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GEOLOGIAN TUTKIMUSKESKUS ESY/Merigeologia ja geofysiikka Espoo 63/2011

Borehole antenna considerations in the EMRE system: Frequency band 312.5–5000 kHz

Arto Korpisalo

GEOLOGIAN TUTKIMUSKESKUS ESY/Merigeologia ja geofysiikka Espoo 63/2011

GEOLOGIAN TUTKIMUSKESKUS 06.12.2011

GEOLOGIAN TUTKIMUSKESKUS KUVAILULEHTI Päivämäärä / Dnro

Tekijät

Arto Korpisalo Raportin laji

Archive report

Toimeksiantaja

Raportin nimi

Borehole antenna considerations in the EMRE system: Frequency band 312.5–5000 kHz Tiivistelmä

The ElectroMagnetic Radiofrequency Echoing (EMRE) system is utilized in radiofrequency imaging (RIM) measurements between two deep boreholes. It is based on radiowave attenuation, making it possible to reconstruct the attenuation distribution of the borehole section (tomogram). The main parts of the EMRE system are a continuous wave (CW) transmitter and superheterodyne-type receiver. The insulated dipole antennas are the transducers between the device and environment or together they form a transmission line. The system is bistatic because the antennas are placed in separate boreholes.

When an antenna is situated in a dissipative medium, e.g. in a water-filled borehole, its performance becomes highly environmentally sensitive. Direct measurements of the feed-point current and radiative characteristics are impossible, and numerical models must therefore be used to investigate the bore-hole effects. A generalized transmission line model of an insulated antenna is a simple and useful way to examine the antenna-related properties. A draw-back is that the borehole water must be excluded from the models due to the high wave number of water. The commercial simulation package FEKO is a numerical modelling package and is a powerful tool when constructing more realistic antenna and borehole models. FEKO models and transmission line models (WKG, CHEN) were compared and the results coincided in the frequency band of 312.5–5000 kHz. According to the FEKO studies, the influence of borehole water and the location of the antenna in the borehole, i.e. centric or eccentric, did not appear to have a significant effect. The scattering parameter s11, the ratio of forward and returned power, is a useful antenna parameter to estimate the power level that is radiated from the antenna to the surrounding rock. According to the FEKO models, the highest measurement frequency (2500 kHz) of the EMRE system seems to suffer the most under the borehole con-ditions due to the low values of s11 (~-2dB). The performance level of the system determines the maximum distances (translumination distance) at which the signals are still detectable. According to the results using a simplified measurement geometry, the EMRE system can operate at distances of <1000 m when the host rock has resistivities of >10000 Ωm and the lowest frequency of 312.5 kHz is used. At minor distances of 400- 600 m, the system operates well at all frequencies. Asiasanat (kohde, menetelmät jne.)

ElectroMagnetic Radiofrequency Echoing, EMRE, radioimaging method, RIM, insulated dipole antenna, transmission line model, FEKO Maantieteellinen alue (maa, lääni, kunta, kylä, esiintymä)

Karttalehdet

Muut tiedot

Arkistosarjan nimi

Arkistotunnus

63/2011 Kokonaissivumäärä

53 Kieli

english Hinta

Julkisuus

julkinen

Yksikkö ja vastuualue

ESY/Merigeologia ja geofysiikka Hanketunnus

7780061 Allekirjoitus/nimen selvennys

Arto Korpisalo Allekirjoitus/nimen selvennys

GEOLOGIAN TUTKIMUSKESKUS 6.6.20121

Contents

1 INTRODUCTION .............................................................................................................................................. 1

2 EMRE INSTRUMENT ...................................................................................................................................... 4

3 BOREHOLE ANTENNA CHARACTERISTICS ............................................................................................ 8

4 NUMERICAL STUDIES AND RESULTS ..................................................................................................... 18

5 DISCUSSION AND CONCLUSIONS ............................................................................................................ 45

6 REFERENCES .................................................................................................................................................. 51

GEOLOGIAN TUTKIMUSKESKUS 1

1 INTRODUCTION

Figure 1. a) The EMRE device and measurement geometry (not to scale). The mobile receiver takes

measurements during movement at a frequency of 2 Hz (Δ ~ 0.25 m, ~ 30 m/min), while the stable trans-

mitter transmits continuously (312.5-625-1250-2500 kHz). The attenuation distribution of the borehole

section is reconstructed (dB/m),with the red colour corresponding to higher attenuation.

The ElectroMagnetic Radiofrequency Echoing (EMRE) system operates in the frequency domain, and

thus differs from ground penetrating radar (GPR) in two ways. GPR is a time domain device and usually

operates in the reflection mode rather than in the transmission mode, which is familiar for the radiofre-

quency imaging method (RIM/EMRE). Electromagnetic methods are usually based on the fact that earth

materials may have large contrasting electrical properties (Korpisalo, 2010b). When operating in the


transmission mode, clearly defined boundaries are not necessities. The first steps in examining wave

propagation below the Earth's surface were taken at the beginning of the 20th century. During an inten-

sive period of development in electronics and device techniques, RIM has become a potential prospecting

method, for instance for the delineation of massive sulphide deposits, where the rock becomes gradually

more conductive towards the centre of the mineralization (Vogt, 2000; Mahrer, 1995; Buselli, 1980). Op-

erating in the transmission mode, the system must have a separate transmitter and receiver antenna, and

the system is referred to as bistatic. When the antennas are embedded in a dissipative medium, many

problems may arise (Figs. 1- 2).

b)

Figure 2. Schematic drawing of the transmitter and receiver dipoles and the effective field components,

showing the field components of the electric dipole. The tangential component EΘ is the dominant compo-

nent in the far-field domain, where the radial component Er vanishes. The magnetic axial component BΦ

(=μHΦ) is not encountered.


The physical behaviour of an electromagnetic field is mathematically governed by Maxwell equations,

which describe the relationship between the electric and magnetic field in a medium and quantify the me-

dium properties. The basic characteristics of the equations, using a plane wave solution, have been pre-

sented by Korpisalo (2010c). The major factor that limits the use of radiofrequencies in geophysics is the

strong absorption of energy in most earth materials, or the penetration may be highly frequency depend-

ent. Thus, the expected attenuation rates of electromagnetic waves in a frequency band should be estimat-

ed when assessing whether the use of RIM is justified in the exploration of the problem. The feasibility of

RIM has been thoroughly treated by Korpisalo (2010b).


2 EMRE INSTRUMENT In Finland, the radiofrequency imaging method (RIM) has been used since the pioneering work by A.

Korpisalo (2008). The heart of the system is a continuous wave (CW) device that simultaneously operates

at a maximum of four frequencies: 312.5, 625, 1250 and 2500 kHz (Korpisalo, 2010b; Korpisalo, 2010c).

The electric dipole antennas are 20/40 m long, consisting of Ø36 mm control tubes (for the corresponding

electronics and voltage source); that are 1.5 m long in the transmitter and 2.5 m long in the receiver. In-

termediate cables of 10/20 m in length are used to connect the antennas to the winch cable. Special damp-

ing filters are used to galvanically isolate the antenna from the winch cable (Fig. 3). The receiver and

transmitter surface units are connected using a ground-level reference line (Korpisalo, 2010b; Korpisalo,

2010c).

Figure 3. RIM instrumentation; (1) antennas (2); intermediate cables; (3) transmitter unit serving as an

amplifier for the reference signal; (4) transmitter and receiver casings; (5) surface filter; (6) surface con-

trol unit of the receiver.


Borehole transmitter

Both the transmitter and receiver have internal crystals of their own. In the transmitter, the basic fre-

quency is 2.5 MHz which is also the highest measurement frequency. The power of the transmitter is 2 W

(33 dBm), but the effective output power is less. Because the broad frequency band (312.5- 2500 kHz) is

sent simultaneously and the electrical properties of the borehole environment may be highly variable, it

has not been possible to properly handle the impedance matching of the antenna, and part of the antenna

power is lost due to the high voltage standing wave ratios (VSWR) generated by the impedance mis-

matches (Korpisalo 2010b).

