OF a MAGNETOTELLUIUC IŒCOI~6ING SYSTEM by John II

TIIE OESIG\1, CONSTTWCTIO~ AND FIELD TESTING

OF A MAGNETOTELLUIUC IŒCOI~6ING SYSTEM

John II. Foster

i\ thesis submitteù to the Faculty of Graduate Studics and Research inpartial fulfilment of the rcquirements for the degree of Mastcr of Science.

Oepartment of Hining Engineering and Applied Geophysics,

McGill t~ivcrsity, ~.fon treal.

April 1964. A C K N 0 l·J L E D r. E ~~ E N T

r It is the author's pleasant duty to acknowleùgc the aid of L.P. r.eldart ùuring this thesis investigation. 1\'ith- out his counscl the topic might not have been discovered, and hecause of his continueù interest, the study was a stimulating and enjoyable experience.

Others who have offered valuahle counsel include

H.ll. l~ooù and n.c. iiest. H.ll. Wood, the designer of the r.uildline amplifier assisted in a variety of ways from field testing of the a."llplifier to theoretical discussions. D.C:. \\'est offered advice on a nUiaber of theorctical matters, and his comments on this thesis wore most helpful.

Ouring the major part of this investigation, the author received a research assistantship from the Oepartment of

Mining Engineering and Applied r.eophysics. Hiss M.A. Standish typed the manuscript: her assistance is gratefully acknowledged. TABLE OF CO:-JTENTS

r INTRODUCTION 1

2. TIIEORETICAL !ŒSISTIVITY r.IODELS 3

3. MORPHOLOGY OF 111E HAGNETOTELLUJHC FIELDS ------9

4. TYPES OF INSTIW~IENTS FOn DETECTINr, HAr;NETIC: 15 FIELD VARIATIONS ------~ s. DESIGN A:-JD CONSTRUCTION OF J\N AIR-C:ORED COlT. SYSTEM FOR TllE DETECTION OF H/\GNETI C 22 FIELD VAHIATIONS ------

A. Amplifier ------22 B. Air-Cored C:oil ------27 c. Leaù- In \\'ire from the Coil to the Amplifier-- 29 n. Input Filter and Grounding System ------30 E. !~esponse Shaping Fil ters ------42 F. Recorders ------48 G. Timing System ------49 !!. Calibration System ------52 I. Bias Stepping C:ircuit ------53

6. llf:SIG~~ ANO C.ONSTRUCTIO~I OF A SYSTml FOR THE DETECTION OF ELECTIHC FIELO VARIATIONS ------57

A. Recording Equipment ------57 B. Electrodes ------57 C. Lead-In llire ------60 o. Input Filter ------61 E. Amplifier ------·------·------62 7. l~ESULTS ------67 A. Hagnctic System ------6778 B. Elcctric System ------c. Conclusions 80

8. BIBLIO(;RA~N ------~------81 APPENDIX 84 LIST OF ILLlJSTRATIONS

Page 1. Example of regular oscillation in 2 eps to 0,2 eps 1 range ------ll 2. Examplc of events \Üth components throughout the broad frcquency range ------12 Example of regular oscillations in .2 eps to .03 eps 13 range ------Examplc of record shmving bias stepping ------20

s. Example of a low frequcney signal .with a very large amplitude ------21 6. Cornparison of curvilinear and rectilincar ehart records ------23 7 • r.Iti\Pll 1 Relative responscs · of the PNL coil-input fil ter combination anù the HcGill coil-input filter comhination. ------·------70 8. GRI\Pll 2 TI1e relative response of the five built-in roll off rcsponse filters of the Guildline amplifier ------71

9. GRI\Pll 3 TI1e superposition of the relative responses of sorne typieal recorders on the responses of the Guildline amplifier. ------72 10. GRAPH 4 TI1e superposition of the response of the lfcGill coil-input filtcr combination \-tith various com binations of amplifier roll fil ters and recorders-- 73

11, GRAPII 5 Thcoretical response curve for magnetic fields with breaks at 0,032 - 1 - 3 eps...... 74

12, GRAPII 6 Theoretical response curve for clcctric fields \dth breaks at 0,01 - 0,2 - 1 - 3 eps...... 75 i

1. INTROOUCTION The sciontific principlc considercd in this thcsis is the relation at the surface of the earth, of the amplitutle, phase and frcquency of orthogonal components of the naturally occurring elcctric and magnetic field fluctuation' to the resistivity profile of the suhsurface geology. A method of rcsisti vi ty pro fi ling, known as magncto te11urics, was presentcd in a paper hy Cagniard, (1953) and extended

in later }Japcrs hy l'lait, (1954~1 Tikhonov and Shakhsuvarov. (1959)1

Cant\'lcll and Madden. (1960)1 Smith, Provazek and Bostick, (1961), Priee,

· (1962)1 Vozoff, llascgawa and Ellis, (1963) and others. Results obtained by these researchers have shmm that the basic theory of magnetotelluric methoùs require sorne modification for extension beyond very simple geologie situations. A major ohject of this thesis is the development of magneto tellurics into a reliable field geophysical tool. This development re quires an cxamination of the theoretical relations and the subsequent dcvolopment of resistivi ty interpretation from observed data. In order to procccd \dth this investigation, the author has designed and con structed a system for the detection and recording of the magnetotelluric signais.

'fue system design criteria for frequency range, amplitude and phase response are implicit in the early literature, and have been

summarized into proposeù standards by Bostick and Smith~(l963). These

standards are the basis of the design describcd in this thesis.

Two contributions to the state of the art have been made in 2 this design. The first is an improvement in the minimum detectable signal.level over other systems previously described in the literature. This extends the period of useful recording to times of relatively weak signals. The second is the descrwtion of a system which may be easily duplicated with a minimum of available technical facilities. Because instruments for magnetotelluric prospecting are not commercially availablc as a package, the 'recording problems must be solved before one can attack the problcms associated with interpretation and application of the technique. It is hoped that this design will facilitate the entrance of other researchers into the study of the magnetotelluric fields,

TI1c term 'magnetotelluric fields' refers to the electromagnetic waves that make up the fluctuating parts of the geanagnetic and geoelectric (or telluric) fields. These electromagnetic waves propagate from the atmosphere into the earth. The sources of these lv-aves are cxternal to the earth and, in general, are not known in detail. In the magnetotelluric method, the relations between the electric and magnetic fields at the earth's surface are interpreted in terms of the variations of resistivities of crustal structures. TI1e relation between the electric and magnetic fields is used to calculatc a function called the apparent resistivity, This apparent resistivity is then related through a theoretical mode! to the frequency and subsurface resistivity variations. for any one frequency the apparent resistivity is equal to the value of the resistivity of a homogeneous medium that produces a wave impedance equal in magnitude to that obtaincd fron the ohserved data. The wave impedance at any frequency is ùefined as the ratio of the spectral 3 density of the electric field to the spectral density of the magnetic field at that frequency. Power spectral density may be defined as the rate of change of the mean square with the frequency of the function. 1 The energy in the magnetotelluric fields is distributed throughout the frequency band from a few cycles per second to a few cycles per week. From time to time quasi-sinusoïdal oscillations of various periods will rise above the background signal level, per sist for a while and then subside again. While these particular fluctuations are important in studies of the sources of the fields, they are of no particular significance in the magnetotelluric method of resistivity analysis. These quasi•sinusoids represent a relatively narrow frequency band in which the energy is enhanced. The magneto telluric analysis is concerned with the general distribution of energy over a relatively wide portion of the spectrum. The lower limit of this band is determined by the depth to which resistivities must be calculated, and the resistivities of the structures above this depth. For investigations down to lOO km, the lowest frequency considered is usually about 0.001 eps. The upper limit is usually taken about one cycle per second. Because the energy in the magnetotelluric field falls off with increasing frequency above o.os eps, considerable difficulty is often experienced in recording above this frequency.

2. THEORETICAL RESISTIVITY MODELS

In discussing the relationship between the electric 4

field and the magnetic field at the carth 1 s surface, one must assume a moùel in which is spccified the nature of the source of the field variations as '"ell as the variations of resistivi ty in the earth below / the point of observation. Investigations of the resistivity variations in the carth are hased on the comparison of relations betlvecn the electric and magnetic fields derived for certain moùels, and the actual relations observed at the carth's surface. If consistency bet1veen theoretical and observcù relations can he estahlished 'hy the appropriatc choice of mode!, then the variations of resistivity with dcpth assumed for the moùel may be used as estimates of the real earth variations. TI1e geological complexity of the earth makes the selection of a mode! \vhich is consistent in detail lvi th the obscrved data an cxtremely unlikcly event. In the present state of the art, success- fui applicatim1 of the magnetotelhuric mc~1où of resistivity analysis seems to be restricteù to areas where the lithology is charactcrized by thick .. horizontal, homogeneous isotropie laycrs of contrasting resistivity. Por these areas, a reasonahly gooù correlation of eross fcatures may be shmm \vith the rcsults ùeriveù from rather simple model:;. In one such simple modol, the earth is represcnted as a somi-infinite, homogcneous, conductive half space s~parated from the atmosphere by a plane interface and the source is taken at infinity. Bostick and Smith (1963) have used this plane earth model, assuming a plane wave to be incident on the earth from above such that the phase normal for the \vaves makes an angle Q 5 with the vertical. For all planes of the polarization and angles of incidence, the instantaneous electric and magnetic field vectors are essentially at right angles and maintai~ a definite amplitude and phase relationship with each other. For this model, an apparent wave impedance is defined as (.t)

If the conductivity of the earth is&mhos/meter, the permeability i~ henrys/meter, and it is assumed that at such low frequencies, the conduction currents are very much larger than the displacement currents, the apparent wave impedance is then , =- '+1-:jwe ' (2 0

The square of the magnitude of 2 11 (w) is given by (s)

where the superscript * denotes the complex conjugate. This is used to define a quantity referred to as the apparent resistivity f'~ . The apparent resistivity of any multilayered model with homogeneous and isotropie layers is defined by (4) 6

This may also be written as (5)

where ~(w) and ~~(w) are the power de:sity spectra of the electric and magnetic fields respectivity.

In the above relations both E and H~ are in the plane of the earth' s surface and the subscript.L on the Il indicates that the magnetic field is perpendicular to the electric field, The terrn (~) is the angular frequency in radians. Unfavourable comparisons between the theoretical and experimental apparent resistivity functions may result from the inadequacy of the mathematical model to represent accurately· the conditions in the real earth, Therefore let us examine this model more critically.

