5 Geomagnetism and paleomagnetism

5.1 HISTORICAL INTRODUCTION

5.1.1 The discovery of magnetism

Mankind's interest in magnetism began as a fascinationwith the curious attractive properties of the mineral lode­stone, a naturally occurring form of magnetite. Calledloadstone in early usage, the name derives from the oldEnglish word load, meaning "way" or "course"; the load­stone was literally a stone which showed a traveller theway.

The earliest observations of magnetism were madebefore accurate records of discoveries were kept, so thatit is impossible to be sure of historical precedents.Nevertheless, Greek philosophers wrote about lodestonearound 800 BC and its properties were known to theChinese by 300 Be. To the ancient Greeks science wasequated with knowledge, and was considered an elementof philosophy. As a result, the attractive forces of lode­stone were ascribed to metaphysical powers. Some earlyanimistic philosophers even believed lodestone to possessa soul. Contemporary mechanistic schools of thoughtwere equally superstitious and gave rise to false concep­tions that persisted for centuries. Foremost among thesewas the view that electrical and magnetic forces wererelated to invisible fluids. This view persisted well into thenineteenth century. The power of a magnet seemed toflow from one pole to the other along lines of inductionthat could be made visible by sprinkling iron filings on apaper held over the magnet. The term "flux" (synony­mous with flow) is still found in "magnetic flux density,"which is regularly used as an alternative to "magneticinduction" for the fundamental magnetic field vector B.

One of the greatest and wealthiest of the ancientGreek city-colonies in Asia Minor was the seaport ofEphesus, at the mouth of the river Meander (modernKucuk Menderes) in the Persian province of Caria, inwhat is now the Turkish province of western Anatolia. Inthe fifth century Be the Greek state of Thessaly foundeda colony on the Meander close to Ephesus calledMagnesia, which after 133 BC was incorporated into theRoman empire as Magnesia ad Maeandrum. In the vicin­ity of Magnesia the Greeks found a ready supply of lode­stone, pieces of which subsequently became known by theLatin word magneta from which the term magnetismderives.

It is not known when the directive power of the magnet- its ability to align consistently north-south - was firstrecognized. Early in the Han dynasty, between 300 and200 BC, the Chinese fashioned a rudimentary compassout of lodestone. It consisted of a spoon-shaped object,whose bowl balanced and could rotate on a flat polishedsurface. This compass may have been used in the searchfor gems and in the selection of sites for houses. Before1000 AD the Chinese had developed suspended andpivoted-needle compasses. Their directive power led to theuse of compasses for navigation long before the origin ofthe aligning forces was understood. As late as the twelfthcentury, it was supposed in Europe that the alignment ofthe compass arose from its attempt to follow the pole star.It was later shown that the compass alignment was pro­duced by a property of the Earth itself. Subsequently, thecharacteristics of terrestrial magnetism played an impor­tant role in advancing the understanding of magnetism.

5.1.2 Pioneering studies in terrestrial magnetism

In 1269 the medieval scholar Pierre Pelerin de Maricourt,who took the Latin nom-de-plume of Petrus Peregrinus,wrote the earliest known treatise of experimental physics(Epistola de Magnete). In it he described simple laws ofmagnetic attraction. He experimented with a sphericalmagnet made of lodestone, placing it on a flat slab of ironand tracing the lines of direction which it assumed. Theselines circled the lodestone sphere like geographical merid­ians and converged at two antipodal points, whichPeregrinus called the poles of the magnet, by analogy tothe geographical poles. He called his magnetic sphere aterrella, for "little Earth."

It was known to the Chinese around 500 AD, in theTang dynasty, that magnetic compasses did not pointexactly to geographical north, as defined by the stars. Thelocal deviation of the magnetic meridian from the geo­graphical meridian is called the magnetic declination. Bythe fourteenth century, the ships of the British navy wereequipped with a mariner's compass, which became anessential tool for navigation. It was used in conjunctionwith celestial methods, and gradually it became apparentthat the declination changed with position on the globe.During the fifteenth and sixteenth centuries the world­wide pattern of declination was established. By theend of the sixteenth century, Mercator recognized that

281

282 Geomagnetism and paleomagnetism

declination was the principal cause of error in contempo­rary map-making.

Georg Hartmann, a German cleric, discovered in 1544that a magnetized needle assumed a non-horizontal atti­tude in the vertical plane. The deviation from the horizon­tal is now called the magnetic inclination. He reported hisdiscovery in a letter to his superior, Duke Albrecht ofPrussia, who evidently was not impressed. The letter layunknown to the world in the royal archives until its dis­covery in 1831. Meanwhile, an English scientist, RobertNorman, rediscovered the inclination of the Earth's mag­netic field independently in 1576.

In 1600 Willianl Gilbert (1544-1603), an English scien­tist and physician to Queen Elizabeth, published DeMagnete, a landmark treatise in which he summarized allthat was then known about magnetism, including theresults of about seventeen years of his own research. Hisstudies extended also to the electrostatic effects seen whensome materials were rubbed, for which he coined the name"electricity" from the Greek word for amber. Gilbert wasthe first to distinguish clearly between electrical and mag­netic phenomena. His magnetic studies followed the workof Peregrinus three centuries earlier. Using small magneticneedles placed on the surface of a sphere of lodestone tostudy its magnetic field, he recognized the poles, where theneedles stood on end, and the equator, where they lay par­allel to the surface. Gilbert achieved the leap of irnagina­tion that was necessary to see the analogy between theattraction of the lodestone sphere and the known mag­netic properties of the Earth. He recognized that the Earthitself behaved like a large magnet. This was the firstunequivocal recognition of a geophysical property, pre­ceding the laws of gravitation in Newton's Principia byalmost a century. Although founded largely on qualitativeobservations, De Magnete was the most important workon magnetism until the nineteenth century.

The discovery that the declination of the geomagneticfield changed with time was made by Henry Gellibrand(1597-1637)'1 an English mathematician and astronomer,in 1634. He noted, on the basis of just three measure­ments made by William Borough in 1580'1 EdmundGunter in 1622 and himself in 1634, that the declinationhad decreased by about 7° in this time. From these fewobservations he deduced what is now called the secularvariation of the field.

Gradually the variation of the terrestrial magneticfield over the surface of the Earth was established. In1698-1700 Edmund Halley, the English astronomer andmathematician, carried out an important oceanographicsurvey with the prime purpose of studying compass vari­ations in the Atlantic ocean. In 1702 this resulted in thepublication of the first declination chart.

5.1.3 The physical origins of magnetism

By the end of the eighteenth century many characteristicsof terrestrial magnetism were known. The qualitative

properties of magnets (e.g., the concentration of theirpowers at their poles) had been established, but the accu­mulated observations were unable to provide a more fun­damental understanding of the phenomena because theywere not quantitative. A major advance was achieved byCharles Augustin de Coulomb (1736-1806), the son of anoted French family. who in 1784 invented a torsionbalance that enabled him to make quantitative measure­merits of electrostatic and magnetic properties. In 1785 hepublished the results of his intensive studies. He estab­lished the inverse-square law of attraction and repulsionbetween slTIaII electrically charged balls. Using thin, mag­netized steel needles about 24 inches (61 em) in length, healso established that the attraction or repulsion betweentheir poles varied as the inverse square of their separation.

Alessandro Volta (1745-1827) invented the voltaic cellwith which electrical currents could be produced. Therelationship between electrical currents and magnetismwas detected in 1820 by Hans Christian Oersted(1777-1851), a Danish physicist. During experimentswith a battery of voltaic cells he observed that a magneticneedle is deflected at rightangles to a conductor carryinga current, thus establishing that an electrical current pro­duces a magnetic force.

Oersted's result was met with great enthusiasm andwas followed at once by other notable discoveries in thesame year. The law for the direction and strength of themagnetic force near a current-carrying wire was soon for­mulated by the French physicists Jean-Baptiste Biot(1774-1862) and Felix Savart (1791-1841). Their compa­triot Andre Marie Ampere (1775-1836) quickly under­took a systematic set of experiments, He showed that aforce existed between two parallel straight current­carrying wires, and that it was of a type different from theknown electrical forces. Ampere experimented with themagnetic forces produced by current loops and proposedthat internal electrical currents were responsible for theexistence of magnetism in iron objects (i.e., ferromagnet­ism). This idea of permanent magnetism due to con­stantly flowing currents was audacious for its time.

At this stage, the ability of electrical currents to gener­ate magnetic fields was known, but it fell to the Englishscien tist Michael Faraday (1791-1867) to demonstratein 1831 what he called "magneto-electric' induction.Faraday came from a humble background and had littlemathematical training. Yet he was a gifted experimenter,and his results demonstrated that the change of magneticflux in a coil (whether produced by introducing a magnetor by the change in current in another coil) induced anelectric current in the coil. The rule that governs the direc­tion of the induced current was formulated three yearslater by a Russian physicist, Heinrich Lenz (1804-1865).Unhampered by mathematical equations, Faraday madefundamental contributions to understanding magneticprocesses. Instead of regarding magnetic and electricalphenomena as the effects of centers of force acting at adistance, he saw in his mind's eye fictional lines of force

r 5.2 THE PHYSICS OFMAGNETISM

traversing space. This image emphasized the role of themedium and led eventually to the concept of magnetic

field. which Faraday first used in 1845.Although much had been established by the early

1830s~ it was still necessary to interpret the strengths ofmagnetic forces by relating magnetic units to mechanicalunits. This was achieved in 1832 by the German scientistand mathematician, Carl Friedrich Gauss (1777-1855).who assumed that static magnetism was carried by mag­netic ....charges," analogous to the carriers of static elec­tricity. Experiment had shown that. in contrast to electriccharge, magnetic poles always occur as oppositely signedpairs, and so the basic unit of magnetic properties corre­sponds to the dipole. Together with Wilhelm Weber( 1804-1891)~ Gauss developed a method of absol utedetermination of the in tensi ty of the Earth's magneticfield. They founded a geomagnetic observatory atGottingen where the Earth 's magnetic field was observedat regular intervals. By 1837 global charts of the totalintensity, inclination and declination were in existence,although the data had been measured at different timesand their areal coverage was incomplete, To analyze thedata-set Gauss applied the mathematical techniques ofspherical harmonic analysis and the separation of vari­ables, which he had invented. In 1839 he established thatthe main part of the Earth's magnetic field was a dipolefield that originated inside the Earth.

The fundamental physical laws governing magneticeffects were now firmly established. In 1872 James ClerkMaxwell (1831-1879)~ a Scottish physicist, derived a setof equations that quantified all known relationshipsbetween electrical and magnetic phenomena: Coulomb'slaws of force between electric charges and magnetic poles;Oersted's and Ampere's laws governing the magneticeffects of electric currents; Faraday's and Lenz's laws ofelectromagnetic induction; and Ohm's law relatingcurrent to electromotive force. Maxwell's mathematicalstudies predicted the propagation of electric waves inspace, and concluded that light is also an electromagneticphenomenon transmitted through a medium called theluminiferous ether. The need for this light-transmittingmedium was eliminated by the theory of relativity. Byputting the theory of the electromagnetic field on a math­ematical basis, Maxwell enabled a greater understandingof electromagnetic phenomena before the discovery ofthe electron.

A further notable discovery was made in 1879 byHeinrich Lorentz (1853-1928)~ a Dutch physicist. Inexperiments with vacuum tubes he observed the deflec­tion of a beam of moving electrical charge by a magneticfield. The deflecting force acted in a direction perpendicu­lar to the magnetic field and to the velocity of the chargedparticles. and was proportional to both the field and thevelocity. This result now serves to define the unit of mag­netic induction.

Since the time of man's first awareness of magneticbehavior. students of terrestrial magnetism have made

283

important contributions to the understanding of magnet­ism as a physical phenomenon. In turn, advances in thephysics of magnetism have helped geophysicists to under­stand the morphology and origin of the Earth's magneticfield, and to apply this knowledge to geological processes.such as global tectonics. The physical basis of magnetismis fundamental to the geophysical topics of geomagnet­ism, rock magnetism and paleomagnetism.

5.2 THE PHYSICS OFMAGNETISM

5.2.1 Introduction

Early investigators conceptualized gravitational, electri­cal and magnetic forces between objects as instantaneouseffects that took place through direct action-at-a­distance. Faraday introduced the concept of the.field of aforce as a property of the space in which the force acts.The force-field plays an intermediary role in the interac­tion between objects. For example, an electric charge issurrounded by an electrical field that acts to produce aforce on a second charge. The pattern of a field is por­trayed bY.field lines. At any point in a field the direction ofthe force is tangential to the field line and the intensity ofthe force is proportional to the number of field lines perunit cross-sectional area.

Problems in magnetism are often 1110re complicatedfor the student than those in gravitation and electrostat­ics. For one thing, gravitational and electrostatic fields actcentrally to the source of force, which varies in each caseas the inverse square of distance. Magnetic fields are notcentral; their directions vary with azimuth. Moreover,even in the simplest case (that of a magnetic dipole or asmall curren t loop) the field strength falls off inversely asthe cube of distance. To make matters more complicated,the student has to take account of IH·'O magnetic fields(denoted by B and H).

The confusion about the B-field and the H-field maybe removed by recalling that all magnetic fields originatewith electrical currents. This is the case even for perrna­nent magnets, as Ampere astutely recognized in 1820. Wenow know that these currents are associated with themotions of electrons about atomic nuclei in the perma­nent magnets, The fundamental magnetic field associatedwith currents in any medium is B. The quantity H shouldbe regarded as a computational parameter proportionalto Bin non-magnetizable materials. Inside a magnetizablematerial, H describes how B is modified by the magneticpolarization (or magnetization, M) of the material. Themagnetic B-field is also called the magnetic ind uction ormagnetic flux densi ty.

Historically. the laws of magnetism were establishedby relating the B-field to fictitious centers of magneticforce called magnetic poles, defined by comparison withthe properties of a bar magnet. Gauss showed that incontrast to electrostatic charges, free magnetic polescannot exist: each positive pole must be paired with a

284 Geomagnetism and paleomagnetism

Fig. 5.1 The characteristic

field lines of a magnetic

dipole are found around (a) a

short bar magnet, (b) a small

loop carrying an electric

current, and (c) a uniformly

magnetized sphere.

(a) (b) (c)

The proportionality constant K was originally defined tobe dimensionless and equal to unity, analogously to thelaw of electrostatic force. This gave the dimensions ofpole strength in the centimeter-gram-second (c.g.s.)system as dyne!" em.

5.2.2.1 The field of a magnetic pole

The gravitational field of a given mass is defined as theforce it exerts on a unit mass (Section 2.2.2). Similarly, theelectric field of a given charge is the force it exerts on aunit charge. These ideas cannot be transferred directly tomagnetism, because magnetic poles do not really exist.Nevertheless, many magnetic properties can be describedand magnetic problems solved in terms of fictitious poles.

5.2.2 Coulomb's lawfor magnetic poles

Coulomb's experiments in 1785 established that the forcebetween the ends of long thin magnets was inversely pro­portional to the square of their separation. Gaussexpanded Coulomb's observations and attributed theforces of attraction and repulsion to fictitious magneticcharges, or poles. An inverse square law for the force Fbetween magnetic poles with strengths PI and P2. at dis­tance r from each other can be formulated as

corresponding negative pole. The most important type ofmagnetic field - and also the dominant component of thegeomagnetic field - is that of a magnetic dipole (Fig. 5.la).This is the field of two magnetic poles of opposite sensethat are infinitesimally close to each other. The geometryof the field lines shows the paths along which a free mag­netic pole would move in the vicinity of the dipole. A tinycurrent loop (Fig. 5.1b) and a uniformly magnetizedsphere (Fig. 5.lc) also have dipole-type magnetic fieldsaround them. Although magnetic poles do not exist phys­ically, many problems that arise in geophysical situationscan be readily solved in terms of surface distributions ofpoles or dipoles. So we will first examine these concepts.

(5.3)

In studying gravitation we also used the concept of a fieldto describe the region around a mass in which its attractioncould be felt by another test mass. In order to move the testmass away from the attracting mass, work had to be doneagainst the attractive force and this was found to be equalto the gain of potential energy of the test mass. When thetest mass was a unit mass, the attractive force was calledthe gravitational field and the gain in potential energy wascalled the change in potential. We calculated the gravita­tional potential at distance r from an attracting point massby computing the work that would have to be expendedagainst the field to move the unit mass from r to infinity.

We can define the magnetic potential Wat a distance rfrom a pole of strength p in exactly the same way. Themagnetic field of the pole is given by Eq. (5.2). Using thevalue /-Lo/47f for K and expressing the pole strengthp in SIunits, the magnetic potential at r is given by

J /-LoPH/= - Bdr=­

47frr

For example, we can define a magnetic field B as the forceexerted by a pole of strength p on a unit pole at distance r.From Eq. (5.1) we get

B(r) = K~ (5.2)

Setting K = 1, the unit of the magnetic B-field hasdimensions dyne!? em -I in c.g.s. units and is called agauss. Geophysicists employ a smaller unit, the gamma(y), to describe the geomagnetic field and to chart mag­netic anomalies (1 ~ = 10-5 gauss).

Unfortunately, the c.g.s. system required units of elec­trical charge that had different dimensions and size inelectrostatic and electromagnetic situations. By interna­tional agreement the units were harmonized and rational­ized. In the modern Systeme Internationale (SI) units theproportionality constant K is not dimensionless. It hasthe value /-Lo/47f, where /-Lo is called the permeability con­stant and is equal to 47fX 10- 7 N A -2 (or henry/meter,H m", which is equivalent to N A -2).

5.2.2.2 The potential of a magnetic pole

(5.1 )F(r) = KP1~2r-

tBI

IIIII

5.2 THE PHYSICS OF MAGNETISM

tI

tF = BP

: d sin e /'i'rP~-------------------~,+.~ ,I .

IIIIIII

:0\

torque =Fd sin e't = Pd B sin e= m x B

285

Fig. 5.2 Geometry for the calculation of the potential of a pair of

magnetic poles. Fig. 5.3 Definition of the magnetic moment m of a pair of magnetic

poles.

The pair of opposite poles is considered to form adipole when their separation becomes infinitesimally smallcompared to the distance to the point of observation (i.e.,d-sri. In this case, we get the approximate relations

5.2.3 The magnetic dipole

In Fig. 5.1 the line joining the positive and negative poles(or the normal to the plane of the loop, or the direction ofmagnetization of the sphere) defines an axis, about whichthe field has rotational symmetry. Let two equal andopposite poles, +p and - p, be located a distance d apart(Fig. 5.2). The potential Wat a distance r from the mid­point of the pair of poles, in a direction that makes anangle (J to the axis, is the sum of the potentials of the pos­itive and negative poles. At the point (r, (J) the distancesfrom the respective poles are r+ and r_and we get for themagnetic potential of the pair

(5.8)

W - J.LOP(-L _ -L)- 41T r+ r_

J.LrP(r- - r+)W=---41T r +r _

(5.4)

(5.5)

Substituting Eq. (5.7) in Eq. (5.5) gives the dipole poten­tial at the point (r, e):

J.Lo (dp )cose J.Lo IncoseW = 41T r2 = 41T~

The quantity m = (dp) is called the magnetic momentof the dipole. This definition derives from observationson bar magnets. The torque exerted by a magnetic fieldto turn the magnet parallel to the field direction is pro­portional to 111. This applies even when the separationof the poles becomes very small, as in the case of thedipole.

The torque can be calculated by considering the forcesexerted by a uniform magnetic field B on a pair of mag­netic poles of strength p separated by a distance d (Fig.5.3). A force equal to (Bp) acts on the positive pole and anequal and opposite force acts on the negative pole. If themagnetic axis is oriented at angle () to the field, the per­pendicular distance between the lines of action of theforces is d sin e. The torque r felt by the magnet is equalto B(pd)sin (J (Le., ,. = mli sin ()). Taking into account thedirection of the torque and using the conventional nota­tion for the cross product of two vectors this gives for themagnetic torque

When d « r, we can write ()= (J' and terms of order (d/r)2and higher can be neglected. This leads to the further sim­plifications

r . - r; = ~ (cosO' + cosO) = dcosO

5.2.4 The magnetic fieldof anelectrical current

The equation used to define the magnetic B-field wasformulated by Lorentz in 1879. Let q be an electricalcharge that moves with velocity v through a magneticfield B (Fig. 5.4a). The charged particle experiences adeflecting force F given by Lorentz's law, which in SIunits is:

dr = r - -cos(J

+ 2

r = r + r1 cos(J ,- 2

d2 ..,r ,. =,.'2 - - cos2(J = r-+ - 4

(5.6)

(5.7)

,.=mXB

F=q(vXB)

(5.9)

(5.10)

286 Geomagnetism and paleomagnetism

BA A

F=q(vxB)

(a)

q'~'~-'~

-7"~II'

/(/_7k--<":II~'1>-~~ \

,\"1 I r "

\':';~'.~S'-;;;:~:~--;~B'·· ~~/ "y

Fig. 5.4 Illustrations of (a) Lorentz's law for the deflecting force F

experienced by an electrical charge that moves with velocity v through amagnetic field B, and (b) the law of Biot and Savart for the forceexperienced by an element dl of a conductor carrying a current I in amagnetic field B.

The electrical current I along the conductor is the totalcharge that crosses A per second, and is given by 1= N'Avq.From Eq. (5.11) we get the law of Biot and Savart for theforce experienced by the element d) of a conductor carry­ing a current I in a magnetic field B:

The SI unit of the magnetic B-field defined by this equa­tion is called a testa; it has the dimensions N A -) m -) .

Imagine the moving charge to be confined to movealong a conductor of length dl and cross-section A (Fig.5.4b). Let the number of charges per unit volume be N.The number inside the element dl is then NA d/. Eachcharge experiences a deflecting force given by Eq. (5.10).Thus the total force transferred to the element dl is

F = laB

F = laB

Q

(b) tIII

F = InB I

+III b

b sin e:I

: e1------I

(a)

Fig. 5.5 Small compass needles show that the magnetic field linesaround an infinitely long straight wire carrying an electrical current formconcentric circles in a plane normal to the wire.

(5.11 )

---~II .//~-----

dl,tf}/

,/ (~'/ ~'-'~~~

1/ dF = I (dl x B )

I I

(b)

dF = NAdlq(v x B) = NAvq(d) x B)

dF=/(dl x B) (5.12) torque =Fb sin e

The Biot-Savart law can be applied to determine thetorque exerted on a small rectangular loop PQRS in a

The orienting effect of an electrical current on mag­netic compass needles, reported by Oersted and Amperein 1820, is illustrated in Fig. 5.5. The magnetic field linesaround an infinitely long straight wire form concentriccircles in the plane normal to the wire. The strength of theB-field around the wire is

/-LolB=­

2'ITf(5.13)

l' = I (ab)B sin e= m x B

Fig. 5.6 (a) Rectangular loop carrying a current I in a uniform magneticfield B; (b) derivation of the torque T experienced by the loop.

magnetic field (Fig. 5.6a). Let the lengths of the sides ofthe loop be a and b, respectively, and define the x-axisparallel to the sides of length a. The area of the loop canbe expressed as a vector with magnitude A = ab. anddirection n normal to the plane of the loop. Suppose thata current I flows in the loop and that a magnetic field Bacts normal to the .r-axis, making an angle () with the

5.2 THE PHYSICS OFMAGNETISM 287

5.2.5 Magnetization and the magnetic field inside amaterial

normal to the plane of the loop. Applying Eq. (5.12), aforce F'.\- equal to (IbB cos £J) acts on the side PQ in thedirection of +x; its effect is cancelled by an equal andopposite force F'.t acting on side RS in the direction of -x.Forces equal to (laB) act in opposite directions on thesides QR and SP (Fig. 5.6b). The perpendicular distancebetween their lines of action is b sin £J, so the torque ,.experienced by the current loop is

The quantity m == fA is a vector with direction parallel tothe normal to the plane of the current loop. This expressionis valid for an arbitrary small loop of area A, regardless ofits shape. By comparing Eqs. (5.14) and (5.9) for the torqueon a dipole, it is evident that m corresponds to the magneticmoment of the current loop. At distances greater than thedimensions of the loop, the magnetic field is that of adipole at the center of the loop (Fig. 5.1b). The definitionof m in terms of a current-carrying loop shows that mag­netic moment has the units of current times area (A m-).

(5.15 )

Fig. 5.7 Schematic representation of the magnetic moments inside amaterial; each magnetic moment m is associatedwith a current loop on

an atomic scale.

Magnetization has the dimensions of magneticmoment (A m'') divided by volume (rn'), so that the SIunits of M are A m - I. The dimensions of BareN A -I m- I and those of /L

oare N A -2; consequently the

dimensions of B1/Lo are also A m -I. In general, the mag­netization M inside a magnetic material will not beexactly equal to BI/Lo; let the difference be H, so that

(5.14),.==mXB

,. == (IaB)b sinf == (fA)B sinf

A true picture of magnetic behavior requires a quantum­mechanical analysis. Fortunately, a working understand­ing of the magnetic behavior of materials can be acquiredwithout getting involved in the quantum-mechanicaldetails. The simplified concept of atomic structure intro­duced by Ernest Rutherford in 1911 gives a readily under­standable model for the magnetic behavior of materials.The motion of an electron around an atomic nucleus istreated like the orbital motion of a planet about the Sun.The orbiting charge forms an electrical current withwhich an orbital magnetic moment is associated. A planetalso rotates about its axis; likewise each electron can bevisualized as having a spin motion about an axis. Thespinning electrical charge produces a spin magneticmoment. Each magnetic moment is directly related to thecorresponding angular 1110111entunl. In quantum theoryeach type of angular momentum of an electron is quan­tized. Thus the spin and orbital magnetic moments arerestricted to having discrete values. The spin magneticmoment is usually more important than the orbitalmoment in the rock-forming minerals (see Section 5.2.6).

A simplified picture of the magnetic moments inside amaterial is shown in Fig. 5.7. The magnetic moment m ofeach atom is associated with a current loop as illustratedin Fig. 5.1b and described in the previous section. The netmagnetic moment of a volume V of the material dependson the degree of alignment of the individual atomic mag­netic moments. It is the vector sum of all the atomic mag­netic moments in the material. The magnetic moment perunit volume of the material is called its magnetization,denoted M:

(5.16)

In the earlier c.g.s. system H was defined by the vectorequation H == B - 41TM, and the dimensions of Hand Bwere the same. For this reason H became known as themagnetizing field (or H-field). It is a readily computedquantity that is useful in determining the value of the truemagnetic field B in a medium. The fundamental differ­ence between the B-field and the H-field can be under­stood by inspection of the configurations of theirrespective field lines. The field lines of B always formclosed loops (Fig. 5.1). The field lines of H are discontinu­ous at surfaces where the magnetization M changes instrength or direction. Magnetic methods of geophysicalexploration take advantage of surface effects that arisewhere the magnetization is interrupted.

