Proc. Indian Acad. Sci. ( Planet. Sci.), Vol. 99, No. 4, December 1990, pp. 441-471. Printed in .

Magnetotellurics: Principles and practice

K VOZOFF Centre for Geophysical Exploration Research, Macquarie University, Sydney, N.S.W. 2109, Australia Abstract. This paper reviews the magnetotelluric (MT) method with emphasis on recent improvements and the emerging applications. Recent improvements are in recognition of statics effects and their treatment, and in analysis of impedance tensors in 3D structural conditions. In spite of substantial progress in the analysis of the tensor, there are still unresolved questions regarding its .information content, in terms of degrees of freedom. There has also been slow but steady progress in inversion, with the development of methods of downward continuation in 1D, 2D and 3D, in time, depth and frequency domains. An improved understanding of the limitations of MT is leading to more joint use with other methods. At shallow depths MT has become an accepted weapon in the arsenal used to explore for petroleum, geothermal resources and epithermal gold and deep base metals. Improved understanding of the relations between conductivity and rock composition and fabric will make MT more useful for engineering purposes in future. Progress in understanding the cause of conduction in the deep crust and has been less rapid, and the many anomalies remain enigmatic. Whereas MT is now a useful technique with some unique applications, there are obviously important and difficult problems remaining to be solved. Keywords. Magnetotellurics; electromagnetic; exploration; electrical conduction in rocks; fields in model earth; anisotropic media; inhomogenoas media; statics effects; source effects; controlled source audio magnetotellurics; resistive layer problem.

1. Introduction

The magnetotelluric method was proposed by Tikhonov (1950), by Kato and Kikuchi (1950), by Rikitake (1950) and by Cagniard (1953), although the principle was recognized much earlier in both Japan and France. Only Cagniard's paper has been easily available in English. With the assistance of Akad. Tikhonov, an English translation of his paper has recently appeared (Vozoff 1986). In its various forms (MT, AMT and CSAMT) the method is now used sparingly in a broad variety of applications. These range from the very deep and large scale studies of the crust and upper mantle, through a wide range of exploration applications for kimberlites, petroleum and geothermal systems, to the shallow problems of epithermal gold, 'deep' base metals and even ground water. In many of these applications MT provides a kind of information which can be obtained in no other way. For exmple, it seems ideally suited to describing the complex, diffuse geothermal systems which are of interest for their association with geothermal power and young porphyry copper and gold deposits. In petroleum exploration it is used in areas where it has been found to be economically and/or technically impracticable to use reflection , but where productive wildcat wells have been drilled, such as in Papua New Guinea and parts of the Andes Mountains of South America. It is unlikely that

441 442 K Vozoff

MT would have been used if these regions had not already been shown to be productive, because it does not provide very high resolution as compared with good seismic data. The successful use of MT in these conditions is possible because of developments in the technology over the past ten years. The aim of this paper is to set out what the metht)d does, and to summarize the more important recent developments. These have been in data processing and interpretation, and in faster turnaround and improved presentation of results through enhanced field computing capabilities. This paper begins with a review of electrical conduction in earth materials, which explains why electromagnetic measurements are carried out. It then goes on to an overview of MT followed by more detailed sections on data processing and analysis, tensor manipulation for complex sites, inversion and interpretation, statics problems, source effects in AMT and CSAMT, and resolving the resistivity in resistive regions.