First, the assurnption that the incident signals are plane wavcs 11 is not correct. The fluctua ti ons of the geomagnetic field probably originate as hydromagnetic waves far out in the earth's exosphere and propagate to the bottom of the ionosphere as magneto- hydrodynamic waves. In the lower portions of the ionosphere these

~UiD waves are changed into electromagnetic waves which are then pro- pagated to the earth's surface. The distance between the lower portion of the ionospherc and the earth's surface is a small fraction of a wavelength at geomagnetic frequencies,

If one could resolve the ~fD waves in the lower portion of the ionosphere into an equivalent current system, the computation 7

of the fields at the earth's surface would require analysis of the ncar fields of this currcnt system rather than the assumption of plane wavcs from an infinitely distant source. This problem is ( quite complex mathematically and has been ,... orked out only for sorne very special cases. The results of these investigations have. indicated that the assumption of incidept plane electric and magnetic waves gives results which are consistent to the first order with the results of the more complex source models. Another objection to the plane homogeneous earth mode! is that the actual conductivity of the earth varies both laterally and vertically. The inclusion of horizontally stratified layers of different conductivities in the plane earth mode! has been investigated by many \IIOrkers. Severa! determinations of apparent resistivity have been compared with those computeù from the layered models to give estimates of the conductivi ty profile lvi thin the earth. The plane layered mode! earth providcs an approximation on the average to the observed data. Small variations are attributecl to local variations of conductivity with depth. The plane layered ea;-th moclel gives resistivity values which are invariant with the orientation of the measuring axis. Most areas on the earth attempted experimentally show a ,.,.ide variation in the values of conductivity as the measuring axis is rotated. For this reason more complex moclels have been proposed. Theoretical investigations

of modcls where the conductivity can vary laterally as well as vertically are rare and the results are inconclusivc. Bostick and Smith (1962) 8

worke<.l \d th an earth model bas cd on the assumption tha t the apparent

\vave impedance is a rank t\vO tensor. Again, howcver, the simpler mo<.lcl gives almost as good a result as the more complicated theory. 1 ror the case of the plane earth model, described by equation(z1 wc may expect that the ratio of the amplitudes of the electric field fluctuations to the magnetiè field fluctuations will increase approximately as the square root of frequency. At the same timc the observed average distribution of energy in the fluctuations of both the electric and magnetic fluctuations decrcases Nith increasing frequency. Thesc factors are sfgnificant in the design of the frequency response of the system. Because of this frequency characteristic a \'lÏde dynarnic range of signais may be observed. ror the most efficient use of an information channel, the detecting equipment should have a relative frequency response which is inversely proportional to the frequency distribution of energy in the signais to be passed through the channel. One objection to this 'prewhitening' of the data is that the recorded signais appear quite hashy and the qualitative character of the original signal is distorted. · . As a compromise, partial pre\'lhi tening is sometimes used to compensate for major increases and decreases of the energy of the recorded signal with frequency, while still retaining sorne of the relative amplitude or character of the signals.

One difficulty of the observed data not predicted by the 9 simple models is that the spectral distribution of energy changes considerably with time. The leve! of geomagnetic activity is often accompanied by a shift in those portions of the spectrum where the maximwn energy occurs. This \~fould requ.fre a different frequency response for every change in spectral distribution. As this is not practical, a compromise response corresponding to the quiet time spectra is usually used, One observed difference in the spectra of the electric and magnetic fluctuations is that the magnetic field fluctuations have somewhat less high frequency energy than the electric field fluctuations. A first approximation to correcting this disparity in the frequency distribution of energy between the two fields is to shift the point of maximum frequency response for the magnetic instruments to a slightly higher frequency than that used in the electric field equipment.

3. MOI

A brief resumé of the characteristics of the natural electric and magnetic field fluctuations is given by Campbell,(l963). Although more detailed classifications have been shown at various times in the literature, Campbell has divided the effects into three classes: regular oscillations in the 2 eps to 0.2 eps range, events with components throughout the broad frequency range, and regular oscillations in the 0.2 eps to 0,03 eps range • .. 10

TI1c regular oscillations in the 2 eps to 0.2 eps range are characterized by a beat frequency appearance as recorded on a strip chart recorder. This phenomenon has often been referred to as 'pcarls'. Usually a frequency near {eps is modulated at a rate of several cycles per minute. A plot of amplitude versus time shows a graduai increase in amplitude from the leve1 of background noise to a maximun amplitude fol1owed by a gradua! decrease in the amplitude down to the level of background noise. TI1e maximum amplitude ~ is reached in about half an hour to one hour following the appearance of the beating abovc the noise. Frequencies of 1 to 2 eps are observed in the middle latitudes. Lower frequencies of 0.2 to 1 eps are observed in the auroral zones. Spectral analysis of pearls by Tepley and \Ventworth (1962) showed that the pearls are composed of a multitude of rising •tones•. Pearls analysed by Pope (1964) at Boulder, Colorado, show an average midfrequency of 1.1 eps and rise from about 0.9 eps to 1.4 eps at the rate of about 0.08 eps per minute. Studies using three orthogonal component receivers make it possible to determine the apparent polarization of thesc pearls. The signal appears to be an elliptically polarized plane wave. The principal component of the magnetic variation is generally north-south. The sense of rotation is usually counterclockwise, but often a reversa! occurs after a transitional period of linear polarization. Reversais in sense of rotation are primarily caused by the superposition of two or more wave trains. 1i

Example of regular oscillation in 2 ·eps to 0,2 eps range, 1.2

NOOfj

llAM

lOAM

Example of events with components throughout the hroad frequency range. 13

NOON

Examplc of regular oscillations in .2 eps to .03 eps ran~e. 1.4

'Pearl' oscillations show a daytime maximum at all latitudes. In the aurora! zones they occur one day in four on the average over a year, with appearances bunched together in groups of one to four days in a row. Signais ire scarce during the equinoxes. Maximum ~plitudes of the order of 0,2 gamma are usual at the high latitudes with a decrease towards the equator of about 50% for every 10° to 15° of latitude. The pearl oscillations seldom appear above the noise at the equator.

Events with components throughout the broad frequency range are spectacular occasions of rapid agitation of the electro magnetic field called micropulsation storms. They contain frequency components ranging from 2 eps to less than 0.005 eps. The north- south magnetic field variations are generally the largest, the vertical field variations being small or undetectable. The polarization sense seems to be random. Micropulsation storms tend to occur more frequently around local geomagnetic midnight. A daylight enhancement of storm amplitude is observed. The probability of a recurrence, with diminished amplitude, within 24 hours is high. Large signal amplitudes of 10 to 20 gammas in the aurora! zones and 1 to 2 gammas in the middle latitudes again indicate a decrease toward the equator of 50% in amplitude for every 10° to 15° lower latitude. Micropulsation storms have not been detected at the equator. :1.5

The period of the regular oscillations in the 0.2 to 0. 03 eps range varies \vi th the time of day. Longer period oscillations are observed near noon whereas shorter periods are noted f near midnight. The oscillations appear to be quite sinusoïdal with sorne evidence of beating. The field variations show an elliptical polarization in the horizontal plane with the major axis in the general north-south direction.

The amplitude of the signais have mid-day maxima~near local noon in the auroral zones. In the middle latitudes the mid-day maxima occur near 1000 hours local mean time, with secondary maxima near 1400 hours local mean time. Amplitudes of 1.4 and o. 7 gammas are usual in the auroral and middle latitudes respectively. TI1ese signals are usually observable at the equator. Although the scientific interest in the frequencies of the magnetotelluric fields has greatly increased in the last ten years it should be mentioned that all the major field type oscillations now investigated were first reported over 25 years ago. To the early magneticians who were extending their frontier to higher frequencies, the appearance of these \11avelengths on slow chart recorders were 'micro' in size. Micropulsations might have been named macropulsations had the early radio researchers, extending downward in frequency, reached this region first.

4. TYPES OF INSTRUMENTS FOR DETECTING MAC";NETIC FIELD VARIATIONS

A survey of micropulsation research conducted as part :16

. . of the Cooperative Geomagnetic Micropulsation Measurement Program

was made by Smith (1963). This survey covered a total of 30 research groups and included approximately 60 fixed or mobile sites.

Smith's results did not cover all of th~ micropulsation research being conducted in Canada and the United States at that time as information about the networks of stations operated by Benioff, Campbell and Maple was not available. The survey showed two basic types of magnetic field transducers. The first type includes total field instruments, such as flux gate, proton precession, rubidium vapour and helium metastable magnetometers. TI1e second type are coil or induction variometer instruments \llhich have a vol tage output proportional to the timo derivative of the local magnetic field. The coil transducers are further subdivided into air cored coils and coils with higher permeability .metal cores. The use of air core coils avoids difficulties arising from the non-linear relation between the magnetic induction B and the magnetic intensity H in a ferromagnetic material. This non-linearity causes distortion of the signais and the production of beat frequencies when severa! frequencies are present at once. Sorne systems listed in the survey by Smith used both air cored and high permeability metal cored coils. The metal cored coils were used for measuring the horizontal components of the timo de-

rivative of the magnetic field, and the air cored detectors for the vertical component. This arrangement was used because large air cored :17 coils are difficult to mount rigidly in the vertical plane, hut can he \vound on level ground to fonn a sensitive detecter for the mcasurcment of the vertical componcnt.

11lis arrangement is used in the installations of Pacifie r Naval Laboratories of the Defence Research Board of Canada. One of thcse installations is presently in operation under contract with the Dcpartment of ~1ining Engineering and Applied Geophysics, r.lcGill

University, and is located at ~1ount St. !lilaire, near Montreal.

TI1c basic types of magnetic field transduccrs differ in that they measurc different quantities. TI1e total field instruments are responsive to fluctuations of the value of the magnetic field without regard to the time factor. On the other hand, the induction coils have a response proportional to the time derivative of one component of the magnetic field. The rising frequency characteristic of the derivative operation may he used to advantage in the prewhitening of magnetic data.