Anomalous magnetic fields arise over geological struc­tures that cause a magnetization contrast between adjacentrock types. Many magnetic anomalies can be analyzed byreplacing the change in magnetization at a surface by anappropriate surface distribution of fictitious magneticpoles. The methodology, though based on a fundamentallyfalse concept, is quite practical for modelling anomalyshapes and is often much simpler than a physically correctanalysis in terms of current distributions. For example, in auniformly magnetized rod, the N-poles of the elementarymagnetic moments are considered to be exposed on oneend of the rod, with a corresponding distribution of S­poles on the opposite end; inside the material the N-polesand S-poles cancel each other (Fig. 5.8a). The H-fieldinside the material arises from these pole distributions and

288 Geomagnetism and paleomagnetism

Fig. 5.8 The magnetization

of a material may be

envisaged as due to an

alignment of (a) small dipoles

or (b) equivalent current

loops; even in a permanent

magnet the physical source of

the B-field of the material is a

system of electrical currents

on an atomic scale.

\

\\

/

I

(a) (b)

The proportionality factor k is a physical property ofthe material, called the magnetic susceptibility. It is ameasure of the ease with which the material can be mag­netized. Because M and H have the same units (A m-1)~ kis a dimensionless quantity. The susceptibility of most

acts in the opposite direction to the magnetization M.Outside the magnet the B-field and H-field are parallel; theH-field is discontinuous at the ends of the magnet.

The same situation can be portrayed in terms ofcurrent loops. The physical source of every B-field is anelectrical current, even in a permanent magnet (Fig.5.8b). Atomic current loops give a continuous B-fieldthat emerges from the magnet at one end, re-enters at theother end and is closed inside the magnet. The alignedmagnetic moments of the elementary current loopscancel out inside the body of the magnet, but the cur­rents in the loops adjacent to the sides of the magnetcombine to form a surface "current" that maintains themagnetization M.

In a vacuum there is no magnetization (M = 0); thevectors Band H are parallel and proportional(8 = J-LoR). Inside a magnetizable material the magneticB-field has two sources. One is the external system ofreal currents that produce the magnetizing field H; theother is the set of internal atomic currents that cause theatomic magnetic moments whose net alignment isexpressed as the magnetization M. In a general,anisotropic magnetic material 8, M and H are not par­allel. However, many magnetic materials are notstrongly anisotropic and the elementary atomic mag­netic moments align in a statistical fashion with the mag­netizing field. In this case M and H are parallel andproportional to each other

materials is temperature dependent, and in some materi­als (ferromagnets and ferrites) k depends on H in a com­plicated fashion. In general, Eq. (5.16) can be rewritten

The quantity JL = (1 + k) is called the magnetic perme­

ability of the material. The term "permeability" recallsthe early nineteenth century association of magneticpowers with an invisible fluid. For example, the perme­ability of a material expresses the ability of the materialto allow a fluid to pass through it. Likewise, the magneticpermeability is a measure of the ability of a material toconvey a magnetic flux. Ferromagnetic metals have highperrneabilities; in contrast minerals and rocks have lowsusceptibilities and permeabilities J.L = 1.

(5.18)B = JLo(H + M) = J.LoH(l + k)

B = JLJLoH

5.2.6 The magnetic properties of materials

The magnetic behavior of a solid depends on the mag­netic moments of the atoms or ions it contains. As dis­cussed above, atomic and ionic magnetic moments areproportional to the quantized angular momenta associ­ated with the orbital motion of electrons about thenucleus and with the spins of the electrons about theirown axes of rotation. In quantum theory the exclusionprinciple of Wolfgang Pauli states that no two electronsin a given system can have the same set of quantumnumbers. When applied to an atom or ion, Pauli's princi­ple stipulates that each possible electron orbit can beoccupied by up to two electrons with opposite spins. Theorbits are arranged in shells around the nucleus. Themagnetic moments of paired opposite spins cancel eachother out. Consequently, the net angular momentum

(5.17)M=kH

5.2 THE PHYSICS OFMAGNETISM 289

(a)

5.2.6.2 Paramagnetism

Fig. 5.9 (a) Variations of magnetization M with applied magnetic fieldH in paramagnetic and diamagnetic materials; (b) the variation ofparamagnetic susceptibility with temperature, and (c) the linear plot ofthe inverse of paramagnetic susceptibility against temperature.

8

-1k 0: (T - 8)

H

-1k ocT

L---"""""--------T

(c)

11k

koc lT

M

-M

o ...

L..-----=======T

(b)

k

is independent of temperature. Many important rock­forming minerals belong to this class, amongst themquartz and calcite. They have susceptibilities around-10-6 in SI units.

and the net magnetic moment of a filled shell must bezero. The net magnetic moment of an atom or ion arisesfrom incompletely filled -shells that contain unpairedspins. The atoms or ions in a solid are not randomly dis­tributed but occupy fixed positions in a regular lattice,which reflects the symmetry of the crystalline structureand which controls interactions between the ions. Hence,the different types of magnetic behavior observed insolids depend not only on the presence of ions withunpaired spins, but also on the lattice symmetry and cellsize.

Three main classes of magnetic behavior can be distin­guished on the basis of magnetic susceptibility: diamagnet­iS111, paramagnetism and ferromagnetism. In diamagneticmaterials the susceptibility is low and negative, i.e., a mag­netization develops in the opposite direction to the appliedfield. Paramagnetic materials have low, positive suscepti­bilities. Ferromagnetic materials can be subdivided intothree categories. True ferromagnetism is a cooperativephenomenon observed in metals like iron, nickel andco balt, in which the lattice geometry and spacing allowsthe exchange of electrons between neighboring atoms.This gives rise to a molecularfield by means of which themagnetic moments of adjacent atoms reinforce theirmutual alignment parallel to a common direction. Ferro­magnetic behavior is characterized by high positive sus­ceptibilities and strong magnetic properties. The crystalstructures of certain minerals permit an indirect coopera­tive interaction between atomic magnetic moments. Thisindirect exchange confers magnetic properties that aresimilar to ferromagnetism. The mineral may display anti-ferromagnetism or ferrimagnetism. The small group of fer­rimagnetic minerals is geophysically important, especiallyin connection with the analysis of the Earth's paleo­magnetic field.

5.2.6.1 Diamagnetism

All magnetic materials show a diamagnetic reaction in amagnetic field. The diamagnetism is often masked bystronger paramagnetic or ferromagnetic properties. It ischaracteristically observable in materials in which all elec­tron spins are paired.

The Lorentz law (Eq. (5.10)) shows that a change inthe B-field alters the force experienced by an orbitingelectron. The plane of the electron orbit is compelled toprecess around the field direction; the phenomenon iscalled Larmor precession. It represents an additionalcomponent of rotation and angular momentum. Thesense of the rotation is opposite to that of the orbitalrotation about the nucleus. Hence, the magnetic momentassociated with the Larmor precession opposes theapplied field. As a result a weak magnetization propor­tional to the field strength is induced in the oppositedirection to the field. The magnetization vanishes whenthe applied magnetic field is removed. Diamagnetic sus­ceptibility is reversible, weak and negative (Fig. 5.9a); it

Paramagnetism is a statistical phenomenon. When one ormore electron spins is unpaired, the net magnetic momentof an atom or ion is no longer zero. The resultant mag­netic moment can align with a magnetic field. The align­ment is opposed by thermal energy which favors chaoticorientations of the spin magnetic moments. The magneticenergy is small compared to the thermal energy, and inthe absence of a magnetic field the magnetic moments areoriented randomly. When a magnetic field is applied, thechaotic alignment of magnetic moments is biassedtowards the field direction. A magnetization is inducedproportional to the strength of the applied field and par­allel to its direction. The susceptibility is reversible, smalland positive (Fig. 5.9a). An important paramagneticcharacteristic is that the susceptibility k varies inverselywith temperature (Fig. 5.9b) as given by the Curie law,'

(5.19)

where the constant C is characteristic of the material.Thus, a plot of 11k against temperature is a straight line(Fig. 5.9c). In solids and liquids mutual interactions

290 Geomagnetism and paleomagnetism

Fig. 5.10 Schematic

representations of the

alignments of atomicmagnetic moments in (a)ferromagnetism, (b)

antiferromagnetism, (c) spin­

canted antiferromagnetism,and (d) ferrimagnetism.

(a)

ferromagnetism

iiiiii

iiiiii

(b)

antiferromagnetism

ititit

tititi

(c)

spin-cantedan tiferromagnetism

(d)

ferrimagnetism

spontaneousmagneticmoment t zero t

For a solid the plot of 11k against (T - 8) is a straight line(Fig. 5.9c). Many clay minerals and other rock-formingminerals (e.g., chlorite, amphibole, pyroxene, olivine) areparamagnetic at room temperature, with susceptibilitiescommonly around 10- 5 - 10- 4 in SI units.

between ions may be quite strong and paramagnetic behav­ior is only displayed when the thermal energy exceeds athreshold value. The temperature above which a solid isparamagnetic is called the paramagnetic Curie temperatureor Weiss constant of the material, denoted by 8; it is closeto zero kelvin in paramagnetic solids. At temperaturesT> (j the paramagnetic susceptibility k is given by theCurie- Weiss law

M

----.---~-I-----I------H

isothermalremanent

magnetiza tion

/flcrremanent :coerci vi ty :

IIIIII

(5.20)C

k== T- 8

5.2.6.3 Ferromagnetism

In paramagnetic and diamagnetic materials the interac­tions between individual atomic magnetic moments aresmall and often negligible. However, in some metals (e.g.,iron, nickel, cobalt) the atoms occupy lattice positionsthat are close enough to allow the exchange of electronsbetween neighboring atoms. The exchange is a quantum­mechanical effect that involves a large amount of energy,called the exchange energy of the metal. The exchangeinteraction produces a very strong molecularfield withinthe metal, which aligns the atomic magnetic moments(Fig. 5.10a) exactly parallel and produces a spontaneousmagnetization (M). The magnetic moments react inunison to a magnetic field, giving rise to a class of strongmagnetic behavior known es ferromagnetism.

A rock sample may contain thousands of tiny ferro­magnetic mineral grains. The magnetization loop of arock sample shows the effects of magnetic hysteresis (Fig.5.11). In strong fields the magnetization reaches a satura­tion value (equal to M), at which the individual magneticmoments are aligned with the applied field. If the magne­tizing field is reduced to zero, a ferromagnetic materialretains part of the induced magnetization. The residual

Fig. 5.11 The magnetization loop of an arbitrary ferromagnetic

material.

magnetization is called the remanence, or isothermal rema­nent magnetization (IRM)~ if the sample is magnetized tosaturation, the remanence is a saturation IRM (Mrs)' For agiven ferromagnetic mineral, the ratio Mr/ Ms depends ongrain size. If a magnetic field is applied in the oppositedirection to the IRM, it remagnetizes part of the materialin the antiparallel direction. For a particular value He ofthe reverse field (called the coercive force) the inducedreverse magnetization exactly cancels the original rema­nence and the net magnetization is zero. If the reverse fieldis removed at this stage, the residual remanence is smallerthan the original IRM. By repeating the process in everstronger reverse fields a back-field Her (called the coerciv­ity of remanence) is found which gives a reverse ren1anencethat exactly cancels the IRM, so that the residual rema­nence is zero. The ratio He/He also depends on grain size.Rock-forming magnetic minerals often have natural rema­nences with very high coercive properties.

5.2 THE PHYSICS OF MAGNETISM

When a ferromagnetic material is heated. its sponta­neous magnetization disappears at the [erromagnetic

Curie temperature (Te>. At temperatures higher than theparamagnetic Curie temperature (8) the susceptibility kbecomes the paramagnetic susceptibility.. so that 11k isproportional to (T - ()) as given by the Curie-Weiss law(Eq, (5.20). The paramagnetic Curie temperature for aferromagnetic solid is several degrees higher than the fer­romagnetic Curie temperature, Tc' The gradual transitionfrom ferromagnetic to paramagnetic behavior is explainedby persistence of the molecular field due to short-rangemagnetic order above Tc'

5.2.6.4 Antiferromagnetism

In oxide crystals the oxygen ions usually keep the metalions far apart, so that direct exchange of electronsbetween the metal ions is not possible. However, incertain minerals, interaction between magnetic spinsbecomes possible by the exchange of electrons from onemetal ion to another through the electron "cloud" of theoxygen ion. This indirect exchange (or superexchangei

process results in antiparallel directions of adjacentatomic magnetic moments (Fig. 5.10b), giving two sub­lattices with equal and opposite intrinsic magneticmoments. As a result, the susceptibility of an antiferro­magnetic crystal is weak and positive, and remanentmagnetization is not possible. The antiferromagneticalignment breaks down at the Neel temperature, abovewhich paramagnetic behavior is shown. The Neel tern­perature TN of many antiferromagnetic substances islower than room temperature, at which they are para­magnetic. A common example of an antiferromagneticmineral is ilmenite (FeTi03), which has a Neel tempera­ture of 50 K.

5.2.6.5 Parasitic ferromagnetism

When an antiferromagnetic crystal contains defects"vacancies or impurities, some of the antiparallel spins areunpaired. A weak "defect moment" can result due tothese lattice imperfections. Also if the spins are notexactly antiparallel but are inclined at a small angle, theydo not cancel out completely and again a ferromagnetictype of magnetization can result (Fig. 5.IOc). Materialsthat exhibit this form of parasiticferromagnetism have thetypical characteristics of a true ferromagnetic 111etaLincluding hysteresis, a spontaneous magnetization and aCurie temperature. An important geological example isthe common iron mineral hematite (a-Fe~03)' in whichboth the spin-canted and defect moments contribute tothe ferromagnetic properties. Hematite has a variable,weak spontaneous magnetization of about 2000 A nl-\"very high coercivi ty and a Curie tern perature aro und675°C. The variable magnetic properties are due to varia­tion in the relative importances of the defect and spin­canted moments,

291

5.2.6.6 Ferrimagnetism

The metallic ions in an antiferromagnet occupy the voidsbetween the oxygen ions. In certain crystal structures. of .which the 1110st important geological example is the spinelstructure. the sites of the metal ions differ from each otherin the coordination of the surrounding oxygen ions.Tetrahedral sites have four oxygen ions as nearest neigh­bors and octahedral sites have six. The tetrahedal andoctahedral sites form two sublattices. In a normal spinelthe tetrahedral sites are occupied by divalent ions and theoctahedral sites by Fe 3+ ions. The 1110st common ironoxide minerals have an inverse spinel structure. Each sub­lattice has an equal number of Fe3+ ions. The samenumber of divalent ions (e.g, Fe 2+ ) occupy other octahe­dral sites .. while the corresponding number of tetrahedralsites is empty,

When the indirect exchange process involves antipar­allel and unequal magnetizations of the sublattices (Fig.5.10d), resulting in a net spontaneous magnetization, thephenomenon is called ferrimagnetism. Ferrimagneticmaterials (called ferritess exhibit magnetic hysteresis andretain a remanent magnetization when they are removedfrom a magnetizing field. Above a given temperature ­sometimes called the ferrimagnetic Neel temperature butmore commonly the Curie temperature - the long-rangemolecular order breaks down and the mineral behavesparamagnetically. The most important ferrimagneticmineral is magnetite (Fe 304) , but maghemite, pyrrhotiteand goethite are also significant contributors to the mag­netic properties of rocks.

5.2.7 Magnetic anisotropy

Anisotropy is the directional dependency of a property.The magnetism of metals and crystals is determined bythe strengths of the magnetic moments associated withatoms or ions, and the distances between neighbors. Herethe symmetry of the lattice plays an important role, andso the magnetic properties of most ferromagnetic materi­als depend 011 direction. Magnetic anisotropy is animportant factor in the dependence on grain size of themagnetic behavior of rocks and minerals. There are threeimportant types: magnetocrystalline, magnetostatic andmagnetostrictive anisotropies.

5.2.7.1 Magnetocrystalline anisotropy

The direction of the spontaneous magnetization (Ms ) in aferromagnetic metal is not arbitrary. The molecular fieldthat produces M; originates in the direct exchange of elec­tron spins between neighboring atoms in a metal. Thesymmetry of the lattice structure of the metal affects theexchange process and gives rise to a magnetocrystallineanisotropy energy, which has a minimum value when M; isparallel to a favored direction referred to as the easy axis(or easy direction) of magnetization. The simplest form of

292 Geomagnetism and paleomagnetism

The anisotropy constants K, and K2 of magnetite areequal to -1.36 x 104 J m- 3 and -0.44 X 104 J m- 3,

respectively, at room temperature. Because these con­stants are negative, the anisotropy energy density Ea isminimum when the spontaneous magnetization is along a[111] body diagonal, which is the magnetocrystalline easyaxis of magnetization at room temperature. (5.23)

,~

s~--~, NI "S~-----\N

\5 ------\N

5 - - - ~~'-::- - ~N

5 -~/-:~i.N5 ----- N

5, ----~N\ ;

S \~'t=7/N

~ :... __ _ _ demagnetizingfield

(a)

(b)

.....;:::~\>. appliedmagnetic field

Fig. 5.12 The origin of shape anisotropy: the distributions of

magnetic poles on surfaces that intersect the magnetization of auniformly magnetized prolate ellipsoid produce internal demagnetizingfields; these are weak parallel to the long axis(a) and strong parallel tothe short axis (b). As a result, the net magnetization is stronger parallel

to the long axis than parallel to the short axis.

The spontaneous magnetization of a uniformly mag­netized material can be pictured as giving rise to a distrib­ution of poles on the free end surfaces (Fig. 5.12). Asnoted above, a property of the magnetic B-field is that itsfield lines form closed loops, whereas the H-field beginsand ends on boundary surfaces, at which it is discontinu­ous. The field lines of the magnetic field H outside amagnet are parallel to the B-field and are directed fromthe surface distribution of N-poles to the distribution ofS-poles. In the absence of an externally applied field theH-field inside the magnet is also directed from the distrib­ution of N-poles on one end to the S-poles on the otherend. It forms a demagnetizing field (Ad) that opposes themagnetization. The strength of the demagnetizing fieldvaries directly with the surface density of the magneticpole distribution on the end surfaces of the magnet, andinversely with the distance between these surfaces. H d

thus depends on the shape of the magnet and the intensityof magnetization; it can be written

(5.22)

(5.21)Ea == Kusin2cjJ

Ku is called the uniaxial magnetocrystalline anisotropyconstant. Its value in hematite is around -103 J m- 3 atroom temperature. The negative value of Ku in Eq. (5.21)means that Ea decreases as the angle cP increases, and isminimum when sin2cjJ is maximum, i.e., when cjJ is 90°. Asa result, the spontaneous magnetization lies in the basalplane of the hematite crystal at room temperature.

Because of its inverse spinel structure, magnetite hascubic anisotropy. Let the direction of the spontaneousmagnetization be given by direction cosines a I' a 2 and a 3relative to the edges of the cubic unit cell (Box 1.5). Themagnetocrystalline anisotropy energy density is thengiven by

magnetic anisotropy is uniaxial anisotropy, when a metalhas only a single easy axis. For example, cobalt has ahexagonal structure and the easy direction is parallel tothe c-axis at room temperature. Iron and nickel have cubicunit cells: at room temperature, the easy axes in iron arethe edges of the cube, but the easy axes in nickel are thebody diagonal directions.

Magnetocrystalline anisotropy is also exhibited by fer­rites, including the geologically important ferrimagneticminerals. The exchange process in a ferrite is indirect, butenergetically preferred easy axes of magnetization arisethat reflect the symmetry of the crystal structure. Thisgives rise to different forms of the anisotropy in hematiteand magnetite.

Hematite has a rhombohedral or hexagonal structureand a uniaxial anisotropy with regard to the c-axis of sym­metry. Oxygen ions form a close-packed hexagonal latticein which two-thirds of the octahedral interstices are occu­pied by ferric (Fe 3+ ) ions. When the spontaneous magne­tization makes an angle cjJ with the c-axis of the crystal,the uniaxial anisotropy energy density can be written tofirst order

5.2.7.2 Magnetostatic (shape) anisotropy

In strongly magnetic materials the shape of the magne­tized object causes a magnetostatic anisotropy. In rocksthis effect is associated with the shapes of the individualgrains of ferrimagnetic mineral in the rock, and to a lesserextent with the shape of the rock sample. The anisotropyis magnetostatic in origin and can be convenientlyexplained with the aid of the concept of magnetic poles.

N is called the demagnetizing factor. It is a dimensionlessconstant determined by the shape of the magnetic grain. Itcan be computed for a geometrical shape, such as a triaxialellipsoid. The demagnetizing factors »; N2 and N3 parallelto the symmetry axes of an ellipsoid satisfy the relationship

(5.24)

The magnetostatic energy of the interaction of the grainmagnetization with the demagnetizing field is called the

5.3 ROCK MAGNETISM 293

5.2.7.3 Magnetostrictive anisotropy

demagnetizing energy (Ed)' For a grain with uniform mag­netization M in a direction with demagnetizing factor N,

which is minimum when M; is parallel to the longestdimension of the grain.

Shape-dependent magnetic anisotropy is important inminerals that have a high spontaneous magnetization. Themore elongate the grain is, the higher the shape anisotropywill be. It is the predominant form of anisotropy in veryfine grains of magnetite (and maghemite) if the longestaxis exceeds the shortest axis by only about 20(~}.

(5.27)

stress to a magnetic material can change its magnetiza­tion; the effect is called piezomagnetism. On a submicro­scopic scale the stress field that surrounds a vacancy,defect or dislocation in the crystal structure can locallyaffect the orientations of ionic magnetic spins.

Magnetostriction is a further source of anisotropy inmagnetic minerals. The magnetostrictive (or magneto­elastic) anisotropy energy density Ea depends on theamount and direction of the stress a. If the saturationmagnetization makes an angle () to the stress, Ea is givenfor a uniaxial magnetic mineral by

s, = ~ AsLTcos2lJ

This is the simplest expression for magnetostrictiveenergy. It assumes that the magnetostriction is isotropic,i.e., that it has the same value in all directions. This condi­tion is fulfilled if the magnetocrystalline axes of the ferri­magnetic minerals in a rock are randomly distributed.The magnetoelastic energy of a cubic mineral is morecomplicated. Instead of a single magnetostriction con­

stant As' separate constants AlOO and AI)I are required forthe saturation magnetostriction along the [100] and [111]directions, respectively, corresponding to the edge andbody diagonal directions of the cubic unit cell.

In magnetite the magnetoelastic energy is more than anorder of magnitude less than the magnetocrystalline energyat room temperature. Consequently, magnetostriction playsonly a secondary role in determining the direction of mag­netization of magnetite grains. However, in minerals thathave high magnetostriction (e.g., titanomagnetites (seeSection 5.3.2.1) with a compositional factor x = 0.65) themagnetoelastic energy may be significant in determiningeasy directions of magnetization, and the magnetizationmay be sensitive to modification by deformation.

5.3 ROCK MAGNETISM

5.3.1 The magnetic properties of rocks

A rock may be regarded as a heterogeneous assemblage ofminerals. The matrix minerals are mainly silicates or car­bonates, which are diamagnetic in character. Interspersedin this matrix is a lesser quantity of secondary minerals(such as the clay minerals) that have paramagnetic prop­erties. The bulk of the constituent minerals in a rock con­tribute to the magnetic susceptibility but are incapable ofany contribution to the remanent magnetic properties,which are due to a dilute dispersion of ferrimagnetic min­erals (e.g., commonly less than 0.010/0 in a limestone). Thevariable concentrations of ferrimagnetic and matrix min­erals result in a wide range of susceptibilities in rocks(Fig. 5.13).

The weak and variable concentration of ferrimagneticminerals plays a key role in determining the magneticproperties of the rock that are significant geologically andgeophysically. The most important factors influencing

(5.26)

(5.25)E == J-L°NM2d 2

Consider the shape anisotropy of a small grain shaped likea prolate ellipsoid. When the spontaneous magnetizationMs is along the long axis of the ellipsoid (Fig. 5.12a), theopposing pole distributions are further away from eachother and their surface density is lower than when M; isparallel to the short axis (Fig. 5.12b). The demagnetizingfield and energy are smallest when M; is parallel to the longaxis, which is the energetically favored direction of magne­tization. The demagnetizing energy is larger in any otherdirection, giving a shape anisotropy. If N) is the demagne­tizing factor for the long axis and N2 that for the short axis(N) < N 2) , the difference in energy between the two direc­tions of magnetization defines a magnetostatic anisotropyenergy density given by

The process of magnetizing some materials causes themto change shape. Within the crystal lattice the interactionenergy between atomic magnetic moments depends ontheir separations (called the bond length) and on theirorientations, i.e., on the direction of magnetization. If anapplied field changes the orientations of the atomic mag­netic moments so that the interaction energy is increased,the bond lengths adjust to reduce the total energy. Thisproduces strains which result in a shape change of the fer­romagnetic specimen. This phenomenon is called magne­

tostriction. A material which elongates in the direction ofmagnetization exhibits positive magnetostriction, while amaterial that shortens parallel to the magnetizationshows negative magnetostriction. The maximum differ­ence in magnetoelastic strain, which occurs between thedemagnetized state and that of saturation magnetization,is called the saturation magnetostriction, denoted As'

The inverse effect is also possible. For example, if pres­sure is applied to one face of a cubic crystal, it willshorten elastically along the direction of the appliedstress and will expand in directions perpendicular to it.These strains alter the separations of atomic magneticmoments, thereby perturbing the effects that give rise tomagnetocrystalline anisotropy. Thus the application of

294 Geomagnetism and paleomagnetism

rutileTi0

2

igneous nxks I

sandstone

sedimentary rock~

10-5....L....-------------------"-10-5

1~----------..,....---------,.-(a) rocks

Fig. 5.13 (a) Median values and ranges of the magnetic susceptibility

of some common rock types, and (b) the susceptibilities of some

important minerals.

Fig. 5.14 Ternary compositional diagram of the iron-titanium oxide

solid solution magnetic minerals (after McElhinny, 1973).

titanohematite series. The minerals of a third series,pseudobrookite, are paramagnetic at room temperature.They are quite rare and are of minor importance in rockmagnetism, The compositions of naturally occurringforms of titanomagnetite and titanohematite usually plotas points on the ternary diagram that are displaced fromthe ideal lines towards the Ti01-Fe103 axis, which indi­cates that they are partly oxidized.

~

.~~t..~

.~ 0.1t 0.01

~ 0

(b) minerals -L-

~

-1.5x 10-5 -1.4 x 10-5 ~ nquartz calcite pyrite hematite pyrrhotite magnetite

0.1

0.01

FeO

wiistite

Fe304

magnetite

Fe203

hematite (a)

maghemite (y)

rock magnetism are the type of ferrimagnetic mineral, itsgrain size, and the manner in which it acquires a remanentmagnetization.