Borehole receiver

Technically, the EMRE receiver (superheterodyne-type) is established in a manner that does not devi-

ate from a normal radio. The receiver has a crystal of 2.6 MHz. The front end of the receiver (RF -

amplifier) and mixer are situated in the borehole unit and the normal components (e.g. detector) in the

surface box. The armoured winch cable is used to feed the signals to the detector. The impedance mis-

match is not such a problem in the receiver. One important functional feature and at the same time a limit-

ing factor in the present receiver is that its dynamic power is <40 dB, and the user thus has to select the

appropriate antennas carefully in order to avoid the saturation of the receiver. Saturation can be eliminat-

ing by changing the antennas, rejecting the problematic frequency or using longer distances between the

transmitter and receiver (Korpisalo, 2010b).


Insulated antennas

The EMRE antennas are symmetrical linear electric dipoles (thin cylindrical antennas) with centre fed

voltage sources. The conductive arms are surrounded by a polyvinyl chloride (PVC) casing (Ø16 mm),

thus effectively isolating the conductors from the environment. They are standing-wave antennas (Zs = ∞)

with total lengths of 20/40 m. Reflections from the open ends are evident, and because it has not been

possible to properly handle the impedance matching between the antenna and generator, the high voltage

standing wave ratios (VSWR) reduce the effective radiative part of the power. When the voltage is turned

on, the generated field moves along the conductor or is guided by the conductor until it reaches the open

ends, where it is reflected and returns towards the source. When reaching the source, additional reflec-

tions are possible due to the impedance mismatch, and the reflected signals have reduced amplitudes due

to losses in the reflection. To maximize the current, the period T of a pulse must be correctly chosen.

When the length of the antenna arm is h = λ/4, the antenna is referred to as a half-wave dipole. The situa-

tion is known as a resonance and the antenna impedance is matched with the impedance of the transmitter

generator. Thus, the antenna can be regarded as a transformer (Korpisalo, 2010b). The current distribution

determines the antenna characteristics. Electromagnetic fields do not exist in a good conductor, and the

current is concentrated on the surface of the conductor, depending on its type (skin depth). Accurate cal-

culation of the currents of an arbitrary antenna is difficult, and numerical methods must be used (e.g.

FEKO/MoM). In numerical models, the antennas are considered to be electrically short and thin. An elec-

trically short antenna means that the radius (a) of the antenna is much less than its length (h); (h >> a)

and 1<<⋅hki , where ki is the wave number of the insulation layer. In an electrically thin antenna, the


signal varies negligibly during the time that it travels a path that equals the diameter of the antenna or

1<<⋅aki .


3 BOREHOLE ANTENNA CHARACTERISTICS The main function of an antenna is to radiate and receive electromagnetic energy. The antennas are the

transducers between the device and environment, or together they form a transmission line. A fundamen-

tal principle of the antennas is reciprocity, meaning that the performance of an antenna is the same

whether the radiation or reception is considered (the same frequency and impedance). Thus, the antenna

parameters could be measured either from the transmitter or receiver. The directivity is the ratio of the

total power fed to the antenna terminals to the total power in the reference (isotropic) antenna. The gain is

a measure of how strong a signal is received or transmitted compared to an isotropic antenna. An ideal

isotropic antenna radiates energy outward in a sphere with a directivity of 1 (0 dB). The gain takes into

account all the losses and can be expressed as G = ηD, where G is the gain, η is the antenna efficiency

and D is the directivity.

However, they both have certain practical characteristics of their own. The transmitter antenna radiates

the radiofrequency field. Directive antennas direct most energy in the desired direction and attempt to

suppress the radiation in other directions. Thus, the goal is to maximise energy radiated. The most im-

portant feature of a receiver antenna is not the maximum receiver power, but rather the maximum signal-

to-noise ratio. The radiation pattern shows the relative intensity of the radiated field in various directions

from the antenna. It is a mathematical representation of the directivity of the antenna (Fig. 4). The effect

of increasing the directivity of a receiver antenna is to increase the signal-to-noise ratio in the receiver, or

otherwise the noise comes from the same direction as the signal. The input impedance Zin of an antenna is

a quantity of great interest and is a function of the radiation resistance, resistive losses in the conductor,

reactive storage fields and impedance effects from the nearby conductors (Fig. 5). The radiation re-

sistance Rr determines the amount of energy that has been radiated, and the ratio of the radiation re-


sistance to the radiation resistance plus all other losses, Rl determines the antenna efficiency η or

( )lrr RRR += /η . (1)

a) b)

d) c) Figure 4. a) Dipole antenna patterns. The black dashed line corresponds to the circular pattern of an iso-

tropic antenna (drawn randomly, thus not related to the 3dB circle). A half-wave dipole (l = 0.5λ) is plot-

ted as a blue line, l = 1.0λ as red, l = 1.25λ as green and l = 1.5λ as yellow. b) A dipole antenna at a

height of h = λ/4 over a conducting surface (f = 1⋅MHz). The blue line corresponds to sea water (σ = 5

S/m, εr = 81), the red line to wet granite (σ = 10-2 S/m, εr = 30), the yellow line to granite (σ = 10-3 S/m,

εr = 15), the green line to dry granite (σ = 10-4 S/m, εr = 3) and the orange line to the dielectric (σ = 10-5

S/m, εr = 1). c) The height is increased (h = λ/2). d) The effect of the conducting medium is to broaden the

pattern. The antenna in air is indicated by blue line and that in the medium (σ = 0.01 S/m, f = 2.5 MHz,

2L = 40 m) is plotted in red. The directivity decreases: Dair = 1.25 dB, Dcond = 1.05 dB.


Figure 4a presents the antenna patterns of the dipole antennas. The length of a half-wave dipole is l = 0.5λ

(λ is the wave length). Its directivity is 2.15 dBi, and a half-wave dipole therefore has a directivity of

2.15 dB over an isotropic source. The directivity and gain increase when the length of the antenna in-

creases (l1.0λ = 3.82 dB, l1.25λ = 5.16 dB, l1.5λ = 3.47 dB), but when the length l >λ, side -lobes appear (e.g.

l = 1.5λ) and the directivity decreases. Figure 4b presents a vertical dipole antenna over an imperfect sur-

face. When the conductivity is finite, no radiation occurs along the ground surface. This does not mean

that the field strength is zero. Over a perfect surface, the radiation would also occur along the surface.

a) b)

c) d)

Figure 5. The impedances of a standing wave dipole antenna (l = 40 m, a= 0.001) as a function of the

length term (l/λ). The wavelengths in air are λ312.5 = 960 m for 312.5 kHz, λ625r = 480 m for 625 kHz,

λ1250 = 240 m for 1250 kHz and λ2500 = 120 m for 2500 kHz. The reactance disappears (~0 Ω) at l = λ/2

(resonance), and the corresponding resistance is ~73.1 Ω (red symbols). Data points corresponding to

l/λ312.5-625-1250-2500 (0.0417, 0.833, 0.1667, 0.333) are shown as brown symbols, respectively. The dipole

antenna is capacitive (reactance <0.0 Ω) when l/λ <~ 0.5 and becomes inductive (reactance >0.0 Ω)

when ~0.5 < l/λ < ~1.0. The reactance continues to alternate cyclically as the dipole length increases in

half-length segments.


When an antenna is situated in a dissipative medium, its performance becomes highly environmentally

sensitive. A bare metal wire antenna can be regarded as a diagnostic probe. The antenna impedance is

strongly influenced by the electrical properties of the medium. When an insulated antenna is used, the di-

agnostic power of the antenna is highly reduced but the impedance is still a function of electrical parame-

ters of the medium. In addition, the insulation layer of an insulated antenna alters the effect of the ambient

medium. The EMRE antennas are 40/20 m long. Thus, at the two highest measurement frequencies, the

antennas may operate as resonance antennas in suitable circumstances (Fig. 5). The longer antenna (40 m)

does not fulfil the requirement to be electrically a short antenna at the two lowest measurement frequen-

cies, but the shorter antenna (20 m) is short across the whole band. It could be used for diagnostic purpos-

es if an additional requirement is fulfilled. Both the ambient medium and the insulation layer should have

similar electrical properties, because the ratio of the relative permittivity of the insulation to that of the

ambient medium determines the impedance. Generally, the relative permittivity of the ambient medium is

larger than the permittivity of the insulation, but ice fulfils the requirement (King, 1981).