2. Electrical conduction in rocks

The first object of geophysical electromagnetic (EM) measurements is to determine the distribution of electrical conductivity in the subsurface. In some applications we are concerned only with real conduction currents, that is conduction such that currents and voltages are in-phase. In other applications, out-of-phase conduction due to the induced polarization effect and/or dielectrics is also of interest. For most purposes the conductivity itself is only a means to an end, that is, to a knowledge (sometimes quantitative) of some aspect of geological composition and conditions. Hence the full use of MT and other EM methods demands two distinct transformations, one from the measurements to the distribution of conductivity in the subsurface (the conductivity structure), and the other from conductivity structure to a quantitative petrographic description of the earth materials being probed. These transformations must be carried out for two different regimes, i.e. for the part of the earth which is accessible to drilling and logging, and for the remainder of the crust, upper mantle and beyond where direct measurement and observation are not yet possible. Petrographic transformation can be done with far greater confidence in the first region, because of the availability of direct evidence. Olhoeft (1983) describes some of the complex reactions which accompany low frequency conduction at surface temperatures and pressures. Interpretation of subsurface EM measurements, i.e., electrical well logs of various kinds, is a technology which has been highly refined for petroleum exploration and engineering purposes. It provides very practical ways of relating the complex electrical conductivity of the (small) region around the borehole to petrographic parameters (Schlumberger 1987). The vast bulk of that work to date has dealt with sedimentary rocks, but the principal parameters are independent of rock type, so the rules apply equally well to most rock types. There is reason to believe that the rules change at some depth beyond that to which drilling has thus far penetrated, and that will also be discussed below. Table 1 lists the electrical resistivities of some common minerals and table 2 lists observed resistivities of common rock types, all at surface temperatures and pressures. The figures are taken Keller (1988), Telford et ai (1976), Van Blaricom (1980) and the Handbook of Chemistry and Physics (1985). Many other common minerals, quartz Magnetotellurics: Principles and practice 443

Table 1. Mineralresistivities (ohm-m).

_ Minimum Maximum Mineral resistivity resistivity

Native copper 3 x 10 -~ 1"2 Graphite 4 x 10 -s 10 -2 Chalcopyrite 150 x 10- 6 10- 3 Pyrite 1.2 x 10-3 0"6 Rock salt (natural) 30 5 x 1013 Quartz 4 x 10 l~ 2 x 1414 Hornblende 2 x 10z 106 Calcite 2 x 1012avg

Table 2. Rock resistivities (ohm-m).

Minimum Maximum Rock resistivity resistivity

Granite 3 x 102 106 Gabbro 103 106 Limestone 50 l0 T Sandstone 1 6.4 x 10s Shales 0"3 2 x 10J Marls 3 70

for example, are considered dielectrics. It is quite striking that, except for a few very conductive minerals such as the metallic sulphides and graphite, the two sets of values show little overlap. The very conductive minerals occur in such small proportions in most circumstances that they cannot explain the discrepancy: another explanation has to be found. It has long been recognized that the difference is due to a common mineral which is not included in table 1, i.e. water. Conduction in accessible rocks (excluding those containing significant graphite or metallic minerals) is due almost entirely to ions dissolved in the water which fills the pores of the rock. The relationship between rock conductivity a, water conductivity aw and fractional porosity q~ is a = aw x ~bm, where m ~ 2. Known as Archie's law, this relationship is thus far purely empirical, and has no firm theoretical basis. Figure 1 shows curves of conductivity versus porosity based on many thousands of sample measurements. As given above, Archie's law assumes that the rock pores are water-saturated; otherwise the fractional saturation appears as another coefficient on the rhs. Thus the main determinants of rock conductivity near the earth's surface are the porosity and the conductivity of the water. The latter depends on salinity and temperature, both of which have regional and depth variations. The relationships between conductivity, salinity and temperature are illustrated in figure 2. It has always seemed curious to me that permeability does not appear in Archie's law and, indeed, that it seems to be uncorrelated to conductivity, although many studies have been carried out on laboratory data to try to establish some relationship. The problem appears to arise because permeability depends on grain size distribution 444 K Vozoff

FORMATION FACTOR VERSUS POROSITY

O. I >.,

o 0 O- O- I

r o O D..

Formation factor - F Figure 1. Formation factor versus percent porosity fo r a wide range of sediments. Formation factor is the ratio of rock resistivity to pore fluid resistivity. (after Schlumbcrger 1978).