TI1c visual chart records may be labelled in uni ts of gamma/sec or gamma. The choice of lahelling is arbitrary, and not dependent on on either the transducer charactcristics or the prewhitening response shaping networks. Even though t)1e choice is arbitrary, the ease of inter- prctation of the recorded signals \

To illustrate the point, consider an example given by

Bostick and Smith (1963). Suppose we amplify the output vol tage of a coi! \vith a flat response amplifier. An amplitude-time pen recorder :1.8

will sho\V" the time derivative of the field lines linking the coil. If the pen recorder chart is calibrated in units of gamma/sec, a frequcncy response plot for the system wouid be a horizontal line on a graph ofrelative rcsponse versus frequency, For a sinusoidal trace on the pen record we could obtain the peak-to-peak fluctuations of the magnetic field from the following calculation. The amplitude of the·record is divided by the relative response of the system which \V"e have assumed to be independent of frequency, This re sul t i:s th en divided by the frequency and the gain constant of the amplifier-coi! comhination. The resul t of this is the amplitude of the sinusoida1 magnetic field variation at the coil. If we consider the same coil and amplifier system, but label the pen record in units of gammas instead of gamma/sec, wc must now supply a frequcncy rcsponse plot which is no longer in dependent of frequency. Since the coil differentiates the time varying field, it has a rising frequency characteristic. For a sinusoidal trace on the record we obtain the same answer as before for the peak-to-peak variations in magnetic field intensity at the coil. From practical considerations, the choice of label for the pen record is usually gamma/sec, This is because actual geo magnetic signals are composed of many frequencies and only on certain occasions do they resemble sinusoidal waves. Since the coi! system is basically a derivative deviee, and we have assumed there is no :1.9

network compensation, i.e. integration in the amplifier for the derivative operation, we could recover the amplitudes of the field variations ohly by Fourier analysis and subsequent inverse transformation to the time domain. Although the changing magnetic flux density in gammas may be obtained from derivative { i.e. time rate of change) records by the use of a computer, it is often desirable to have it available as a separate response for the system. To do this, a filter is added to the output of the amplifier. The filter is used to give the system an amplitude response with an attenuation· rate of 20 decibels per decade over the frcquency range of interest. This is the response for the transfer charactcristic 1/wT, which is the transfer function needed for integration of a sinusoïdal input signal. For accurate integration, the phase shift of the circuit should lag by as near 90° as possible. One disadvantage of the integrated response from a coil instrument, or the output from a total field instrument, is the com paratively low amplitude of higher frequencies of the signal. Pre whitening of the data prior to recording is one remedy for this difficulty. Another remcdy is the use of a 'bias stepper' to dis place the recording pen when it reachcs the limits of the paper chart. This system allows one to increase the gain of the recording channel to a level which allows the smaller, higher frequency components to be adequately recordèd. 20

Examplc of record sholving hias stcpping. • 21.

1 ()

6AM

SAM

Example of a low frei'J.uency signal tdth a very large amplitude. 22

In this discussion of detecting instruments, the use of rectilinear recordcrs has heen presumed. Records of a curvilinear nature may be compared with rectilinear records by the use of appro- priate graticules for scale correction. The labour involved in this process is considerable, and in general prevents extensive use of cuvilinear records for other than monitor purposes. For lengthy analyses, direct recording of the signais onto magnetic tape is preferrcd, to facilitate data handling ~or analysis.

5. DESIGN A.~D CONSTRUCTION OF AN AIR CORED COlL SYSTEM FOR TIIE DETECTION OF MAf.NETIC FIELD VARIATIONS

An air cored coil system for the detection of one component of magnetic field variations consists of an air cored coil, lead-in wire, input filter and grounding system, amplifier, response shaping filters for timc derivative output, response filters for integrated output, response filters for prewhitening integrated output, one recorder for each of the outputs desired, timing system and a calibration system. In most installations, three orthogonal components of magnetic field variations are recorded. The timing and calibration system is usually common to all three components.

A. Ampli fier Although sorne research organizations, for example, Pacifie Naval Laboratories, have designed and built their own amplifiers for 23

. '

:z 0 ):· z ';> "n 0·-

Comparison of curvilinear and rectiiinear chart records. 24

use with their coil systems, most researchers use commercially available amplifiers. The procedure· followed in this research was to select an amplifier and design the optimum coil for use with this amplifier.

This procedure was then repeated for a number of amplifiers and final selection made on the basis of the optimum coil-amplifier combination.

The factors to be considered in the selection of an amplifier arc: input impedance, bandwidth, noise, drift, temperature stability, line voltage stability, overload recovery, life of major components such as choppers, ease and cost of maintenance, initial cost. The amplifier selected \'las the Guildline model 9790, known in the u.s. as the Sensitive Research Instrument Corporation model 9790. This amplifier was designed and developed in 1963 by Hr. Herbert Wood of the Canadian Industries Limited, Central Research Laboratories, in McMasterville, near Montreal, and is manufactured by Guildline Instruments, Smith's Falls, Ontario. Although researchers at c.I.L. have expressed a pre ference to buy rather than design amplifiers, they found that no commercially available amplifiers could meet their performance re quirements. Further indications of this lack of commercially avail able amplifiers suitable for very low level signals in the o.c. to 1 eps range are that researchers at the University of Texas extensively modified the Leeds and Northrup ~iicrovol ter amplifier to meet their 25

requirements, while Pacifie Naval Laboratories designed their own amplifier. The specifications of the Guildline 9790 amplifier show a significant improvement over both these privately built amplifiers. A cobperative geomagnetic measurement program of The Pacifie Naval Laboratory and the University of Texas reported by Smith (1962) showed the Pacifie Naval Laboratory amplifier to be the better of the two. Comparison of the Pacifie Naval Laboratory amplifier wi th the Guildline 9790 at St. Hilaire showed the Gui! dU neto be superior. The Guildline 9790 amplifier incorporates severa! features not previously available in low level amplifiers, for cxample, immediate recovery from overloads of 10,000 times full scalc, 0.03 microvolt inp1,1t for full scale output on the lowest range, 0.003 microvolts peak-to-peak stability over a 24 hour period. The amplifier output can be switched to give 1 ma into a 1500-ohm pen recorder, such as an Esterline Angus Rccording Milliammeter, or may be switched onto one of three interna! voltage

dividers to give outputs of approximately 100 1 10, or 1 mv at currents suitable for the operation of most self-balancing recorders. Full scale adjustment for any particular recorder is made with the fine gain control. An output filter is built in to vary the high frequency roll-off of the amplifier. Five alternative responses can be selected on the filter output switch. Response times in the range from 1 second full scale to 6 seconds full scale are available. 26

The input impedance of the amplifier depends on the chopper speed and the input transformer supplied. With a chopper speed of 5.6 eps, input transformcrs are available to provide an effective input impedance in the range of 50 to 1000 ohms. Higher and lower impedance values might be achieved '"i th other transformers, but this has not yet been tried. The transformers for 50 ohm and

1000 ohm '"cre designed for l0\4 noise, low microphonic response and high stability with respect to temperature fluctuations. Trans-- formers to provide an input impedance much above 1000 ohms could be designed, but only with sorne increase in the noise level. \Vider bandwidth and much higher input impedances (also a some\-vhat higher noise level) can be obtained by increasing the chopper speed. The chopper, a Guildline type 9742, has been used successfully in other applications at speeds up to lOO eps. Another method of raising the input impedance is through the use of feedback in a circuit configuration known as bootstrapping, but again this results in an increase in the noise level. Calculations \-vere made for various input impedance values, the noise levels corresponding to these impedances, and the signal levels from coils designed within predetermined limits of size and weight. As a general rule, the lower the input impedance levels, the more sensitive the system. This agrees \YÎ th the results obtained by P.N.L. and incorporated into their design of coil and amplifier combination •. 27

B. Air Cored Coil

The predetermined limits for the size and weight of the co il were a diameter of two meters anù weight of 200 lbs. The impedance limit ùetermined by the amplifier design was a D,C, resistance of less than 50 ohms, the lower the better. The inùuced voltage in a coil is proportional to the rate of change of the magnetic flux, that is, E =NA dB/dt volts where N is the number of turns of wire on the coi 1, A the areâ in square meters, and B the magnetic flux density in webers per square -3 meter. Converting the above equation to gammas, we have E = 10 NA dr ar· microvolts where y is the flux density in gammas. For a sinusoïdal frequency component of the magnctic flux linking the coil, the voltage -3 induced in the coil per gamma of magnetic flux density is e m 10 NA~ microvolts/gamma where GO is the frequency in radians per second.

For a coil 2 meters in diameter with 1000 turns of wire the vol tage induced \~ill be 20 microvol ts for one gamma per second,

TI1e noise leve! of the Guildline 9790 amplifier, 0,003 microvolts peak-to-peak, corresponds to 0.00015 gamma per second, and the full scale maximum sensitivity of 0.03 microvolts is equivalent to an input of 1.5 milligammas per second for full scale output.

About twenty thousand fëet of wire are ~equired to wind

1000 turns on a coil 2 meters in diameter. To keep within the weight and resistance limits, it was necessary to use #10 aluminum magnet wirc covered with heavy formel insulation •. This wire has a resistance 28

of 1.5 ohms per 1000 feet and a \'leight of 9.6 lbs per 1000 fect. This gives a coil of 30 ohms resistance and weight about 200 lbs. Specifications of the coil construction are as follows: rectangular cross section, 32 turns per layer, 31 complete layers and a top layer of 8 turns. The coil was wound on a plywood mold on a base of epoxy cemented fiberglass cloth. The layers were impregnated with epoxy during winding and separated with a layer of fiberglass cloth. The epoxy was allowed to harden, the coil ;emoved from the plywood mold, and spiral wrapped with aluminum foil to act as an electrostatic shield. A final spiral wrapping \...Ïth epoxy impregnated fiherglass type provided mechanical protection and additional rigidity. The coil terminais were imbedded in a block of aluminum and located as close together as possible to minimize any temperature difference betwcen the terminais. Similar terminal protection is in corporated on the amplifier. Although the thermal compensator bàlance controls on the amplifier may be used to null out steady thermocouple voltages, the terminal protection is required to minimizc fluctuations in the thermoelectric voltages generated at the coil and amplifier terminals. To minimize local interference, the detector coils are located 500 feet away from the rest of the system, In the case

of a three-coil system1 the three coils are oriented in such a way that they are all mutually perpendicular. One coil, laid horizontally, 29 moasures the vertical component of the geomagnetic variations. The .. ether two coils, one with its axis north-south and the ether with its axis east-west, ùetect the two horizontal components. The coils are arranged in such a manner that the coupling coefficient between the coils is practically zero.

C. Lead-In Wire From The Coil To The l\mplifier

A very low pick-up, or radiation type, of lead-in cable known as lnter-8 ~~eave cable, was selected. This cable is manu factured by the Magnetic Shield Division of Perfection Mica Company, Chicago.

A twisted cable pair is somewhat more effective in reducing inductive pickup and radiation than single cables. This is because a twisted cable pair consists of a series of loops which, by their phase relationship, tend to reduce the fields radiated or picked up. This effect has becn further cnhanced in the Inter-S Weave arrangement which uses four wh·es in place of the normal tNisted pair to give two interlocking loops with very small enclosed areas in each loop. Laboratory test arrangements shown in the manufacturer's literature may be used to verify the claim of 20 db improvement in 60 cycle pick-up in comparison with a twisted pair cable.

The Inter-8 \~eave cable selected also had a shield braid of Co-Netic high leve! magnetic shielding material and an overall PVC jacket. This shield was used to connect the electrostatic shield 30

enclosing the coil to the grounding system.