In water, the velocity of an electromagnetic wave is about three times lower than in common rocks.

This could cause some part of the energy to be trapped in the borehole and result in the waves propagat-

ing as guided waves along the borehole with the velocity of the surrounding rock, thus being able to radi-

ate energy along the borehole. However, theoretical studies suggest that the waveguide effects are only

significant as long as the dominant wavelength of an electromagnetic wave is less than 5- 10 times the

diameter of the borehole (Holliger et al., 2001). In highly conductive (1 S/m) water, the dominant wave-

lengths are from 10 m (100 kHz) to 1.2 m (6000 kHz). In more resistive borehole water (250 Ωm), the

wavelengths increase substantially being from 15 m (100 kHz) to 5.5 m (6000 kHz). Thus, in the 312.5 -


2500 kHz band, the waveguide phenomenon is not significant and may be bypassed in typical boreholes

(Ø56 -76 mm).

When an antenna is situated near an interface across which the electrical properties change, the anten-

na is coupled to the interface and the radiation pattern changes when compared to the full-space situation.

At the air -earth interface, the electric properties change considerably and the coupling effects may be se-

vere, resulting in a modified radiation pattern (Fig. 4b). The Earth has a finite conductivity, which swings

the maximum direction of the pattern out from the interface, and no radiation therefore occurs in the di-

rections along the ground plane. In air, the antenna pattern of the dipole antenna is a well-known and

simple symmetrical pattern (Fig. 4a), but in a conducting medium the pattern becomes broader due to the

contributions from the different parts of the antenna (Fig. 4d). The refracted (along the air -earth surface)

and reflected waves may interfere with the direct waves and cause significant artefacts if they are not tak-

en into account. The artefacts may be avoided by ensuring that the transmitter (receiver) antenna is al-

ways situated at least one dominant wavelength from the air -earth surface.

Earth materials have relative permittivity and conductivity values that are higher than those of air, so

the wavelength is shorter along a buried bare wire than it is along a wire used in air. In air, the wavelength

is equal to 300/f, where f is the frequency in MHz. In any medium other than free space, the wavelength

is equal to 300/Nf. N -factor is a function of relative permittivity and conductivity in the material. When

N -factor has a value of 4, it means that a half-wave dipole at 2.5 MHz is 60 m long in air, but 15 m long

when buried in rock. The earth materials surrounding the wire dipole forces its length to be reduced by a

factor of 4 in order to achieve the antenna characteristics that are normally attributed to a half-wave di-

pole. The same occurs with insulated antennas, but because the relative permittivity values of the insula-

tion layers are εr ~ 2, 3, the effect is not as strong.


The essential electrical earth parameters that have a strong effect on the antenna are the conductivity

and dielectric permittivity. Normally, these parameters are complex quantities with conductivity in the

form of σσσ ′′+′= i and permittivity εεε ′′+′= i . The conductivity is the response of free charges to an

applied field. It describes the ability of the material to pass free charges. A certain relaxation phenomenon

can also be related to the conductivity but its effect is small in conductors. At low frequencies, the charg-

es respond instantaneously to an applied field. Thus, the current varies in -phase with the electric field and

the conductivity can be represented by a static value (DC). However, at much higher frequencies the re-

laxation times τ (the relaxation time or the time needed to align the charges with the applied field) are

large, resulting in an out-of-phase component (σ''). The permittivity is a measure of the response of bound

charges to an applied field (polarization). It describes the ability of a material to store or release energy.

Now, the relaxation phenomenon can also be an important factor in the EMRE frequency band. In the re-

laxation phenomenon, the time-dependent displacement mechanism (charges are accelerated, generating

an out-of-phase displacement current) act at different rates to an applied electric field. Below the relaxa-

tion frequency ( πτ2/1=rf ), the charges quickly react to an applied field and remain in phase with its

changes. As frequencies increase, the polarization lags behind the changing field, resulting in an out-of-

phase component (ε''). Thus, the real component ε' of permittivity is related to the energy storage effects

and the complex component ε'' to the losses in polarization and displacement. The relaxation mechanisms

can be divided to two groups: bound charge effects (e.g. electronic, atomic, dipolar) and free charge ef-

fects (e.g. Maxwell-Wagner). Bound charge polarization is related to much higher frequencies than the

EMRE band and can be ignored. However, the Maxwell-Wagner effect, where free ionic charges can be

trapped in porous water and on grain surfaces, can already be notable from a frequency level of 100 kHz.


The parameters are expressed in Helmholtz equations (time-dependence e-iωt) in the following combina-

tion (Korpisalo, 2010c)

i ωεσε −=) (2)

Taking into account the complex representations and using Eq. 2, the effective conductivity and permit-

tivity which are the directly measurable quantities, can be written as

εωσσ ′′+′=e

ωσεε /′′−′=e (3)

According to Eq. 3, σ ′ and ε ′′ both produce a current that varies in -phase with the applied electric field,

and σ ′′ and ε ′ both produce a current out -of -phase with the electric field. Generally, the magnetic per-

meability is real and can be expressed as μ = μ0μr, where μ0 = 4π∗10-7 H/m. The relative permeability μr

is equal to unity in most rocks, or μ = μ0 is a valid assumption.

The wave number k is an important parameter that binds the conductivity, permittivity, permeability

and frequency. The wave number can be expressed as k = 2π/λ, where λ is the wavelength of an electro-

magnetic wave. Generally, the wave number is a complex quantity

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

=

>∗+==+=

0 when ,i

0 when ,)lossi(1)( ik

er

ere

εωμσ

εμεωμεωαβ

e

e (4)

where β is the phase constant (rad/m), α is the attenuation constant (Np/m), losse is the loss tangent and

eeeloss ωεσ /= . The relative permittivities of most earth materials are positive and larger than 1, or εr1 ≥

1.


112

112

22 −+=>++= ee

ee lossloss

μεωα

μεωβ (5)

The Q -factor is equal to the inverse value of the loss tangent. The behaviour of the Q -factor is closely

related to the behaviour of the field in a medium where the field exists. It is thoroughly treated in a paper

by Korpisalo (2010b). Figure 6 presents the attenuation and phase constants as a function of frequency.

The cut-off frequencies determine the frequencies when a quasi-static condition is valid or α ≈ β. When

the cut-off frequency has been reached, both the attenuation and phase curve deviate from the quasi-static

curve (black) and the field propagates as waves through the medium. In a moderate conductive medium

(σ = 0.01S/m), the cut-off frequency for quasi-static condition is at ≈1000 kHz while in highly resistive

medium (σ = 0.0001 S/m) the quasi-static limit is at 10 kHz (Fig. 6a). The effect of increasing the relative

permittivity is to decrease the cut-off frequency. In a moderately conductive medium (σ = 0.01S/m), the

quasi-static condition is valid up to 100 kHz, while in a highly resistive medium (σ = 0.0001 S/m) the

quasi-static condition can reach up to 10 kHz (Fig. 6b).

a) b)

Figure 6. a) The phase and attenuation constants in a dissipative medium with εr = 10. b) The phase and

attenuation constants in a dissipative medium with εr = 20. α is the attenuation (blue lines) and β is the

phase constant (red lines). The m -curve is valid when α ≈ β (black lines).


In a dissipative medium, the calculations become more complicated and no analytical solutions exist.