I0 r u i

q

,01 %

1Oq

0 0!10~ f I 104 105 ~06 NoCI Concenrrofion p.p.m. Figure 2. Dependence on temperature and NaCl concentration of brine resistivity. Magnetotellurics: Principles and practice 445 as well as on porosity, as recognized in the Kozeny-Carman formula (Bear 1972) whereas conductivity does not directly depend on grain sizes, assuming the grains are much smaller than the rock sample. There is currently a great deal of research under way into the problems of modelling the physical properties of rocks, including velocities, permeability and conductivity, for given configurations of pores, cracks and solid. Yale (1985) reviews this work, which has been reasonably successful in predicting, for example, porosity and conductivity from SEM scans. A recent paper by Katz and Thompson (1987) relates permeability and conductivity in porous rocks, using only measured quantities and without resorting to empirical constants, while shedding new light on Archie's law. (Archie's law figures strongly in most books on well log analysis, and is reviewed in a recent article in the Schlumberger journal 'The Technical Review', July 1988.) As depth increases, porosity and permeability decrease due to increasing pressure. At the same time, some of the water is driven into hydration in the rock-forming minerals, and the remaining free water enters the vapour phase because of temperature and pressure. For these reasons it has been generally assumed that water is no longer the major medium of conduction in the deep crust and upper mantle, and that another mechanism has to be found. In seeking other conduction mechanisms, it is known that most of the minerals expected at depth are semiconductors, whose conductivity increases exponentially with increasing temperature. This increase is of the form

,r = ao exp [- (E,, + PA V)/kT], where a is the conductivity, a o is a constant, Eo is the activation energy, P the pressure, A V the activation volume, k the Boltzmann's constant and T the absolute temperature (e.g., Tozer 1959). Thus conductivity increases exponentially with temperature and decreases with pressure. The parameters ao, AV and E a are different for different minerals, so the conductivity of a semiconducting mineral depends on composition and temperature. Minor impurities can also have very large effects on mineral conductivity. The conductivity of an assemblage of different semiconducting minerals depends on the geometric distribution of the most conductive components: a small amount of a highly conductive mineral can have a dominant effect if it is continuous over large distances (Madden 1976). Pressure also seems to play a part, since it appears that phase changes which change conductivity, or the rate of change of conductivity with temperature, may occur with increasing pressure (Tyburczy and Waft 1983). For these reasons one would anticipate that, at sufficient depths, conductivity will increase to large values even though water no longer plays an important part. In fact it is generally found in deep MT results that, from the generally high values near surface, conductivity decreases to very low values over some depth range, and then it seems to increase abruptly. The depth at which it increases depends on location, but is typically between 100 and 300 km. It is also found that, in many places, an intermediate conductive zone exists within the deep crust (e.g. Shankland and Ander 1983). The reasons for these variations are not u.nderstood in detail. The depth at which water is no longer important is still not known, but in any case it might be expected to depend on the geological environment and tectonic history. The role of semi- conduction is probably somewhat better understood, since both temperature and 446 K Vozoff composition are reasonably well constrained by other geological and geophysical data, but the actual contribution of impurities is unknown. There is evidence that certain basic rocks become conductive under conditions expected in the lower crust due to the effect of hydrous minerals, and that water can retain a very important role if, for tectonic reasons, it is under near-lithostatic pressures (Lee et al 1983). Thus, in summary, although we understand some of the mechanisms involved, we do not yet understand adequately the conditions responsible for most observed-conductivity behaviour beyond the depth of drilling. Despite this, it appears that the joint interpretation of EM and other data will help explain particular situations in the near future. For example, Liischen et ai (1987) combine MT results with near-vertical and wide-angle seismic data in an effort to explain conditions beneath the Black Forest. This work is coupled with plans to drill a hole to a depth of 15 km, so as to directly observe mineralogy, temperature, fluid content and pressure. From such intensive programmes of , and geochemistry combined with drilling we will obtain a better understanding of conditions at these depths, enabling us to interpret deeper geophysical results.

3. Overview of the method

Although the MT method is simple in principle, its successful application requires the use of an increasingly sophisticated set of procedures which have been evolving for the past 30 years, and which continue to develop. It is assumed that the reader is familiar with conventional single-site procedures, as summarized in Vozoff (1972). Volume 5 in the SEG Reprint Series (Vozoff 1986) contains a broad collection of papers up to 1986, and the new SEG EM volume 2 (Nabighian 1991) includes newer reviews of MT and CSAMT. I will start from the front end, i.e., with the signals, anti follow them through the acquisition and processing stages to the interpretation of the results. In the course of this I will touch on equipment and field procedures, as well as on modelling and inversion. Examples are referenced to serve as guides by which results can be judged. After an overview we will return to the more technical details. The signals used for MT are the natural electric and magnetic fields in the frequency range 10-4Hz to 10§ although in general only a part of this broad range is used in any particular application. In addition, artificial fields are sometimes applied at frequencies above 10-100Hz, where the natural fields are so weak. The latter method is called controlled source audio magnetotellurics (CSAMT). The natural signals have two major sources. At frequencies above a few hertz, most of the signal energy is from electrical storms, mainly in tropical regions of the earth (Volland 1982). The spectrum of this radiation peaks around 10kHz. Signals at frequencies below 1 Hz arize mainly from currents flowing in the lower part of the ionosphere (Rostoker 1979; Orr 1984). These currents flow in large systems extending over major portions of the earth. They are excited indirectly by the flux of energy from the sun, acting on the (Shawan 1979). Figure 3 shows a segment of low frequency signal, and figure 4 is a higher frequency transient from a discharge. This difference in character arises from the differing nature of the sources. Figure 5 is an envelope of observed spectra over the broad range of frequencies. The band of low energies between 0.1 and 10Hz arises because signals from the two Ma#netotellurics: Principles and practice 447