D. Input Filter And Grounding System

The grounding system consists of the spiral wrapped aluminum foil shielù on the coil, the shield braid on the leaù-in wire and the ground terminal of the amplifier. The purpose of the grounding system is to prevent static charges from collecting on the coil windings and thereby producing o.c. or slm.Jly varying potentials. The input filter is required to rejcct higher frequency interference, notably 60 cycle and higher harmonies. Because of the derivative action of the coil, fairly \veak high frequency inter ference fields result in large voltage signais from the coil. These voltages cause saturation of the first amplification stage which results in less sensitivity. The input filter designed by P.N.L. consists of three separate filters. The first filter consists of a large shunt capacitance across the lead-in wires. For loN frequencies, an equivalent circuit for the coil is a resistance in series with an inductance, the t\110 bèing shunted_ by a capacitance. The capacitance consists of the distributed capacitance of the coil windings and the lead-in cable. The shunt capacitance added as a filter is very much larger than the distributed capacitance. The shunt capacitance and. the internai resistance and inductance of the coil comprise a two terminal lm-r-pass fil ter \'<'hich attenuates the higher frcquency inter ference. Thi:; filter is sho\-m in the ùiagram beloN. 3:1

ovr

HL TER

,, FliC<;.'(' 1 SGC.t>Ntl SIICTIO., ~~~~ r1oN'

TI1is shunt capacitor filtcr was uscd alonc, 1vithout

the aùdeù rcjection of hridgcd T fil tcrs by researchors at the

University of Texas. This \vas possible hccause the coil use1l by

tho Texas group has a much hir,hcr inductance than the coils uscù hy PNL or the co il of this dcsi;.;n.

The resistance of the coil is dictatcù by the Hire sizc, and is sir:1ply calculated from a kno\vn lcngth of wirc used to wind the coil.

Tiw calculation of self-inductance has hcen simplificd to routine calculations hy Graver (194 7). ror each coil design a simple working fomula is providcd in Nhich appear, in addition to the given dimensions, numcrical constants that"may be

interpolatcù from tables in l'lhich the coil shape rations are argu:nents.

With these formulae an accuracy of 1 part in .1000 is ohtainahle. llmvcver, errors in measurement of the dimensions of coils are usually the limit ing factors to the accuracy. 32

TI1c coi! designcd for this system is a circular coil of square cross section for a comhination of large attainahle in- ductancc Nith simplicity of construction. A simple channel in an insulating disk providcs a \o~inding form that enablcs a large numbcr of turns to he wound in close proximity to each other. Thus each individual turn has a relatively large mutual inductance with the others, and large inductance for the \-lhole co il resul ts for the amount of wirc used. The nomenclature for the $-!eometry of suéh a coil is illustrated as follm-1s

~------~- -·r ~ ~-J

.. b • a = mean radius of the turns

b = axial dimension of the cross section c = radial. dimension of the cross section N = total number ·of turns

nb :: numher of turns pcr layer ne = number of lay crs pb = pi teh of the Nin ding in the layer

= the distance hetween centers of adjacent turns in a layer

p a: distance beb1een centcrs of corresponding wires in cor.. c responding wires in consecutive layers. 33

For a circular coil of square cross section the parameter c/2a may have any dcsired value between 0 and 1 but h/c = 1. The inductance is given hy 2 L O.OOlaN P ,'uh = 0

in which P ' is a function of c/2a alone and may be interpolated 0 from table 21 of Grover (1947).

= = a = 42 inches = 108.3cm

3 6 L = 10- X 108,3 X 10 X 41.5 uh = 4.48 henrys

4.5 henrys

\Ji th this value of inductance for the co il i t is possible to calculate the rcsponse of the coi! and shunt input

capacitor.

' E'. 1 (. Eo . -- - - ...... C OIL

For this circuit we have a transfer function of

1 E sc: 0 = E. R+Sf.+ .!_ l sc 34

11w capacitor used as a shunt lol\' pass fil ter also affects the series resonance of the RLC: combination. To provide effective rejection of the higher harmonies of 6o~cps, the coil should he detuncd from its natural resonant frequcncy to something below 60 eps, hut ahove the highest frequcncy of interest to avoicl attenuating the weak high frequency signais. \Vith in the limi ts detcrmined hy the desirable resonance frequencies, the choice of the size of shunt capacitor rests with what attenuation is needed at 60 cycles and the higher harmonies. In general the 180 cycle harmonie is larger than the 120 cycle harmonie. For the purposcs of chccking the filter design, voltage !'lcasurcmcnts wcre made on the unfil terccl input leads from the PNL system using a Tectronic 122 low noise prca.nplifier. The preamplifier was set with a banclwidth of 8 eps to 40 kc. The output \\'as monitored on an oscilloscope. The output Navcfôrm shoNcd a 60 cycles component from lOO to 600 micro volts, varying with the component coil measurcd and the time of the measurement, and a harmonie content of less than 10% of the strength of the 60 cycle. To bring this interference to a love! equivalent to the amplifier noise, lOO dh of rejcction at 60 eps and 60 db of rejection at 180 eps arc requircd. Ignoring the resonance limita ti ons, 100 db of rej ection at 60 eps requires a shunt capacitor across the coi! designcd for this system of 160,000 ufd. Large values of low voltage elcctrolytic capacitors arc available from severa! manufacturors. A selection of thcse was testcd as shunt filters. Howcvcr, the leakagc and capacitance 35

of thcse large clectrolytics are vol tage and temperature depenJcmt. :Jo electrolytics Ni th sufficient stability were found, and they \iere rejected for this filter design. Oil-filled paper capacitors \vere found to have suitable stability, but are not corrrnonly availahle in values over 25 ufd.

To meet the 180 eps rejection requircments of 60 db,

'"ith the resonant frequcncy above the highest frcqucncy of intercst, a shunt capacitor of 160 ufd \vas used. This capacitor resonatc~ Nith the coil in this system at about 6 eps and p1·ovided 40 db of 60 eps rejection.

'Notch' rejcction filters providcd;:another 60 dh at 60 eps for the re quired lOO db rejection.

FollO\·ling the example of the PNL design, bridge T filters were selectcd for this. The rcason for this choice is that other filter designs have a greater insertion loss in the frequencies of interest in this application.

In the PNL design, thcre are two hridgcd-T filtcrs, one in each line to maintain a balanced line, for increascd 60 cycle rcjection.

TI1ese P~JL hridgecl-T fil tcrs uscd very large toroidal incluctors to minimize the series n.c. resistance of the filter. Although .larger toroids can be wound commcrcially, it appears that the PNL desir,n has carried that approach as far as practical with toroid coils of 8 inches outside diameter. llo,~ever, filter theory shows tha t large toro ids are not needeJ. llence a new input filter was designed. 36

The bridged T sections of the P~H. fil ter arc shown

in the diagram hel oh•.

At the notch frequcncy, this section may be resolvcd into

the equivalent circuit shown in the diagram below.

~ ... + l)f] t<., ----~--~ v----~~---- X L=r;it<>• .. .. ~ ... R-.. ~ ... qr..o R..... lf'o. X.c..,: -)">'X> ''- c ..... -~>}o C-e. c,T I I I

From this, the response at the notch frequency is seen

to be an open circuit, ie the rejection notch is of infinite depth.

Considcr the theory of bridgeù T filters. TI1e cor.1-

poncnts of the general case arc shm.:n in the diagram be low.

rf 37

The circuit equations arc

E • Il (Zl + Z3) 12Zl ( 1)

0 = -IlZl + 12 (Zl + z2 + Z4) (2)

For Vo • o, 1 z + 0 (3) 2 2 11Z3 =

For a non-trivial solution of these equations in I and 1 thq. 1 2 determinants of the coefficients must vanish.

Thus, (4)

This condition cannot be satisfied with all branches pure positive resistances. Unless all the branches are pure reactances, which cannot be achieved in practice, there will be sorne positive real terms in equation (4). To cancel these, we must have at least two complex impedances to provide a negative real term in their product. A particular case of interest is given by z = z = wC making the balance condition 1 2 1/j

(5)

We are at liberty to make either z or z pure resistance. 3 4 Let us examine both cases. 38

First let R as in the P.N.L. bridged-T filter. z3 = Then equation (5) becomes

Then, • • r + j'X

So that Z can be a series combination of resistance and inductance, 4

r =

These equations are the balance equations of the circuit below.

If on the other band we chose • R z4

Z (R + ....3:-- ) = 3 1w(. = 1

making the reciprocal of z3 a simple sum. This suggests interpreting as a parallel combination. A series combination:could be used z3 but this yields more complicated balance conditions as shown later in this section. 39

2 2 Sin ce 1 w c R - 2jNC: = 1 + 1 = JWL z3 r

wc have r = 1 2 w Rc2

wL = 1 2wC

as balance conditions for the figure helow.

For ideal inductors L in the parallel case, the rejection notch will he of infinite uepth, ie, a truc balance will he achicveù. llo1vever, a prototype filter hasoù on this design resulteu in a very shallO\v rejection notch. This is because real inùuctors have an appreciahle resistance, which is effectively in series with the inductor L. 11\is resistance defines a parameter of the coil knO\m x as the q,uality factor Q, by the relation q,~_!;_ • The Q of the coil does R not appear in this simple parallel balance condition. ror this rcason the series halance condition must be used as a design for the bridged

T fil ter. Derivation of the series balance condition follo\vs in the appendii. 40

To st~marize the series balance conditions derived in the Appcndix, wc have

R r = L = 1 4

TI1ese conditions apply to the circuit shown below, wherc r is the DC resistance of the toroid L

c c. L

Com~on sizcs of toroids for use in a 60 cycle hridged T filter, say 2 inches in diameter, have a quality factor

Q = ~L of the order of 10 or 20. TI1e large toroids wound hy PNL,

9 inchcs in diameter, have Q of 60 with a o.c. resistance of 10 ohms. This lmv o.c. resistance is desirable for. toroids in the series arm or position to prevcnt excessive~signal loss in the filter. z4 If, however, the coil is placed in the shunt ann, or z position, one may spccify a value for R in the z position, and 3 4 calculate the balance conditions. Por R = 10 ohms, the coil should have r = R = 2.5 ohms, Por common sizes of toroids, this small 4 value of r indicates a small value for 1 and hence large values for c.

Por the choice of C = 16 ufd, L = _l__ = 0,285 H. This requires 2w2c a Q of about so. which is readily availahle for such a small inductance value, 4i

As R approaches zero, the resistance r should also approach zero. For real inductors this is not possible, and an RLC comhination is left shunting the signal line. The impedance of such a combination is Z n + j(wL - _l_) and wi th wL • -1-- givcs = 1 1 1 \-IC: wC . 1 a shunt resistance R across the s1gnal line. This results in a 1 less thun infinite depth of rejection notch for the filter. TI1e input filtcr for this system is shown in the .. diagram helow.

IN OUT

For comparison the P'lL input filter is shown ih the diagram belm-1.