Numerical methods must therefore be taken into use. Of course, it is possible to estimate, for instance the

power density using the same methods as in a non-conducting medium, but now the electrical parameters

of the medium are complex quantities. The total average power is now strongly dependent on the distance

R. In air, the radius R does not matter and the same power flows through any sphere. In a dissipative me-

dium, there is a large difference in energy flow through different spheres, especially in the vicinity of the

dipole. Thus, it is not meaningful to estimate the values of antenna parameters (e.g. antenna pattern, gain,

directivity) in a dissipative medium, or the distance R from the source must be included in the definitions

of these parameters. Normally, when antennas are concerned, they are situated in a free space and the

mathematical formulation to determine the antenna properties is relatively straightforward. However, if

we add conductive material near an antenna or if the antenna is near to the Earth's surface, its operation

may be severally disturbed, and its efficiency depends on the energy lost as heat. When a vertical infini-

tesimal dipole is placed over a conductive half-space (l = 2zo), an analytical formula (Eq. 6) determines

the changes in the impedance ( XiRZ Δ+Δ=Δ )

( )( )

( ) ( ) ( ) ⎥⎥⎦

⎤

⎢⎢⎣

⎡+++

∗++

∗∗=

Δ −−......

411613

3213 lklki

lkNelik

lkei

RZ

ooo

liko

o

lik

o

oo (6)

where R0 is free space radiation resistance of the antenna (2

280 ⎟⎠⎞

⎜⎝⎛λ

π h ) and h is the length of the dipole

(Wait, 1969). ωεωεσ

oiiN 11

1+

= , where σ1 and ε1 = εr1εo are half-space properties and ω is the angular fre-

quency. The phase angle is determined as 1

12tanσωεϕ = . Figure 7 presents the impedance changes as a

function of relative permittivity (εr1 = 10), conductivity (σ = ∞, 10, 1, 0.1, 0.01, 0.001, 0.0001 S/m) and


several height parameter values kol ( oook μεω= ) at a frequency of 106 Hz. The corresponding phase

angle values are ϕ = 0.0, 0.0, 0.0, 0.006, 0.06, 0.6, 1.4. The dielectric half-space (σ ≈ 0) with ϕ = 1.4 and

the conducting half-space (σ ≈ ∞) with ϕ = 0 are illustrated. The curves behave similarly when the con-

ductivity ranges from σ = 1S/m to σ = ∞, and the resistance changes approach unity when kol→0. This

means that doubling of the radiation resistance or the antenna would operate more efficiently. In addition,

the reactance changes approach infinity when kol → 0. The effect of reducing conductivity (N1 decreases)

is to increase resistance changes.

Figure 7. A vertical electric dipole over a dissipative half space. The reactance changes (ΔX/Ro) as a

function of resistance changes (ΔR/Ro) are plotted for several values of the height parameter kol.


4 NUMERICAL STUDIES AND RESULTS In this paper, a commercial simulation package FEKO (FEKO, 2012) is utilized for the numerical

modelling of characteristics of the insulated antennas. FEKO is an electromagnetic simulation package

developed by EM Software and Systems and runs in the frequency domain. The Methods of Moments

(MoM) is a full wave solution of Maxwell’s integral equations in which only the structures in question are

discretized, not free space. The shapes of objects can be arbitrary (Fig. 8). The preliminary step is to de-

termine the electric currents on the conducting surfaces and the equivalent electric and magnetic surface

currents on the surface of dielectric solids. The electromagnetic fields and, for instance, the antenna im-

pedances are then calculated from the current distributions.

Figure 8. The FEKO model. An insulated antenna (-20 < z < 20, yellow) is centred in a water-filled

borehole (-250 < z < 250, diameter 76 mm, black tube. The yellow bar represents the antenna.


An antenna tuner (ATU) would match the transmitter generator (characteristic impedance) to the load

(antenna) impedance. The mismatch is usually caused when a non-resonant antenna is used. The radiated

power is a complex quantity and consists of an active and a reactive component. The reactive power

component oscillates in the near field of the antenna. To cancel the complex component and to make the

antenna resonant at the operating frequency, an inductor or a capacitor is connected to the antenna sys-

tem. These components are passive and they do not change the active power, but they change the reactive

power in the system to ensure that the reactance is zero. In the EMRE system, the ATU is lacking. In ad-

dition, open-end terminations (Zs = ∞) are used. Thus, high voltage standing wave ratios (VSWR) are evi-

dent. When looking at the complete circuit (e.g. transmitter, antenna) and its functionality, the borders

with the outer space are of greatest interest. Thus, when isolating the circuit and defining a limited num-

ber of ports, where it interacts with the outer space, simple notations (scattering parameters) can be used

to describe its functionality. The scattering parameter s11 defines the relationship between the reflected

and incident voltage in the input port of the antenna. When the antenna is well -matched with the trans-

mitter or the input impedance of the antenna is equal to the characteristic impedance, the incident voltage

is not reflected, and s11 thus equals 0. In Figures 9 -10, the components of the input impedance of an insu-

lated dipole antenna are presented.

Figure 9. The resistance component of the input impedance of an insulated dipole antenna.


Figure 10. The reactive component of the input impedance of an insulated dipole antenna.

The characteristic impedance of the generator is 50 Ω. The reactance alternates cyclically (capacitive -

inductive -capacitive, etc.) and the zero -values corresponds to the different resonance positions. The re-

sistive component of the antenna impedance should equal 50 Ω (well matched) with a zero reactive com-

ponent. This occurs at ∼1.6 MHz, which is the first resonance point of the antenna. At the second and

third positions, ∼3.3 MHz (100 Ωm) and ∼3.7 MHz (1462 and 2825 Ωm), the resistive component of the

impedance is much higher (hundreds of Ωm).

Figure 11. Scattering parameter s11.

Figure 11 presents the behaviour of scattering parameter s11. At a frequency of ∼1.6 MHz, s11 is -15.95dB,

meaning that only 2.5% is reflected and 97.5% is delivered to the antenna, embedded in a moderate con-


ductive medium (100 Ωm). Respectively, at a frequency of ∼1.8 MHz, s11 is -7.7dB, meaning that 16.7%

is reflected and 83.3% is delivered to the antenna (1462 Ωm). At a frequency of ∼1.9 MHz, s11 is -9.35dB,

meaning that 11.1% is reflected and 88.9% is delivered to the antenna (2825 Ωm). (s11(dB) =

20*log10(s11(lin)) or s11(lin) = 10^(-s11

(dB)/20) = √(Pref/Pfw)).

One of the distinctive features of the EMRE system is that both antennas are situated in deep bore-

holes, which are usually water-filled. They are classified as insulated antennas due to the presence of in-

sulation layers around the central conductors of the antennas. When a bare wire antenna resides in even a

weakly conductive material, the current in the antenna will diminish along the antenna axis, because the

surrounding material acts as a complementary path for the current. As the current in the antenna is very

sensitive to the surrounding material, a bare metal wire could be used as a diagnostic probe to investigate

the electric parameters of the borehole vicinity. In general, the antennas are highly insulated. Depending

on its thickness, the insulation will not only prevent the leakage of conducting charges from the antenna

but will also greatly reduce the sensitivity of the entire current distribution to the electrical properties of

the ambient medium. The current distributions of an insulated and a bare wire antenna (Probe dipole)

were compared in a water-filled borehole, where the relative permittivity of rock is εr r= 8.0 and that of

the insulation εri = 2.0. Water has a high relative permittivity value of εrw = 81. The resistivity of rock is ρr

= 10000 Ωm and that of water ρw = 1, 1000 Ωm. The antennas are 40 m long. The FEKO model of a bur-

ied insulated antenna is illustrated in Figure 8. When the borehole water is conductive, i.e. σw = 1 S/m, it

effectively serves as a complementary path for the current in the bare wire antenna (Fig. 12).


|tnerruC|Currents

Probe dipole (1250 kHz)Position z [m]

Curre

nt [A

]

20151050-5-10-15-20

1.4

1.2

1.0

0.8

0.6

0.4

0.2

0.0

|tnerruC|Currents

EMRE insulated dipole (1250 kHz)Position z [m]

Curre

nt [A

]

20151050-5-10-15-20

0.12

0.10

0.08

0.06

0.04

0.02

0.00

Figure 12. The frequency is 1250 kHz and the conductivity of borehole water is σw = 1 S/m. The water is

a complementary current path in a bare wire antenna and the current is concentrated near the feeding

point (having a peak value of 1.3 A). An insulated antenna is approaching its first resonance length and

the current waveform becomes sinusoidal (current peak value is ∼ 0.1 A).