5.3.2 The ternary oxide system of magnetic minerals

The most important magnetic minerals are iron-titaniumoxides, which are naturally occurring ferrites. The mineralstructure consists of a close-packed lattice of oxygen ions,in which sorne of the interstitial spaces are occupied byregular arrays of ferrous (Fe 2+ ) and ferric (Fe 3+ ) iron ionsand titanium (Ti4+) ions. The relative proportions ofthese three ions determine the ferrimagnetic properties ofthe mineral. The composition of an iron-titanium oxidemineral can be illustrated graphically on the ternary oxidediagram (Fig. 5.14), the corners of which represent theminerals rutile (Ti02), wustite (FeO), and hematite(Fe203) . The proportions of these three oxides in amineral define a point on the ternary diagram. The verti­cal distance of the point above the FeO-Fe203 baselinereflects the amount of titanium in the lattice. Hematite isin a higher state of oxidation than wustite: hence the hori­zontal position along the FeO-Fe~03 axis expresses thedegree of oxidation.

The most important magnetic minerals belong to twosolid-solution series: (a) the titanomagnetite, and (b) the

5.3.2.1 The titanomagnetite series

Titanomagnetite is the name of the family of iron oxideminerals described by the general formula Fe 3_xTi.\.04

(0 ~ X ~ 1). These minerals have an inverse spinel structureand exemplify a solid-solution series in which ionicreplacement of two Fe 3+ ions by one Fe2+ and one Ti 4+

ion can take place. The compositional parameter xexpresses the relative proportion of titanium in the unitcell. The end members of the solid-solution series are mag­netite (Fe

304) , which is a typical strongly magnetic ferrite,and ulvospinel (Fe1Ti04) , which is antiferromagnetic atvery low temperature but is paramagnetic at room temper­ature. An alternative form of the general formula isxFe1Ti04 (1 - x)Fe304. Written in this way, it is apparentthat the compositional parameter x describes the molecu­lar fraction of ulvospinel, As the amount of titanium (x)

increases, the cell size increases and the Curie temperature(J and spontaneous magnetization M; of the titanomag­netite decrease (Fig. 5.15).

Magnetite is one of the most important ferrimagneticminerals, It has a strong spontaneous magnetization(M, = 4.8 X 105 Am") and a Curie temperature of578°C. Because of the high value of Ms' magnetite grainscan have a strong shape anisotropy. The magnetic suscep­tibility is the strongest of any naturally occurring mineral

,5.3 ROCK MAGNETISM 295

600.-------,--~--:------:--.,----.--,.....------.--, R.5-~ ilmenite is antiferrornagnetic at low temperature andparamagnetic at room temperature, For titanium contents0.5 <x<0.95 titanohematite is ferrimagnetic and for.v< 0.5 it exhibits parasitic ferromagnetism,

The end member hematite (Cl-Fe~O~) is an extremelyimportant magnetic mineral. Its magnetic propertiesarise from parasitic ferromagnetism due to the spin­canted magnetic moment and the possible defect 1110111entof its otherwise antiferromagnetic lattice. Hematite has aweak spontaneous magnetization (AJs =2.2 X 1O~ A 111- 1 )

and a strong uniaxial magnetocrystalline anisotropy(Ku ~ 103 J nl- 3). Hematite is paleomagnetically irnpor­tant because of its common occurrence and its high mag­netic and chemical stability. It often occurs as asecondary mineral, formed by oxidation of a precursormineral, such as magnetite, or by precipitation fromfluids passing through a rock.

8.50 oS

8.42

c

-8A6]~v

.-*:5

0.8

I

0.6

I

0.4

Mole fraction of Fe 2T i 04

0.2

E-lOO-

Fig. 5.15 Variations of Curie temperature and unit-cell size withcomposition in titanomagnetite (after Nagata, 1961).

tk = 1-10 SI). For many sedimentary and igneous rocksthe magnetic susceptibility is proportional to the mag­netite content.

Maghemite ()'-Fe~03) can be produced by low­temperature oxidation of magnetite. It is a strongly mag­netic mineral (M s=4.5 X 105 A In-I). Experiments onmaghemite doped with small amounts of foreign ions indi­cate that it has a Curie temperature of 675 °C. However, itis metastable and reverts to hematite (a-Fe20J) whenheated above 300-350 °C. The low-temperature oxidationof titanomagnetite leads to a "titanomaghernite" solid­solution series.

Titanornagnetite is responsible for the magnetic prop­erties of oceanic basalts. The basaltic layer of the oceaniccrust is the main origin of the marine magnetic anomaliesthat are of vital importance to modern plate tectonictheory. The magnetic properties of the 0.5 km thickbasaltic layer are due to the presence of very fine grainedtitanomagnetite (or titanornaghemite, depending on thedegree of ocean-floor weathering). The molecular frac­tion (x) of Fe 2TiO4 in titanomagnetite in oceanic basaltsis commonly around 0.6.

5.3.2.2 The titanohematite series

The minerals of the titanohematite solid-solution seriesare also variously referred to as "hemoilmenite,""hematite-ilmenite ~~ or "ilmenohematite, ~~ They have the

general formula Fe 2_xTixOy The unit cell has rhombohe­draI symmetry, Ionic substitution is the same as for titano­magnetite, and the compositional parameter x has thesame implications for the titanium content of the unit cell.The end mern bers of the solid-solution series are hematite(Fe 203) and ilmenite (FeTi03) . The chemical formula canbe written in the alternative form xFeTi03 . (1 - x)Fe103•

where x represents the molecular fraction of ilmenite,As in the case of titanornagnetite, the cell size increasesand the Curie point decreases as the titanium contentincreases. The Curie point of hematite is 675°C, while

5.3.3 Other ferrimagnetic minerals

Although the iron-titanium oxides are the dominantmagnetic minerals, rocks frequently contain other miner­als with ferromagnetic properties. Although pyrite (FeS2)

is a very COlTIIUOn sulfide mineral, especially in sedimen­tary rocks, it is paramagnetic and therefore cannot carry aremanent magnetization. As a result it does not con­tribute directly to the paleomagnetic properties of rocks,but it may act as a source for the formation of goethite orsecondary magnetite.

Pyrrhotite is a common sulfide mineral which canform authigenically or during diagenesis in sediments,and which can be ferrimagnetic in certain compositionalranges. It is non-stoichiometric (i.e., the numbers ofanions and cations in the unit cell are unequal) and hasthe formula Fe1_xS. The parameter x refers to the propor­tion of vacancies among the cation lattice sites and islimited to the range 0<x<0.14. Pyrrhotite has a pseudo­hexagonal crystal structure and would be antiferrornag­netic but for the presence of the cation vacancies. TheNeel temperature at which the fundamental antiferro­magnetism disappears is around 320°C. Pyrrhotite withthe formula Fe 7S S is ferrimagnetic with a Curie tempera­ture close to the Neel temperature and a strong sponta­neous magnetization of about 105 A 111- 1 at roomtemperature. The magnetocrystalline anisotropy restrictsthe easy axis of magnetization to the hexagonal basalplane at rOO1l1 temperature.

The iron oxyhydroxide goethite (FeOOH) is anothercommon authigenic mineral in sediments, Like hematite,goethite is antiferromagnetic, but has a weak parasitic fer­romagnetism. It has a very high coercivity (with maximumvalues in excess of 5 T) and a low Curie point around 100°C or less. It is thermally unstable relative to hematiteunder most natural conditions, and decomposes onheating above about 350°C. It is a common (and paleo­magnetically undesirable) secondary mineral in lime­stones and other sedimentary rocks.

296 Geomagnetism and paleomagnetism

200 400 600

Temperature (OC)

Fig. 5.16 Identification of the ferromagnetic minerals in a pelagic

limestone by determination of their Curie temperatures in concentrated

extracts (after Lowrie and Alvarez, 1975).

(5.28)

(5.29)

fig =goethite

8m = magnetite

8" =hematite

1 (VKlI )T = Voexp kT

magnetization parallel to the easy direction is equal to vKll

•

Thermal energy, proportional to the temperature, has theeffect of disturbing this alignment. At temperature T thethermal energy of a grain is equal to k T~ where k isBoltzmann's constant (k= 1.381 X 10- 23 J K-l). At anyinstant in time there is a chance that thermal energy willdeflect the magnetic moment of a grain away from its easydirection. Progressively, the net magnetization of the mate­rial (the sum of all the magnetic moments of the numerousmagnetic grains) will be randomized by the thermal energy,and the magnetization will be observed to decay. If theinitial magnetization of the assemblage is MrO~ after time f

it willdecrease exponentially to Mr(t), according to

In this equation T is known as the relaxation time ofthe grain (Box 5.1). If the relaxation time is long, theexponential decrease in Eq. (5.28) is slow and the magne­tization is stable. The parameter T depends on propertiesof the grain and is given by the equation

The constant Vo is related to the lattice vibrational fre­quency and has a very large value (=108-1010 S-I). Thevalue of K

lldepends on whether the easy direction of the

magnetic mineral is determined by the magnetocrystallineanisotropy or the magnetostatic (shape) anisotropy. Forexample, in hematite the magnetocrystalline anisotropyprevails because the spon taneous magnetization isvery weak, and Ku is equal to the magnetocrystalline

5.3.4 Identification offerrimagnetic minerals

It is often difficult to identify the ferrimagnetic mineralsin a rock, because their concentration is so low, especiallyin sedimentary rocks. If the rock is coarse grained, ferri­magnetic minerals may be identified optically among theopaque grains by studying polished sections in reflectedlight. However, in many rocks that are paleomagneticallyimportant (e.g., basaltic lava.. pelagic limestone) opticalexamination may be unable to resolve the very fine grainsize of the ferrimagnetic mineral. The ferrimagneticmineral fraction may then be identified by its propertiesof Curie temperature and coercivity.

The Curie temperature is measured using a form ofbalance in which a strong magnetic field gradient exerts aforce on the sample that isproportional to its magnetization,The field (usually 0.4-1 T) is strong enough to saturate themagnetization of many minerals. The sample is heated andthe change of magnetic force (i.e., sample magnetization) isobserved with increasing temperature. When the Curiepoint is reached, the ferromagnetic behavior disappears; athigher temperatures the sample is paramagnetic. The Curiepoint is diagnostic of many minerals. For exarnple, anextract of magnetic minerals from a pelagic limestone (Fig.5.16) shows the presence of goethite (--100°C Curie point,sample SR3A), magnetite (--570°C Curie point, allsamples) and hematite (---650°CCurie point, sample SR 11 ).Some Curie balances are sensitive enough to analyze wholerock samples, but this is generally only possible in stronglymagnetized igneous rocks. For most rocks it is necessary toextract the ferrimagnetic minerals, or to concentrate them.The extraction is sometimes difficult, and often it is notcertain that the extract is representative of the rock as awhole. This is also a drawback of optical methods, whichonly allow description of large grains.

To avoid the difficulties and uncertainties associatedwith making a special extract or concentrate of the ferri­magnetic fraction, alternative methods of ferrirnagneticmineral identification, based on bulk magnetic properties,are more widely used. One simple method makes use ofthe coercivities and Curie temperatures, as expressed inthe thermal demagnetization of the isothermal remanentmagnetization (see Section 5.3.6.4). Another method,useful for pure magnetite and hematite, takes advantageof the low-temperature variations of the magnetocrys­talline anisotropy constants of these minerals.

5.3.5 Grain size dependence of ferrimagnetic properties

The ferromagnetic properties of metals and ferrites varysensitively with grain size. Consider an assemblage of uni­formly magnetized grains of a ferrimagnetic mineral char­acterized by a spontaneous magnetization A4s and uniformgrain volume V. Let the spontaneous magnetization beoriented parallel to an easy direction of magnetization(crystalline or shape determined) .. defined by the anisotropyenergy K

lIper unit volume. The energy that keeps the

,5.3 ROCK MAGNETISM

Box 5.1: Magnetic relaxation

297

where the negative sign indicates a reduction in lV"j'

Similarly, the number changing in the opposite sensefrom state 2 to state 1 is

bility A per unit time, the number of particles iiN, thatchange from state 1 to state 2 is proportional to the timeinterval dt and to the number of grains N, in state 1. It isgiven by

Relaxation behavior is characterized by the exponen tialreturn of a physical property with time from a state ofelevated energy to a state of lower energy. The 1110stfamiliar example is radioactive decay (Section 4.1.3.1)~

but the magnetizations of natural materials also exhibitrelaxation behavior, as explained in Section 5.3.5.

In the absence of an external field, the easy directionof magnetization of a single domain magnetic grainwith volume v and anisotropy energy Ku per unit volumeis determined by the anisotropy energy vKu (Section5.2.7). The probability that the grain's thermal energykT can overcome this energy barrier and allow the grainmagnetization to change direction is determined by theMaxwell-Boltzmann distribution of energies, and isproportional to exp(-vK

l/k1).The probability per unit

time, A, of a magnetic moment changing to a differenteasy axis is given by the Arrhenius equation for a ther­mally activated process

The net change in magnetization is therefore

dM== J.LdN} - J.LdN2 == J.Ld(N j - N2)

dM= -AJ.L(N j - N2)dt== -AMdt

(3)

(4)

(5)

( VKu)A == Cexp - kT (1)

The solution of this differential equation is

(6)

where T, the relaxation time, is the inverse of A in Eq. (1):

Equations (6) and (7) are very important in paleornag­netism, The strong anisotropy of fine grained ferromag­netic minerals can result in very long relaxation times,and consequently the magnetizations of fine grainedrocks can be extremely stable over geological lengths oftime.

The parameter C is called the frequency factor; here it isthe lattice vibration frequency, l'o' At a particular tem­perature, all parameters on the right side of Eq. (I) areconstant and so the probability A per unit time of amagnetic moment changing to a different easy axis isconstant.

Now suppose an assemblage of identical non­interacting single domain particles, of which N, aremagnetized initially in one direction (state 1) and N2 inthe opposite direction (state 2). The net magnetization isproportional to (N} - N 2) . Assuming a constant proba-

I (VKu )T==voexp kT (7)

anisotropy. In grains of magnetite the value of Ku isequal to«K/3)+ (K2/27)), if magnetocrystalline anisotropy con­trols the magnetization (as in an equidimensional grain). Ifthe magnetite grain is elongate with demagnetizing factorsN, and N2, shape anisotropy determines Ku' which is thenequal to the energydensity Ea givenby Eq. (5.26).

This theory applies only to very small grains that areuniformly magnetized. Fine grained ferrimagnetic miner­als are, however, very important in paleomagnetism androck magnetism. The very finest grains, smaller than a crit­ical size, exhibit an unstable type of magnetic behaviorcalled superparamagnetism, with relaxation times typicallyless than 100 s.Above the critical size the uniformly magne­tized grain is very stable and is called a single domain grain.

5.3.5.1 Superparamagnetism

In a ferromagnetic material the strong molecular fieldskeep the atomic spin magnetic moments uniformly aligned

with each other, and the grain anisotropy requires thisspontaneous magnetization to lie parallel to an "easy"direction. If the temperature is too high, thermal energy(k1) may exceed the anisotropy energy (l'Ku) but still betoo small to break up the spontaneous magnetization,The thermal energy causes the entire magnetic 1110n1ent ofthe grain to fluctuate coherently in a manner similar toparamagnetism (the theory of which applies to individualatomic magnetic moments). The grain magnetizationhas no stable direction, and the behavior is said to besuperparaniagnetic. It is important to note that superpara­magnetic grains themselves are immobile: only theiruniform magnetization fluctuates relative to the grain.Whether the ferrirnagnetic grain exists in a stable or super­paramagnetic state depends on the grain size, the grainshape (if the origin of K u is magnetostatic) and the tem­perature. If the grain volume F is very small, unstablemagnetic behavior due to superpararnagnetism becomeslikely. Magnetite and hematite grains finer than about

298 Geomagnetism and paleomagnetism

aciculargrain

sphericalgrain

,/

,//-/-~~-~""""",-

+\+

\..

~~ s;"n;gledo11lt1i71

r~lOOS~ ~/--~

(a)

(b)

-/- -\-

//// -."'~,~-' ',-~~-~.//

0.01

r-

-3':::

..c:'toc~

c::.~

0.1 0

1.00.80.6

multldomain

0.4

Axial ratio ([)/n)

superparumagnctic

Coercivity (T)

0.25 0.20 0.15 0.10 0.05

0.20.0

0.01

Fig. 5.17 Rangesof grain sizesand shapes for superparamagnetic,

single domain and multidomain magnetic behavior in ellipsoidal

magnetite grains (after Evansand McElhinny, 1969).

(5.30)

0.03 J-Lm in diameter are superparamagnetic at room temp­erature.

5.3.5.2 Single domain particles

When the anisotropic magnetic energy (vKu) of a grain isgreater than the thermal energy (k1), the spontaneousmagnetization direction favors one of the easy directions.The entire grain is uniformly magnetized as a singledomain. This situation occurs in very fine grains of ferri­magnetic minerals.

In magnetite Ku is the magnetostatic energy related tothe particle shape. The theoretical range of single domainsizes in magnetite is narrow, from about 0.03 to 0.1 J.Lm inequant grains and up to about 1 J.Lm in elongate grains(Fig. 5.17). In hematite Ku is the large magnetocrystallineanisotropy energy, and the range of single domain sizes islarger, from about 0.03 to 15 urn.

The magnetization of a single domain particle is verystable, because to change it requires rotating the entireuniform spontaneous magnetization of the grain againstthe grain anisotropy, which requires a very strong magneticfield. The magnetic field required to reverse the direction ofmagnetization of a single domain grain is called its coerciv­ity Beand is given by:

2KuBc =¥

s

The maximum coercivity of single domain magnetite isaround 0.3 T for needle-shaped elongate grains. The mag­netocrystalline anisotropy of hematite gives it highermaximum coercivities, in excess of 0.5 T. However, themagnetic properties of hematite are very variable and itsmaximum coercivity commonly exceeds 2 T. Because of

(c)

Fig. 5.18 Subdivision of (a) the uniform magnetization of a large grain

into (b) two oppositely magnetized magnetic domains and (c) four

alternately magnetized domains.

their stable remanent magnetizations, single domain par­ticles playa very important role in paleomagnetism.

5.3.5.3 Multidomain particles

Single domain behavior is restricted to a limited range ofgrain sizes. When a grain is large enough, the magneticenergy associated with its magnetization becomes toolarge for the magnetization to remain uniform. This isbecause the demagnetizing field of a uniformly magne­tized grain (Fig. 5.18a) interacts with the spontaneousmagnetization and generates a magnetostatic (or self­demagnetizing) energy. To reduce this energy, the magne­tization subdivides into smaller, uniformly magnetizedunits, called Weiss domains after P. Weiss, who theoreti­cally predicted domain structure in 1907. In the simplestcase the magnetization divides into two, oppositely mag­netized domains (Fig. 5.18b). The net magnetization isreduced to zero, and the magnetostatic energy is reducedby about a half. Further subdivision (Fig. 5.18c) reducesthe magnetostatic energy correspondingly. In a grain with1"1 domains of alternately opposed spontaneous magneti­zations the magnetostatic energy is reduced by lIn. The

5.3 ROCK MAGNETISM

domains are separated from one another by thin regions,about 0.1 J..Lm thick. that are usually much thinner than thedomains they divide. These regions are called Blochdomain walls in recognition of F. Bloch., who in 1932 pro­posed a theory for the structure of the domain wall on anatomic scale. Within the domain wall the magnetizationundergoes small progressive changes in direction fromeach atom to its neighbor. The crystalline magneticanisotropy of the material attempts to keep the atornicmagnetic spins parallel to favored crystalline directions.while the exchange energy resists any change of directionfrom parallel alignment by the molecular field. The energyof these competing effects is expressed as a domain wallenergyassociated with each unit area of the wall.

The magnetization of a multidomain grain can bechanged by moving the position of a domain wall., whichcauses some domains to increase in size and others todecrease. A large multidomain grain may contain manyeasily movable domain walls. Consequently, it is mucheasier to change the magnetization of a multidomaingrain than of a single domain grain. As a result multido­main grains are less stable carriers of remanent magneti­zation than single domain grains.

The transition between single domain and multido­main behavior occurs when the reduction of magnetosta­tic energy is balanced by the energy associated with thedomain wall that has been added. If magnetite grains areelongate, they can persist as single domain grains up toabout 1 J..Lm (Fig. 5.17). Magnetite grains larger than afew micrometers in diameter are probably multidomain.In equidimensional grains of magnetite the transitionshould occur in grains of about 0.05-0.1 urn diameter.However, at this point the grain is not physically largeenough to contain a wall, which has a thickness of about0.1 urn. Grains in the intermediate range of sizes, andthose large enough to contain only a few walls, are said tocarry a pseudo-single domain magnetization. True mul­tidomain behavior in magnetite is observed when thegrain size exceeds 15-20 urn,

In a pseudo-single domain grain that is large enoughto contain only two domains, the domain wall separatingthem is not able to move freely. Its freedom of movementis restricted by interactions with the grain surface. A smallgrain in this size range has more stable magnetic proper­ties than a multidomain particle but is not as stable as atrue single domain grain. Magnetite grains between about0.1 m and several micrometers in diameter have pseudo­single domain properties.

5.3.6 Remanent magnetizations in rocks

The small concentration of ferrimagnetic minerals in arock gives it the properties of magnetic hysteresis. Mostimportant of these is the ability to acquire a remanentmagnetization (or remanence). The untreated remanenceof a rock is called its natural remanent magnetization(NRM). It may be made up of several components

299

acquired in different ways and at different times, The geo­logically important types of remanence are acquired atknown times in the rock's history. such as at the time of itsformation or subsequent alteration. The remanence of arock can be very stable against change; the high coercivity(especially of the fine grains) of the ferrimagnetic mineralassures preservation of the magnetic signal during longgeological epochs.

A remanence acquired at or close to the time of for­mation of the rock is called a primary magnetization:a remanence acquired at a later time is called asecondary magnetization. Examples of primary rema­nence are thermoremanent magnetization. which anigneous rock acquires during cooling., and the remanentmagnetizations acquired by a sediment during or soonafter deposition. Secondary remanences may be causedby chemical change of the rock during diagenesis orweathering., or by sampling and laboratory procedures.

5.3.6.1 Thermoremanent magnetization

The most important type of remanent magnetization inigneous (and high-grade metamorphic) rocks is thermore­manent magnetization (TRM). Igneous rocks solidify attemperatures well above 1000 °C. At this temperature thegrains are solid and fixed in a rigid matrix. The grains of aferrimagnetic mineral are well above their Curie tempera­ture, which in magnetite is 578°C and in hematite is675°C. There is no molecular field and the individualatomic magnetic moments are free to fluctuate chaoti­cally: the magnetization is paramagnetic (Fig. 5.19).

As the rock cools, the temperature eventually passesbelow the Curie temperature of the ferrimagnetic grainsand a spontaneous magnetization appears. In singledomain grains the relaxation time of the grain magnetiza­tion is governed by Eq. (5.29), which can be modified bywriting the anisotropy energy density Ku in terms of thespontaneous magnetization M; and coercivity Be of thegrain. This gives the relaxation time as follows

(5.31)

At high temperature the thermal energy (k1) is largerthan the magnetic energy (vM sB/2) and the magnetiza­tion is unstable. Although the individual atomic mag­netic moments are forced by the molecular field to act ascoherent units" the grain magnetizations are superpara­magnetic. As the rock cools further, the spontaneousmagnetization and the magnetic anisotropy energy K u ofthe grain increase. Eventually the temperature passesbelow a value at which the thermal energy., whose effectis to randomize the grain magnetic moments, is nolonger greater than the magnetic anisotropy energy. Thespontaneous magnetization then becomes "blocked"along an easy direction of magnetization of the grain. Inthe absence of an external magnetic field the grain

300 Geomagnetism and paleomagnetism

M t. Etna lavas(ChC7)nlier,1925)

Temperature

Curiepoint

.>,

)60C

'\

j

90°

f270+-

I

t\-

• direction of magnetic field during eruption

o direction of magnetization of lava sample

ferromagnetisnl <!

Fig.5.19 On cooling through the Curie temperature the magnetic

state of magnetite grains changes from paramagnetism to

ferromagnetism. On cooling further the magnetizations in the

magnetite grains become blocked along easy directions of

magnetization close to the field direction. The resultant

thermoremanent magnetization is parallel to the field direction.

magnetic moments will be randomly oriented (assumingthe easy axes to be randomly distributed). If the graincools below its blocking temperature in a magnetic field,the grain magnetic moment is "blocked' along the easyaxis that is closest to the direction of the field at that time(Fig. 5.19). The alignment of grain magnetic momentswith the field is neither perfect nor complete; it repre­sents a statistical preference. This means that in anassemblage of grains more of the grains have their mag­netic moments aligned close to the field direction thanany other direction. The degree of alignment depends onthe strength of the field.

It is important to note that the mineral grains them­selves are immobile throughout the process of acquisitionof TRM. Only the internal magnetizations of the grainscan change direction and eventually become blocked. Theblocking temperatures of TRM are dependent on thegrain size, grain shape, spontaneous magnetization andmagnetic anisotropy of the ferrimagnetic mineral. If therock contains a wide range of grain sizes and perhapsmore than a single magnetic mineral, there may be abroad spectrum of blocking temperatures, Maximumblocking temperatures may range as high as the Curiepoint and the spectrum can extend to below ambienttemperature, If the magnetic field is applied only while therock is cooling through a limited temperature range, onlygrains with blocking temperatures in this range are acti­vated. and a partial TRM (or pTRM) results.

r->. matrix\.-) mineral

\ magnetization~ direction

Fig. 5.20 Agreement of directions of thermoremanent magnetization

in a basaltic lava flow on Mt. Etna (Sicily) with the direction of the

geomagnetic field during eruption of the lava (based upon data from

Chevallier, 1925).

TRM is a very stable magnetization which can existunchanged for long intervals of geological time. Theability of TRM to record accurately the field direction isdemonstrated by the results from a lava that erupted onM1. Etna at a time for which a record of the magnetic fielddirection is available from observatory data. The direc­tions of the TRM in the lava samples are the same as thedirection of the ambient field (Fig. 5.20).

5.3.6.2 Sedimentary remanent magnetizations

The acquisition of depositional remanent magnetization(ORM) during deposition of a sediment takes place atconstant temperature. Magnetic and mechanical forcescompete to produce a physical alignment of detrital ferri­magnetic particles. During settling through still waterthese particles are oriented by the ambient magnetic fieldin the same way that it orients a compass needle. The par­ticles become aligned statistically with the Earth's mag­netic field (Fig. 5.21). The action of mechanical forcesmay at times spoil this alignment. Water currents causehydromechanical forces that disturb the alignment duringsettling, giving rise to a declination error. On contact withthe bottom of the sedimentary basin, the mechanicalforce of gravity rolls the particle into a stable attitude,causing an inclination error. The pressure of overlyingsediment during deep burial results in compaction, whichcan produce further directional errors. The DRM isfinally fixed in sedimentary rocks during diagenesis.

A modified form of post-depositional remanence(pORM) is important in fine grained sediments. A water­logged slurry forms at the sediment-water interface. Finegrained magnetic minerals in the water-filled pore spaces in

5.3 ROCK MAGNETISM 301

Fig. 5.21 Acquisition of depositional remanent magnetization (DRM)

in a sediment; gravity causesan inclination error between the

magnetization and field directions.

geomagneticfield direction

30° 60°

Inclina tion of field

O°-t'-~---r--,.....-----,..---r----r---r--~--,

0°

(b)

of bioturbated sediment by the burrowing organismsassists the Brownian motion of the magnetic particles.Under these conditions the pDRM is acquired at the baseof the bioturbated zone.