I:-J OUT

The advantagc of this filter over the PNI. design is that it does not rcquire the use of large, specially constructed toro id co ils. 42

E. Response Shaping Fil ters

The derivation of fonnulae for the calculation of filter elements used with operational amplifiers for response shaping \'lere given by Boothe, Fannin and Bostick (1960). To quote these fonnulae without explanation would be pointless. The explanation of the formulae is found in their derivation. For this reason the derivation is repeated here. for two responses. To correct the response of the coil, input filter and amplifier combination so that a frcquency response plot for the output in' gamma/sec shows no attentuation below one cycle per second the response shaping network shown below is used.

c, PHIL BR tc K f'b~ll our OPcRATIONAL A~PLJFIER +

For this circuit the transfer characteristic is given by

= (1)

Th en (2) WHIAE. !>=j. ...

= G ( 1 -~-&T,) (3), (4) (,.,.s'li )(!1-..S/)) 43

where G = (5)

(6)

T • R2c2c3· 2 (7) (c2 + c3)

(8)

and \oJhere T , T , T are 'breaks' in the response curve. 1 2 3 Fix R1 large enough so as not to load the preceding sta$e and calculate the remaining elements in terms of R1•

From equation (8)

(9)

Substitution of equation (6) into (7) gives

(10)

Substitution of (9) into (5) gives

T3 (11)

Replace (C + c ) or (10) by (11) to get 2 3 C3 = T3T2 (12) ----TlGRl

Substituting (12) into (11)

(13) 44

Substituting (13) into (6)

::l R2 Tl T GR = = 1 1 (14) ""ë2 T1T3-T2T3

Collecting tho results we have

T3 cl = (9) R1

T2T .. c3 = 3 (12) T1GR1

T3 T cz . -- ( 1 .. _:__, (13) GR 1 Tl

T GH 1 1 R2 = (14) T3(1 .. T2) T3

A similar calculation of filter elements for integration response \o:as made by Boothe, Fannin and Bostick (1960) along the lines of the following. The response network shown below has the transfer characteristic.

r: 0 •. (1) 45

IN PHILSRICK P6S"/i our + OPE.RATIONAL AMPLI FIER _:,.

1 1\2 (R3 + ) /C TI1en ., r.l s 2s

E R2 + R3 + 1/r. s - 0 1 = (2) E. l R2 (R3 + 1/C S) 1 R ( 1 c s ) 2 1( + R + 1/C S ) R2 3 1

0 = R,.. (3)

That is, E 0 = (4) E. ~

where G = (5)

R C (6) 3 l 46

= R c + R C + R C (7) 2 1 2 2 3 1

(8)

Select R large enough not to load the preceding stage and solve for 1 the other elements in terms of R 1 substituting (6) in (7) and (8) gives

= R C + R C (9) 2 1 2 2

TT and = 1 3 (10)

Replace R c of (9) by (10) and suhstituting (5) into (9) for 2 2 R one has 2 TT 1 3 T + T - T = + GR c (11) 1 3 2 T2 1 1 since rcarrangemcnt of (5) gives R • GR (12) 2 1 from equation (11) one may solve for c1 'l' _1_.._ cl = (13) GR ( Tl + T3 - T2 - TlT3/T2 ) 1

Similarly from (6) and (13) 2 G\T2 (14) H = T2 = 3 --ç- Tz(Tl+T3-T2)-TlT3 4.7

Substitution of (5) into (10) gives

= =

Collecting the final resu1 t"s

R = GR 2 1

T T 1 1 3 c = Tl + T3 - T 2 1 GR 1 T2

R = 3

TT 1 3 =

A discussion of the rcsults of these designs applied to this system:. :1ay he found in a la ter section. 48

F. Recorders

Recorders suitable for use in magnetotellurics may be dividcd into ttoJO types: paper chart recorders and magnetic

tape recorders. These can be further subdivided into six basic recorder types as shown in the sketch below.

Choices of Recorder Types

The most useful of the six types of recordersin general are (2), (4), and (6). In an ideal data analysis system probably all three would be used simultaneously. However each type bas its advantages for a particular type of analysis. For rapid visual inspection of large amounts of data type (2) is preferable. The paper chart records can be laid out on the floor, rolled on a multiple chart inspecter or folded. into convenient lengths for inspection and correlation by eye. For sub sequent analysis of portions of the records, curve followers, either manual or automatic may be used to transpose the data from paper records into suitable form for analog or digital analysis. 49

For analog analysis of records type (4) is preferable. Type (4) is preferable to type (3) because faster input and output of signals are usual, and there are fewer opportunities to introduce noise, distortion and phase shifts into the records. Type (4) records can be eut into suitable lengths for a tape-loop transport input· to analog analysing deviees. For digital analysis of records, type (6) is preferable. rype (6) is preferable to (5) because the data are stored in an IBM compatable format in the exact spacing required for maximum efficiency of reading tape. With'the low frequencies involved in magnetotellurics, type (5) is mostly blank tape.

G. Timing System

For recording in cooperation with widely separated stations, accurate absolute time values are essential if meaningful cross correlation studies are to be made on the concurrent data samples. For a micropulsation having a period of twenty seconds, one second represents eighteen degrees of phase. Accurate timing is then clearly an essential feature when phase delay between two locations is to be investigated. Consequently an accurate timing signal must be recorded simultaneously with the geomagnetic data. A suitable timing circuit was described by Caner and i'Jhitham (1962). A description of this circuit follows.

Timing pulses are provided by a crystal tuned \VivY or CHU .. ::! ~ l. ~ l.'

:::t. ()

~ \Q )...... J

0 u. ~ Q \A \.A ...... ,~ ~ <:!( <;c; ~ \1 N \.) 11'1 ~ \0 <:!( "" "" q::< li. 3 3

Timing C:ircuit Aftcr C:ancr & Whitham (1962). 51

r- ~~ >< -Ill '1: !:! ,.. t:c: -, ~wct () ':z- .. ""' ,...

~~ ;:~ 0~ 'Il- .q'- ""2-

~ , ~ ÔQ 'CI.\11 !~ l;~ ~v 1!! v ~~ ~~~- ~ 1- ~ t ...... t '> 0 > IJ) <:. 0 2 !JI + ~

Timing Circuit Pm.,or Supply After Caner & Nhi tham (1962). 52

receiver, The audio signal from the receiver is passed through sharp 'tick' filters and amplifiers, and the rectified pulse can be applied to a recorder or event pen. Timing pulses can be applied to a calibration coil for the magnetic system and to series resistors for the telluric system to provide a reliable assessment of any possible parallax between timing and signal channels, including tirne delays of the amplifier chain as well as mechanical offset of the recorder pens. For rough timing \iork to the nearest second, this is not necessary. But for accurate timing it is important to have a reliable measure of all factors affecting timing accuracy in order to take advantage of high timing resolution.

H. Calibration System

TI1e principles of a calibration system for magnet~c systems have been discussed in section 4. The internally generated test voltages are used with the fine gain control to provide the full scale deflections calculated from the transfer characteristics of the system. One of the t\170 o. 07-ohm resistors of the thermal compensator circuit is used for the injection of calibration signals in series with the circuit connected across the input terminais. This system is in use at the University of Texas for air cored coils. P.N.L. also use this system for their air-cored vertical 53

component coil as the sensitivity can be calculated from the kno\m area and turns. The P.N.L. metal cored coils are calibrated by means of a single turn of wire arourid the center of the core, the relation ship between the current in the \'lire and the effective field strength having been previously determined. A discussion of the results of calibration of the system may be found in a later section.

I. Bias Stepping Circuit

A bias stepping network designed by Varian Associates was described by Ward and Douglass (1962) .for a telluric recording system. 1'/ith the adjustments provided in the circuit,· it may be used to extend the range of recorders in other applications. The bias stepper effectively widens the chart paper when necessary, by adding or subtracting steps of voltage bias to keep the recording pen on the chart. \vhenever the pen rcaches either end of its travel, it closes a limit switch in the recorder, thus energizing a stepping relay which in turn moves a wiper across a voltage divider. The voltage divider consists of 35 resistors of

50 ohms each, in series with a 30 K potentiometer and a 1.34 volt mercury cell. The 30 K pot may be set so that any given voltage increment is set at a value such that, when the pen goes off scale in one direction, it will immediately return to 60% of full scale in the other direction. The response time of the stepping is governed 54

by the response time of the recorder. The basie stepping circuit referred to above operates aùequately undcr most conditions. However, if large changes occur* the stepping rclay may not have time to complete its action on the first off-scalc drive before the second change is required. Sin ce the limi t s\qi teh would only be closed once, only one bias step would result. TI1is situation is handled by an interrupter circuit which pulses the stepping circuit repeatedly until the pen moves away from the limit switch.

The circuit is wired such that the last step on each end of the range disconnects the signal input and returns the recorder pen to zero. This feature prevents damage to a high sensitivity recorder from micropulsation storm activity, but results in the loss of data until the recorder is reset. · Bias stepping is a standard feature on many total field instruments commercially available at the present, but is not often found on coil systems. MALLORY 30K RM-12

1 STEP~ALD IOK

{.tl 0 0- ~p son.each 1'1' BIAS STEPS ..... 0 . ·~.0------....l Hl

~. BL\JE su !A - - n-~~~~~~~------~------~B~l~U~E~ ~·SIGNAL INPUTS CHANNEL ouTPVTS 1meq --·-·_.:::;:_.Q---- 1 T~~~~-~117VAC

~ REl> 1'1' RED .tiQ CHANt-EL :;;;; su c.ti .t:'ll IOK El ..... ' p ~ r lA lA ~~ ,...... 11..::) e N ......

CHANNELS IDENTICAL EXCEPTFOR TlMER ON REDCHANNEL c.n Ci't 1

C')..!

tn: r

COILS

RELAY

IR-RAS-IZ

GUARDI

STEPPlNG

l-4-

DRlVE

ANNEC

BlUE

IN2482/f2.

SMKESTARZIAN

Q-l

BRATOR

----

2-2N24lA

---

MUL

---

lNTERRUPTE.R

4.7K

---

-15

T25

ANNEL

RED

---

+ -

~Il

470.!1

j_50J.tftl50,ufd

LTE.R

F2l?.

470Q

T2.5v

l55pfd

lt\120

1 1 ',

1 r

:_-

1 1

25v

C\J

-·IOO~fd:

-·

Ill

1 l

DPDT

CHANNEL

SELECT

CHANNEL

111

SUPP

BLUE

COHMON

TIMER

- +

t~PCHANNELt

STEP

------

•

MANUAL -

POWER.

"""':--6

LIMIT Ft

SWITCUES

f(f.COfU>E.I!..S

1171/J

l---

lU trt:

trt

ç;

01~

:::::~'

>"!

rt > Q

....