In Figure 13, the conductivity of borehole water has been reduced to a value of σw = 0.001 S/m, resulting

in similar current waveforms. Thus, the water layer has lost its power to serve as a complementary path

for the current. Both antennas are near resonance: the bare wire antenna has just past it, but the insulated

antenna is still short.

|tnerruC|Currents

Probe dipole (1250 kHz)Position z [m]

Curre

nt [A

]

20151050-5-10-15-20

0.12

0.10

0.08

0.06

0.04

0.02

0.00

|tnerruC|Currents

EMRE insulated dipole (1250 kHz)Position z [m]

Curre

nt [m

A]

20151050-5-10-15-20

100

90

80

70

60

50

40

30

20

10

0

Figure 13. The frequency is 1250 kHz and the conductivity of borehole water is σw = 0.001 S/m. The

probe dipole has past its half-wave length (current peak value is 0.12 A). An insulated antenna is still

short compared to the wavelength and the current waveform has not changed. (Current peak value is 0.1

A).


Figure 14 presents a model of an insulated antenna in a water-filled borehole.

Figure 14. An insulated one -layer antenna in a water-filled borehole (not to scale).

Normally, MoM is used to solve the integral equations, e.g. when metal wires are of interest. However,

after King (1981), a generalized transmission line model (coaxial line model) can be used to eliminate the

tedious integrals (Fig. 15). It is assumed that the inequalities 12 <<bk , 13 <<ck and h >> c> b are satis-

fied, or the layers are narrow compared to the wavelengths.

Figure 15. Transmission line model of an insulated dipole antenna with two identical sections. The outer

and inner conductor (black) are metal regions.


The wave numbers associated to the different layers are

( ) ( )2/1

12/111 2

1 ⎟⎠⎞

⎜⎝⎛+==ωμσωμσ iik conductor

( )2/1

2

22/122 1 ⎟⎟

⎠

⎞⎜⎜⎝

⎛+=ωεσμεω ik first insulator (8)

( )2/1

3

32/133 1 ⎟⎟

⎠

⎞⎜⎜⎝

⎛+=ωεσμεω ik second insulator

( ) ( )2/1

42/144 2

1 ⎟⎠⎞

⎜⎝⎛+==ωμσωμσ iik conductor

It has been shown by King (1981) that even if the antenna has two or more insulation layers (ε2 and ε3), it

is possible to determine the effective relative permittivity as

⎥⎥⎦

⎤

⎢⎢⎣

⎡

+=

)/ln()/ln()/ln(

223

2,bcab

acreff

ηεε , (7)

where a is the conductor radius, b is the radius of the first insulator and c is the radius of the second insu-

lator. Factor η23 is defined by k2/k3 (ratio of wave numbers in the insulation layers).

According to King (1981), the current of the open-end section of a thin antenna driven by voltage Vo

can be assumed to be sinusoidal

hk

zhkZVi

hkzhk

IzIh

h

c

o

h

ho cos

)(sin2*

cos)(sin

)(−

=−

= (9)

and the corresponding input impedance of the antenna is given by

)*cot(2* hkZiZ hcin −= (10)


where Zc is the characteristic impedance of the transmission line and kh is the complex wave number of

the transmission line (Sato, 1991; Gouws, 2006). As can be seen from Eq. 10, the antenna serves as a

transformer.

In the WKG -model (Wu-King-Giri), the impedance of the transmission line consist of three serial im-

pedances z1, z2 and z3, and a shunt impedance y2 (Gouws, 2006). The complex wave number kh of the

transmission line is defined as

hhh yzk −= (14)

The model is accurate to 22

24 16 kk > , which greatly restricts its usefulness (King, 1991). Strictly, the

model could only be used when the antenna is embedded in water (Gouws, 2006).

The CHEN -model (Chen and Warne) introduced the admittance of the ambient medium to the model.

The impedance consist of three serial impedances, z1, z2 and z3, and two shunt impedances, y2 and y4

(Gouws, 2006). The transmission line wave number kh is given by Gouws (2006) and Sato (1991) as

{ } 2/1

4)2(

14244

)2(0

22

4)2(

144)2(

024

2)()/ln()(

)()/ln()(

⎥⎥⎦

⎤

⎢⎢⎣

⎡

+

+=

bkHabbkkbkHk

bkHabbkbkHkkkh (15)

where )2(nH is the Hankel function of second kind of order n. The CHEN model is assumed to be accu-

rate, when 22

24 2 kk > is satisfied, and the model can be used in both conductive and dielectric condi-

tions. The water-filled borehole must be excluded in both of these transmission line models (WKG and

CHEN), because the wave number of water is much larger than that of ambient rock and cannot be intro-

duced (Gouws, 2006). Thus, the outer conductor of the transmission line model must correspond to the

ambient rock.


In the FEKO -model, a lumped port element (port between the conductive arms of the dipole) is used

as a voltage source (Fig. 8). The conductive arms are assumed to be perfectly electric conductors (PEC).

Using the PEC assumption, only the surface of a conductor must be discretized in FEKO/MoM.

The comparisons of the different methods (WKG/CHEN/FEKO) were performed with the water layer

removed from the model in Figure 14. The ambient medium has resistivity values of ρr = 100, 1462, 2825

and 11000 Ωm, and relative permittivity εrr = 8, 32, and that of the antenna insulation εri = 1, 3. Figures 16

-17 present the effect of changing the relative permittivity of the insulation layer from a value of εri = 1 to

a value of εri = 32. The FEKO results are plotted in dark blue, WKG results in red and CHEN results in

green.

a) b)

c) d)

Figure 16. Input impedance. Relative permittivities εrr = 8 for rock and εri = 1 for insulation. a.) Re-

sistance. Rock resistivity has values of ρr = 2825, 11000 Ωm. b). Resistance. Rock resistivity has values of

ρr = 100, 1462, 2825 Ωm. c). Reactance. Rock resistivity has values of ρr = 2825, 11000 Ωm. d). Reac-

tance. Rock resistivity has values of ρr = 100, 1462, 2825 Ωm.


In Figure 16, the wave number ratio is 8/ 22

24 =kk . It is evident that the WKG –model (red curves) most-

ly suffers from the low permittivity value of the external medium (εrr = 8), because the accuracy condi-

tion 22

24 16 kk ≈ is not achieved. The first resonance point of the WKG -model is at 1.4 MHz and that of

other models at 1.9 MHz. The correspondence between the FEKO- and CHEN -models become better

when the resistivity of the external medium decreases, and is very good at 100 Ωm across the whole fre-

quency band (Fig. 16).

a) b)

c) d)






In Figure 17, the wave number ratio is 32/ 22

24 =kk . The effect of increasing the permittivity value of the

external medium (εrr = 32) is to improve the results at the higher resistivity values. FEKO- and CHEN -

models have excellent correspondence across the whole frequency band. The gap between the first reso-

nance point of all models has been narrowed and occurs now at ~1.6MHz (Fig. 17).

a) b)

c) d)






The increase in the relative permittivity of the insulation layer (εri = 3) has a pronounced effect on all

models, but it is quite evident that the WKG –model suffers from the disadvantageous wave number rela-

tionship of 22

24 3kk ≈ . The first resonance points of all models have moved towards lower frequencies,

occuring at ~920 kHz in WKG and at ~1.4 MHz in FEKO and CHEN. The favourable frequency band for

the EMRE measurements has decreased. The correspondence between the FEKO- and CHEN -model is

good in a moderately conductive medium (100 Ωm) across the whole frequency band, but becomes worse

when the resistivity of the external medium increases (Fig. 18).

a) b)

c) d)






The wave number ratio is 10/ 22

24 ≈kk . A further increase in the relative permittivity value of the exter-

nal medium (εrr = 32) makes the correspondence between all models better across the whole frequency

band (Fig. 19). When comparing with the results in Figure 17 (εri = 1), the correspondence between

FEKO and CHEN has become worse. In all models, the characteristic effect of increasing the permittivity

value of rock and insulation, is to move the first resonance point towards lower frequencies (wavelength

increases).