5.3.6.3 Chemical remanent magnetization

Fig. 5.22 (a) Post-depositional remanent magnetization (pDRM) isacquired by reorientation of ferromagnetic grains in the pore spaces ofa deposited sediment. (b) Comparison of the pDRM inclination with thefield inclination in a redeposited deep-sea sediment (after Irving andMajor, 1964).

(a)

Chemical remanent magnetization (CRM) is usually asecondary form of remanence in a rock. It occurs whenthe magnetic minerals in a rock suffer chemical alterationor when new minerals form authigenically. An example isthe precipitation of hematite from a goethite precursor orfrom iron-saturated fluids that pass through the rock. Themagnetic minerals may also experience diagenetic modifi­cation or oxidation by weathering, which usually happenson the grain surface and along cracks (Fig. 5.23). Thegrowth of a new mineral (or the alteration of an existingone) involves changes in grain volume v. spontaneous

water

,'geomagnetic" field direction,

,,,,,,,~ /" ~,,,,

magnetitegrains

r#4 c1inationDRM " error,,,,

field Ji'direction

the sediment are partially in suspension and may be reori­ented by the magnetic field, if they are free enough to move(Fig. 5.22a). The energy for this motion of the particles isobtained from the Brownian motion of the water mole­cules, which continuously and randomly collide with theparticles in the pore spaces. Large particles are probably incontact with the surrounding grains and are unaffected bycollisions with the water molecules. Very fine particles thatare virtually floating in the pore spaces may acquireenough freedom from the Brownian agitation to align sta­tisticallywith the Earth's magnetic field. Laboratory exper­iments have established that the direction of pDRM is anaccurate record of the depositional field, without inclina­tion error (Fig. 5.22b). The pDRM is acquired later thanthe actual time of sedimentation, and is fixed in the sedi­ment during compaction and de-watering at a depth of....... l Ocm. This may represent a lock-in time delay of 100yrin lacustrine sediments or 10,000yr in pelagic marine sedi­ments, where it is no tnore important geologically than theerrors involved in locating paleontological stage bound­aries. The pDRM process is particularly effective in finegrained sediments containing strongly magnetic magnetitegrains. For example, pDRM is the most important mecha­nism of primary magnetization in pelagic limestones,Compaction may cause a flattening of the inclinationunder some conditions.

Bioturbation may mix the sediment, typically to a depthof about 10em in pelagic sediments. This affects the posi­tions of stratigraphic marker levels. First occurrence datumlevelsof fossils are carried deeper. and last occurrences arecarried higher than the true stratigraphic levels. Agitation

302 Geomagnetism and paleomagnetism

Fig.5.23 Acquisition of chemical remanent magnetization (CRM)

accompanies the diagenetic modification or oxidation by weathering of

magnetic minerals; this often happens on the grain surface and along

cracks.

575=350

350150325675

80-120

Maximumblockingten1perature[Oe]

200 -100 600

Temperature (OC)

Maximumcoercivity[T]

lOO 80e. • low coercivity

(a)...,

+ intermediate

80~ o high coercivity\60 \

"I I

6 \6 6U

1 140 \Cretaceous limestone, \:E -to Scaglia Rossa, Italy :E

e:: ~~

2020

0 0 2 3 200 -100 600

Field (T) Temperature (OC)

200 150

(b)• low coercivity

+ intermediate

k-' -, o high coercivity,./

• -.100 0--.'78 1'6

'q,.\~1100 1

~~e:: 50

2 3

Field (T)

Fig. 5.24 Examples of the identification of magnetic minerals by

acquisition and subsequent thermal demagnetization of IRM. Hematite

is present in both (a) and (b), because saturation IRM requires fields

> 1T and thermal demagnetization of the hard fraction persists to

T= 675°(. In (a) the soft fraction that demagnetizes at T= 575°C is

magnetite, while in (b) no magnetite is indicated but pyrrhotite is

present in all three fractions, shown by thermal unblocking atT = 300-330 O( (after Lowrie, 1990).

Ferromagneticmineral

Magnetite 0.3Maghemite 0.3

Titanomagnetite (Fe) _ xTix04):.\=0.3 0.2x= 0.6 0.1

Pyrrhotite 0.5-1Hematite 1.5-5Goethite > 5

these properties provides a method of identification of thepredominant magnetic minerals in rocks. Starting with thestrongest field available, IRM is imparted in successivelysmaller fields, chosen to remagnetize different coercivityfractions, along two or three orthogonal directions. Thecompound IRM is then subjected to progressive thermaldemagnetization. The demagnetization characteristics of

Table 5.1 Maximum coercivities and blockingtemperatures for some C0111111011 ferromagnetic minerals

hemntit»in cracks and

along grain rims

c =secondary

CRM

M=primary

remanentmagnetiza tion

magnetization u, and coercivity Be' The chemical changeaffects the relaxation time of the grain magnetization,according to Eq. (5.31). The grains eventually growthrough a critical volume, at which the grain magnetiza­tion becomes blocked. The new CRM is acquired in thedirection of the ambient field during the chemical change,and so it is younger than the host rock. It has stable mag­netic properties similar to TRM. A common example isthe formation of hematite during diagenesis or weather­ing. Hematite that originates in this way typically carries asecondary remanent magnetization.

5.3.6.4 Isothermal remanent magnetization

Isothermal remanent magnetization (IRM) is induced ina rock sample by placing it in a magnetic field at constanttemperature. For example, rock samples are exposed tothe magnetic fields of the sampling equipment and toother magnetic fields during transport to the laboratory.A common technique of rock magnetic analysis consistsof deliberately inducing IRM via a known magnetic fieldproduced in a large coil or between the poles of an elec­tromagnet. The magnetic moments within each grain arepartially aligned by the applied field. The degree of align­ment depends on the field strength and on the resistanceof the magnetic mineral to being magnetized, looselyreferred to as its coercivity. After removing the samplefrom the applied field an IRM remains in the rock (seeFig. 5.11). If the rock sample is placed in progressivelystronger fields the IRM increases to a maximum valuecalled the saturation IRM, which is determined by thetype and concentration of the magnetic mineral. Theshape of the progressive acquisition curve and the fieldneeded to reach saturation IRM depend on the coercivi­ties of the magnetic minerals in the rock (Fig. 5.24).

The maximum coercivities of the most common ferro­magnetic minerals in rocks are fairly well known (Table5.1). These minerals also have distinctive maximum block­ing temperatures (Section 5.3.6.1). The combination of

5.3 ROCK MAGNETISM

Time Is)

Fig. 5.25 Viscous remanent magnetization (VRM) in pelagic limestone

samples, showing logarithmic growth with increasing time (after Lowrie

and Heller, 1982).

the different coercivity fractions help to identify the mag­netic mineralogy (Fig. 5.24).

5.3.6.5 Other remanent magnetizations

If a rock containing magnetic minerals with unstable mag­netic moments experiences a magnetic field, there is a finiteprobability that some magnetic moments opposite to thefield may switch direction to be parallel to the field. As timegoes on, the number of magnetic moments in the directionof the field increases and the magnetization grows loga­rithmically with time (Fig. 5.25). The time-dependentremanence acquired in this way is called a viscous remanentmagnetization (VRM). The VRM also decreases logarith­mically when the field is removed or changed and is oftenidentifiable during laboratory analysis as an unstable time­dependent change in remanence. The direction of a VRMis often parallel to the present-day field direction, whichcan be useful in its identification. However, it is always asecondary remanence and it can mask the presence of geo­logically interesting stable components. Techniques of pro­gressive demagnetization have been designed to removeVRM and IRM, effectively "cleaning" the remanence of arock of undesirable components.

An important form of remanent magnetization can beproduced in a rock sample by placing it in a coil that carriesan alternating magnetic field, whose amplitude is thenslowly reduced to zero. In the absence of another field, thisprocedure randomizes the orientations of grain magneticmoments with coercivities less than the peak field. If,however, the rock sample is exposed to a small constantmagnetic field while the amplitude of the alternating mag­netic field is decreasing to zero, the magnetic moments arenot randomized. Their distribution is biassed with a statis­tical preference for the direction of the constant field. Thisproduces an anhysteretic remanent magnetization (ARM)in the sample. The intensity of ARM increases with theamplitude of the alternating field, and also with the

303

strength of the constant bias field. ARM may be produceddeliberately, as described, and it is commonly observed as aspurious effect during progressive alternating field demag­netization of rock samples when the shielding from exter­nal fields is imperfect (Section 5.6.3.2).

Stress and the associated strains of magnetostrictioncombine to produce magnetoelastic energy (see Section5.2.7.3). This acts as a source of magnetic anisotropy thatcan modify the easy directions of magnetization in somemagnetic minerals. As a result, stress caused by tectonicdeformation or by defects in the crystal structure of con­stituent minerals may influence the direction of magnetiza­tion in a rock. The effect of high hydrostatic pressure, suchas might be encountered at depth in the Earth's crust, is todeflect the magnetizations of individual grains away fromexisting easy axes, which leads to a net demagnetization ofthe rock. On the other hand, the effect of non-hydrostaticstress in the presence of a magnetic field is to produce apiezoremanent magnetization (PRM) that is added to, ormay replace, any pre-existing remanent magnetization. Themodification of rock magnetization by deformationalstress, whether elastic or plastic, can overprint the originalmagnetization in rocks that have been deeply buried, or sub­jected to high stress and temperature during deformation.

A related type of magnetization has been observed interrestrial and lunar rocks that have been shocked by mete­oritic impact. The event causes very high local stress ofshort duration, and gives rise to a shock remanent magneti­zation (SRM) by a similar mechanism to PRM. The colli­sion of a meteorite with another planetary body imposes acharacteristic shock' texture on the impacted rocks, so thatSRM and PRM are not exactly equivalent. Moreover, muchof the energy of the collision is released as heat, which canmodify and reduce the SRM over a much longer time thanthe brief duration of the impact. However, SRM may haveplayed a role in the origin of anomalous crustal magnetiza­tions on the Moon, Mars and other extraterrestrial bodiesthat have suffered extensive meteoritic bombardment.

5.3.7 Environmental magnetism

Since the mid-1980s rock magnetic properties have foundimportant new applications in environmental research,where they can serve as tracers for pollution or as indica­tors of past climates. Heavy metals from industrialprocesses enter the environment, contaminating both theground surface and the water in lakes, rivers and thegroundwater. Magnetic minerals such as magnetite andhematite accompany more toxic elements in the emis­sions. Magnetic susceptibility surveys can provide a rapidmethod of determining the geographic dispersal and rela­tive concentration of the heavy metal pollution. Motor­vehicle exhaust emissions also pollute the environment byloading it with heavy metals as well as sub-micrometersized particles of soot, a fraction of which consists ofnanoparticle sized magnetic minerals. Rock magneticparameters and investigative techniques provide ways of

304 Geomagnetism and paleomagnetism

Fig. 5.26 Comparison of the

magnetic susceptibility

variation in a section of loess

and paleosols at Xifeng,

China, with the oxygen

isotope record in marine

sediments cored at ODPsite

677 (after Evansand Heller,

2003). 100

Age(kyr)

200

300

400

ODP 677

() 180 (%0 to PDB)

XifengSusceptibility

(10-8 m3 kg-1)

100 200

Lithology300

characterizing these particles and of describing theirregional distribution and concentration.

The magnetic grain fraction in a sediment or soil usuallyconsists of hematite, magnetite, maghemite or an ironsulfide. The magnetic mineral composition may be modi­fied by the climatic conditions at or after deposition. Theseaffect magnetic properties of the sediment that depend ongrain size and mineral composition, such as magnetic sus­ceptibility, coercivity and the various remanent magnetiza­tions. These magnetic parameters can act as proxies forpaleoclimatic change. Numerous studies have been devotedto understanding the processes involved and their applica­tion. The following example illustrates the potential ofmagnetic methods for analyzing a paleoclimatic problem.

Great thicknesses of loess sediments up to 100m inthickness occur in Central China. The loess are very finegrained (10-50 J.1m size) wind-blown sediments that aredeposited in cold, dry conditions. Alternating with thebeds of loess are layers of paleosol, the name given tofossil soils. These form by conversion of the loess to soils(a process called pedogenesis), which takes place duringinterglacial periods of warmer, humid conditions. Inturn, later loess deposits bury the soils. The alternation ofloess and paleosol is therefore a record of past climaticvariations. The magnetic susceptibility correlates with thelithology of the loess-paleosol sequences. In the loessbeds the susceptibility measures around 25 SI units, but inthe paleosol layers the values exceed 200 SI units (Fig.5.26). Rock magnetic analysis showed that the dominantmagnetic mineral in both lithologies is magnetite. Thehigher susceptibility of the paleosols is thus due to higherconcentrations of magnetite. The susceptibility variationcorrelates very well with the oxygen isotope stratigraphymeasured in deep-sea sediments at site 677 of the OceanDrilling Program (ODP). The oxygen isotope ratio (seeBox 5.2) is a record of climatic variation, with the mostnegative values corresponding to warmer temperature,

and it has been dated by comparison to magnetostratigra­phy in marine sediments (Section 5.7.2). The correlationin Fig. 5.26 provides a way of dating the loess-paleosolsequence and shows that the paleosols were formed underwarmer conditions than the loess. Possibly the change toa warmer, humid climate encouraged the in situ formationof a new phase of magnetite in the paleosols, with a con­sequent increase in susceptibility.

The new phase of magnetite in the paleosols originatesby a chemical process. However, magnetite can be producedby the action of bacteria in sediments deposited in lakesand in the sea. This is referred to as a biogenic process andthe bacteria that can produce magnetite are called magneto­tactic bacteria. The magnetite forms as tiny crystallitescalled magnetosomes, less than 0.1 J.1m in size and thus ofsingle domain type, which occur as chains of particlesenclosed in a membrane. The most common magnetosomemineral is magnetite, but greigite, an iron sulfide with struc­ture similar to magnetite, has also been found. The chain­like assembly imparts a dipole magnetic moment to thebacteria. This is evidently an evolutionary feature, whichhelps the bacteria to survive. If the sediment is disturbed,the magnetic moment of the bacteria enables them to movealong the Earth's magnetic field lines. The dipping fieldlines guide them back down into the sediment where theyfind nutrition needed for their survival. It was long believedthat magnetite in deep-sea sediments was mainly of detritalorigin, washed in from the continents and ocean ridges, butit is now clear that a large portion must be biomagnetic.

Magnetite of biogenic origin has been identified in manyunusual settings. For example, submicroscopic magnetiteoccurs in the brains of dolphins and birds; whether it plays arole in their guidance during migration is unclear.Magnetite of nanometer size has been located in the humanbrain, where it may be related to neurological disorders suchas epilepsy, Alzheimer's disease and Parkinson's disease. Italso occurs in other human organs. The magnetic properties

5.4 GEOMAGNETISM 305

o

o

-20

-60(

(180 / I60) sample - (

180 / I60) standard)

8180 = 1000 X ('80/ 160)

standard

Box 5.2:Oxygen isotope ratio

The element oxygen has two important stable isotopes.These are a "light" isotope 160 , with 8 protons and 8neutrons in its nucleus, and a "heavy" isotope 180 , with8 protons and 10 neutrons. Mass spectrometers arecapable of determining accurately the masses of theseisotopes, and so the mass ratio 180 /160 can be measuredin quite small samples. In order to describe the deviationof the 180 /160 ratio in a given sample from a standardvalue, a useful parameter, 8180 , is defined as follows:

40

The standard value is taken to be the 180 /160 ratio inthe modern oceans at depths in the 200-500 m range, oralternatively the ratio in a fossil belemnite known asPDB. The factor 1000 causes 8180 values to beexpressed in parts per thousand. The global climate atpresent is relatively warmer than in the past, so 180 /160ratios measured in ancient samples tend to be smallerthan the standard value and give negative 8180 values.

The 180 /160 ratio in water is dependent on tempera­ture, as evident in the plot of 8180 in the annual precipi­tation against the mean temperature at a global set ofsites (Fig. B5.2). Two factors determine this correlation:cool air holds less moisture than warm air, and the"heavy' isotope 180 condenses more easily than the"light" isotope 160 . From an air mass that moves pole­wards, precipitation in warmer regions is relatively richin 180 whereas in colder regions it is enriched in 160 .

The situation is reversed in the oceans. During globalwarm periods, polar ice sheets melt, adding fresh waterenriched in 160 to the oceans. As a result, low (i.e., largenegative) 8180 values in the oceans indicate intervals ofglobal warming. In contrast, during glacial intervalswater is transferred from the oceans to the ice sheets

-40 -20 0 20

Temperature (OC)

Fig. 85.2 Observed correlation between a180 in precipitation andtemperature for the present-day climate (after Jouzel et al., 1994).

primarily as 160 , so the remaining ocean water isenriched in 180 , which increases the 8180 value. Thus,high (i.e., small negative or even positive) 8180 values inoceanic water and sediments indicate cool intervals.Conversely, the same conditions result in the oppositerelationships between global temperature and 8180values measured in polar ice.

Paleoclimatology uses the 8180 parameter as a guideto past climates, as illustrated by the use of the record insediment cores from the Ocean Drilling Project to inter­pret the paleoclimate that affected. Chinese loess-pale­osol profiles (Fig. 5.26). Samples can be used from avariety of sources: polar ice cores, ocean sediments, andfossil shells. In the last case, biological and chemicalprocesses disturb the simple relationship with tempera­ture, but this can be taken into account and corrected.

of the magnetite, its source and the mechanism of its forma­tion in human tissue are exciting fields of modem research.

5.4 GEOMAGNETISM

5.4.1 Introduction

The magnetic field of the Earth is a vector, that is, it hasboth magnitude and direction. The magnitude, or intensityF, of the field is measured in the same units as other B­fields, namely in tesla (see Eq. (5.10». However, a tesla isan extremely strong magnetic field, such as one wouldobserve between the poles of a powerful electromagnet.The Earth's magnetic field is much weaker: its maximumintensity is reached near to the magnetic poles, where itamounts to about 6 X 10- 5 T. Modern instruments for

measuring magnetic fields (called magnetometers) have asensitivity of about 10- 9 T; this unit is called a nanotesla(nT) and has been adopted in geophysics as the practicalunit for expressing the intensity of geomagnetic field inten­sity.There is a practical reason for adopting this unit. Mostgeomagnetic surveys carried out until the 1970s used thenow abandoned c.g.s. system of units, in which the B-fieldwas measured in gauss, equivalent to 10- 4 T. The practicalunit of geophysical exploration was then 10- 5 gauss, calleda gamma ('y). Thus, the former unit ('y) is convenientlyequal to 10- 9 T, which is the new unit (nT).

The magnetic vector can be expressed as Cartesiancomponents parallel to any three orthogonal axes. Thegeomagnetic elements are taken to be components parallelto the geographic north and east directions and the verti­cally downward direction (Fig. 5.27). Alternatively, the

306 Geomagnetism and paleomagnetism

iV

vertical

Fig. 5.27 Definition of the geomagnetic elements. The geomagneticfield can be described by north (X), east (Y)and vertically downward (Z)

Cartesian components, or by the angles of declination (0) andinclination (I) together with the total field intensity (F).

geomagnetic elements can be expressed in spherical polarcoordinates. The magnitude of the magnetic vector isgiven by the field strength F~ its direction is specified bytwo angles. The declination D is the angle between themagnetic meridian and the geographic meridian; the incli­nation I is the angle at which the magnetic vector dipsbelow the horizontal (Fig. 5.27). The Cartesian (X, Y, Z)and spherical polar (F, D, l) sets of geomagnetic elementsare related to each other as follows:

This is a rather formidable expression, but fortunatelythe most useful terms are quite simple, The summationsigns indicate that the total potential is made up of aninfinite number of terrns with different values of 11 and I.We will only pay attention here to the few terms for which11= 1. The expression in parentheses describes the varia­tion of the potential with distance r. For each value of n

there will be different dependences (e.g., on r, r 2, }.3, ]"-2,

]"-3, etc.). The function Y:l(8.cP) describes the variation ofthe potential when r is constant. i.e., on the surface of asphere. It is called a spherical harmonicfunction, becauseit has the same value when ()or cP is increased by an inte­gral multiple of 21T (Box 2.3). For observations made onthe spherical surface of the Earth, the constants Andescribe parts of the potential that arise from magneticfield sources outside the Earth, which are called the geo­magnetic field of external origin. The constants B

ll

describe contributions to the magnetic potential fromsources inside the Earth. This part is called the geomag­

neticfield 0.[internal origin.The potential itself is not measured directly. The geo­

magnetic elements X, Yand Z (Fig. 5.27) are recorded atmagnetic observatories. Ideally these should be distrib­uted uniformly over the Earth's surface but in fact they arepredominantly in the northern hemisphere. The geomag­netic field components are directional derivatives of themagnetic potential and depend on the same coefficients AJ1and Bn . Observations of magnetic field elements at a largenumber of measurement stations with a world-wide distri­bution allows the relative importance of A 11 and B

I1to be

assessed. From the sparse data-set available in 1838 Gausswas able to show that the coefficients An are very muchsmaller than BJ1' He concluded that the field of externalorigin was insignificant and that the field of internal originwas predominantly that of a dipole.

Y=FcoslsinD Z=Fsinl

-:""~v'" 7P'j.r:\:-~~//~~'\: / :<,,0.''-

X= FcoslcosD

F'2=X2+ y2+Z2

z"Y------J

5.4.2 Separation of themagnetic fields of external andinternal origin

The magnetic field B and its potential Wat any point can beexpressed in terms of the spherical polar coordinates (r, 8, cP)of the point of observation. Gauss expressed the potentialof the geomagnetic field as an infinite series of terms involv­ing these coordinates. Essentially, his method divides thefield into separate components that decrease at differentrates with increasing distance from the center of the Earth.The detailed analysis is complicated and beyond the scopeof this text. The magnitude of the potential is given by

where R is the Earth's radius.

W= R~(Al,r" + J~:I)~ y;,(O,c/»1/=1 1 1=0

D = arctan(-:f:) 1= arctan( ~X2~ yJ (5.32)

(5.33)

5.4.3 The magnetic fieldof external origin

The magnetic field of the Earth in space has been mea­sured from satellites and spacecraft. The external field hasa quite complicated appearance (Fig. 5.28). It is stronglyaffected by the solar wind, a stream of electrically chargedparticles (consisting mainly of electrons, protons andhelium nuclei) that is constantly emitted by the Sun. Thesolar wind is a plasma. This is the physical term for anionized gas of low particle density made up of nearlyequal concentrations of oppositely charged ions. At thedistance of the Earth from the Sun (1 AU) the density ofthe solar wind is about 7 ions per cm', and it produces amagnetic field of about 6 nT. The solar wind interactswith the magnetic field of the Earth to form a regioncalled the magnetosphere. At distances greater than a fewEarth radii the interaction greatly alters the magnetic fieldfrom that of a simple dipole.

The velocity of the solar wind relative to the Earth isabout 450 km S-I. At a great distance (about 15 Earth radii)from the Earth. on the day side, the supersonic solar wind

5.4 GEOMAGNETISM

--------- ............<,

20". 30 Earth 4U

radii

Fig. 5.28 Schematic cross-section through the magnetosphere,

showing various regions of interaction of the Earth's magnetic field

with the solar wind.

collides with the thin upper atmosphere. This produces aneffect similar to the build-up of a shock wave in front of asupersonic aircraft. The shock front is called the bow-shockregion (Fig. 5.28); it marks the outer boundary of the mag­netosphere. Within the bow-shock region the solar wind isslowed down and heated up. After passing through theshock front the solar wind is diverted around the Earth in aregion of turbulent motion called the magnetosheath, Themoving charged particles of the solar wind constitute elec­trical currents. They produce an interplanetary magneticfield, which reinforces and compresses the geomagneticfield on the day side and weakens and stretches it out on thenight side of the Earth. This results in a geomagnetic tail,or magnetotail, which extends to great distances "down­wind" from the Earth. The Moon's distance from the Earthis about 60 Earth radii and so its monthly orbit about theEarth brings it in and out of the magnetotail on eachcircuit. The transition between the deformed magnetic fieldand the magnetosheath is called the magnetopause.

5.4.3.1 The Van Allen radiation belts

Charged particles that penetrate the magnetopause aretrapped by the geomagnetic field lines and form the VanAllen radiation belts. These constitute two doughnut­shaped regions coaxial with the geomagnetic axis (Fig.5.29). The inner belt contains mainly protons, the outerbelt energetic electrons. Within each belt the charged par­ticles move in helical fashion around the geomagnetic fieldlines (Fig. 5.30). The pitch of the spiraling motion getssmaller as the particle comes ever closer to the Earth andthe field intensity increases; eventually it reaches zero andreverses sense. This compels the particles to shuttle rapidlyfrom one polar region to the other along the field lines.The inner Van Allen belt starts about 1000 km above theEarth's surface and extends to an altitude of about

307

3000 krn (Fig. 5.29)~ the outer belt occupies a doughnutshaped region at distances between about 3 and 4 Earthradii (20,000-30~OOOkm) from the center of the Earth.

5.4.3.2 The ionosphere

The effects described above illustrate how the Earth's mag­netic field acts as a shield against much of the extra-terres­trial radiation. The atmosphere acts as a protective blanketagainst the remainder, Most of the very short-wavelengthfraction of the solar radiation that penetrates the atmos­phere does not reach the Earth 's surface. Energetic "t: andx-rays and ultraviolet radiation cause ionization of themolecules of nitrogen and oxygen in the thin upper atITIOS­phere at altitudes between about 50 km and 1500 krn,forming an ionized region called the ionosphere. It isformed of five layers, labelled the D~ E, F I' F2 and G layersfrom the base to the top. Each layer can reflect radio waves.The thicknesses and ionizations of the layers changeduring the course of a day; all but one or two layers on thenight side of the Earth disappear while they thicken andstrengthen on the day side (Fig. 5.31). A radio transmitteron the day side can bounce signals off the ionosphere thatthen travel around the world by multiple reflectionsbetween the ground surface and the ionosphere. Conse­quently, radio reception of distant stations from far acrossthe globe is best during the local night hours. The 0 layer isclosest to the Earth at an altitude of about 80-100 km. Itwas first discovered in 1902, before the nature of the ionos­phere was known, because of its ability to reflect long­wavelength radio waves, and is named the Kennelly­Heaviside layer in honor of its discoverers. The E layer isused by short-wave amateur radio enthusiasts. The F layersare the most intensely ionized.