.::;-.>

:"") o.:.:

.... ::s l-I)

Cil

~ C.

Cil

0':1

"'::l

>-;:;:

0\0 ...... •

l.:j>"! Nt:

'-'

...... 57

6. DESIGN AND CONSTRUCTION OF A SYSTEM FOn THE DETECTION OF ELECTRIC FIELD VAlUATIONS

A. Recording Equipment A system for the detection of one component of the elcctric field intensity consists of a pair of electrodes, lead-in 1dre, input filtcr, amplifier, response filter for prewhitening output, recorder, timing system and calibration system. In most installations ti.YO horizontal components are recorded. The only • vertical electrode sprcad reportcd in the CGJ'.·NP survey by Smith

(1963) is part of the magnetotelluric recording system of Jersey

Production Rescarch Co., at Leonard, Oklahoma, /\part from the expcnse and difficulty of horehole rncasurements of earth currcnts, another rcason for the lack of intercst in the vertical componcnt of the elcctric field intensity is that magnctotclluric and telluric interpretations are hascd on horizontal componcnts only.

l3. Electrodes

Earth currents were first observed in the early

1840' s on the single \vire grounded telegraph systems (Burhank, 1905), and their connection \vith aurora! and geomagnetic activity 1>1as soon noted. An earth current system was installed at the Ebro Ohservatory,

Tortosa, Spain in 1910 and recording continued through 1938. Reports of other systems installed since 1910 provide over 50 years of experience in recording techniques for the designer of present day 58

+ I fi;;.

2.00 ro posrnve l=l..ow '2.000 PT OF c. Utl.. t.6tVT To N o~TH liNO ro &Il~ r (f~OM IUGG- ) fl.I;.SOi..Vï/OAI ler5'

,.....-.--1 + N S s fJMPL W + 1..,_ ___ .'2.00 T0-----tol- é. '2.ooo ~r

E.'vl Il fi PL

Schcmatic of Earth Currcnt Station Layout Showing Convention of · Polarities. 59 telluric installations.

The early literature shO\\'S a preoccupation with methods for lowering earth contact resistance, improving chemical stability and compensating for thermally generated voltages. One approach to these problems was the design of non-polarizable electrodes, such as copper in copper sulfate, zinc in zinc sulphate and other metal-metal salt pairs. One design improvement in these wet electrodes to retard fluid loss is the use of gelled metal salt solutions. Another im provement to permit the use of wet electrodes in subfreezing temperatures is the addition of antifreeze to the water of the metal salt solution.

A second approach to the problems of electrode resist ance and stability is the use of rather stable metals, such as lead or aluminum. Improved perfonnance is obtained by increasing the electrode dimensions and incorporating salt in the backfill. Fortunately, high input impedance amplifiers permit the use of extremely simple elect:z-odes. An electrode uscd \vi th success at Mt. St. Hilaire· in this telluric system consists of a foot or so of the lead-in wire stripped bare of insulation and buried a few inches helow the' surface of the soi!. Simul taneous recording with this electrode and non-polarizable electrodes con sisting of copper rods immersed in gellcd copper sulfate showcd no dctectable improvement through the use of the more elaborate electrodes. This conclusion is in agreement with the findings of

Vozoff (1963) of the lfuiversity of Alberta. 60

C. Lead-In Wire

The linos leacling from the electrodes to the

recorder carry only minute currents. Thus any type of insulated conductor having the required mechanical strength and insulation

resistance is satisfactory. High insulation resistance is required to prevent leakage currents from forming sorne complex and unknown electrode configuration. Shielded lead-in wires are not required . bccause static potentials leak off through the earth as they are

formed. Thcsc static potentials result in very minute currents which may be neglected at the signal levels of telluric recording. One of the !east expensive wires designed for direct burial in the earth, and honce suitahle for a telluric 1ead-in, is a single conductor, polyvinyl chloride-covered wire known as nvu. Standard or solid copper are standard conductors for nvu. If \... eight is an important factor in the wire choice, nvu is also available with aluminum conductors. The smallest available sizc, number 14 wire, weighs 28 lbs pcr 1000 feet and 10 lbs per 1000 fcet for copper and aluminum rcspectively and is availahle in lengths of 500 and 1000 feet. The regular nvu must be handlcd \"i th care in freezing temperatures. A type known as TWIJ minus 40F is available for use in temperatures clown to minus 40 degrees F. Either type is suitable for low temperature use if it is left undistuvbed. Si

D. Input Filter Sorne of the currents obscrved in the ground are not gcncratcd in the ionosphere. Sorne natural sources of these non tclluric currcnts are lightning discharges, atmospheric elcctrical gradients, temperature differences, chemical potentials, filtration potentials and snowfall potentia.ls. Man-made currcnt sources include clectrified trains and street cars, ground-return telegraph and telephone systems, power !ines, radio stations and arc weldingr operations. Lightning is an casily recognizable event on the records and can be.disregarded in picking data for data analysis. The lightning strokes appear as short spikes on one side or the other of a center zero scale recorder, depcnding on the location and polarity of the stroke. Othcr natural potentials are small and slowly varying or constant. These may be eliminated by a combination of high pass filtering and the insertion of an equal but opposite bias voltage. The circuit \'lhich produces the bias, or offset, or zero suppression as it is variously known, is usually part of the amplifier. Most of the man-made signais may be eliminated from a telluric system by low pass filtering. Low and high-pass filtering may be achieved hy adding capaci tors in parallel and series wi th an op erational amplifier respectively. Details of this procedure arc covered in the section dealing with the amplifier. 62

E. Amplifier

To avoid excessive signal loss in the electrode and input fil ters, the amplifier should opera tc wi th very small input currcnts, i.e., have a very high input impedance. The term

'input impedance' of an amplifier is simply the ratio of the voltage drop to the current through the input elements.

For very small input currents one can use electro- meter tubes, such as CK 5886's which operate with input grid -14 currents of the order of 10 amperes. TI1e next order of size of input currents, about 10-12 amperes, can be obtaincd with nuvistors such as 6CW4's conncctcd as cathode followers. A further increasc in the input current through the range of 10-ll ataperes up through 10-8 amperes is obtained for various solid state operational ~1plifiers connected as followers.

TI1e rcasonable leve! of input currents is governed by the impedance of the èlcctrocles and input filters. For a permanent installation, electrode resistances of a fc\-1 hundred ohms have heen achieved Nith wet electrodes. Most permanent installations reported have electrode resistances of less than 10,000 ohms. For portable work, the electrodes tend to be smaller and thus of higher impedance. It is also possible that a portable telluric system be requircd to operate on such extrcmes of conductivity as sand dunes in one case and a swamp in another. Other variables of electrode impedance involve local rainfall. snow cover and permafrost. 63

The level of input currents should not be very much smallcr than the level necessary to avoid loading the source, i.e., electrodes and filters, as the problems of noise and stability increase \Ü th decreasing current levels.

To permit the use of simple electrodes, an amplifier with an input impedance of 1 megolun \vas selected. For an input signal of·lO mv through the input resistor of 1 meg, the input current ~s. o f the oruer.1 o f 10 .s ampercs. Tclluric recordings are the measurement of changes of the vol tage differences c1 - e2 \'lhere c1 is the vol tage difference betwccn one electrode and sorne reference point, and e2 is the voltage difference hetwecn the second electrode and the same reference point.

11le reference point is usually the earth at the location of the amplifier, The magnitude of vol tage that is common to both e and e 1 2 is known as the common mode voltage. A differentiai amplifier with both inputs insulated from ground provides a high degree of common mode rejection. In the Philbrick P2 differentiai opcrational amplifier, hundreds of volts of common mode voltage are tolerable without causing damage, In contrast, most solid state operational amplifiers have a common mode tolerance of tens of volts. Sources of high common mode voltages are nearhy lightning strikes, and power line transients.

The use of an operational amplifier rather than a normal amplifier in the first stage permi ts the use of the input 64

and feedhack components for high-1)ass and low pass fil tering as requircd for telluric recording.

ovr IN PHIL8RlCJ( P2. + OPE.~IITIONAI.. RMPL/Pié~ +

For this circuit the transfer characteristic is

1 R2 -R- + 1 E zf c S c s 0 = 2 2 = 2 = z:- 1 R + 1 R +....L- 2 1 c s c:2s 1 R + 1 1 c1s

R2 c s 2 R C:.,S + 1 R., 2 .. .. c s n2r:2s + 1 = 2 = R1c:1s + 1 I

R C S = 2 1 2 R C R C S + R C S + R C S + 1 1 1 2 2 1 1 2 2

n ...'") T = 1 R2C2 1~ c s + 1 + + 1 ..'") 2 RlCl a{1s

= G T TS+l+ 2 + 1 2

;~he re T = R C 1 1 1

R C T2 = 2 2

~~2 G = iÇ 66

In the rcsponse curves suggested as standards by

Smith (1963)

= 1 = 1 = 1 = 16 sec. 2lf (.01) .063

T = 1 = 1 = 0.8 sec. and 2 2'!1" (0.2)

T = 1 = 1 = .16 sec. 3 w 211'(1.0) 3

iVith R 1.21 meg, to avoicl loading the electrodes 1 =

RlCl = 16 or = 13 ufd,

For R..,.. = 2.37 mcg, to avoid magnifying input instability,

R{2 = 0.8 = 0.34 ttfd. ror R3 = 1.21 rncg, to pen1it a high gain in the scconJ stage,

R3C3 = 0.16 or c3 = .13 ufd.

R is variable bct\veen lK and llO K to permit gain control for the systen, 5 TI1esc components lvcrc combincd in the circuit shmvn next. 67

J. '2.1 f'tli6r

- E ovr

1 0.01 C.f$

lŒSliLTS

1\. ~.. lagnctic System

TI1c rcsults of primary importance are the absolute and relative output responscs to ~he magnctic field fluctuations. One important relative output response is the standard proposed for the CGM~·lP by !3ostick and Smith (1963). This standardized response makes possible the direct comparison of records \vi thout additional data processing. T\vo other relative responses are 68

desirable. One is a response lvith no appreciable relative attenu

ation in the output voltage of the coil. Tiüs permits the

recording of the derivative, or time rate of change, of the changes

in flux lin king the coil. The uni ts of the output are gamma/soc.

Tilc second rosponse is one in Nhich the output vol tage of the coil

is intcgrated, ie attenuated proportional to frequency, to mcasure

the changes in magne tic flux linking the co il • TI1e uni ts of the output of this response are gammas. Other responses \vl th emphaSis

in certain portions of the spcctrum are generâ.lly obtained by band pass filtcring one of the more usual responscs.

TI1e relative respOJ!Se of the system is the super position of the responses of the coil, input filter, anplificr, responsc-shaping amplifier, hand pass fil ter and recorder. The response-shaping nnpli fier and band pass fil ter are only inscrtcd

in the chain for certain responses.