The control tubes of EMRE are slim (Ø36 mm), and EMRE can therefore used in almost all boreholes.

It is also usual that the boreholes are water-filled. Using the FEKO model (Figs. 8 & 14), the effect of the

water layer on the antenna impedance is estimated in a Ø76 mm borehole. In the model, the relative per-

mittivity of rock has the values of εrr = 8, 32 and the antenna insulation, εri = 1, 3. Rock resistivity has val-

ues of ρr=100, 1462, 2825 and 11000 Ωm and that of the borehole water, ρw=1, 250, 500, 750 and 1000

Ωm. Both components of the antenna impedance (resistance and reactance) are presented in Figures 20 -

23.

a) b)


c) d)

Figure 20. Comparison of a water-filled borehole and one without water. The input impedance of an an-

tenna. Relative permittivities -εrr = 8 for rock and εri = 1 for insulation. Resistivity of the external medi-

um: a) 100 Ωm, b) 1462 Ωm, c) 2825 Ωm, d) 11 000 Ωm. The solid lines represent resistances and the

dashed lines reactances. The green lines represent the situation without a water layer.

The water layer appears to have insignificant effects in the EMRE band. At the higher frequencies (>2

MHz) and with a moderately conductive water layer (1 Ωm), the response from the water layer clearly

deviates from the other responses. An increase in the external resistivity causes the curves to diverge

more and the disadvantageous frequency band covers the upper EMRE band. The peaks move towards

higher frequencies and at the same time they become broader or the area under the peaks expands. The

trend increases when rock resistivity increases. An increase in rock resistivity from 100 Ωm to 11 000

Ωm moves the first resonance point from ~1.6 MHz to ~1.8MHz.


a) b)

c) d)

Figure 21. Comparison of a water-filled borehole and one without water. The input impedance of an an-

tenna. Relative permittivities - εrr = 32 for rock and εri = 1 for insulation. Resistivity of the external medi-

um: a) 100 Ωm, b) 1462 Ωm, c) 2825 Ωm, d) 11 000 Ωm. The solid lines represent resistances and the

dashed lines reactances. The green lines represent the situation without a water layer.

An increase in the relative permittivity of the ambient medium (εrr = 32) reduces the effect of the water

layer. The result with a moderately conductive water layer (1 Ωm) deviates from the others. There are no

differences in the first resonance points compared with the previous results (Fig. 20), but the same trend

of points moving towards higher frequencies continues when the resistivity of the medium increases. The

overall behaviour of the input impedance is that the borehole water layer does not appear to have a per-


ceptible effect on the resistance and reactance values in the EMRE band (Figs. 20 -21). The differences in

the curves can be seen starting from the level of ~2.6 MHz and are emphasized at ~3.4 MHz, which is the

second resonance point. Beyond the level of 4.1 MHz, the behaviour is again similar. The increase in

rock’s relative permittivity evens up the disadvantageous frequency range (2.5 -4.1 MHz) and cancels out

the reverse effect of the increase in rock resistivity.

a) b)

c) d)

Figure 22. Comparisons of a water-filled borehole and one without water. The input impedance of an

antenna. Relative permittivities - εrr = 8 for rock and εri = 3 for insulation. Resistivity of the external me-

dium: a) 100 Ωm, b) 1462 Ωmm, c) 2825 Ωm, d) 11 000 Ωm. The solid lines represent resistances and

the dashed lines reactances. The green lines represent the situation without a water layer.


An increase in the relative permittivity value of insulation (εri = 3) moves the first resonance points to-

wards lower frequencies, being dependent on the increase in rock resistivity (~1.0 -1.4 MHz). Thus, the

1.25 MHz frequency could be favourable. In a moderately conductive external medium (100 Ωm), all re-

sponses are almost identical. The disadvantageous frequency band has broadened and the highest EMRE

frequency should now be problematic. The water layer appears to already be significant at the highest fre-

quency of the EMRE band (2.5 MHz). Despite the second resonance point occurs at ~2.5 MHz in a more

resistive medium, the corresponding resistance values of ~800 -1300 Ω result in the mismatch problem.

a) b)

c) d)

Figure 23. Comparisons of a water-filled borehole and one without water. The input impedance of an

antenna. Relative permittivities - εrr = 32 for rock and εri = 3 for insulation. Resistivity of the external

medium: a) 100 Ωm, b) 1462 Ωm, c) 2825 Ωm, d) 11 000 Ωm. The solid lines represent resistances and

the dashed lines reactances. The green lines represent the situation without a water layer.


An increase in the relative permittivity value of rock (εrr = 32) makes the situation worse when the lower

limit of the disadvantageous band approaches 1.25 MHz and covers the 2.5 MHz frequency. There is no

gap between the first reference points. In a moderately conductive medium (100 Ωm), the responses are

almost identical. The middle frequencies (625 kHz and 1.25 MHz) are perhaps the most effective ones,

but the highest frequency (2.5 MHz) must be problematic. More resonance points have appeared (third,

fourth). Thus, the water layer alone has a minor effect in the EMRE band, but combined with the resistivi-

ty of the external medium the influence is significant at higher frequencies. It is the highest frequency that

may suffer and introduce its effects on the active power delivery of the antenna into the external medium.

As vertical boreholes (Θr = 90o) are rare, the antenna may lie against the borehole wall (Fig. 1). Models

(Fig. 24) can be used to examine how the input impedance of the antenna and the scattering parameter s11

changes, when the antenna is moved away from borehole’s midpoint closer to the borehole wall. Three

models are presented. In first model, the antenna is located in a central position and the outer surface is 30

mm from the borehole wall (insulation Ø16 mm, borehole Ø76 mm). In second model, the antenna is

moved 20 mm and the outer surface is 10 mm from the borehole wall. In the third model, the antenna is

moved 28 mm and the outer surface is 2 mm from the borehole wall. Figures 25 -32 present the effects of

the movements.


Figure 24. An insulated antenna in a water-filled borehole. The diameter of the borehole is Ø76 mm and

that of the antenna Ø16 mm. The antenna is moved from its central position: on the left the outer surface

is 30 mm from the borehole wall; in the middle the outer surface is 10 mm from borehole wall; on the

right the outer surface is 2 mm from the borehole wall (not to scale).


Figure 25. The components of antenna impedance and s11 in a water-filled borehole. a) Resistance b).

Reactance and s11. Resistivity ρr = 2500 Ωm for rock and ρw = 1, 500, 1000 Ωm for borehole water. Rela-

tive permittivities εrr=8 for rock, εri = 1 for antenna insulation, and εrw = 81 for borehole water.

The capacitive cycle (reactance is <0.0 Ω) ends or the first resonances occurs at ∼1.8 MHz in the central

case, 1.75 MHz in the eccentric 10 mm case and at ∼1.65 MHz in eccentric 2 mm case. This is followed

by an inductive cycle (reactance is >0.0 Ω). The resistances are <200 Ω across almost the whole EMRE

band. In the eccentric 2 mm case, the resistances increase to >200 Ω at the ends of the band. The

reactances are >-300 Ω during the capacitive cycle and <300 Ω during the inductive cycle across the

EMRE band. The maximum s11 -values are (-7dB, -7.5dB, -7.5dB) in the central case (brown), (-5.5dB, -

5.8dB, -5.8 dB) in the eccentric 10 mm case (black) and (-4.6dB, -4.2dB, -4.2dB) in eccentric 2 mm case

(red), meaning that (19.8%, 17.8%, 17.8%), (27.8%, 26.8%, 26.8%) and (34.8%, 37.8%, 37.8%) are re-

flected and (80.2%, 82.2%, 82.2%), (72.2%, 73,2%, 73,2%) and (65.2%, 62.2%, 62.2%) are delivered to

the antenna. Thus, the delivered power is dependent on the antenna position. In the frequency range of 2.5

-5.1 MHz, the s11-values are at a low level and the antenna operates inefficiently.


Figure 26. The components of antenna impedance and s11 in a water-filled borehole. a) Resistance b).