5.4.3.3 Diurnal variation and magnetic storms

The ionized molecules in the ionosphere release swarms ofelectrons that form powerful, horizontal, ring-like electri­cal currents. These act as sources of external magneticfields that are detected at the surface of the Earth. Theionization is most intense on the day side of the Earth,where extra layers develop. The Sun also causes atmos­pheric tides in the ionosphere, partly due to gravitationalattraction but mainly because the side facing the Sun isheated up during the day. The motions of the charged par­ticles through the Earth's magnetic field produce an elec­trical field, according to Lorentz's law (Eq. (5.10»)~ whichdrives electrical currents in the ionosphere. In particular,the horizontal component of particle velocity interactswith the vertical component of the geomagnetic field toproduce horizontal electrical current loops in the ionos­phere. These currents cause a magnetic field at the Earth'ssurface. As the Earth rotates beneath the ionosphere theobserved intensity of the geomagnetic field fluctuateswith a range of amplitude of about 10-30 nT at theEarth's surface and a period of one day (Fig. 5.32a). This

308 Geomagnetism and paleomagnetism

outerVan Allen

rJ! belt

//

<~.>i .... i.••·.../·<.~ -~

'~

dipolefieldaxis

\\ .. "~

<.':',/.:

5

Distance(Earth radii)

Fig. 5.29 Schematicrepresentation of the inner

and outer Van Allen belts ofcharged particles trapped bythe magnetic field of the

Earth.

geomagneticaxis

auroraborealis

belt

auroraaustralis

belt

dipole 7'field lines

N

(a)

S L..--- --' L..--- -----I L..--- -----I

Fig. 5.30 Charged particles from the solar wind are constrained tomove in a helical fashion about the geomagnetic field lines (afterVestine, 1962).

northcomponent

(X)

eastcomponent

(Y)

verticalcomponent

(2)

Fig. 5.31 Cross-section through the Earth showing the layeredstructure of the ionosphere (after Strahler, 1963).

Fig. 5.32 (a) The time-dependent daily (or diurnal) variation of the

components of geomagnetic field intensity at different latitudes (after

Chapman and Bartels, 1940), and (b) the variation of horizontal fieldintensity during a magnetic storm (after Ondoh and Maeda, 1962).

v

Macquarie observatory16.2.1958

II I I I I II I I I I II I I II III III III II I III II I I

6 12 18 24 6 12 18Universa I time

Horizontalintensity

500lnTJ(b)

time-dependent change of geomagnetic field intensity iscalled the diurnal (or daily) variation.

The magnitude of the diurnal variation depends on thelatitude at which it is observed. Because it greatly exceedsthe accuracy with which magnetic fields are measuredduring surveys, the diurnal variation must be compensatedby correcting field measurements accordingly. The intensity

nightday

radiation

solar

5.4 GEOMAGNETISM 309

5.4.4 The magnetic field of internal origin

To understand how geophysicists describe the geomagneticfield of internal origin mathematically we return toEq. (5.33). First, we follow Gauss and omit the coefficientsAn of the external field. The spherical harmonic functionsy~~(0,4» that describe the variation of potential on a spher­ical surface are then written in expanded form (Box 2.3).The potential Wof the field of internal origin becomes

of the effect depends on the degree of ionization of theionosphere and is therefore determined by the state of solaractivity. As described in Section 5.4.7.1, the solar activity isnot constant. On days when the activity of the Sun is espe­cially low, the diurnal variation is said to be of solar quiet(Sq)type. On normal days, or when the solar activity is high,the Sqvariation is overlaid by a solar disturbance (SD)vari­ation. Solar activity changes periodically with the ll-yrcycle of sunspots and solar flares. The enhanced emissionof radiation associated with these solar phenomenaincreases the ionospheric currents. These give rise to rapidlyvarying, anomalously strong magnetic fields (called mag­

netic storms; with amplitudes of up to 1000 nT at theEarth's surface (Fig. 5.32b). The ionospheric disturbancealso disrupts short-wave to long-wave radio transmissions.Magnetic surveying must be suspended temporarily while amagnetic storm is in progress, which can last for hours ordays, depending on the duration of the solar activity.

Here, R is the Earth's radius, as before, and P~;'(cosO) arecalled Schmidt polynomials, which are related to the asso­ciated Legendre polynomials (Box 2.2).

Equation (5.34) is a multipole expression of the geo­magnetic potential. It relates the potential of the mea­sured field to the potentials of particular combinations ofmagnetic poles (Box 5.3). The constants g7z1 and h~;l in thegeomagnetic potential are called the Gauss (or Gauss­Schmidt) coefficients of order n and degree In. Inspectionof Eq. (5.34) shows that they have the same dimensions(nT) as the B-field. Their values are computed fromanalysis of measurements of the geomagnetic field.

Data from several sources are integrated in modernanalyses of the Earth's magnetic field. Until the dawn ofthe satellite era. continuous records at magnetic observa­tories were the principal sources of geomagnetic data.Average values of the geomagnetic elements were deter­mined, from which optimum values for the Gausscoefficients could be derived. Currently, about 200 perma­nent observatories make continuous measurements of thefield. However, satellites orbiting the Earth in low near­polar orbits now provide most of the high-quality dataused to model the field. The Polar Orbiting Geophysical

n=XI11=tI(R)ll+ IW= R~,~) r Cg,;'cosm¢

+ Iz~;'sin md: )P~~'( cos 0) (5.34)

Observatory (POGO), launched in 1965, was the first todeliver field measurements, but the greatest advance camewith the Magnetic Field Satellite (MAGSAT), whichdelivered high-quality data during a six-month mission in1979-1980. In 1979, a Danish satellite, 0RSTED, wasplaced in an elliptical, low-polar orbit, with altitudebetween 650 km and 865 km. It carried a vector magne­tometer and a total field magnetometer, each with a sensi­tivity of 0.5 nT; the mission was dedicated to a survey ofthe geomagnetic field. The German satellite CHAMP (seealso Section 2.4.6.4), was launched in 2000 in a lower,near-circular orbit on a planned five-year mission. Inaddition to measuring the gravity field, this satellitewas also equipped to make scalar and vector measure­ments of the magnetic field. The low orbit and improvedinstrumentation were designed to provide magnetic mea­surements with high resolution.

In principle, an infinite number of Gauss coefficientswould be needed to define the field completely. Thecoefficients of order and degree 8 and higher are very smalland the calculation of Gauss coefficients must usually betruncated. A global model of the field is provided by theInternational Geomagnetic Reference Field (IGRF),which is based on coefficients up to n == 10, although analy­ses of higher order have been made. It is updated at regularintervals. The IGRF also gives the rate of change of each ofthe Gauss coefficients (its secularvariation), which permitscorrection of the current values between update years.

The Gauss coefficients get smaller with increasingorder n: this decrease provides a way of estimating theorigin of the internal field. The analysis involves a tech­nique called power spectral analysis.. The distance across afeature of the magnetic field (for example, a region wherethe field is stronger than average) is called the wavelengthof the feature. As in the case of gravity anomalies, deep­seated magnetic sources produce broad (long-wave­length) magnetic anomalies, while shallow sources resultin narrow (short-wavelength) anomalies. Spectral analysisconsists of calculating the power (alternatively calledthe energy density) associated with each "frequency" inthe signal. This is obtained by computing the sum of thesquares of all coefficients with the same order. In the caseof the geomagnetic field. the spectral analysis is based onthe values of the Gauss coefficients. The spatial frequencyof any part of the observed field is contained in the ordern of the coefficients. Low-order terms (those with smallvalues of 11) correspond to long-wavelength features,high-order terms are related to short-wavelength features.

Measurements of the geomagnetic field from theMAGSAT Earth-orbiting satellite at a mean altitude of420 km above the Earth's surface have been analyzed toyield Gauss coefficients to order 11 = 66, special techniquesbeing invoked for orders 11 > 29. A plot of the energydensity associated with each order n of the geomagneticfield shows three distinct segments (Fig. 5.33). The high­frequency terms of order 11 >40 are uncertain and theterms with 11> 50 are in the "noise level" of the analysis

310 Geomagnetism and paleomagnetism

Box 5.3: Multipole representation of thegeomagnetic field

Each term in Eq. (5.34) is the potential of the magneticfield due to a particular combination of magnetic poles.For example, Eq. (5.34) contains three terms for which 11

== 1. Each corresponds to a dipole field. One dipole isparallel to the axis of rotation of the Earth and theother two are at right angles to each other in the equato­rial plane. The five terms with 11== 2 describe a geometri­cally more complex field, known as a quadrupole field.Just as a dipole field results when two single poles arebrought infinitesimally close to each other (see Section5.2.3)~ a quadrupole field results when two opposingcoaxial dipoles are brought infinitesimally close end-to­end. As its name implies, the quadrupole field derivesfrom four magnetic poles of which two are "north ~~

poles and two are "south" poles. The terms with 11== 3describe an octupole field which is characterized byeight (23) poles. The terms with 11 == N describe a fieldthat arises from a configuration of 2N poles.

The configurations of axial dipole. quadrupole andoctupole fieldsrelative to a reference sphere are illustratedin Fig. B5.3.1 for the case where the order 171 of the Gausscoefficients is zero. If 111 == 0 in Eq, (5.34), the potentialdoes not vary around a circle of "latitude ~~ defined by achosen combination of () and r, This kind of field is said tohave zonal symmetry, Any cross-section that contains theaxis of symmetry is representative for the symmetry, Fig.85.3.1 shows axial cross-sections of the simplest field linegeometries corresponding to (a) dipole, (b) quadrupoleand (c) octupole fields:each field is rotationally symmetri­cal about the axis of the configuration. The correspond­ing zonal spherical harmonics are illustrated symbolicallyby shading the alternate zones in which magnetic fieldlines leaveor return to the surface of a sphere.

The dipole field is horizontal at the equator. In thesouthern hemisphere the field lines leave the referencesphere: in the northern hemisphere they return to it. Inthe northern hemisphere the field of an axial quadrupoleis horizontal at latitude 35.3°N. North of this latitude thefield lines of the quadrupole leave the reference sphere.An equivalent circle of latitude is located in the southernhemisphere at 35.3°S~ south of this latitude the quadru­pole field lines also leave the Earth. The field lines re­enter the Earth in the band of latitudes between thosewhere the field is horizontal. The symmetry of thequadrupole field is described by these three zones aroundthe axis. The axial octupole field exhibits zonal symmetrywith four zones: two zones in which the field leaves theEarth alternate with two zones in which it re-enters it.

Tenus in the potential expansion for which the degree171 of the Gauss coefficients is equal to the order /1 (e.g., x],h 1. g~~ h~) are called sectorial harmonics. Their symmetryrelative to the Earth's axis is characterized by an evennumber of sectors around the eq uator in which the fieldlines alternately leaveand re-enter the Earth (Fig. B5.3.2).

L\\IS 01rotational"Yllll11clry

(.1) (b) (e)

dipole quadrupole ociupole

~. (:) ~<c::11=1 11=2 11=3

ZUlU"harmonics

Fig.B5.3.1 Axial cross-sections showing the field line geometries of

(a) dipole, (b) quadrupole and (c) octupole fields; each field is

rotationally symmetrical about the axis of the configuration. The

corresponding zonal spherical harmonics are illustrated symbolically

by shading the alternate zones in which magnetic field lines leave or

return to the surface of a sphere.

-ectorial harmonic pattern

tesseral harmonic pattern

Fig.B5.3.2 Symmetry relative to the axis of rotation of sectorial and

tesseral spherical harmonic functions.

The potential terms for which 171 1= /1 (e.g., g~, h~, g~~ 171) areknown as tesseral harmonics. Their pattern of symmetryis defined by the intersections of circles of latitude andlongitude, which outline alternating domains in whichthe field lines leave and re-enter the Earth, respectively.

Multipole representation allows the very complexgeometry of the total field to be broken down into contri­butions from a number of fields with simple geometries.

8y superposing many terms corresponding to thesesimple geometries a field of great complexity can begenerated. It 111USt be kept in mind that this is not aphysical expression of the magnetic field. because mag­netic poles do not exist. It is a convenient technique fordescribing the field mathematically

5.4 GEOMAGNETISM311

MAGSAT data(mean altitude 420 krn)

Note that Br vanishes at the equator iH> 90°) and thefield is horizontal: comparing Eqs. (5.37) and (5.39) weget that the horizontal equatorial field BtJ is equal to g? Ata point (r~ 0) on the surface of a uniformly magnetizedsphere the magnetic field line is inclined to the surface atan angle J. which is given by

(5.38)

(5.39)

(5.40)Br

tanl= B = 2cotO = 2tan.Ae70605040302010

Order, 11

5.4.4.1 The dipole field

Fig. 5.33 The energy density spectrum derived from measurements of

the geomagnetic field made by the MAGSAT Earth-orbiting satellite(after Cain, 1989).

Note that the spatial variation of this potential dependson (cos OIi·2) in the same way as the potential of a dipole,which was found (Eq, (5.8» to be

Comparison of the coefficients of (cos OIi·2 ) in Eq. (5.35)and Eq. (5.36) gives the dipole moment of the Earth'saxial dipole in terms of the first Gauss coefficient:

(5.41 )

The angle I is called the inclination of the field, and () isthe angular distance (or polar angle) of the point ofobservation from the magnetic axis. The polar angle is thecomplement of the magnetic latitude, .A (i.e., 0 = 90° - .A).Equation (5.40) has an important application in paleo­magnetism, as will be seen later.

The terms gl and Izj are the next strongest in the poten­tial expansion. They describe contributions to the potentialfrom additional dipoles with their axes in the equatorialplane. The total dipole moment of the Earth is thenobtained from the vector sum of all three components:

111 = t: RJ-Y(g?)2 + (gl)2 + (hi>"

The analysis of the geomagnetic field for the year 2005gave the following values for the dipole coefficien ts: g? =-29~556.8 nT~ gl=-1671.8 nT~ 17}=5080.0 nT. Thestrength of the Earth's dipole magnetic moment obtainedby inserting these values in Eq. (5.41) is 111 = 7.7674 X 1022

A n1 2. Note that the sign of if is negative. This 111eanS thatthe axial dipole points opposite to the direction of rota­tion. Taken together, the three dipole components describea geocentric dipole inclined at about 11.2° to the Earth'srotation axis. This tilted geocentric dipole accounts formore than 90lXl of the geomagnetic field at the Earth 'ssurface. Its axis cuts the surface at the north and south geo­

magnetic poles. For epoch 2005 the respective poles werelocated at 79.7°N, 71.8°W (i.e.~ 288.2°E) and 79.7°S,108.2°E. The geomagnetic poles are antipodal (i.e., exactlyopposite) to each other.

The magnetic poles of the Earth are defined as the loca­tions where the inclination of the magnetic field is ± 90°(i.e.. where the field is vertically upward or downward). Anisoclinal map (showing constant inclination values) for theyear 1980 shows that the location of the north magneticpole was at 77.3°N, 258.2°E while the south magnetic polewas at 65.6°S~ 139.4°E (Fig. 5.34a). These poles are notexactly opposite one another. The discrepancy betweenthe magnetic poles and the geomagnetic poles arisesbecause the terrestrial magnetic field is somewhat 1110recomplex than that of a perfect dipole. The intensity of thegeomagnetic field is generally stronger in high latitudesthan near the equator (Fig. 5.34b). The intensity is

(5.35)

(5.36)

(5.37)

JLo,ncos()w=---­41Tr2

The most important part of the Earth's magnetic field atthe surface of the Earth is the dipole field, given by theGauss coefficients for which /1 = 1. If we write only thefirst term of Eq. (5.34) we get the potential

R3g0 cosOW=_L_'__,.2

41T ., 0/71=-R-'a

JLo b'

and cannot be attributed any geophysical importance, Theterms 15~ /1 < 40 are due to short-wavelength magneticanomalies associated with the magnetization of the Earth 'scrust. The terms /1~ 14dominate the Earth's magnetic fieldand are due to much deeper sources in the fluid core.

The term g? is the strongest component of the field. Itdescribes a magnetic dipole at the center of the Earth andaligned with the Earth 's rotation axis. This is called thegeocentric axial magnetic dipole.

The magnetic field B of a dipole is symmetrical aboutthe axis of the dipole. At any point at distance r from thecenter of a dipole with moment 111 on a radius that makesan angle () to the dipole axis the field of the dipole has aradial component B, and a tangential component Btrwhich can be obtained by differentiating the potentialwith respect to ,. and ()~ respectively:

312 Geomagnetism and paleomagnetism

Fig. 5.34 (a) The isoclinal

map of the geomagnetic field

for the year 1980 AD (afterMerrill and McElhinny, 1983),

and (b) the total intensity of

the InternationalGeomagnetic Reference Field

(in IJ..T) for 2000 (source:

http://geomag.nasa.gov).

especially low over the South Atlantic, where it is about 20J.LT weaker than expected. The cause of this "SouthAtlantic magnetic anomaly" is not understood. Becausethe geomagnetic field shields the Earth from cosmic radia­tion and charged particles of the solar wind, this protec­tion is less effective over the South Atlantic. Orbitingsatellites note increased impacts of extra-terrestrial parti­cles over this region. The feature poses hazards for astro­nauts in low-orbiting spacecraft and also for pilots andpassengers in high-altitude aircraft that pass through theregion. The enhanced particle flux can interfere with theiron-board computers, communications and guidancesystems.

5.4.4.2 The non-dipole field

The part of the field of internal origin (about 5(Yo of thetotal field), obtained by subtracting the field of theinclined geocentric dipole from the total field, is collec­tively called the non-dipole field. A map of the non-dipolefield consists of a system of irregularly sized, long­wavelength magnetic anomalies (Fig. 5.35). To describethis field requires all the terms in the potential expansionof order n~2 in Eq. (5.34).

The distribution of positive and negative non-dipolefield anomalies suggests an alternative representation ofthe non-dipole field to the multipole portrayal. The posi­tive and negative anomalies have been modelled byinward or outward oriented radial dipoles in the core atabout one-quarter the Earth's radius. Each dipole is pre­sumed to be caused by a toroidal current loop parallel tothe surface of the core. A single centered axial dipole andeight auxiliary radial dipoles are adequate to representthe field observed at the Earth's surface. The secular vari­ation at a site (Section 5.4.5.2) is explained by this modelas the passage of one of the auxiliary dipoles under thesite. This model may be a little closer to physical realitybut it is more unwieldy to handle. The multipole represen­tation is the most convenient way of modelling the geo­magnetic potential for mathematical analysis.

5.4.5 Secular variation

At any particular place on the Earth the geomagnetic fieldis not constant in time. When the Gauss coefficients of theinternal field are compared from one epoch to another,slow but significant changes in their values are observed.The slow changes of the field only become appreciable

,5.4 GEOMAGNETISM

313

10,1-------------__. (a)

-I

8°

J(b)' I , , .

12°-+ --- -- ----- ---- --- --- -- ---- ---- ----

..... <,

1'1

6r~N

S20' .....,...

Qjoc 6

06<lJ"0c,0

-s1800 900W 0° yO<)E 1800

IJ)·xC'l:lQ)

"0c,~

'0.....~

Fig. 5.35 The vertical component of the non-dipole magnetic field for

the years 1780 AD (after Yukutake and Tachinaka, 1968) and 1980 AD

(after Barton, 1989).

Fig. 5.36 Secular variations of the tilted geomagnetic centered dipole

from 1550 AD to 1900 AD. (a) Decrease of dipole moment; (b) slowchanges of the tilt of the dipole axis relative to the rotation axis, and (c)longitude variation indicating westward drift of the geomagnetic poles(after Barton, 1989).

century. Less reliable data, enlarged by archeomagneticresults (see Section 5.6.2.1), allow estimates of the secularvariation of the dipole axis since the middle of the six­teenth century. The earlier data suggest that in the six­teenth century the dipole axis was tilted at only about 3°to the rotation axis; a gradual increase in tilt took placebetween the sixteenth and nineteenth centuries. Duringthe last 200 yr the dipole axis has maintained an almostconstant tilt of about 11-12° to the rotation axis (Fig.5.36b).

For the past 400 yr the longitude of the geomagneticpole has drifted steadily westward (Fig. 5.36c). Before thenineteenth century the pole moved westward at about0.14° yr: I; this corresponds to a pseudo-period of 2600 yrfor a complete circle about the geographic pole. However..since the early nineteenth century the westward motionof the pole has been slower, at an average rate of0.044° vr: I ~ which corresponds to a pseudo-period of8200 yr.

over decades or centuries of observation and so they arecalled secular variations(from the Latin word saeCU1UlJ'1 fora long age). They are manifest as variations of both thedipole and non-dipole components of the field.

5.4.5.1 Secular variation of thedipole field

The dipole field exhibits secular variations of intensityand direction. Calculations of the Gauss coefficients fordifferent historical epochs show a near-linear decay ofthe strength of the dipole moment at a rate of about 3.2<Yoper century between about 1550 AD and 1900 AD. Atthe start of the twentieth century the decay became evenfaster and has averaged about 5.8°;{) per century duringthe last 80 yr (Fig. 5.36a). If it continues at the samealmost linear rate, the field intensity would reach zero inabout another 2000 yr. The cause of the quite rapid decayin intensity is not known; it may simply be part of alonger term fluctuation. However, another possibility isthat the dipole moment may be decreasing preparatoryto the next reversal of geomagnetic field polarity.

The position of the dipole axis also shows secularvariation. The changes can be traced by plotting thecolatitude (the angle between the dipole axis and the rota­tion axis) and longitude of the geomagnetic pole as afunction of time. Data are only sufficiently abundant forspherical harmonic analysis since the early nineteenth

1500 1600 1700 1800

Year

1900 2000

314 Geomagnetism and paleomagnetism

0.2'---L---l---L--l------l.-.---l.----!.......---'-

0.4

core

core

outer

inner

-0.4 -0.2 0 0.2Angular velocity of corerelative to mantle (0yr")

o-!--I--:--------;-----;----,-----;-------+-----""":"""-...........-:----,--~

-0.6

~ 2000

Q)u~

J3en~~

~C'I:3

~ 1000-

Fig. 5.38 Interpreted velocity distribution (relative to the mantle) for amulti-layered core model in which the change of angular momentum ofeach layer due to convectional fluid motion is balanced byelectromagnetic forces (after Watanabe and Yukutake, 1975).

3000

the rotational axis) its angular rate of rotation must speedup. This results in a layered structure for the radial profileof angular rate of rotation relative to the mantle (Fig.5.38). The outer layers of the core probably rotate moreslowly than the solid mantle, imparting a westward driftto features of the magnetic field rooted in the fluidmotion.

5.4.6 Origin of the internal field

Analysis of the Gauss coefficients and the wavelengths offeatures of the non-dipole field indicate that the mainfield is produced in the fluid outer core of the Earth. Thecomposition of the fluid core has been estimated fromseismic and geochemical data. The major constituent isliquid iron, with smaller amounts of other less dense ele­ments. Geochemical analyses of iron meteorites suggestthat the core composition may have a few percent ofnickel, while shock-wave experiments require 6-100/0 ofnon-metallic light elements such as silica, sulfur oroxygen. The solid inner core is inferred from seismic andshock-wave data to consist of almost pure iron.

For the generation of the magnetic field the importantparameters of the core are its temperature, viscosity andelectrical conductivity. Temperature is known verypoorly inside the Earth, but probably exceeds 3000 °C in

•angularrateofdrift forconstantlinear velocityof0.58mm/«at top of core

0.3

i

O.4~I

~ ::1~ I

Latitude N

Fig. 5.37 The variation with latitude of average westward drift ratesestimated from inclination and declination observations at geomagneticobservatories in the northern hemisphere. The curve gives the angular

rotation rate at the surface of the core for a linear velocity of0.058 cm S-1 (after Yukutake, 1967).

5.4.5.2 Secular variation of thenon-dipole field

Comparison of maps of the non-dipole field for differentepochs (Fig. 5.35) show two types of secular variation.Some anomalies (e.g., over Mongolia, the South Atlanticand North America) appear to be stationary but theychange in intensity. Other anomalies (e.g., over Africa)slowly change position with time. The secular variation ofthe non-dipole field therefore consists of a standing partand a drifting part.

Although some foci may have a north-south compo­nent of motion, the most striking feature of the secularvariation of the recent non-dipole field is a slow westwarddrift. This is superposed on the westward drift of thedipole, but can be separated readily by spherical har­monic analysis. The rate of drift of the non-dipole fieldcan be estimated from longitudinal changes in selectedfeatures plotted for different epochs. The mean rate ofwestward drift of the non-dipole field in the first half ofthe last century has been estimated to be 0.18° yr- 1, corre­sponding to a period of about 2000 yr. However, somefoci drift at up to about 0.7° yr- I , much faster than theaverage rate. Results from several geomagnetic observato­ries show that the rate of drift is dependent on latitude(Fig. 5.37).

Westward drift is an important factor in theories ofthe origin of the geomagnetic field. It is considered to be amanifestation of rotation of the outer layers of the corerelative to the lower mantle. Theoretical models of thegeomagnetic field (discussed in the next section) presumeconservation of angular momentum of the fluid core. Tomaintain the angular momentum of a particle of fluidthat moves radially inwards(decreasing the distance from

5.4 GEOMAGNETISM

the liquid core. The electrical conductivity of iron at20°C is 107 0, -} m -1 and decreases with increasing tem­perature. At the high temperatures and pressures in thecore the electrical conductivity is estimated to be around(3-5) X 105 0, -} m -}, which corresponds to a goodelectrical conductor. For comparison, the conductivityof carbon (used for many electrical contacts) is3x 1040,-lm - l at 20 °C.

5.4.6.1 Magnetostatic and electromagnetic models

As observed by Gilbert in 1600, the dipole field of theEarth resembles that of a uniformly magnetized sphere.However, permanent magnetization is an inadequateexplanation for the geomagnetic dipole. The mean mag­netization of the Earth would need to be many timesgreater than that of the most strongly magnetic crustalrocks. The Curie point of the most important minerals atatmospheric pressure is less than 700°C, which is reachedat depths of about 25 km so that only a thin outer crustalshell could be permanently magnetized. The necessarymagnetization of this shell is even greater than valuesobserved in crustal rocks. Moreover, a magnetostaticorigin cannot account for the temporal changes observedin the internal field, such as its secular variation.

The main magnetic field of the Earth is thought to beproduced by electrical currents in the conductive core.Although the core is a good conductor, an electricalcurrent system in the core continually loses energythrough ohmic dissipation. The lost electrical energy isconverted to heat and contributes to the thermal balanceof the core. The equations of electromagnetism applied tothe core show that an electrical current in the core woulddecay to zero in around 10,000-20,000 yr unless it is sus­tained. Paleomagnetic evidence in the form of coherentlymagnetized rocks supports the existence of a geomag­netic field since Precambrian time, i.e. for about 3000Myr. This implies that it must be continuously main­tained or regenerated. The driving action for the mainfield is called the dynamo process, by analogy to the pro­duction of electrical power in a conductor that rotates ina magnetic field.