TI1e relative rcsponses of the P~L coil-input

fil ter combinat ion, and the ~1cGill coil-input fil ter combination

are shown in: graph 1. TI1e PNL comhination has a derivative rcsponse

from bclm·; 0.001 eps up to n 'break', or 3 db. attenuation, at 1 eps

to a broad maximum at 2.5 eps and a low pass roll off a.hove 2.5 eps.

TI1e McGill comhination has a derivative response \vith a break at

4 eps to a maximum at G eps and a 10\v pass roll off above 6 eps.

The position of the maximum for a coil-input fil ter combina tian is Jetermined by the LC time constant. TI1e sharpness of the 69

maximun is ùctcrmincd hy the Q of the induetor. The lower n.c. resistan'ec of the HeGill coil is evitlent in the sharpcr maximum of the responsc eurvc.

The relative response of the fivo huilt-in roll off rcsponsc filtcrs of the Guildlinc amplifier are shm·m in graph 2. For filter 1, the break is at 1 eps; for filtcr 2 the l1reak is at 0,6 eps; for fi1ter 3 at 0.3 eps; fi1ter 4 at 0.2 eps and filtcr 5 at 0.03 eps. Bccause of the chopper spced of 5.6 'eps, in the amplifier normally supplied, there is no useful response ahove 2 eps. As pointcd out in the discussion of this amplifier, the hir,h frcquency rcsponse cou1d be extcndcd by increasing the chopper spced up to a maximum of 100 eps, 11/Ï th an increasc in the noise. 1bc superposition of the relative rcsponscs of some typical rccordcrs on the responses of the Guihllinc anplifier arc shown in graph 3. For c1arity in the graph, only the filtcr rcsponscs 1 and 5 are shmvn. Filters 2, 3 and 4 \vould gencratc intcmcdiate response curvcs. A responsc-sharing rost ampl:lfier could be useù to compcnsatc for the roll off of the responsc of a recorJer. llowcver, the system operation is simplcr and more relia ble \vÏth the use of a recorder tvhich has a flat response to a frequcncy slit!htly ahove the highest dcsircd frequency. An examplc of such a recorder is the Estcrline Angus S601S Scrvo Recorder. This recorder ô

.c ·=" :S.. E ~ >< (j)_2!-"'.., (l)

"'a. " >- ~ v :z uJ u ::> 0' LIJ

1 9 --!--:...----'

x Ol.!:- "' . ~ CX)<.> 1!1": -~ E .<: ., ~ '""""ë., "'

0 3

' 1 ! t -f--l ;0 2

0 () \ ~ N S.L701\ ..si 1 1 1 ..()

.t::..., .5., =.s ;; >(~ 3 m- "'z.. ~ .~0 q)U'!; 2 Cl"""''0 ·ê t ~ :;; ..0 -! ·o 1 Ë~.. 9 "' 8 7 6

...."'v 4 >- u 3 ::,. 0 \Il ::> <::r 2 I,,J ~ 1.1.

1 . - 9 ô 8 ·.7 6 5 4

2 i.IC: u~-~~ \)a: ~ :::0: 1 9 8 7 6 5

3 !" .....

0 2

() () ..... 'IP - S.L"'70A a ..Q 1 1 ' 1 9 8-- 1 .ti. 6 "' .:... 5 =e 4 s >! 2 ~!~"""'·ê;• Q ·;:=., 0.. -1 ë 1 .. 9 "' 8 7 G ... '-\1 4 >- 3 0 "'~ Id ' '::> <> 2 lU c;{ 1&.

1 9 8 7 6 5

l ,~ 0 ~ 9 8 7 6 5

0 2 1---.~~~~~,_.,,-~~rr_,-..,-,~~~-rrT,-rT,-OT~r 9--~~~+-~+-~+-~-r-~-r~~~~~~~+-~ 8--~~~+-r++-r++-r+-rr+-r~~~-r~-r+-rT- 7--~~~+-~+-r++- 6---r~-r~~r++-~ 5--~~~+-~+-~;-r+~~~

4---4~+-~~+-~~+-~-++-~

l---+--~+-~-r~-r+4~+4-r~~+-~+-~~~~+4~·+4-r~~~~ 0 9---+~~~~~+~-r+4~~~~L++-~ 8---+~r+~~~~-r~-r~~~~~+-~ 7--~~~-r+4-r+.~~~ 6---++-~+-~~~

5---+,·~··r++-~~+-

1---+~-r~-rr+-r~lh-r+,_-++-r++-r+~~~--+>-rr+-rr+-r-+,_-+~r++-r+~~~~~~ 9--~~~-r+-~~~-~~~~~-r,_~~~-++-~--~-++-~~~-++-~~~r+~~ 8---+4-r+~-+~+4-r~-r+4~+-~+-r++-~~+4~+4~+4~+-~+-~+-~~~~+ 7---++--++-~+-~-r~~-r~-r+--++--++--++-+4~~-r~~+--++--+~-+~~~ 6--~~+-~~~+44+-~~~+4~~~~+;~~~~~~~~~~~~~~

5---+~-++-~~r+-H~~~~~r++--++-r++-~~~-r+4~~~+-~+-~+-r+~~~

4---++--++--+~+4-H·~-r+4~~-++--++--+~-+~+4~+4~~~+--++--++--+~+4-r+4~+

~==t==H4=I+~;ê~~=rt-;==~jjlt+ttt~~±±==rttc~Jt±tt 8--~~~~~-++--+~~~-++--+~-+~-r+4~~ 1--~~~~~~-~~~~~~~~~~~~~~ 6---+~-+~-+-+-+-r+>-r~~r--++--+~-+-r~-r~~~~ S---++--+~-+-++>-r+>-T-

4---4~~~~--~-++-~-+- 0

....() $..! "70"' :.fli.L f/73 ~ ~ B. 1 1 ' 76

has a~ljust~tblc damping for a choicc of response tir.1cs of 1/ s sec to 1 sec. TI1csc responsc tiMes provide breaks at 4 eps and 0.2 eps

respcctivoly. This latter response corresponds to the rcsponsc of the Estcrline Angus A601C: recorder. Internec.liate rcsponscs hetlvccn thesc .times are ohtainable With co:amon scrvo recorders such as the Varian Gll.

The superposition of the rcsponsc of the r.tcGill

coil-input fil ter combinat ion wi th various comhinations of arap.lifier roll off filtcrs and recordcrs are shown in graph 4. The dcrivat:ive

rcsponsc is ohtained from the comhination of roll off filtcr 1 and

the S601S recorder. TI1c CG~f'IP rcsponse is ohtained wi th the corn- bination of roll off filtcr 5 nnd the S601S recorder. Tite integrated

responsc may hè ohrained from the cornhination of roll off filter 5,

the S601S recorder and a response-shaping amplifier vith a response characteristic sho11n in the sketch below.

1•l ! 77

From the relation clerivecl in the section on rcsponsc-shaping o.mplifiers wc have

1 T = = = 1 = 100 sec. 1 2 ( .0016) 0.01

= 4 sec. T = = 1 = 1 2 2 (. 04) 0.252

1 T = 1 3 \\1 = = = 0.04 sec. 3 2 ( 4 ) 25.2

Typica1 values to achieve this responsc are

6 R = 10 ohms 10 ufcl 1 \.1 =

6 = 10 X 10 ohms 0.104 ufù '~ 2 c2

6 R = 0.4 x 10 ohms 3

This 'provicles a responsc essontially flat from

0.0016 to 1 eps, but 25 db belO\~ the flat portion of the r.t.~1'1P 78

response, and 50 dl1 hclm~ the derivative response at 1 eps. The re lative attentuation of the higher frequc-ncics with this integratcd rcsponse indicates the desirability of the derivative response for the stuùy of \veak high-frcquency signals.

Ni th the system dcscrihed the change from the de rivative response to the CQNP. response r.w.y he made \vi th the action of one huil t-in slvitch on the C.uildline amplifier, lvhile the in tegrated response or any ether response requires the introduction of an amplifier with a suitahle transfer characteristic.

The ahsolutc responsc of the system is also important.

The relative rcsponsc of the PNL system Nith an Estcrlinc Angus A601C recorder is closely approximatcd by the relative response of the 1'1cC:ill system wit!'l roll off filter 5 and a sinilar A601C: recorder. llowever the relative response of the P~H, system at maximum gain is at an absolute rcsponsc levcl of 30 dh l1clow the responsc of the ~lcGill system at maximum gain. The lcvels of the output voltages are the samc. The difference in the levcls of ahsolutc rcsponsc is a rosult of the 30 db lo1•cr noise lcvel of the r!cGill system. It should be s't:ressed at this point that improvcments in ahsolutc rcsponsc levcl arc only obtainable hy lmvcring the lcvel of the minimum dctectablc input. 111e addition of a post amplifier to the output amplifies both the signal and the no'ise wi th no improvement in the rilinimum input signal.

il. Electric System

'I11c princip les of ahsolute and rclati ve res pons es tliscusscd in the rcsults of the mar,netic systern also apply tc the elcctric system. The physical rcalization of the response objectives 79

is much simpler for the electric system for tt-.•o reasons. rirst~ the output from the electrodes is proportional to the changes of the clcctric field with a flat frequcncy response from n.c. to frcqucncies much higher than those of interest for this work,

;.rhile the coil has an output proportional to the derivative of the changes of the magnetic field. with no response at D.C:., i.e. zero frequcncy, and a res panse incrcasing 1-:ith frequcncy to the resonant frequcncy of the coil-input filter combination. The second reason is that for this system, the telluric signal leve! is al)out a factor of 3 10 grcatcr than the signal from the coil.

As ùcscribed in the section on al7lplifier design, the RC input and feeùback components may be sclcctcd for a ùesircd shape of rcsponsc. Tiw derivativ!j:~ CG'~

S601S recorder. The CGvP·1P response for the electric fielù is shifted to a rclatively lo,.,rcr frequency than the respcnsc for the ma~nctic field, Tids permi ts the A601C recorder to be used for this rcsponse for the telluric system.

TI1ere is no telluric equipment in the PNL installation at St. Hilaire. For this rcas.on no direct comparisons of absolutc response coulù be made. The critcrion useù in this design was useù to proville relative gain and noise levels for the telluric system \'lhich provide recorder signals of about the same strength

\dth analogous gain settings on the magnetic systet:l, 80

CO~CL\JSIO~S

As stated in the introduction, a major abject of this thesis is the development of magnetotellurics into a reliable field gcophysical tool. This developr~ent is a very broad subj ect.

1i1e division of the problem into two parts has provided a convenient limit to the scope of this thesis. The first part is the collection of magnetotelluric data, while the second part is the interpretation . of the data. It is true that this thesis has shmm a preoccupation hrith the engineering details of the design and construction of a magnetotclluric system. llmv-ever, i t must be emphasized that a grasp of the requirements of interpretation was a prerequisite to the solution of the problems of design.

