Last Time: Magnetic Methods (Intro) • Governed by Laplace’ eqn: 2u = f (sources)• Differs from gravity in that the source is a dipole rather than a monopole• Magnetic field strength relates to force exerted by one “monopole” on the other: • Intensity of induced magnetization by an external field is

(where k is magnetic susceptibility)

• Crustal minerals can be diamagnetic (k ~ –10-5); paramagnetic (k ~ 0.02–0.2); antiferromagnetic (k ~ 0.05); or ferrimagnetic (k ~ 0.5–10)• Core minerals are ferromagnetic…

Geology 5660/6660Applied Geophysics

€

rH

€

rH =

r F

p2

= ˆ r p1

μr 2

€

rI = k

r H

26 Mar 2014

© A.R. Lowry 2014For Fri 26 Mar: Burger 429-449 (§7.4–7.6)

Last Time Cont’d: Magnetic Methods (Intro)• Magnetic anomaly is the measured perturbation of the external (core) magnetic field’s vector magnitude by crustal magnetization (i.e., vector component of the total change in the field in the direction of measurement!)

• Must know strength & direction of the Earth’s main field!• Magnetic field strength decays as 1/r3

• Total intensity of magnetization:

where remanent magnetization IR is in the direction of HE at the time of magnetization…

€

rI T = k

r H E +

r I R

Geology 5660/6660Applied Geophysics

26 Mar 2014

© A.R. Lowry 2014For Fri 26 Mar: Burger 429-449 (§7.4–7.6)

Field Exercises Tomorrow:West Cache Fault near Mendon, UT

(Thanks for the legwork Michael!)

http://ugspub.nr.utah.gov/publications/special_studies/SS-98.pdfTwo events on a 7 m (!) scarp: One4.4–4.8 ka; the other 15–25 ka. Long-term slip rate ~ 0.13 mm/year…

Would imply a~27 ka recurrencefor a 3.5 m event(but with caveats!)

The Earth’s Main Field (Core Field):

Earth’s main field is generated by convection of Earth’s

fluid Ni-Fe outer core. As the solid innercore cools & grows, released heat drivesthermo-chemical convection. Motion of the electrically-conductive molten ironproduces electric currents which in turngenerate a magnetic field.

Rotation of the Earth Coriolis forces which cause a Magnetohydrodynamic Dynamo Effect, in which magnetic fields organize in a way that amplifies the current flow. Positive feedbacks are self-stabilizing & produce a verylarge, predominantly dipolar magnetic field (with smallerhigher-order terms).

Core-generated magnetic field is a vector quantity so has magnitude and direction. Most often described by: intensity HE (i.e., magnitude) inclination i ( from horiz) declination d ( from true N)

These vary depending on location on Earth’s surface, and also change nonlinearly with time!

Intensity HE varies from ~25k nT at equator to ~65k nT at poles

Here blue is negative (i is positive down)

HE

i

d

World magnetic model 2010

Westward drift of “non-dipole” field(& precession of magnetic aboutrotation pole) declination changes relatively rapidly

IGRF Inclination 1995

Can express vector where aregeographical East, North, Up directions. Then

intensity

inclination i is the angle of field direction from horizontal (positive downward):

declination d is angle (positive clockwise) from true north to magnetic north:

€

rH E = ˆ x XE + ˆ y YE + ˆ z ZE

€

ˆ x , ˆ y , ˆ z

€

HE =r

H E = XE2 +YE

2 + ZE2

€

i = tan−1 ZE

XE2 +YE

2

⎛

⎝

⎜ ⎜

⎞

⎠

⎟ ⎟

€

d = tan−1 YE

XE

⎛

⎝ ⎜

⎞

⎠ ⎟

Intensity of Earth’s total dipole field also changes through time… Paleointensitymeasurements are very noisy but they and models of coredynamo suggest field is strong immediately after a reversal & weakens (~ exponential decay) for some period to near zero, then jumps to high value… Reversal may or not accompanythe jump. This “sawtooth” pattern is basis for suggestion by some that Earth will experience a reversal in next ~2000 years. But it’s not nearly that predictable!

500 yrs beforereversal

mid-reversal 500 yrs afterreversal

Glatzmeier modeling revealed:• Solid inner core magnetized opposite main field; forced to rotate by applied torque precession (~0.2°/yr for real Earth)• Inner core stabilizes field dipole; long time required to diffuse outer core field to inner core controls reversal timescale