5.4.6.2 The geomagnetic dynamo

When a charged particle moves through a magnetic field,it experiences a deflecting electrical field (called theLorentz field) proportional to the magnetic flux density Band the particle velocity v, and acting in the directionnormal to both Band v. The Lorentz field acts as an addi­tional source of electrical current in the core. Its strengthis dependent on the velocity of motion of the conductingfluid relative to the magnetic field lines. When this term isincluded in the Maxwell electromagnetic equations, amagnetohydrodynamic equation relating the magneticfield B to the fluid flow v and conductivity a in the core isobtained. It is written

315

aB 1 2at = /Loa V B + V X (v X B) (5.42)

This vector equation, although complicated, has imme­diate consequences. The left side gives the rate of changeof magnetic flux in the core: it is determined by two termson the right side. The first is inversely dependent on theelectrical conductivity, and determines the decay of thefield in the absence of a driving potential; the better theconductor, the smaller is this diffusion term. The second,dynamo term, depends on the Lorentz electrical field,which is determined by the velocity field of the fluidmotions in the core. The conductivity of the outer core«3-5) X 105 0- 1 m- I) is high and for a fluid velocity ofabout 1mm s-1 the dynamo term greatly exceeds thediffusion term. Under these conditions, the lines of mag­netic flux in the core are dragged along by the fluid flow.This concept is called thefrozen:tlux theorem, and it is fun­damental to dynamo theory. The diffusion term is onlyzero if the electrical conductivity is infinite. There is proba­bly some diffusion of the field through the fluid, because itis not a perfect conductor. However, the frozen-fluxtheorem appears to approximate well the conditions in thefluid outer core.

The derivation of a solution of the dynamo theory isdifficult. In addition to Maxwell's equations with the addi­tion of a term for the Lorentz field, the Navier-Stokesequation for the fluid flow, Poisson's equation for the grav­itational potential and the generalized equation of heattransfer must be simultaneously satisfied. The fluid flowconsists of a radial component and a rotational compo­nent. The energy for the radial flow comes from twosources. The slow cooling of the Earth produces a temper­ature gradient in the core, which results in thermallydriven convection in the iron-rich fluid of the outer core.This is augmented by latent heat released at the boundarybetween the inner and outer cores as the inner core solidi­fies. The solidification of the pure iron inner core depletesthe fluid of the outer core of its heaviest component. Theremaining lighter elements rise through the liquid outercore, causing a buoyancy-driven convection.

The rotational component of the fluid flow is the resultof a radial velocity gradient in the liquid core, with innerlayers rotating faster than outer layers (Fig. 5.38). The rel­ative rotation of the conducting fluid drags magnetic fieldlines around the rotational axis to form ring-like, toroidalconfigurations. The toroidal field lines are parallel to theflow and therefore to the surface of the core. This meansthat the toroidal fields are confined to the core and cannotbe measured; their strengths and configurations must beestimated from models. Their interactions with theupwelling and descending branches of convective cur­rents create electrical current systems that producepoloidal magnetic fields. These, in their turn, escape fromthe core and can be measured at the surface of the Earth.The fluid motions are subject to the effects of Coriolisforces, which prove to be strong enough to dominate theresultant flow patterns.

316 Geomagnetism and paleomagnetism

5.4.6.3 Computer simulation ofthegeodynamo

Important advances in understanding the geomagneticdynamo (or geodynatnoi have been made by simulatingthe related core processes with supercomputers. In 1995,G. A. Glatzmaier and P. H. Roberts presented a numeri­cal model for the generation of a magnetic field assuminga hot convective fluid outer core surrounding a solid innercore, with rotation rate akin to that of the Earth. The heatflow, electrical conductivity and other material propertieswere made as similar as possible to those of the Earth'score. The simulated dynamo had dominantly dipole char­acter and intensity similar to the Earth's, and it exhibiteda westward drift of the non-dipole field comparable tothat measured at the Earth's surface. It also reversedpolarity spontaneously, with long periods of constantpolarity between short polarity transitions, as is the casefor the history of geomagnetic reversals in the last160 Myr (Section 5.7). During a polarity reversal, the fieldintensity decreased by an order of magnitude, as is alsoobserved in paleomagnetic studies (see Fig. 5.71).

The simulations showed that the ability to reversepolarity was increased when the heat flow across thecore-mantle boundary was non-uniform, as in the Earth,showing that thermal conditions in the lower mantleinfluence the formation of the magnetic field in the fluidcore. The solid inner core evidently plays an importantrole in the reversal process. Magnetic fields in the outercore can change quickly, accompanying convection, andmay act to initiate reversals. However, magnetic fields inthe solid inner core change more slowly by diffusion andthus the inner core may act to stabilize the field againstreversals. A reversal occurs occasionally, on a longer timescale than the core processes.

A prediction of this model is that the magnetic fieldcouples the inner core to the eastward flowing fluid aboveit, so that the inner core rotates slightly faster than themantle and crust (Fig. 5.38). There is seismic evidencethat this indeed occurs. The solid inner core is seismicallyanisotropic, with cylindrical symmetry about an axisclose to the rotation axis. The axis of symmetry rotates ata rate about 10 faster than that of the mantle and crust.

5.4.7 Magnetic fields of theSun, Moon and planets

Our knowledge of the magnetic fields of the Sun andplanets derives from two types of observation. Indirectobservations utilize spectroscopic effects. All atoms emitenergy related to the orbital and spin motions. The energyis quantized so that the atom possesses a characteristicspectrunl of energy levels.The lowest of these is called theground state. When an atom happens to have been excitedto a higher energy level, it is unstable and eventuallyreturns to the ground state. In the process the energy cor­responding to the difference between the elevated andground states is emitted as light. For example atomichydrogen gas in the Sun and galaxies emits radiation at

1420 MHz, with corresponding wavelength of 21 em.This frequency is in the microwave range and can bedetected by radio telescopes. If the hydrogen gas is inmotion the frequency is shifted by the Doppler effect,from which the velocity of the motion can be deduced.

In the presence of a magnetic field a spectral line cansplit into several lines. This "hyperfine splitting" is calledthe Zeeman effect. When a hydrogen atom is in theground state its hyperfine structure has only one line.However, if the atom is in a magnetic field, it acquiresadditional energy from the interactions between the atomand the magnetic field and hence it can exist in severalenergy states. As a result the spectral lines of energyemitted by the atom are split into closely spaced lines, rep­resen ting transitions between the different energy states.The energy differences between these states are dependenton the strength of the magnetic field, which can be esti­mated from the observations.

Direct observations of extra-terrestrial magnetic fieldshave been carried out since the 1960s by space probes.Magnetometers mounted in these spacecraft haverecorded directly the intensity of the interplanetary mag­netic field as well as the magnetic fields around severalplanets. The manned Apollo missions to the Moonresulted in a large amount of data obtained from theorbiting spacecraft. The materials collected on theMoon's surface and brought back to Earth by the astro­nauts have provided valuable information about lunarmagnetic properties.

5.4.7.1 Magnetic field of theSun

The Sun has nearly 99.9°10 of the mass of the solar system.About 990/0 of this mass is concentrated in a massivecentral core that reaches out to about 800/0 of the Sun'sradius. The remainder of the Sun consists of an outerconducting shell, which contains only 1°/0 of the Sun'smass but has a thickness equivalent to about 20DA) of thesolar radius. Thermonuclear conversion of hydrogen intohelium in the dense core produces temperatures of theorder of 15,000,000 K. The visible solar disk is called thephotosphere. Its diameter is about 2,240,000 km (about175 times the diameter of the Earth) and its surface tem­perature is about 6000 K. The lower solar atmosphere iscalled the chromosphere; the outer atmosphere is calledthe corona. The chromosphere includes spike-like emis­sions of hydrogen gas called solar prominences thatsometimes can reach far out into the corona.

The heat from the core is radiated out to the outer con­ducting shell, where it sets up convection currents. Someof these convection currents are small scale (about1000 km across) and last only a few minutes; others arelarger scale (30,000 knl across) and persist for about a(terrestrial) day. The convection is affected by the Sun'srotation and is turbulent.

The rotation of the Sun has been estimated spectro­scopically by measuring the Doppler shift of spectral

5.4 GEOMAGNETISM

lines. Independent estimates come from observing themotion of solar features like sunspots, etc. The rotationalaxis is tilted slightly at 7° to the pole to the ecliptic. Nearthe Sun's equator the rotational period is about 25 Earthdays; the polar regions rotate more slowly with a periodof 35-40 days. The Sun 's core may rotate more rapidlythan the outer regions. Turbulent convection and velocityshear in the outer conducting shell are conducive to adynamo origin for the Sun's magnetic field. The surfacefield is dipolar in higher latitudes but has a more compli­cated pattern in equatorial latitudes.

Temperatures in the outer solar atmosphere (corona)are very high, around 1~000,000K. The constituent parti­cles achieve velocities in excess of the escape velocity ofthe Sun's gravitational field. The supersonic stream ofmainly protons (H+ ions), electrons and a-particles(He2+ ions) escaping from the Sun forms the solar wind.The flow of electric charge produces an interplanetarymagnetic field (IMF) of varying intensity. At the distanceof the Earth from the Sun the IMF measures about 6 nT.

Sunspots have been observed since the invention of thetelescope (ca. 1610 AD). A sunspot is a dark fleck on thesurface of the Sun, measuring roughly 1000 to 100,000 krnin diameter. It has a lower temperature than the surround­ing photosphere and represents a strong disturbanceextending far into the Sun's interior. Sunspots last forseveral days or weeks and move with the Sun's rotation,providing a means of estimating the rotational speed. Thefrequency of sunspots changes cyclically with a period of11 years.

Intense magnetic fields are associated with thesunspots. These often occur in unequally sized pairs ofopposite polarity. The predominating magnetic polarityof sunspots changes from one period of maximumsunspot activity to the next, implying that the period is infact 22 years. The magnetic field of each sunspot istoroidal. It can be imagined to resemble a vortex, ortornado, in which the magnetic field lines leave the solarsurface in one sunspot and return to it in the othermember of the pair. The polarity of the Sun's dipole fieldalso reverses with the change of polarity of the sunspots,indicating that the features are related.

Associated with the sunspots and their strong mag­netic fields are emissions of hydrogen gas, called solarflares. The charged particles ejected in the flares con­tribute to the solar wind, which consequently transfersthe sunspot cyclicity to fluctuations in the Earth's mag­netic field of external origin and to ancillary terrestrialphenomena such as magnetic storms, brilliant aurorasand interference with radio transmissions.

5.4.7.2 Lunar magnetism

Classical hypotheses for the origin of the Moon - rota­tional fission, capture or binary accretion - have beensuperseded by the Giant Impact hypothesis. According tothis model, the Earth experienced a catastrophic collision

317

with a Mars-sized protoplanet early in its development.Sorne debris from the collision remained in orbit aroundthe Earth, where it re-accumulated as the Moon about4.5 Ga ago. This origin accounts for why the Earth andMoon have the same oxygen isotope composition. At thetime of the Giant Impact the Earth's mantle and core hadalready differentiated and dense iron had settled in to thecore. This may also have taken place in the impactor sothe Moon formed from the iron-depleted rocky mantlesof the impacting bodies. The Moon has only a small core,whereas if it had originated like the other planets its corewould be proportionately larger.

The early Moon was probably covered by an ocean ofmolten magma at least a hundred kilometers thick, therelicts of which are now the major constituents of thelunar highlands. After cooling and solidification, the lunarsurface was bombarded by planetesimals and meteoroidsuntil about 4Ga ago. The huge craters left by the impactswere later filled by molten basalt to form the lunar maria,Rock samples recovered from the maria in the mannedApollo missions have been dated radiometrically at3.1-3.9 Ga. The volcanism may have continued after thistime but probably ceased about 2.5 Ga ago. Since then thelunar surface has been pulverized by the constant born­bardrnent by meteorites, micrometeorites and elementaryparticles of the solar wind and cosmic radiation. Exceptfor the lunar highlands the surface is now covered by alayer of shocked debris several meters thick called thelunar regolith.

Our knowledge of lunar magnetism derives from mag­netic field measurements made from orbiting spacecraft,magnetometers set up on the Moon and rock samples col­lected from the lunar surface and brought back to Earth.Measurements of the lunar surface field from orbitingspacecraft have been made by on-board magnetometersand by the electron reflection method, the principle ofwhich is basically the same as used to explain the origin ofthe Van Allen belts in the Earth's magnetosphere (seeSection 5.4.3.1). Electrons rain abundantly upon thelunar surface, in part from the solar wind and in part fromthe charges trapped in the Earth's magnetotail, which iscrossed by the monthly orbit of the Moon about theEarth. In the absence of a lunar magnetic field the elec­trons would be absorbed by the lunar surface. As in theEarth's magnetosphere, an electron incident on the Moonis forced by the Lorentz force to spiral about a magneticfield line (see Fig. 5.30). As the electron approaches thelunar surface the magnetic field strength increases and thepitch of the helix decreases to zero. At the point of closestapproach (also called the mirroring point) the electronmotion is completely rotational about the field line. Theelectron path then spirals with increasing pitch backalong the field line, away from the Moon. The effective­ness of the electron reflection is directional; for a givenelectron velocity there is a critical angle of incidencebelow which reflection ceases. By counting the number ofelectrons with a known energy that are reflected past a

318 Geomagnetism and paleomagnetism

Table 5.2 Magnetic characteristics 0..( the planets (data source: Van Allen and Bagenal, 1999)

Mean Mean Period Magnetic Equivalent Dipoleorbital radius of dipole equatorial tilt toradius of planet rotation moment magnetic rotation

Planet [AU] [kn1] [days] [nl E] field [nT] axis [0]

Mercury 0.3830 2.440 58.81 0.0007 300 14Venus 0.7234 6,051 243.7(R) < 0.0004 <3Earth 1 6,371 1 1 30,500 10.8Moon 0.00257 1.738 27.32Mars 1.520 3,390 1.0275 < 0.0002 < 30Jupiter 5.201 69.910 0.414 20.000 428.000 9.6Saturn 9.576 58,230 0.444 600 22,000 <1Uranus 19.19 25,362 0.720(R) 50 23,000 58.6Neptune 30.05 24,625 0.671 25 14,000 47

satellite in known directions, the surface field B. can bes

estimated from the field Bomeasured at the altitude of thesatellite.

The lunar magnetic field was surveyed extensively in1998 by the Lunar Prospector orbiting spacecraft. Themeasurements show that the Moon currently has nodetectable dipole moment. It has only a very weak non­dipolar magnetic field due to local magnetization ofcrustal rocks. Estimates of surface anomalies suggest thatthe largest are of the order of 100 nT. From records ofmeteoritic impacts and moonquakes made by seismo­meters left on the Moon for several years it has beeninferred that, if the Moon has a core (necessary for alunar dynamo), it must be smaller than 400-500 km inradius, representing less than 20/0 of the Moon's volumeand l-3(/{) of its mass. In contrast, the Earth's core occu­pies about 16(/{) of the planet's volume and has about 33~)of its mass. Lunar Prospector detected magnetic fieldchanges due to electrical currents induced in the Moon asit traversed the stretched out tail of Earth's magnetos­phere. They suggest an even smaller, iron-rich metalliccore, with radius 340 ± 90 km (Hood et al., 1999).

Although the Moon now has no global dipole mag­netic field, samples of lunar rocks recovered in themanned Apollo missions possessed quite strong naturalremanent magnetizations. Rock magnetic studies onApollo samples with radiometric ages of ........ 3.6-3.9 Gasuggest that they were magnetized in fields of the order of100100fJ-T (0.1-1 gauss). much stronger than presentfields on the Moon. As yet, the ancient lunar magneticfield is not well understood. The interior of the Moonmay have acquired a primordial remanent magnetizationin the external field of the Sun or Earth. In turn this mayhave provided the fields for acquisition of the observedcrustal magnetizations. The small lunar metallic core iscurrently solid, and the core heat flux is too low to havepowered an internal dynamo at the time of formation ofthe Apollo samples. However, models suggest that a thinlayer of the Moon's mantle adjacent to the core mayhave first blanketed the core, then later provided enoughradioactive heating to assist dynamo activity that

persisted for a limited period during a "magnetic era"about 0.5-1.0 Ga after the Moon was formed (Stegman etal.,2003).

5.4.7.3 Extra-terrestrial magnetic exploration

Jupiter and Saturn, like the Earth, have magnetic fieldsthat are strong enough to trap charged particles. Themotions of these charged particles generate electromag­netic radiation which is detectable as radio waves far fromthe planet. The magnetic field of Jupiter was first detectedin this way. Moreover, the radio emissions are modulatedby the rotation of the planet. Analysis of the periodicityof their modulated radio emissions provides the best esti­mates of the rotational rates of Jupiter and Saturn.

Most data concerning the magnetic fields of theplanets (Table 5.2) have been obtained with flux-gatemagnetometers (see Section 5.5.2.1) installed in passingor orbiting spacecraft. When the spacecraft traverses themagnetosphere of a planet, the magnetometer registersthe passage through the bow shock and rnagnetopause(Fig. 5.39). A bow shock results from the supersonic colli­sion of the solar wind with the atmosphere of a planetjust as it does for the Earth (see Fig. 5.28). Counters ofenergetic particles register a sudden increase in frequencyand the magnetometer shows a change in magnetic fieldstrength during passage through the bow shock into themagnetosheath. When the spacecraft leaves the magne­tosheath and crosses the magnetopause it enters theregion that is shielded from the solar wind by the mag­netic field of the planet. The magnetopause is where thekinetic energy of the plasma is equal to the potentialenergy of the planetary magnetic field. The existence of abow shock may be regarded as evidence for a planetaryatmosphere, while the magnetopause is evidence that theplanet has a magnetic field.

5.4.7.4 The magnetic fields of theplanets

Mercury was visited by the Mariner 10 spacecraft., whichmade three passes of the planet in 1974 and 1975. The

5.4 GEOMAGNETISM

Fig. 5.39 Changes with timeof particle density and

magnetic field along the path

of the Mariner 10 spacecraftduring its flight past the

planet Mercury (data fromOgilvie et a/., 1977).

319

Mariner 10 flyby of Mercury

rr:1, l B~ Magneto- ~:,~ h M : bow

~ .. h h ,.~ magnetosp ere --.:.b § 40-1 :: : seat : : :sh~ck I 40

~120~~A~:,~ _.j~~20~ " ·v '~L ~ , :: I

,I,;, I I I,I! I! I '1iIiiiiiI~1' 1;1 ';1:. i I' "

III

~ 80£'"0Q) 60 " ,u::.~~

40OJCbD(Ij

:;E 20

40

20

I I I I I I I I I I I I I' I I 1'1 1'1 I I I I II I"; I I I I I I I

2030 2040 2050 2100 UT

on-board magnetometer detected a bow shock and amagnetopause (Fig. 5.39), which imply that the planethas a magnetic field. On the first encounter a magneticfield of about 100nT was measured at an altitude of700 km (radial distance of 3100 km), which was the pointof closest approach. In estimating the magnetic field ofthe planet compensation must be made for the magneticfield of the solar wind. Different models have given esti­mates of the strength of the dipole moment in the range(2-7) X 10- 4 of the Earth's magnetic moment (111E =7.7674 X 1022 Am2 in 2005), which would give a surfaceequatorial magnetic field of about 100-400 nT. Thesource of the magnetic field is uncertain. It is possible, butunlikely, that Mercury has a global magnetic moment dueto crustal remanent magnetization; it would be difficult toexplain the uniformity and duration of the external fieldneeded to produce this. Mercury is believed to have alarge iron core with a radius of about 1800 km, propor­tionately larger than Earth's. Probably part of this core ismolten, so it is possible that Mercury has a small activeinternal dynamo. This would however be unlike Earth's. Itmight be of thermoelectric origin, or it could be due todynamo processes in a thin shell-like liquid outer coresurrounding a solid inner core.

Venus was investigated by several American andRussian spacecraft in the 1960s. The instruments onMariner 5 in 1967 clearly detected a bow shock from thecollision of the solar wind with the planetary atmosphere.Magnetometer data from later spacecraft found no evi­dence for a planetary magnetic field. If a magnetopauseexists, it must lie very close to the planet and may wraparound it. Data from the Pioneer Venus orbiter in 1978 setan upper limit of 10- 5 111E for a planetary dipole moment,which would give a surface equatorial field of less than InT. The absence of a detectable magnetic field was notexpected. As shown by Eq. (5.37) the dipole magneticmoment is proportional to the eq uatorial field times the

cube of the planetary radius. The strength of a dynamofield is expected to be proportional to the core radius andto the rotation rate. These considerations give a scalinglaw whereby the dipole magnetic moment of a planet isproportional to its rotation rate and the fourth power ofthe core radius. The rotation of the planet is very slowcompared to that of the Earth: one sidereal day on Venuslasts 243 Earth days, but the size of the planet is close tothat of the Earth. It was therefore expected that Venusmight have an internal dynamo with a dipole momentabout 0.20/0 that of the Earth and an equatorial surfacefield of about 86 nT. It seems likely that the slow rotationdoes not provide enough energy for an active dynamo.

Mars was expected to have a magnetic momentbetween that of Earth and Mercury, because of its sizeand rotation rate. Mariner 4 in 1965 was the firstAmerican spacecraft carrying magnetometers to visitMars; it detected a bow shock but no conclusive evidencefor a magnetopause. In September 1997, the Mars GlobalSurveyor spacecraft entered orbit around the planet.Since 1999 it has mapped the Martian magnetic field froman almost circular orbit about 400 ± 30 km above theplanet's surface. The survey measurements have nearlyuniform global coverage and show that there is no signifi­cant global magnetic field at present. This does notexclude the possible existence of a dynamo-generatedglobal field in the planet's distant past. The measuredmagnetic field consists of large regional magnetic anom­alies, which are attributed to remanent magnetization ofthe Martian crust. At the survey altitude the crustal mag­netic anomalies have amplitudes up to 220 nT, an order ofmagnitude larger than the crustal anomalies of Earth atthat altitude, which attests to the presence of stronglymagnetic minerals in the Martian crust. The crustal mag­netic field shows some features with circular geometry,some of which may be related to impact processes.However, the most striking anomalies are prominent

320 Geomagnetism and paleomagnetism

east-west trending linear features over a region in theplanet's southern hemisphere. These sub-parallel lin­eations are attributed to alternating bands of stronglymagnetized crust. It is tempting to interpret their origin inthe same way as the generation of oceanic magnetic lin­eations on Earth by a plate tectonic process in the pres­ence of a reversing field. However, as yet the origin of themagnetic anomalies on Mars is not understood.

Jupiter has been known since 1955 to possess a strongmagnetic field, because of the polarized radio emissionsassociated with it. The spacecraft Pioneer 10 and 11 in1973-4 and Voyager 1 and 2 in 1979 established that theplanet has a bow shock and magnetopause. From 1995to 2003 the spacecraft Galileo made extensive surveysof Jupiter's magnetosphere. The huge magnetosphereencounters the solar wind about 5,OOO~000km "upwind"from the planet; its magnetotail may extend all the way toSaturn. Two reasons account for the great size of the mag­netosphere compared to that of Earth. First, the solarwind pressure on the Jovian atmosphere is weaker due tothe greater distance from the Sun; secondly, Jupiter'smagnetic field is much stronger than that of the Earth.The dipole moment is almost 20,0001nE which gives apowerful equatorial magnetic field of more than400,000 nT at Jupiter's surface. The quadrupole and octu­pole parts of the non-dipole magnetic field have beenfound to be proportionately much larger relative to thedipole field than on Earth. The dipole axis is tilted at 9.7°to the rotation axis, and is also displaced from it by 10(0)of Jupiter's equatorial radius. The magnetic field ofJupiter results from an active dynamo in the metallichydrogen core of the planet. The core is probably verylarge, with a radius up to 75% of the planet's radius. Thiswould explain the high harmonic content of the magneticfield near the planet.

Saturn was reached by Pioneer 11 in 1979 and theVoyager 1 and 2 spacecraft in 1980 and 1981, respectively.The on-board magnetometers detected a bow shock anda magnetopause. In 2004 the Cassini-Huygens spacecraftentered into orbit around Saturn. In 2005 the Huygenslander descended to the surface of Saturn's largest moonTitan while Cassini continued to orbit and measure theparent planet's properties. Saturn's dipole magneticmoment is smaller than expected, but is estimated to bearound 500nl E. This gives an equatorial field of 55,000nT, almost double that of Earth. The magnetic field has apurer dipole character (i.e., the non-dipole componentsare weaker) than the fields of Jupiter or Earth. The sim­plest explanation for this is that the field is generated byan active dynamo in a conducting core that is smaller rel­ative to the size of the planet. The axis of the dipole mag­netic field lies only about I° away from the rotation axis, incontrast to 11.4° on Earth and 9.7° on Jupiter.

Uranus is unusual in that its spin axis has an obliquityof 97.9°. This means that the rotation axis lies very closeto the ecliptic plane, and the orbital planes of its satellitesare almost orthogonal to the ecliptic plane. Uranus was

visited by Voyager 2 in January 1986. The spacecraftencountered a bow shock and magnetopause and subse­quently entered the tnagnetosphere of the planet, whichextends for 18 planetary radii (460,000 km) towards theSun. Uranus has a dipole moment about 50 timesstronger than Earth's, giving a surface field of 24,000 nT,comparable to that on Earth. Intriguingly, the axis of thedipole field has a large tilt of about 60° to the rotationaxis; there is no explanation for this tilt. Another oddity isthat the magnetic field is not centered on the center of theplanet, but is displaced by 300/0 of the planet's radiusalong the tilted rotation axis. The quadrupole componentof the field is relatively large compared to the dipole. It istherefore supposed that the magnetic field of Uranus isgenerated at shallow depths within the planet.

Neptune, visited by Voyager 2 in 1989, has a magneticfield with similar characteristics to that of Uranus. It istilted at 49° to the rotation axis and is offset from the plan­etary center by 55(~) of Neptune's radius. As in the case ofUranus, the magnetic field has a large quadrupole termcompared to the dipole and thus probably originates in theouter layers of the planet, rather than in the deep interior.

It is not yet known whether Pluto has a magnetic field.The planet is probably too small to have a magnetic fieldsustained by dynamo action.

There is reasonable confidence that Mercury, Earth,Jupiter, Saturn, and Uranus have active planetary dynamostoday. The magnetic data for Mars and Neptune are incon­clusive. All available data indicate that Venus and theMoon do not have active dynamos now, but possibly eachmight have had one earlier in its history.

5.5 MAGNETIC SURVEYING

5.5.1 The magnetization of the Earth's crust

The high-order terms in the energy density spectrum ofthe geomagnetic field (Fig. 5.33) are related to the rnagne­tization of crustal rocks. Magnetic investigations cantherefore yield important data about geological struc­tures. By analogy with gravity anomalies we define a mag­netic anomaly as the difference between the measured(and suitably corrected) magnetic field of the Earth andthat which would be expected from the InternationalGeomagnetic Reference Field (Section 5.4.4). The mag­netic anomaly results from the contrast in magnetizationwhen rocks with different magnetic properties are adja­cent to each other, as, for example, when a strongly mag­netic basaltic dike intrudes a less magnetic host rock. Thestray magnetic fields surrounding the dike disturb thegeomagnetic field locally and can be measured with sensi­tive instruments called magnetometers.