The interpretations of magnetotelluric data reported up to the present time have indicated that there:arc difficultics related to the theoretical models and data analysis. It is the opinion of the author that many of the difficulties arc the result of faulty data caused by the successive applications of seeminMy harmless assumptions of the quality and characteristics of the detecting and recording equipment. 1ilis belief prompted the design and construction of a system in \vhich the author has complete con- fidence in the quality and complete familiarity 'dth the limitations.

1i1e education in the fundamentals of magnetotellurics thus attained should facilitate the presentation of a Ph.n. thesis on magnetotelluric interpretation. 81.

13 I B L I 0 G R A P H Y

i300TIIE, R.R., FANN'IN, BJI. and ilOSTICK, F.X.; "A Geomagnetic ~licropulsation Hcasuring System lltilizing Air-Core coils as Detcctors", lleport No. 115, E1ectrica1 Engineering Rescarch Laboratory, TI1e University of Texas, August 1960.

BOSTICK, F.X., and Jl,\'J, S~HTII; "An Ana1ysis of the Magncto- telluric ~lcthod for Determining Suhsurface Rcsistivities", Report No, 120, E1ectrical Engineering Rcsearch tahoratory, The University of Texas, February, 1961.

"Investigation of Large Scale Inhomogencities in the Earth by Magnetotelluric Methocl.", Report No. 127, Electrical Engineering Research Lahoratory, TI1e llni versi ty of Texas, June, 1962.

"Factors Involved in the Choicc of the Geomagnetic Hicropulsation 1·feasurement System Used at the University of Texas", Henorandum No. 17, Electrica1 Ent;ineering Hesearch Lahoratory, The University of Texas, Auuust, 1963.

BURBANK, J.E.; Earth Currents; and a Proposed ~1ethod for their Investigation, Terr. Mag., 10, 23-43, 1905.

CAGNIARD, L.; "Basic TI1eory of the Hagnetotelluric Hethod of Geophysical Prospccting", Geophysics, 18, 605-635, 1953.

CAMPBELL, \'J.H.; "Natural Electromagnetic Field Fluctua ti ons in the 3,0 to 0.002 eps Range',', Proc. IEEE, 51, 1337-1342, Oct., 1963,

C.i\"lER, B. • and Nl!ITIIN-f, K.: "A Geomagnetic Observation of a lligh Altitude Nuclear Detonation", Can. J. Phys. 40, 1846-1851, 1962,

CA"lTIVf:LL, T., and MADOEN, T.R.; "Preliminary Report on Crustal ~fagnetotclluric Measurements",. J.G. Res., 65, 4202-4205, nec. 1960. 82

GROVER, F.lv,; Inductance Calculations, 0, Van Nostrand Co, Inc., 1947.

POPE, J.ll.; "An Explanation for the Apparent Polarization of Sorne Geomagnetic ~licropulsations (Pearls) .. , J.G. Res., 69, 399-405, 1964.

PRICE, A.T.; "The Theory of Magnetotelluric Methods l'ihen the Source Field is Considered", J.G. Res., 67, 1907-1918, 1962.

SMITil, II.W.; "Report of Cooperative Geomagnetic Measurement Program of The Pacifie Naval Lahoratory, The University of British Columbia, TI1e University of Alberta, The University, of Texas", Report No. 128, Electrical Engineering Lahoratory, The University of Texas, ~fay, 1962,

"A Survey of r.eomagnetic Micropulsation Research Conducted in C:onnection l-

Micropulsation ~~1easurement Program" 1 Report No, 130, Electrical Engineering Research Lahoratory, The University of Texas, Hay, 1963.

Stv!I111, ii.I'l,, PHOVAZEK, L.D. and BOSTICK, F.X.; "Directional Properties and Phase Relations of the Hagnetotelluric Fields of Austin, Texas", .J.G. Res., 66, 879-888, 1961.

TEPLEY, L. R. and WENTivORTII, R.C., "llydromagnetic Emissions 1 X-Ray Bursts and Electron Bunches: 1. Experimental Results, 2. Theoretical Interpretation'', J.G. Res., 67, 3317-3343, 1962.

TIKIIONOV 1 A.N. and SIIAKI!SllVAROV 1 D.N.; "On the Possibili ty of Using the Impedance of the Natural Electromagnetic Helù of the Earth in Exploration of" the Upper Layers", Izv. Akad. Nauk. SSSR Ser. Geofiz. 4, 410-418, 1956. AGU Trans la ti on.

VOZOFF, K, liASEGA\vA, Il. and ELLIS, R.H.; "Results anù Limitations of Hagnetotelluric Surveys in Simple r.eologic Situations", Geophysics, 28, 778-792, 1963. · 83

WAIT, ,J ,lt.; "On the Relation Bctwcen Tell urie Currents and the Earth's Magnetic Field", Geophysics, 19, 281-289, 1!:>54. l'lARD, S.ll. and DOlJ(';LASS, J.L.; "11te Recording of Earth Currents" Series 3, Issue 28, Space Sciences Lahoratory, University of California, Berkeley, Octoher 1962. APPENDI X 84

lt may be shown that the balance conditions for this bridged T filter are not functions of input or load impedances. Consider the more general circùit be1ow

The circuit equations are

n = Il(Z7 + zs) + 12 C-zs) + 13(0) + 14(0)

0 = r1c-zs) + IzCZs + z1 + z3) + I 3( -Z3) + (14(-Z1)

p = 11 (0) + ~.IzC-Z1) + 13(-Zz) + 14(Zl+Z4+Zz)

0 = 1 l (0) + ~rz( -z3) + 13(Z3+Zz+Z6) + 14(-Zz)

Â = (Z7 +, Zs) c-zs) 0 0

C-zs) (ZS+Zl+Z3) ( -Z3) ( ~Z1)

0 t-Zl) C-Zz) (Z +Z +Z ) 1 4 2 0 ( -Z3) (Z3+Zz+Z6) (~Z2)

13 = (Z7 + zs) c-zs) E 0 C-z s) (Zs+Zl+Z3) 0 ( -Zl) 0 ( -Zl) 0 (Zl+Z4+Zz)

0 0 C ( -Z3) -z 2 J .0 85

For r 0, numerator is zero 3 =

Expand about E

E ( .z ) + + Z3) C-z ) 5 czs zl 1 0 ( -Zl) (Zl + z4 + Z2) = 0

0 ( -Z3) ( -Z2)

Expand about ( -z5) -EZ ( -Zl) 0 5 zl + z4 + z2 = ( -Z3) -z2

= 0

This result is the equation 4 of the simpler case. and will again lead to the relation

= 1

This may be re\~ritten as

1 = z3

1 1 As a parallel combina ti on y3 :: + -r jWl:"'

with r = 1 and wL = 1 w2Rc2 2wC as derived before. 86

For the series combinution Y r - XL ::: 3 = (Z) 2 this case has

r - j\vL = r L r"'f""+ w2l.2 ~

separating real and imaginary terms

r = wl. = 2wC

r = l. :::

No\v consider the equation in J! and L

::: 0

2 2 l. ::: 1 :[1 .. 16w c i 4\i2C

squaring both si des

2 2 2 + 2 2 2 l 1.2 = 1 + 1 - l6w c r 2Jl 16\v c r 2 16H4 C

But =

1 2 2 16w r.r ) = 0 87

= 0

2 2 2 .. r 16w C r

R) 2 R2 (r = ( 1 - l6142c2r 2) 8 ;z r2 - rR + R2 = R2 1 w2c2r 2R2 4 64 64 4

2 r ( 1 - 1 w2C2R2 ) - R r = 0 4 4

R r = o or r= 4 2 2 2 1 + lw c R 4

So as a design approximation lie have the series resistance

Now put r = R into equation for .L

2 2 L = 1 ~ J 1 - 16w2c r , 41v2c 88

l-16tlc2R2 + 1 - T6 2 (l+lw c2R2) 2 L = 4w2c

1 2C2R2 + 2 2 2 1 + 1\1 - 1 ; 1w C R = 4 4 4w2c (1 + ~ w2c2R2) 4

TI1e two cases are ]._ w2C2H2 2 • l = 2 and L = 2 1 2 2 2 2 1 2 2 2 4w C( 1 +- \\1 C R ) 4~.,. C(l~-l\1 C R ) 4 4

1 2 = = CI~ 2w 2C( 1+~.,. 2 c 2 R 2 ) 8(1 + i'"2C2R2) 4 ,., 2 CR .. 2 = 'le = 4 + w2C2R2 4 + ,.,.2c2R2

2 -2- \\1 c = 2. Test the root of L = ') 2 2 ... · 2 . 4 + w... C R 'wC D 4 4 2 L2 \\1 c TI1en = and r = H 2 n IT

2 2 2 L = 2Cr + 2'" Cl 89

2 4 2 \v C 2 ~ ,,,4c;2 = 2CR + 2wC nz oz n2

2 2 2 2 2 --- (4 +wC R) 2CR + 8 = 2 w2c \\' c

2 8 8 + = 2CR + An iùentity 2 2 w c w c

2 2 2 4 2 2 Test the same root into r = w C R + ,.,. C 1. R

4 2 2 R2 4 2 4 2 Rn = w c R + w C R w c 2 ? 7 n· n~

2 2 2 2 2 3 H( 4 + ,.,. C R ) = w C R + 4R

2 'l 3 4R + w C R = + 4R also an iùentity.

Now test the other root of l =

Th en 2.. 2 2 L- = r = R and r = R o n2 90

2 2 2 L = 2Cr + 2w CL:

? CR"" D 2 2 = + 2w C 2 D

2 3 4 = w C R 2

2 2 2 2 2 ,ic:3R 4 ~ (4+w CR) = 2CR + 2

2 2 3 4 2 3 4 2CR + \ic R = 2CR + "-' C R an identity 2 2

Test this othcr root into

4 2 2 r = + wC L R

4 2 2 4 + w C R C R = -4-

2 2 2 2 2 3 4 4 5 R(4+w c R ) = \<1 C R + w C R 4

w4C4RS R = 16

4 4 R ( w c é = 16 ) 91

,.,.2C2R2 )2 w2C2R2 R = R ( True only for = 1 4 4 wCR or -2- = 1

:-.!ote that 2 = If wCR ,le -2- = 1

Sin ce 2 2 = w c 4

So as a design approximation

2 2 1 w c becomes L ~ L = 2 2w c

2 wCR = . CR or for -2- 1 L = -B-

To summarize the balance conditions wc have

R . R r = ·~"'71 = -- 4 + ~2c2R2 4

2 w2c 1 L = ~ 2 4 = w4c2R2 2w c