Reactance and s11. Resistive ρr = 12500 Ωm for rock and ρw = 1, 500, 1000 Ωm for borehole water. Rela-

tive permittivities εrr = 8 for rock, εri = 1 for antenna insulation, εrw = 81 for borehole water.

An increase in rock's resistivity slightly raises the first resonance frequencies, or they occur at ∼1.85 MHz

in the central case, at ∼1.8 MHz in the eccentric 10 mm case and at ∼1.7 MHz in the eccentric 2 mm case.

The resistances and reactances behave as in the previous case. The maximum s11 -values are (10dB, -

11.3dB, -11.3dB) in the central case, (-7.2dB, -7.7dB, -7.7 dB) in the eccentric 10 mm case and (3.8dB, -

3.6dB, -3.6dB) in the eccentric 2 mm case, meaning that (10%, 7.4%, 7.4%), (19%, 17.2%, 17.2%) and

(41.5%, 43.5%, 43.5%) are reflected and (90%, 82.6%, 82.6%), (81%,82.8%, 82.8%) and (58.5%, 56.5%,

56.5%) are delivered to the antenna. Thus, the increase in the resistivity value clearly improved the opera-

tional level of the antenna. In the central position, the antenna operates well. At the higher frequencies,

the antenna operates inefficiently, having low s11 -values.


Figure 27. The components of antenna impedance and s11 in a water-filled borehole. a) Resistance b) Re-

actance and s11. Resistivity ρr = 2500 Ωm for rock and ρw = 1, 500, 1000 Ωm for borehole water. Relative

permittivities εrr = 32 for rock, εri = 1 for antenna insulation and εrw = 81 for borehole water.

An effect of increasing rock permittivity (εrr = 32) is to reduce the first resonance frequencies. The capac-

itive cycle (reactance <0.0 Ω) ends or the first resonances occur at ∼1.65 MHz in the central case, at ∼1.6

MHz in the eccentric 10 mm case and ∼1.5 MHz in the eccentric 2 mm case. Resistances are <200 Ω

across almost the whole EMRE band, but in the eccentric 2 mm case resistances increase to >200 Ω earli-

er. Maximal s11 -values are (-4.8dB, -4.5dB, -4.5dB) in the central case, (-7.0dB, -6.5dB, -6.5dB) and (-

12.3dB, -15.3dB, -15.3dB) in the eccentric cases, meaning that (33%, 35%, 35%), (20%, 22.5%, 22.5%)

and (5.8%, 3.0%, 3.0%) are reflected and (67%, 65%, 65%), (80%, 77.5%, 77.5%) and (94.2%, 97%,

97%) are delivered to the antenna. Second resonances occur at ∼3.4 MHz, 3.2 MHz and ∼3.0 MHz, hav-

ing low s11 -values and high resistances, but the third resonance at ∼5.1 MHz has high enough s11 -values

and low resistances and the antenna could maintain its effectiveness at third resonance occurring at ∼5.1

MHz. At the first resonance, highly conductive borehole water has larger effect on the s11 -parameters

(decreasing s11 -value) in the eccentric 2 mm case. Eccentricity has a profound influence on the s11 -

parameters. The effectiveness of the antenna increases when dipole is moved from its central position or

the reflected portion of power decreases.


Figure 28. The components of antenna impedance and s11 in a water-filled borehole. a) Resistance b) Re-

actance and s11. Resistivity ρr = 12500 Ωm for rock and ρw = 1, 500, 1000 Ωm for borehole water. Rela-

tive permittivities εrr = 32 for rock, εri = 1 for antenna insulation and εrw = 81 for borehole water.

The first resonances occur at ∼1.65 MHz in the central case, at ∼1.6 MHz in the eccentric 10 mm case

and ∼1.5 MHz in the eccentric 2 mm case. Resistances are almost <200 Ω across the EMRE band, but in

the eccentric 2 mm case the resistances increase >200 Ω earlier. Maximal s11 -values are (-4.7dB, -4.3dB,

-4.3dB) in the central case, (-7.0dB, -6.4dB, -6.4dB) and (-13.1dB, -16.9dB, -16.9dB) in the eccentric

cases, meaning that (34%, 37%, 37%), (20%, 23%, 23%) and (5%, 2%, 2%) are reflected and (66%, 63%,

63%), (80%, 77%, 77%) and (95%, 98%, 98%) are delivered to the antenna. The second resonances occur

at ∼3.4 MHz, ∼3.2 MHz and ∼3.0 MHz having low s11 -values and high resistances, but the third reso-

nance at ∼5.1 MHz has high enough s11 -values and low resistances, and the antenna could maintain its

effectiveness at the third resonance occurring at ∼5.1 MHz. At the first resonance, highly conductive

borehole water does not have a larger effect on s11 -parameters in the eccentric 2 mm case. Eccentricity

has a profound influence on the s11 -parameters. The effectiveness of the antenna increases when dipole is

moved from its central position or the reflected portion of power decreases.


The highest measurement frequency, 2500 kHz, suffers mostly in the borehole conditions (Figs. 25 -

32) but halving the transmitter power only means a loss of 3 dB. According to Vogt (2000), the directivity

would seem to be closely comparable with a free-space antenna, but the gain suffers from the borehole

environment (e.g. low s11 values). The high reactive component values of the input impedance mean

higher reactive power values, which are lost in the near field of the antenna.

In EMRE system, the transmitter power source is an accumulator unit of 12 volts. The current con-

sumption is highly dependent on the value of the antenna impedance. The output power of the EMRE sys-

tem is 2 W. Thus, if the antenna impedance is 34+174i [Ω] and impedance matching is not performed, to

get 2 W power delivered to the antenna using 12 V, a current of 0.87 A is needed. When the reactive

component is reduced and the impedance is 34+74i [Ω], the corresponding current is 0.4 A. Thus, it is

evident that the antenna impedance effectively controls the duration when the transmitter is able to oper-

ate at a reasonable level without an accumulator recharging period. In Figure 33, the antenna current and

impedance are represented as a function of frequency (100–6000 kHz). The resistivity of rock has a value

of ρr = 5555 Ωm and that of borehole water ρw = 500 Ωm. The relative permittivities are εrr = 8 for rock

and εrw = 81 for borehole water and εri = 1 for antenna insulation.

Figure 33. The antenna current and impedance as a function of frequency. Resistivities ρr = 5555 Ωm for

rock and ρw = 500 Ωm for borehole water. Relative permittivities are εrr = 8, εrw = 81 and εri = 1.


The antenna current burdens the voltage source and consumes current more effectively at lower frequen-

cies, having a maximum value of 1.4 A at 100 kHz, while the current follows a strong decreasing trend

until 350 kHz (0.8 A) is reached. In the interval between 350 and 1100 kHz, the current is almost constant

but decreases strongly after 1100 kHz, having a minimum of 0.2 A at 1900 kHz and remaining constant at

higher frequencies. The dependence of the current on frequency should be examined more closely, but it

is evident that the lowest frequency of the EMRE band (312.5 kHz) is the most current-consuming fre-

quency (Fig. 33).

The performance level of the system determines the maximum distance through the rock at which a

signal can be detected. To estimate the maximum transmitter ranges in different situations, a simplified

measurement geometry can be used (Pralat & Zdunek, 2005; Korpisalo 2010b). The model consists of

vertical boreholes separated by d metres. The scanning depth is h or the area of interest is defined by a

h×d rectangle. The maximum distance between the transmitter and receiver is equal to the diagonal of the

rectangle (Fig. 34).

Figure 34. Modeling geometry. Borehole distance is d metres and scanning length is h metres (Pralat &

Zdunek, 2005; Korpisalo, 2010b).


The total attenuation (dB) is calculated along the diagonals and the results are presented in Table 1

(Korpisalo, 2010b). Calculations are performed with four radio frequencies from 312 kHz to 5000 kHz

and with two relative permittivity values of εr =10 and 40.

Table 1. The total attenuation (dB) losses along the diagonal as a function of material parameters and

frequency. All other losses (e.g. in the device, different polarizations in transmission and reception) are

excluded.