As discussed in Section 5.3.1~ each grain of mineral ina rock can be classified as having diamagnetic, pararnag­netic or ferromagnetic properties. When the rock is in amagnetic field, the alignment of magnetic momentsby the field produces an induced magnetization (M)

5.5 MAGNETIC SURVEYING321

rock is not paraJIel to the geomagnetic field. If the intensi­ties of M, and M, are similar, it is difficult to interpret thetotal magnetization. Fortunately, in many important situ­ations M r and M, are sufficiently different to permit somesimplifying assumptions. The relative importance of theremanent and induced parts of the- magnetization isexpressed in the Konigsberger ratio (Qn)' defined as theratio of the intensity of the remanent magnetization tothat of the induced magnetization (i.e., Q

n== /tIf

r/ M).

Two situations are of particular interest. The first iswhen Qn is very large (i.e., Qn~ I). In this case (Fig. 5.4Gb),the total magnetization is dominated by the remanent com­ponent and its direction is essentially parallel to lVI

r.

Oceanic basalts, formed by extrusion and rapid underwatercooling at oceanic ridges, are an exampleof rocks with highQn ratios. Due to the rapid quenching of the molten lava,titanomagnetite grains form with skeletal structures andvery fine grain sizes. The oceanic basalts carry a strongthermoremanent magnetization and often have Qn values of100 or greater. This facilitates the interpretation of oceanicmagnetic anomalies, because in many cases the inducedcomponent can be neglected and the crustal magnetizationcan be interpreted as if it were entirely remanent.

The other important situation is when Qn is very small(i.e., Qn~ 1). This requires the remanent magnetization tobe negligible in comparison to the induced magnetization.For example, coarse grained magnetite grains carry multi­domain magnetizations (Section 5.3.5.3). The domainwalls are easily moved around by a magnetic field. The sus­ceptibility is high and the Earth's magnetic field can inducea strong magnetization. Any remanent magnetization isusually weak, because it has been subdivided into anti par­allel domains. These two factors yield a low value for Qn'Magnetic investigations of continental crustal rocks forcommercial exploitation (e.g., in ancient shield areas) canoften be interpreted as cases with Qn~ I. The magnetiza­tion can then be assumed to be entirely induced (Fig.5.40c) and oriented parallel to the direction of the present­day geomagnetic field at the measurement site, which isusually known. This makes it easier to design a model tointerpret the feature responsible for the magnetic anomaly.

5.5.2 Magnetometers

The instrument used to measure magnetic fields is called amagnetometer, Until the 1940s magnetometers weremechanical instruments that balanced the torque of themagnetic field on a finely balanced compass needle againsta restoring force provided by gravity or by the torsion in asuspension fiber. The balance types were cumbersome,delicate and slow to operate. For optimum sensitivity theywere designed to measure changes in a selected compo­nent of the magnetic field, most commonly the verticalfield. This type of magnetometer has now been super­seded by more sensitive, robust electronic instruments.The most important of these are the flux-gate, proton­precession and optically pumped magnetometers,

inducedMj

,,,,,,,,,,,,,,,

,,,,,

"'l

remanentMr

(a)

(b) Qn ~ 1

Fig. 5.40 Theremanent(Mr) , induced(M), and total (Mt ) magnetizationsin a rock. (a)Foran arbitrarycase Mt liesbetween M,and Mr, (b) for a verylarge Konigsberger ratio (On~ 1)M t iscloseto Mr, and (c)for a verysmallKonigsberger ratio (On~1) M t isalmost the sameasMi'

proportional to the field, the proportionality constantbeing the magnetic susceptibility, which can have a widerange of values in rocks (see Fig. 5.13). The geomagneticfield is able to produce a correspondingly wide range ofinduced magnetizations in ordinary crustal rocks. Thedirection of the induced magnetization is parallel to theEarth's magnetic field in the rock.

Each rock usually contains a tiny quantity of ferro­magnetic minerals. As we have seen, these grains canbecome magnetized permanently during the formation ofthe rock or by a later mechanism. The remanent magneti­zation (M r ) of the rock is not related to the present-daygeomagnetic field, but is related to the Earth's magneticfield in the geological past. Its direction is usuallydifferent from that of the present-day field. As a result thedirections of M, and M, are generally not parallel. Thedirection of M, is the same as that of the present field butthe direction of M, is often not known unless it can bemeasured in rock samples.

The total magnetization of a rock is the sum of theremanent and induced magnetizations. As these havedifferent directions they must be combined as vectors (Fig.5.40a). The direction of the resultant magnetization of the

322 Geomagnetism andpaleomagnetism

Fig. 5.41 Simplified principle of the flux-gate magnetometer. (a)

Primary and secondary electrical circuits include coils wrapped around

parallel strips of Mumetal in opposite and similar senses, respectively.

(b) The output signal in a magnetic field is proportional to the net rate

of change of magnetic flux in the Mumetal strips (after Militzer et el.,1984).

core 1

secondarycircuit

primarycircuit

:H u H

: Earth's: fieldIIIII

(b) B

(a)

5.5.2.2 The proton-precession magnetometer

Since World War II sensitive magnetometers have beendesigned around quantum-mechanical properties. Theproton-precession magnetometer depends on the factthat the nucleus of the hydrogen atom, a proton, has amagnetic moment proportional to the angular momen­tum of its spin. Because the angular momentum is quan­tized, the proton magnetic moment can only havespecified values, which are multiples of a fundamentalunit called the nuclear magneton. The situation is analo­gous to the quantization of magnetic moment associatedwith electron spin, for which the fundamental unit is theBohr magneton. The ratio of the magnetic moment to thespin angular momentum is called the gyromagnetic ratio(Yp) of the proton. It is an accurately known fundamentalconstant with the value yp = 2.675 13 X 108 S-1 T-J.

The proton-precession magnetometer is simple androbust in design. The sensor of the instrument consists of aflask containing a proton-rich liquid, such as water.Around the flask are wound a magnetizing solenoid and adetector coil (Fig. 5.42); some designs use the same sole­noid alternately for magnetizing and detection. When thecurrent in the magnetizing solenoid is switched on, itcreates a magnetic field of the order of 10mT~ whichis about 200 times stronger than the Earth's field. The

5.5.2.1 The flux-gate magnetometer

Some special nickel-iron alloys have very high nlagneticsusceptibility and very low remanent magnetization.Common examples are Permalloy (78.5(~) Ni, 21.511'0 Fe)and Munietal (7TYo Ni, 161Yo Fe~ 51j';) Cu, 2(~) Cr). Thepreparation of these alloys involves annealing at veryhigh temperature (1100-1200 °C) to remove lattice defectsaround which internal stress could produce magnetostric­tive energy. After this treatment the coercivity of the alloyis very low (i.e.~ its magnetization can be changed by avery weak field) and its susceptibility is so high that theEarth's field can induce a magnetization in it that is a con­siderable proportion of the saturation value.

The sensor of a flux-gate magnetometer consists oftwo parallel strips of the special alloy (Fig. 5.41a). Theyare wound in opposite directions with primary energiz­ing coils. When a current flows in the primary coils, theparallel strips become magnetized in opposite directions.A secondary coil wound about the primary pair detectsthe change in magnetic flux in the cores (Fig. 5.41b),which is zero as soon as the cores saturate. While theprimary current is rising or falling., the magnetic flux ineach strip changes and a voltage is induced in the sec­ondary coil. If there is no external magnetic field, thesignals due to the changing flux are equal and oppositeand no output signal is recorded. When the axis of thesensor is aligned with the Earth's magnetic field, thelatter is added to the primary field in one strip and sub­tracted from it in the other. The phases of the magneticflux in the alloy strips are now different: one saturatesbefore the other. The flux changes in the two alloy stripsare no longer equal and opposite. An output voltage isproduced in the secondary coil that is proportional tothe strength of the component of the Earth's magneticfield along the axis of the sensor.

The flux-gate magnetometer is a vector magnetometer,because it measures the strength of the magnetic field in aparticular direction, namely along the axis of the sensor.This requires that the sensor be accurately oriented alongthe direction of the field component to be measured. Fortotal field measurements three sensors are employed.These are fixed at right angles to each other and con­nected with a feedback system which rotates the entireunit so that two of the sensors detect zero field. The mag­netic field to be measured is then aligned with the axis ofthe third sensor.

The flux-gate magnetometer does not yield absolutefield values. The output is a voltage, which must be cali­brated in terms of magnetic field. However, the instru­ment provides a continuous record of field strength. Itssensitivity of about 1 nT makes it capable of measuringmost magnetic anomalies of geophysical interest. It isrobust and adaptable to being mounted in an airplane, ortowed behind it. The instrument was developed duringWorld War II as a submarine detector. After the war itwas used extensively in airborne magnetic surveying.

5.5 MAGNETIC SURVEYING323

signal frequency gives an instrumental sensitivity ofabout 1 n'T, but requires a few seconds of observation.Although it gives an absolute value of the field, theproton-precession magnetometer does not give a continu­ous n .ord, Its portability and simplicity give it advan­tages for field use.

The flux-gate and proton-precession magnetometersare widely used in magnetic surveying. The two instru­ments have comparable sensitivities of 0.1-1 nT. Incontrast to the flux-gate instrument, which measures thecomponent of the field along its axis, the proton-preces­sion magnetometer cannot measure field components; itis a total-field magnetometer, The total field B

1is the

vector SU111 of the Earth's magnetic field BEand the straymagnetic field LlB of, say, an orebody. Generally, ~B<{BE'so that the direction of the total field does not deviate farfrom the Earth's field. In some applications it is often ade­quate to regard the measured total field anomaly as theprojection of LlB along the Earth's field direction.

magnetizingfield F

(::::10mT)

flask ofproton-rich

I?~ tluid (e.g.,water, alcohol)

magnetizingcoil

//

geomagnetic field, e, .;(:::: 0.03-0.06 mT)

(a)

(b)

//

The intensity of the Earth's magnetic field is in therange 30,OOO-60,000nT. The corresponding precessionalfrequency is approximately 1250-2500 Hz, which is in theaudio-frequency range. Accurate measurement of the

5.5.2.3 The absorption-cell magnetometer

The absorption-cell magnetometer is also referred to asthe alkali-vapor or optically pumped magnetometer. Theprinciple of its operation is based on the quantum­mechanical model of the atom. According to theirquantum numbers the electrons of an atom occupy con­cen tric shells about the nucleus with different energylevels. The lowest energy level of an electron is its groundstate. The magnetic moment associated with the spin ofan electron can be either parallel or antiparallel to anexternal magnetic field. The energy of the electron isdifferent in each case. This results in the ground statesplitting into two sublevels with slightly different ener­gies. The energy difference is proportional to the strengthof the magnetic field. The splitting of energy levels in thepresence of a magnetic field is called the Zeeman effect.

Absorption-cell magnetometers utilize the Zeemaneffect in vapors of alkali elements such as rubidium orcesium, which have only a single valence electron in the out­ermost energy shell. Consider the schematic representationof an alkali-vapor magnetometer in Fig. 5.43. A polarizedlight-beam is passed through an absorption cell containingrubidium or cesium vapor and falls on a photoelectric cell,which measures the intensity of the light-beam. In the pres­ence of a magnetic field the ground state of the rubidium orcesium is split into two sublevels, G) and G 2• If the exactamount of energy is added to the vapor, the electrons maybe raised from their ground state to a higher-energy level,H. Suppose that we irradiate the cell with light from whichwe have filtered out the spectral line corresponding to theenergy needed for the transition G,H. The energy for thetransition G I H has not been removed, so the electrons inground state G 1 will receive energy that excites them to levelH, whereas those in ground state G., will remain in thisstate. The energy for these transitions -comes from the inci­dent light-beam, which is absorbed in the cell. In due

(5.43)

(c)

B =2'ITft 'Yp

// precession of

/ proton spin withIt-Bt frequency f about

field direction

Fig. 5.42 (a) The elements of a proton-precession magnetometer. (b)

Current in the magnetizing coil produces a strong field Fthat aligns themagnetic moments ("spins") of the protons. (c) When the field Fis

switched off, the proton spins precessabout the geomagnetic field 8t'inducing an alternating current in the coil with the Larmor precessionalfrequency f.

magnetizmg field aligns the magnetic moments of theprotons along the axis of the solenoid, which is orientedapproximately east-west at right angles to the Earth's field.After the magnetizing field is interrupted, the magneticmoments of the proton spins react to the couple exerted onthem by the Earth's magnetic field. Like a child's top spin­ning in the field of gravity, the proton magnetic momentsprecess about the direction of the ambient magnetic field.They do so at a rate known as the Larmor precessionalfre­quency. The motion of the magnetic moments induces asignal in the detector coil. The induced signal is amplifiedelectronically and the precessional frequency is accuratelymeasured by counting cycles for a few seconds. Thestrength Bt of the measured magnetic field is directly pro­portional to the frequency of the signal (f), and is given by

324 Geomagnetism and paleomagnetism

D/~-=--=--=--i-=--=--=--=--=-~_-=.-=.-=.-=.-=. -=--=--=-~~Ol,~ - --- - ----- ------ --- - / /~

", ~~~~- i:': ~~~~~~ ~~~- /

/

cell becomes curr~nt istransparent maxImum

!o:;f;~e~ D1J-~~~]~~~~~O---0--o~ 'V::::::U::::::J-j

resonant RF signal // cell becomesis applied to cell opaque

pumpingpreferentially fills

energy level G2of ground state

1

:••••.1i-•

H electrons are initially Photo-

diVid;~o:~~~r.,~:tween '~-=--=--=-i-=--=--=--=--=-8 0~---»0,-::::: ::::: ------ --- ---~Cs ---- -----

lamp .filter removes Cs-vapor current IS

spectral line absorption minimumG~ cell

G., ••••G- ••••

I

pumping 8nullified byRF signal eieeii.,

• 1: ~ ~ .

Fig. 5.43 The principle ofoperation of the opticallypumped magnetometer (after

Telford et al., 1990).

(5.44)

course, the excited electrons will fall back to one of themore stable ground states. If an electron in excited state Hfalls back to sublevel G} it will be re-excited into level H;but if it falls back to sublevel G 2 it will remain there. Intime, this process - called "optical pumping" - will emptysublevel G I and fill level G 2• At this stage no more energycan be absorbed from the polarized light-beam and theabsorption cell becomes transparent. If we now supplyelectromagnetic energy to the system in the form of a radio­frequency signal with just the right amount of energy topermit transitions between the populated G 2 and unpopu­lated G} ground sublevels, the balance will be disturbed.The optical pumping will start up again and will continueuntil the electrons have been expelled from the G} level.During this time energy is absorbed from the light-beamand it ceases to be transparent.

In the rubidium-vapor and cesium-vapor magnetome­ters a polarized light-beam is shone at approximately 45° tothe magnetic field direction. In the presence of the Earth'smagnetic field the electrons precess about the field directionat the Larmor precessional frequency. At one part of theprecessional cycle an electron spin is almost parallel to thefield direction, and one half-cycle later it is nearly antiparal­leI. The varying absorption causes a fluctuation of intensityof the light-beam at the Larmor frequency. This is detectedby the photocell and converted to an alternating current.By means of a feedback circuit the signal is supplied to acoil around the container of rubidium gas and a radio­frequency resonant circuit is created. The ambient geomag­netic field B, that causes the splitting of the ground state isproportional to the Larmor frequency, and is given by

B = 21T j't 'Ye

Here, 'Ye is the gyrornagnetic ratio of the electron, whichis known with an accuracy of about I part in 107. It is

about 1800 times larger than 'Yp ' the gyromagnetic ratio ofthe proton. The precessional frequency is correspondinglyhigher and easier to measure precisely. The sensitivity ofan optically pumped magnetometer is very high, about0.01 nT, which is an order of magnitude more sensitivethan the flux-gate or proton-precession magnetometer.

5.5.3 Magnetic surveying

The purpose of magnetic surveying is to identify anddescribe regions of the Earth's crust that have unusual(anomalous) magnetizations. In the realm of applied geo­physics the anomalous magnetizations might be associ­ated with local mineralization that is potentially ofcommercial interest, or they could be due to subsurfacestructures that have a bearing on the location of oildeposits. In global geophysics, magnetic surveying overoceanic ridges provided vital clues that led to the theoryof plate tectonics and revealed the polarity history of theEarth's magnetic field since the Early Jurassic.

Magnetic surveying consists of (1) measuring the terres­trial magnetic field at predetermined points, (2) correctingthe measurements for known changes, and (3) comparingthe resultant value of the field with the expected value ateach measurement station. The expected value of the fieldat any place is taken to be that of the InternationalGeomagnetic Reference Field (IGRF), described in Section5.4.4. The difference between the observed and expectedvalues is a magnetic anomaly,

5.5.3.1 Measurement methods

The surveying of magnetic anomalies can be carried outon land, at sea and in the air. In a simple land survey anoperator might use a portable magnetometer to measurethe field at the surface of the Earth at selected points that

5.5 MAGNETIC SURVEYING325

B

(b)

economical way to reconnoitre a large territory in a shorttime. It has become a routine part of the initial phases ofthe geophysical exploration of an uncharted territory.

The magnetic field over the oceans may also be sur­veyed from the air. However, most of the marine magneticrecord has been obtained by shipborne surveying. In themarine application a proton-precession magnetometermounted in a waterproof "fish' is towed behind the ship atthe end of a long cable (Fig. 5.44b). Considering that mostresearch vessels consist of several hundred to several thou­sand tons of steel, the ship causes a large magnetic distur­bance. For example, a research ship of about 1000 tonsdeadweight causes an anomaly of about 10 nT at a dis­tance of 150 m. To minimize the disturbance of the shipthe tow-cable must be about 100-300 m in length. At thisdistance the "fish " in fact "swims" well below the watersurface. Its depth is dependent on the length of the tow­cable and the speed of the ship. At a typical survey speedof 10 km h -1 its operational depth is about 10-20 m.

5.5.3.2 Magnetic gradiometers

The magnetic gradiometer consists of a pair of alkali-vapormagnetometers maintained at a fixed distance from eachother. In ground-based surveying the instruments aremounted at opposite ends of a rigid vertical bar. In airborneusage two magnetometers are flown at a vertical spacing ofabout 30 m (Fig. 5.44c). The difference in outputs of thetwo instruments is recorded. If no anomalous body ispresent, both magnetometers register the Earth's fieldequally strongly and the difference in output signals is zero.If a magnetic contrast is present in the subsurface rocks, themagnetometer closest to the structure will detect a strongersignal than the more remote instrument, and there will be adifference in the combined output signals.

The gradiometer emphasizes anomalies from localshallow sources at the expense of large-scale regionalvariation due to deep-seated sources. Moreover, becausethe gradiometer registers the difference in signals from theindividual magnetometers, there is no need to compen­sate the measurements for diurnal variation, which affectseach individual magnetometer equally. Proton-precessionmagnetometers are most commonly used in ground­based magnetic gradiorneters, while optically pumpedmagnetometers are favored in airborne gradiometers.

5.5.3.3 The survey pattern

In a systematic regional airborne (or marine) magneticsurvey the measurements are usually made according to apredetermined pattern. In surveys made with fixed-wingaircraft the survey is usually flown at a constant flight ele­vation above sea-level (Fig. 5.45a). This is the procedurefavored for regional or national surveys, or for the investi­gation of areas with dramatic topographic relief Thesurvey focuses on the depth to the magnetic basement,which often underlies less magnetic sedimentary surface

------- ..:

--r-30m

-- f--30m

_J__Fig. 5.44 (a) In airborne magnetic surveying the magnetometer may be

mounted rigidly on the airplane at the end of a boom (A), or towed in

an aerodynamic housing behind the plane (8). (b) In marine studies the

magnetometer must be towed some distance d behind the ship to

escape its magnetic field. (c) A pair of sensitive magnetometers in the

same vertical plane act as a magnetic gradiometer (after Slack et ai.,1967).

(a)

(c)

form a grid over a suspected geological structure. Thismethod is slow but it yields a detailed pattern of the mag­netic field anomaly over the structure, because the mea­surements are made close to the source of the anomaly.

In practice, the surveying of magnetic anomalies is mostefficiently carried out from an aircraft. The magnetometermust be removed as far as possible from the magnetic envi­ronment of the aircraft. This may be achieved by mountingthe instrument on a fixed boom, A, several meters long(Fig. 5.44a). Alternatively, the device may be towed behindthe aircraft in an aerodynamic housing, B, at the end of acable 30-150m long. The "bird" containing the magne­tometer then flies behind and below the aircraft. The flightenvironment is comparatively stable. Airborne magne­tometers generally have higher sensitivity (=0.01 nT) thanthose used in ground-based surveying (sensitivity = 1 nT).This compensates for the loss in resolution due to theincreased distance between the magnetometer and thesource of the anomaly. Airborne magnetic surveying is an

326 Geomagnetism and paleomagnetism

Fig. 5.45 In airborne magnetic surveying the flight-lines may be flown

at (a) constant altitude above sea-level, or (b) constant height above

ground-level. The flight pattern (c) includes parallel measurement lines

and orthogonal cross-tie lines.

rocks at considerable depth. In regions that are flat or thatdo not have dramatic topography, it may be possible to flya survey at low altitude, as close as possible to the mag­netic sources. This method would be suitable over ancientshield areas, where the goal of the survey is to detect localmineralizations with potential commercial value. If ahelicopter is being employed, the distance from the mag­netic sources may be kept as small as possible by flying ata constant height above the ground surface (Fig. 5.45b).

The usual method is to survey a region along parallelflight-lines (Fig. 5.45c), which may be spaced anywherefrom 100 m to a few kilometers apart, depending on theflight elevation used, the intensity of coverage, and thequality of detail desired. The orientation of the flight­lines is selected to be more or less normal to the trend ofsuspected or known subsurface features. Additional tie­lines are flown at right angles to the main pattern. Theirseparation is about 5-6 times that of the main flight-lines.The repeatability of the measurements at the intersec­tions of the tie-lines and the main flight-lines provides acheck on the reliability of the survey. If the differences(called closure errors) are large, an area may need to be re­surveyed. Alternatively, the differences 111ay be distributedmathematically among all the observations until theclosure errors are minimum.

(5.45)

(5.46)

The altitude correction is given by the vertical gradient ofthe magnetic field, obtained by differentiating the inten­sity B, with respect to radius, r. This gives

aBt /Lo,n ~1 + 3cos2lJ 37ir == - 3 411" ,A == - rBt

The vertical gradient of the field is found by substitutingr == R = 6371 km and an appropriate value for Bt• It clearlydepends on the latitude of the measurement site. At themagnetic equator (B, ~ 30,000 n'T) the altitude correctionis about 0.015 nT m -1; near the magnetic poles(B, ~ 60,000 nT) it is about 0.030 nT m-1. The correctionis so small that it is often ignored.

In regional studies the corrections for latitude and longi­tude are inherent in the reference field that is subtracted. Ina survey of a small region, the latitude correction is givenby the north-south horizontal gradient of the magneticfield, obtained by differentiating B, with respect to polarangle, lJ. This gives for the northward increase in B, (i.e.,with increasing latitude)

1aB, /Lon? 1 a ~ 3BtsinO coslJ--A-=---- 1+3cos2lJ= (547)

'alJ 411" 1'4 ao r( 1+ 3cos20) .'

The latitude correction is zero at the magnetic pole (()= 0°)and magnetic equator (lJ== 90°) and reaches a maximumvalue of about 5 nT per kilometer (0.005 nT m-1) at inter­mediate latitudes. It is insignificant in small-scale surveys.

5.5.4 Reduction of magnetic fieldmeasurements

In comparison to the reduction of gravity data, magneticsurvey data require very few corrections. One effect thatmust be compensated is the variation in intensity of thegeomagnetic field at the Earth's surface during the courseof a day. As explained in more detail in Section 5.4.3.3this diurnal variation is due to the part of the Earth's mag­netic field that originates in the ionosphere. At any pointon the Earth's surface the external field varies during theday as the Earth rotates beneath different parts of theionosphere. The effect is much greater than the precisionwith which the field can be measured. The diurnal varia­tion may be corrected by installing a constantly recordingmagnetometer at a fixed base station within the surveyarea. Alternatively, the records from a geomagneticobservatory may be used, provided it is not too far fromthe survey area. The time is noted at which each field mea­surement is made during the actual survey and the appro­priate correction is made from the control record.

The variations of magnetic field with altitude, latitudeand longitude are dominated by the vertical and horizontalvariations of the dipole field. The total intensity B, of thefield is obtained by computing the resultant of the radialcomponent B, (Eq. (5.38» and the tangential componentBe(Eq. (5.39»:

B =.1 2 2 _ J-Loln ~1 + 3cos2(J

t ~Br + Be - 411' ,.3

,cross-tieight-line

constant height(e.g. 100-200 H\)

above ground-level

t.:I'"

flight altitude #1e.g. 4 km above

t.:I'" sea-level

~,-... F"' r: f', f"\,

~ ""\

t---j>

fl

-;U l....,....J '-....,....J U ............ U

mainflighline

(c)

(b)

(a)

(5.49)

5.5 MAGNETIC SURVEYING

In some land-based surveys of highly magnetic terrains(e.g., over lava flows or mineralized intrusions), the disturb­ing effect of the magnetized topography may be seriousenough to require additional topographic corrections.

5.5.5 Magnetic anomalies

The gravity anomaly of a body is caused by the densitycontrast (~p) between the body and its surroundings.The shape of the anomaly is determined by the shape ofthe body and its depth of burial. Similarly, a magneticanomaly originates in the magnetization con trast (~M)between rocks with different magnetic properties.However, the shape of the anomaly depends not only onthe shape and depth of the source object but also on itsorientation to the profile and to the inducing magneticfield, which itself varies in intensity and direction withgeographical location. In oceanic magnetic surveyingthe magnetization contrast results from differences in theremanent magnetizations of crustal rocks, for which theKonigsberger ratio is much greater than unity (i.e.,Qn~ 1). Commercial geophysical prospecting is carriedout largely in continental crustal rocks, for which theKonigsberger ratio is much less than unity (i.e., Qn~ I)and the magnetization may be assumed to be induced bythe present geomagnetic field. The magnetization con­trast is then due to susceptibility contrast in the crustalrocks. If k represents the susceptibility of an orebody, kothe susceptibility of the host rocks and F the strength ofthe inducing magnetic field, Eq. (5.17) allows us to writethe magnetization cantrast as

(5.48)

Some insight into the physical processes that give rise toa magnetic anomaly can be obtained from the case of avertically sided body that is magnetized by a vertical mag­netic field. This is a simplified situation because in practiceboth the body and the field will be inclined, probably atdifferent angles. However, it allows us to make a few obser­vations that are generally applicable. Two scenarios are ofparticular interest. The first is when the body has a largevertical extent, such that its bottom surface is at a greatdepth; the other is when the body has a limited verticalextent. In both cases the vertical field magnetizes the bodyparallel to its vertical sides, but the resulting anomalieshave different shapes. To understand the anomaly shapeswe will use the concept of magnetic pole distributions.

5.5.5.1 Magnetic anomaly of asurface distribution ofmagnetic poles

Although magnetic poles are a fictive concept (see Section5.2.2.1), they provide a simple and convenient way tounderstand the origin of magnetic field anomalies. If aslice is made through a uniformly magnetized object,simple logic tells us that there will be as many south polesper unit of area on one side of the slice as north poles on

327

the opposite side: these will cancel each other and the netsum of poles per unit area of the surface of the slice iszero. This is no longer the case if the magnetizationchanges across the interface. On each unit area of thesurface there will be more poles of the stronger magneti­zation than poles of the weaker one. A quantitativederivation shows that the resultant number of poles perunit area a (called the surface density of poles) is propor­tional to the magnetization contrast IiAf.

The concept of the solid angle subtended by a surfaceelement (Box 5.4) provides a qualitative understanding ofthe magnetic anomaly of a surface distribution of mag­netic poles. Consider the distribution of poles on the uppersurface with area A of a vertical prism with magnetizationM induced by a vertical field B=, as illustrated in Fig. 5.46a.At the surface of the Earth, distant r from the distributionof poles, the strength of their anomalous magnetic field isproportional to the total number of poles on the surface,which is the product of A and the surface density a ofpoles. Equation (5.2) shows that the intensity of the field ofa pole decreases as the inverse square of distance r. If thedirection of r makes an angle ()with the vertical magnetiza­tion M, the vertical component of the anomalous field at Pis found by multiplying by cosO. The vertical magneticanomaly ~B= of the surface distribution of poles is

(aA) cosO~B_(X ') C( (~M)O

- r:

A more rigorous derivation leads to essentially thesame result. At any point on a measurement profile, themagnetic anomaly ~B= of a distribution of poles is pro­portional to the solid angle ° subtended by the distribu­tion at the point. The solid angle changes progressivelyalong a profile (Fig. 5.46b). At the extreme left and rightends, the radius from the observation point is very obliqueto the surface distribution of poles and the subtendedangles 0, and 04 are very small: the anomaly distant fromthe body is nearly zero. Over the center of the distribution,the subtended angle reaches its largest value !lo and theanomaly reaches a maximum, The anomaly falls smoothlyon each side of its crest corresponding to the values of thesubtended angles 02 and 03 at the intermediate positions.A measurement profile across an equal distribution of"north" poles would be exactly inverted. The north polescreate a field of repulsion that acts everywhere to opposethe Earth's magnetic field, so the combined field is lessthan it would be if the "north" poles were not there. Themagnetic anomaly over "north' poles is negative.

5.5.5.2 Magnetic anomaly ofa vertical dike

We can now apply these ideas to the magnetic anomaly ofa vertical dike. In this and all following examples we willassume a two-dimensional situation, where the horizon­tal length of the dike (imagined to be into the page) isinfinite. This avoids possible complications related to"end effects. ~~ Let us first assume that the dike extends to

328 Geomagnetism and paleomagnetism

p

n"JJ, I. _I

reii

+.18-

:ill l' i7Ce

distribution ofSouth poles

.... liMdistribution of North~ ..~~." .......,.~~._.". ///Pl))CS is at great depth

(a)Box 5.4: Solid angles

A solid angle is defined by the ratio between the areaof an element of the surface of a sphere and the radiusof the sphere. Let the area of a surface element be Aand the radius of the sphere be 1\ as in Fig. B5.4. Thesolid angle n subtended by the area ..4 at the center ofthe sphere is defined as

Fig. 85.4 Definition of the solid angle n. subtended by an area Aon the surface of a sphere with radius r.

The angle subtended by any surface can be deter­mined by projecting the surface onto a sphere. Theshape of the area is immaterial. If an element of areaA is inclined at angle a to the radius r through a pointon the surface, its projection normal to the radius (i.e.,onto a sphere passing through the point) is Acosa, andthe solid angle it subtends at the center of the sphere isgiven by

north poledistribution

CIt great depth

Fig. 5.46 Explanation of the magnetic anomaly of a vertical prism withinfinite depth extent. For simplicity the magnetization M and inducingfield B, are both assumed to be vertical. (a) The distribution of magneticpoles on the top surface of the prism subtends an angle n at the pointof measurement. (b) The magnetic anomaly ~Bz varies along a profile

across the prism with the value of the subtended angle n.

(b)

t~B:

i

very great depths (Fig. 5.47a), so that we can ignore thesmall effects associated with its remote lower end. Thevertical sides of the dike are parallel to the magnetizationand no magnetic poles are distributed on these faces.However, the horizontal top face is normal to the magne­tization and a distribution of magnetic poles can beimagined on this surface. The direction of magnetizationis parallel to the field, so the pole distribution will consistof "south" poles. The magnetized dike behaves like amagnetic monopole. At any point above the dike wemeasure both the inducing field and the anomalous "strayfield" of the dike, which is directed toward its top. Theanomalous field has a component parallel to the Earth'sfield and so the total magnetic field will be everywherestronger than if the dike were not present. The magneticanomaly is everywhere positive, increasing from zerofar from the dike to a maximum value directly over it(Fig.5.46b).

If the vertical extent of the dike is finite, the distributionof north poles on the bottom of the dike may be closeenough to the ground surface to produce a measurablestray field. The upper distribution of south poles causes apositive magnetic anomaly, as in the previous example, Thelower distribution of north poles causes a negativeanomaly (Fig. 5.47b). The north poles are further from themagnetometer than the south poles, so their negativeanomaly over the dike is weaker. However, farther along

( I )

(2)n = Ac~sar:

A solid angle is measured in units of steradians,which are analogous to radians in planar geometry.The minimum value of a solid angle is zero, when thesurface element is infinitesimally small. The maximumvalue of a solid angle is when the surface completelysurrounds the center of the sphere. The surface area ofa sphere of radius r is A = 4'1l'r2 and the solid angleat its center has the maximum possible value, whichis 4'1l'.

0=4t":

5.5 MAGNETIC SURVEYING329

(b) finite depth extent:dipole model

: inducing'V mt7gl/l·ticjield

I 111101l1l110/IS field l~f

~ magnetizedbody

COmpOIIl'Ilt of+IIIIOIII/llous .#eldparallc! toinducingfield

Distance

i1R> 0

(a) infinite depth extent:monopole model

Fig. 5.47 (a) The vertical-field

magnetic anomaly over a

vertically magnetized block

with infinite depth extent is

due only to the distribution of

poles on the top surface. (b) If

the block has finite depth

extent, the pole distributionson the top and bottom

surfaces both contribute tothe anomaly.

field ofN-poles

Fig. 5.48 Explanation of the origin of the magnetic anomaly of aninfinitely long vertical prism in terms of the pole distributions on top,bottom and side surfaces, when the magnetic field (or magnetization) isinclined.

account in forward-modelling of an anomaly. However,as in other potential field methods, the inverse problem ofdetermining these factors from the measured anomaly isnot unique.

//

I/

//

( : inducing~ l1lagl/eticfield

! anomatousfieid ofmagnetized body

component ofI anomnlou« field~ parallel to

inducingfield

the profile the deeper distribution of poles subtends alarger angle than the upper one does. As a result, thestrength of the weaker negative anomaly does not fall offas rapidly along the profile as the positive anomaly does.Beyond a certain lateral distance from the dike (to the leftof L and to the right of R in Fig. 5.47b) the negativeanomaly of the lower pole distribution is stronger than thepositive anomaly of the upper one. This causes the mag­netic anomaly to have negative side lobes, which asymptot­ically approach zero with increasing distance from the dike.

The magnetized dike in this example resembles a barmagnet and can be modelled crudely by a dipole. Far fromthe dike, along a lateral profile, the dipole field lines have acomponent opposed to the inducing field, which results inthe weak negative side lobes of the anomaly. Closer to thedike, the dipole field has a component that reinforces theinducing field, causing a positive central anomaly.

5.5.5.3 Magnetic anomaly of aninclined magnetization

When an infinitely long dike is magnetized obliquely ratherthan vertically, its anomaly can be modelled either by aninclined dipole or by pole distributions (Fig. 5.48). Themagnetization has both horizontal and vertical compo­nents, which produce magnetic pole distributions on thevertical sides of the dike as well as on its top and bottom.The symmetry of the anomaly is changed so that the nega­tive lobe of the anomaly is enhanced on the side towardswhich the horizontal component of magnetization points;the other negative lobe decreases and may disappear.

The shape of a magnetic anomaly also depends on theangle at which the measurement profile crosses the dike,and on the strike and dip of the dike. The geometry, mag­netization and orientation of a body may be taken into

330 Geomagnetism and paleomagnetism

(5.54)

(5.52)

(5.55)

(5.53)

The vertical magnetic field anomaly jB_ over thehorizontal cylinder is

1 ') (z2- x2)s», = 2 J.1-oR-d M: (z2 + xl)2

Assuming the same dimensions and a magnetiza­tion contrast iJM_~ the potential of the magneticanomaly over a vertically magnetized sphere accord­

ing to the Poisson relation is

(5.51)

By differentiating with respect to x or z we get thehorizontal or vertical field anomaly, respectively.The vertical field magnetic anomaly iJB_ of the

sphere is

(3) Horizontal crustal block. The gravity anomaly for athin horizontal sheet of thickness t at depth d betweenhorizontal positions Xl and x2 (Fig. 2.54 b), extendingto infinity normal to the plane of observation, is givenby Eq. (2.96). Let the width of the block be 2n1, andlet the horizontal position be measured from the mid­point of the block, so that Xl = X -111 and x 2 == x + 111.

Applying Poisson's relation, we get the magneticpotential for a semi-infinite horizontal thin sheet ofvertically magnetized dipoles, of thickness t at depth z

(2) Horizontal cylinder. The gravity anomaly dg: over acylinder of radius R with horizontal axis centered atdepth 2 and with density contrast ~p (representing ananticline or syncline) is given by Eq. (2.93). If thestructure is vertically magnetized with magnetizationcontrast dM:, Poisson's relation gives for the mag­netic potential

130

DO

(b) after reduction to the pole

2m~--L-----II

13U

(a) magnetic anomaly map

Fig. 5.49 Effect of data-processing by reduction to the pole on themagnetic anomaly of a small vertical prism with an inclinedmagnetization. In (a) the contour lines define a dipole type of anomalywith regions of maximum and minimum intensity (in nT); in (b) the

anomaly after reduction to the pole is much simpler and constrainsbetter the location of the center of the prism (after Lindner et al.,1984).

The asymmetry (or skewness) of a magnetic anomalycan be compensated by the method of reduction to the pole.This consists of recalculating the observed anomaly for thecase that the magnetization is vertical. The method involvessophisticated data-processing beyond the scope of thistext. The observed anomaly map is first converted to amatrix of values at the intersections of a rectangular gridoverlying the map. The Fourier transform of the matrix isthen computed and convolved with a filter function tocorrect for the orientations of the body and its magnetiza­tion. The reduction to the pole removes the asymmetry ofan anomaly (Fig. 5.49) and allows a better location of themargins of the disturbing body. Among other applications,the procedure has proved to be important for detailed inter­pretation of the oceanic crustal magnetizations responsiblefor lineated oceanic magnetic anomalies.

5.5.5.4 Magnetic anomalies of simple geometric bodies

The computation of magnetic anomalies is generally morecomplicated than the computation of gravity anomalies. Inpractice, iterative numerical procedures are used. However,the Poisson relation (Box 5.5) enables the computation ofmagnetic anomalies for bodies for which the gravityanomaly is known. This is most easily illustrated for verti­cally magnetized bodies, such as the following examples.

(1) Sphere. The gravity anomaly dg: over a sphere ofradius R with density contrast dp and center at depthz (representing a diapir or intrusion) is given by Eq.(2.83), repeated here:

5.5 MAGNETIC SURVEYING 331

Substituting this result in (3) gives

(5)

(J

r

v

dV

z

II

11M I

Z 'f

surface

Fig. 85.5 Definition of parameters used in the derivation of Poisson'srelation.

(1)

(2)

Box 5.5: Poisson's relation

Poisson (1781-1840) observed a relationship between thegravitational and magnetic potentials of a body, whichallows a simple method of computing magnetic fieldanomalies if the gravity anomaly of the body is known.Consider an arbitrary volume V with homogeneousdensity and vertical magnetization (Fig. B5.5). If thedensity of the body is lip a small element with volume d Vhas mass (lipd V). The gravitational potential U at apoint on the surface at a distance I' from the element is

U == - G LlpdVI'

If the body is vertically magnetized with uniformmagnetization liM:, the magnetic moment of thevolume element is (liM: d V). The magnetic moment isdirected downward as in Fig. B5.5. The radius vectorfrom the element to a point on the surface makes anangle ('IT - 0) with the orientation of the magnetization.The magnetic potential Wat the point (I', 0) is

The vertical gravity anomaly Jg: of the volumeelement is found by differentiating Uwith respect to z

a ( lipd V) a (1)g == -- -G -- == GlipdV-:- -z az I' az I'

JLo liM_ d Vcos ('IT - 0)w== 4'IT '- 1'2

== _ JLo liMz dVcosO == _ JLo IiMz d V(~)4'IT 1'2 41T 1'2 I'

(3)

Comparing Eq. (2) and Eq. (5) and eliminating thevolume Ii Vwe get Poisson's relation:

Note the following relationship

1 ar- 2, az (4)

This derivation for a small element is also valid for anextended body as long as the density and magnetizationare both uniform.

Assume that the horizontal crustal block is madeup of layers of thickness t == dz. If the top of theblock is at depth z1 and its base at depth z2' the mag­netic potential of the block is found by integratingEq. (5.55) between Zo and zl'

W = ILO::=J[ tan - {x ~ m )

- tan- 1( x-; m) JdZ (5.56)

Differentiating with respect to z gives the verticalmagnetic field anomaly over the block:

liB == - d,W= az

JLOliM=f=2 a. [ _ (x + In)== - --- ---= tan I -~-21T d..;, ...

(5.59)

where the angles ai' a2, a 3 and a4 are defined in Fig.5.50a. Note that the angles (a l - a2) and (a3 - a4) arethe planar angles subtended at the point of measure­ment by the top and bottom edges of the verti­cally magnetized crustal block respectively. This issimilar to the dependence of magnetic anomalies of

332 Geomagnetism and paleomagnetism

Fig. 5.50 The effect of block width on the shape of the magnetic

anomaly over a vertically magnetized thin crustal block. (a) The block

has width W= 2m, and its top and bottom surfaces are at depths Z1 and

Z2' respectively. For each of the calculated anomalies in (b), (c) and (d)

these depths are Z1 = 2.5 km and Z2 = 3 km, and only the width of the

block is varied. The amplitude of the anomaly is in arbitrary units.

for which 1171.:) == 1, a block of width] 0 km (111/Z 1 == 2), and

a wide block of width 40 km tml: 1 == 8).The narrowest block gives a sharp" positive central

anomaly with negative side lobes (Fig. 5.50b), asexplained in Section 5.5.5.2. As the block widens withrespect to its depth, the top of the central anomaly flat­tens (Fig. 5.50c), its amplitude over the middle of theblock decreases" and the negative side lobes grow. Whenthe block is much wider than the depth to its top (Fig.5.50d), a dip develops over the center of the block. Thepositive anomalies are steep sided and are maximum justwithin the edges of the block, while the null values occurclose to the edges of the block. The negative side anom­alies are almost as large as the positive anomalies.

The pronounced central dip in the anomaly is due tothe limited vertical thickness of the layer. If the layer isvery wide relative to its thickness, the central anomalymay diminish almost to zero. This is because the angle(a

3- (

4)subtended by the magnetized base of the layer is

almost (but not quite) as large as the angle (a) - ( 2) sub­tended by the top of the layer. For a very large width-to­thickness ratio, the central anomaly is zero, the edgeanomalies separate and become equivalent to separateanomalies over the edges of the block.

Examination of Fig. 5.50a shows that the subtendedangles (a) - ( 2) and (a3 - ( 4), and thus the anomalyshape, depend also on the height of the measurementprofile above the surface of the block. A low-altitudeprofile over the block will show a large central dip, while ahigh-altitude profile over the same block will show asmaller dip or none at all.

In contrast to the example of a thin layer describedabove, if the crustal block is very thick, extending to greatdepth, the angle (a

3- ( 4) is zero and the effects of the

magnetization discontinuity (or pole distribution) on itsbase are absent. The shape of the anomaly is then deter­mined by (a l - ( 2) and is flat topped over a wide block.

+x

(.r/m)3

(x/m)

-l 5

(.r/111)1.5 2

-60

180

150(c)

block width(2m) = 10 90

B

30-3 -1

-60

(d)90

block width B(2m) = 40

-1 -0.530

0.5

-x

(b)

block width(2m) = 5

-5 -4 -3 -2

(a) model

three-dimensional bodies on solid angles subtendedby surfaces of the body at the point of observation"as illustrated in Fig. 5.46. As was the case for gravitysurveys" magnetic profiles normal to the strike ofelongate bodies may be regarded as two-dimen­sional, as long as the third dimension of the body islarge enough for variations normal to the profile tobe negligible.

5.5.5.5 Effect ofblockwidth onanomalyshape

The effect of the width of a crustal block on anomalyshape is illustrated by use of Eq. (5.59) to Inodel the verti­cal field magnetic anomaly of a vertically magnetizedblock with its top at depth 2.5 krn and base at depth 3 kn1.The block is effectively a thin magnetized layer, similar tothe source of oceanic magnetic anomalies. Three cases areconsidered here: a narrow block of width \t' == (2111) == 5 km

5.5.6 Oceanic magnetic anomalies

In the late 1950s marine geophysicists conducting mag­netic surveys of the Pacific ocean basin off the west coastof North America discovered that large areas of oceaniccrust are characterized by long stripes of alternating posi­tive and negative magnetic anomalies. The striped patternis best known from studies carried out across oceanicridge systems (see Fig. 1.13). The striped anomalies arehundreds of kilometers in length parallel to the ridge axis,10-50 krn in width, and their amplitudes amount toseveral hundreds of nanotesla. On magnetic profiles per­pendicular to a ridge axis the anomaly pattern is found toexhibit a remarkable symmetry about the axis of theridge. The origin of the symmetric lineated anomalypattern cannot be explained by conventional methods ofinterpretation based on susceptibility contrast.

Seismic studies indicate a layered structure for theoceanic crust. The floor of the ocean lies at water depths

5.5 MAGNETIC SURVEYING 333

B

GoB

~J

I

orr=n=oJ

(c)

.r

B

~o

III

~:.~

1 n M n IL7 c;==; : ~ CJIII

o

[JJ

(d)

G

[j]G

(b)

Fig. 5.51 Explanation of the

shape of a magnetic profile

across an oceanic spreading

center: (a) the anomalies of

individual oppositely

magnetized crustal blocks on

one side of the ridge, (b)

overlap of the individual

anomalies, (c) the effect for

the opposite sequence of

blocks on the other side of

the ridge, and (d) the

complete anomaly profile.

G o B B o G

of 2-5 km, and is underlain by a layer of sediment ofvariable thickness, called seismic Layer 1. Under the sedi­ments lie a complex of basaltic extrusions and shallowintrusions, about 0.5 krn thick, forming seismic Layer 2A,under which are found the deeper layers of the oceaniccrust consisting of a complex of sheeted dikes (Layer 2B)and gabbro (Layer 3). The magnetic properties of theserocks were first obtained by studying samples dredgedfrom exposed crests and ridges of submarine topography.The rocks of Layers 2B and 3 are much less magnetic thanthose of Layer 2A. Samples of pillow basalt dredged nearto oceanic ridges have been found to have moderate sus­ceptibilities for igneous rocks, but their remanent magne­tizations are intense. Their Konigsberger ratios arecommonly in the range 5-50 and frequently exceed 100.Recognition of these properties provided the key tounderstanding the origin of the lineated magnetic anom­alies. In 1963 the English geophysicists F. 1. Vine and D.H. Matthews proposed that the remanent magnetizations(and not the susceptibility contrast) of oceanic basalticLayer 2 were responsible for the striking lineated anomalypattern. This hypothesis soon became integrated into aworking 1110del for understanding the mechanism of sea­floor spreading (see Section 1.2.5 and Fig. 1.14).

The oceanic crust fanned at a spreading ridge acquiresa thermoremanent magnetization (TRM) in the geomag­netic field. The basalts in Layer 2A are sufficientlystrongly magnetized to account for most of the anomalymeasured at the ocean surface. For a lengthy period oftime (measuring several tens of thousands to millions ofyears) the polarity of the field remains constant; crustformed during this time carries the same polarity as thefield. After a polarity reversal, freshly fanned basaltsacquire a TRM parallel to the new field direction, i.e.,opposite to the previous TRM. Adjacent oceanic crustal

blocks of different widths, determined by the variabletime between reversals, carry antiparallel remanent mag­netizations.

The oceanic crust is magnetized in long blocks parallelto the spreading axis, so the anomaly calculated for aprofile perpendicular to the axis is two dimensional, as inthe previous examples. Consider the case where theanomalies on a profile have been reduced to the pole, sothat their magnetizations can be taken to be vertical. Wecan apply the concept of magnetic pole distributions toeach block individually to determine the shape of its mag­netic anomaly (Fig. 5.51a). If the blocks are contiguous,as is the case when they form by a continuous processsuch as sea-floor spreading, their individual anomalieswill overlap (Fig. 5.51b). The spreading process is syrn­metric with respect to the ridge axis, so a mirror image ofthe sequence of polarized blocks is fanned on the otherside of the axis (Fig. 5.51c). If the two sets of crustalblocks are brought together at the spreading axis, a 111ag­netic anomaly sequence ensues that exhibits a symmetricpattern with respect to the ridge axis (Fig. 5.51d).

This description of the origin of oceanic magneticanomalies is over-simplified, because the crustal magneti­zation is more complicated than assumed in the blockmodel, For example, the direction of the remanent magne­tization, acq uired at the time of formation of the oceancrust is generally not the same as the direction of the mag­netization induced by the present-day field. However, theinduced magnetization has uniformly the same direction inthe magnetized layer, which thus behaves like a uniformlymagnetized thin horizontal sheet and does not contributeto the magnetic anomaly. Moreover, oceanic rocks havehigh Konigsberger ratios, and so the induced magnetiza­tion component is usually negligible in comparison to theremanent magnetization, An exception is when a magnetic

334 Geomagnetism and paleomagnetism

survey is made close to the magnetized basalt layer, Inwhich case a topographic correction may be needed.

Unless the strike of a ridge is north-south, the magne­tization inclination must be taken into account. Skewnessis corrected by red ucing the magnetic anomaly profile tothe pole (Section 5.5.5.3). A possible complication mayarise if the oceanic magnetic anomalies have two sources.The strongest anomaly source is doubtless basaltic Layer2B, but, at least in some cases, an appreciable part of theanomaly may arise in the deeper gabbroic Layer 3. Thetwo contributions are slightly out of phase spatially,because of the curved depth profiles of cooling isothermsin the oceanic crust. This causes a magnetized block in thedeeper gabbroic layer to lie slightly further from the ridgethan the corresponding block with the same polarity inthe basaltic layer above it. The net effect is an asymmetryof inclined magnetization directions on opposite sides ofa ridge, so that the magnetic anomalies over blocks of thesame age have differen t skewnesses.

5.6 PALEOMAGNETISM

5.6.1 Introduction

A mountain walker using a compass to find his way in theSwiss Alps above the high mountain valley of theEngadine would notice that in certain regions (forexample, south of the Septimer Pass) the compass-needleshows very large deviations from the north direction. Thedeflection is due to the local presence of strongly magne­tized serpentinites and ultramafic rocks. Early compasseswere more primitive than modern versions, but the falsifi­cation of a compass direction near strongly magnetic out­crops was known by at least the early nineteenth century.In 1797 Alexander von Humboldt proposed that therocks in these unusual outcrops had been magnetized bylightning strikes. The first systematic observations of rockmagnetic properties are usually attributed to A. Delesse(1849) and M. Melloni (1853), who concluded that vol­canic rocks acquired a remanent magnetization duringcooling. After a more extensive series of studies in 1894and 1895 of the origin of magnetism in lavas, G.Folgerhaiter reached the same conclusion and suggestedthat the direction of remanent magnetization was that ofthe geomagnetic field during cooling. By 1899 he hadextended his work to the record of the secular variation ofinclination in ancient potteries. Folgerhaiter noted thatsome rocks have a remanent magnetization opposite tothe direction of the present-day field. Reversals of polar­ity of the geomagnetic field were established decisivelyearly in the twentieth century.

In 1922 Alfred Wegener proposed his concept of conti­nental drift based on years of study of paleoclimatic indi­cators such as the geographic distribution of coaldeposits. At the time. there was no way of explainingthe mechanism by which the continents drifted. Onlymotions of the crust were considered, and the idea of rigid

continents ploughing through rigid oceanic crust wasunacceptable to geophysicists. There was as yet no way toreconstruct the positions of the continents in earlier erasor to trace their relative motions, Subsequently, paleomag­netism was to make important contributions to under­standing continental drift by providing the means to tracepast continental motions quantitatively.

A major impetus to these studies was the invention of avery sensitive astatic magnetometer. The apparatus con­sists of two identical small magnets mounted horizontallyat opposite ends of a short rigid vertical bar so that themagnets are oriented exactly antiparallel to each other.The assembly is suspended on an elastic fiber. In this con­figuration the Earth's magnetic field has equal and oppo­site effects on each magnet. If a magnetized rock is broughtclose to one magnet, the magnetic field of the rock pro­duces a stronger twisting effect on the closer magnet thanon the distant one and the assembly rotates to a new posi­tion of equilibrium, The rotation is detected by a lightbeam reflected off a small mirror mounted on the rigid bar.The device was introduced in 1952 by P. M. S. Blackett totest a theory that related the geomagnetic field to theEarth's rotation. The experiment did not support the pos­tulated effect. However, the astatic magnetometer becamethe basic tool of paleomagnetism and fostered its develop­ment as a scientific discipline. Hitherto it had only beenpossible to measure magnetizations of strongly magneticrocks. The astatic magnetometer enabled the accurate mea­surement of weak remanent magnetizations in rocks thatpreviously had been unmeasurable.

In the 1950s, several small research groups wereengaged in determining and interpreting the directions ofmagnetization of rocks of different ages in Europe, Africa,North and South America and Australia. In 1956 S. K.Runcorn put forward the first clear geophysical evidencein support of continental drift. Runcorn compared thedirections of magnetization of Permian and Triassic rocksfrom Great Britain and North America. He found that thepaleomagnetic results from the different continents couldbe brought into harmony for the time before 200 Ma agoby closing the Atlantic ocean. The evaluation of the scien­tific data was statistical and at first was regarded as con­troversial. However, Mesozoic paleomagnetic data weresoon obtained from the southern hemisphere that alsoargued strongly in favor of the continental drift hypothe­sis. In 1957 E. Irving showed that paleomagnetic data con­formed better with geological reconstructions of earlierpositions of the continents than with their present-daydistribution. Subsequently, numerous studies have docu­mented the importance of paleomagnetism as a chronicleof past motions of global plates and as a record of thepolarity history of the Earth's magnetic field.

5.6.2 The time-averaged geomagnetic field

A fundamental assumption of paleomagnetism is that thetime-averaged geomagnetic field corresponds to that of