Thus, in a normal situation where the host rock is highly resistive (>10000 Ωm), the borehole separa-

tion can be ~1000 metres and the signals are detectable at the lowest measurement frequency (312.5 kHz),

at least. However, at longer distances, the boreholes must also be deeper so that a reasonable angle cover-

age is met. At usual borehole separations of 400 -600 meters (rock resistivity ≈ 7500 Ωm, borehole depth

≈ 1000 m), the EMRE system can be used across its whole frequency band, despite device-based losses,

which have not been taken into account at all.


5 DISCUSSION AND CONCLUSIONS The operation of an antenna is strongly dependent on the medium in which the antenna exists. The

main function of an antenna is to radiate and receive electromagnetic energy, serving as a transducer be-

tween the generator and the environment. The Q -factor determines the behaviour of the generated elec-

tromagnetic field in a medium, or whether the field propagates as waves or diffuses through the medium.

Figure 6 presents the cut-off frequencies at which the diffusive movement turns into waves (Korpisalo,

2012b). The most natural medium is air, where modeling studies and the antenna characteristics for all

antenna types are straightforward to calculate. However, even in air, when the antenna is placed near an

interfering obstacle or the altitude from the Earth's surface is low, the operation may be severely dis-

turbed. In Figure 7, the impedance changes are presented with several values of the height parameter (kol).

Thus, power is lost as heat and the effectiveness is reduced when the antenna is near the surface. Most of

us may have observed that the relocation of the device or a slight movement of the antenna makes the sit-

uation better in the most cases.

When a bare wire antenna resides in a weakly conductive material, the current in the antenna will di-

minish along the antenna axis, because the surrounding material acts as a complementary path for the cur-

rent. Thus, a bare metal wire could be used as a diagnostic probe to investigate the electric parameters of

the borehole vicinity. In general, the antennas are highly insulated and the insulation will not only prevent

the leakage of conducting charges but also greatly reduces the sensitivity of the entire current distribution

to the electrical properties of the ambient medium (King, 1981). In Figures 12 -13, the current distribution

of a bare metal wire and an insulated dipole antenna are compared as a function of the conductivity of

borehole water and frequency. It is evident that the high conductivity of borehole water (1 S/m) makes the

surrounding material act as a complementary path for the current, and the current in a wire antenna will


effectively diminish along the antenna axis. The effect of reducing the water conductivity (0.001 S/m) is

to diminish the diagnostic power of the wire antenna. The thickness of the insulation layer effectively

prevents the leakage of charges in the insulated antenna and the sensitivity to the electrical properties of

the environment. In addition, the electrical length of an antenna is shorter than it should be in air. This is

due the difference in the electrical parameters; permittivity and conductivity. In air, the relative permittiv-

ity is εrair = 1 and the conductivity null and the electromagnetic wave propagates at the speed of light.

However, in a dissipative material, the parameters are different or εrr>>εrair and the conductivity may

range over several decades, varying from 108 to 10-14 S/m. Thus, the speed of the electromagnetic wave

may be much lower and the wave length is reduced by the N -factor. The relative permittivity of the insu-

lation layer is smaller than in rock and the conductivity is slightly greater. However, the electrical length

of the insulated antenna is shorter.

The mathematical treatment of the operation of an antenna when situated in a dissipative medium such

as seawater or in deep water-filled boreholes, becomes much worse. Modelling studies become compli-

cated and numerical methods must be used. The traditional transmission line technique is feasible and the

implementation is easy to perform, e.g. in MatLab, but in deep water-filled boreholes, the models cannot

include a water layer at all. Despite the lack of a water layer, the transmission line models (WKG-CHEN)

can give valuable information on the operation of the antenna in a hostile environment. These models can

be the first steps to becoming familiar with the behaviour of the antenna. On the other hand, the water

layer is not the most important factor in the borehole models if an insulated antenna is considered. The

transmission line models (WKG-CHEN) were compared with the FEKO results in Figures 16 -19. There

was a restriction on using the WKG/CHEN models, as a water layer could not be included in the models.

When the relative permittivity of the insulation layer increases from εri = 1 to εri = 3, both the insulation


speed and the wavelength decrease. This means that the resonance points move towards lower frequen-

cies. On the other hand, an increase in the resistivity and relative permittivity of the rock has the same ef-

fect on the resonance points, and the models approach to each other. Due to the movement of the reso-

nance points, the favourable resistance area (<200 Ω) becomes narrower in the EMRE band. When the

resistivity of the rock is ρr = 11 000 Ωm and the relative permittivity εrr = 8, and the relative permittivity

of the insulation εri=1, the first resonance point occurs at ~1.4 MHz (WKG)/1.6 MHz (FEKO, CHEN). It

moves to a level of <1 MHz in all models when the rock’s relative permittivity is εrr = 32 and the relative

permittivity of insulation is εri = 3. The second resonance point occurs at ~3.0 MHz/3.8 MHz (ρr = 11 000

Ωm, εrr = 8 and εri = 1). It moves to 1.8 MHz/2.1 MHz (εrr = 32, εri = 3), meaning that at the first and se-

cond resonance points, the antenna operates inductively. The cycle continues and the capacitive period is

followed.

More sophisticated tools must be used when more detailed models are designed (e.g. FEKO). The

principle characteristics (e.g. power density, antenna pattern, radiation resistance) of an antenna can be

calculated by using the same approach as in a non-conducting (non-dissipative) medium, but the electrical

parameters of the medium are now complex quantities and the results are different from one point to an-

other (dependent on the radius R). The characteristic effect of the conducting medium on the antenna pat-

terns is to broaden the pattern and swing the maximum direction of the pattern. Even the determination of

the origin (central or end) may lead to confusing solutions in the conducting medium and the modifica-

tions in antenna patterns become more pronounced, unlike in air where the coordinates of the origin in the

proximity of an antenna yields the same result. The phase shift and the attenuation due to the contribution

from one end of the antenna relative to that from the other end are not significant. However, it must kept

in mind that the pattern modifications merely represent a different viewpoint and not changes in the field


structure. Boreholes are most typically water-filled, and a water layer might influence the impedance and

power delivery of an antenna. Because the water layer is thin, its influence is not perceptible, and the

most notable effects are generated by both the resistivity and permittivity of the rock and the permittivity

of the insulation (Figs. 20 -23). Thus, when the resistivity of the rock decreases, visible effects on the im-

pedance of the antenna are evident and contribute to the power delivery, or more power may be lost as

heat (Fig. 33).

Vogt (2000) has examined the operation of a borehole antenna in his dissertation, and the final conclu-

sion was that the gain and directivity of an insulated antenna may be reasonable; thus, they are well suited

for radio tomography applications. I have theoretically examined the variations in antenna impedance,

and antennas do not appear to suffer much from the hostile environment because of the insulation layer.

The EMRE band is sent simultaneously, and impedance matching has been impossible. The highest fre-

quency, 2500 kHz, suffers the most in the borehole conditions, but on the other hand a halving of the

transmitter power, only means a decrease of 3 dB. Thus, the borehole conditions alone are not the most

important issue when considering the transmission of radio waves through geological transformations

(Figs. 24 -32) (Korpisalo, 2010b). In the EMRE system, the transmitter is a continuous wave (CW) device

with a power of 2 W (33 dBm) and an estimated performance level of ~135 dB. According to the theoreti-

cal calculations, where a simplified geometry (Fig. 34) was used, it was possible to estimate the maxi-

mum transmitter ranges. The results imply that borehole separations could be up to 1000 m when the

lowest system frequency of 312.5 kHz is used (Table 1).

In summary, insulated antennas maintain their effectiveness and feasibility at an acceptable level in the

typical borehole situations in the frequency band of 312.5–2500 kHz. In addition, the first empirical re-


sults from the field revealed that the EMRE system appears to operate according to theoretical expecta-

tions, or even better.


Acknowledgements

I wish to acknowledge RF -specialist Mika Niemelä, who maintained the proper functioning of the EMRE

device. Geophysicists Tapio Ruotoistenmäki and Kimmo Korhonen aided in the preparation of this paper.


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