Figure 3. Typical ULF signals, arranged (from top) E~o Ey, Hx, Hy. Time marks on top trace are 1rain (from Hopkins 1966).

IO0-

o

-I00 I I I I 0 2 4 6 8 I0 TIME msec ~4. Typical audio frequencytransient.

distinct source regions weaken as frequency approaches 1 Hz. The other band of low energy, near 2 kHz, is due to a change in the mode of propagation within the waveguide, resulting in a very high effective attenuation. For that reason, the gap is most pronounced in transients that have travelled the farthest and is undetectable in signals from nearby storms. In practice it is found that the high frequency gap is much narrower and causes less difficulty than the one near 1 Hz. Pierce (1977) includes a great deal of useful information about spherics. components are usually measured with induction coils, although superconducting SQUIDS were widely used in the 1970s and early 1980s. SQUIDS appear to have fallen into disfavour for several reasons: in survey operation they never achieved the low noise levels expected of them, they are less robust than induction coils, and it is often difficult to obtain and keep liquid helium in remote operational areas. At the same time, the performance of newer induction coils has improved, putting SQUIDS at a further disadvantage. 448 K Vozoff

T--T ~ T /. f s S , I I0 le o!o " I /-t S ; oS S oS SS tD S S S I /oo o o S oS I ;i S

iO.n

e- 9 10.2

. fl_ . /,.

/o o S ea ~J" 10.3

~o-4

I0"

.L ! t .L I0 4 I0 3 I0 2 I0 t I I()~ l()2 IC) 3 FREQUENCY Hz Figure 5. Envdol~ of observed SL0~tra t~cn from all av~lable sources.

Figure 6 is a collection of published noise spectra of commercial and other induction coil . As can be seen, the low noise figures of the SQUID are only really useful below 1 Hz. More recent research suggests that lower SQUID noise levels are possible (Hastings 1986). However Nichols (pers. comm., 1986) showed that the noise limitation on SQUIDS is, determined by microseismic vibration rather than by intrinsic noise levels, so there seems little point in pursuing that avenue unless some practical means of seismic isolation is devised. Electric fields are of course obtained by measuring time variations in the voltages between pairs of electrodes. Contact resistance and noise can be reduced by installing the electrodes in wet pits several hours, or days, before they are to be used, to allow the electrochemical environment to stabilize. The definitive study of electrode noise is still that of Petiau and Dupis (1980). FiUoux et al (1985) describe the use of MT in the deep oceans, while Filloux (1987) includes a very recent review of instrumentation for sea floor MT. Hoehn and Warner (1983) discusses the measurement in shallow waters of the Gulf of Mexico. Data recording and processing are now almost universally done digitally. In some Magnetotellurics: Principles and practice 449

I0 i i I

16'

M

C

.J hl II

ILl

----S/ hl .J

$2

166~ F-M

I I I I I Io4 Ioa Io 2 Io t i Io"~ io "z io-3 FREQUENCY Hz Figure 6. Noisespectra reported for various commercialand research magnetometers.S1 and $2 are, respectively,typical observed and theoretical noise levels for SQUIDS. systems the data are simply recorded for a predetermined length of time, and are processed later. In other systems the data are processed more or less in real time, and no raw data are saved. All new commercial systems are built around micro- computers and include the capability of processing on-site. Survey procedures vary according to geological objective and conditions. From experience it has been found necessary to depart from Cagniards's (1953) ideal of widely-separated sites in several respects. It is now common practice for recording sites to be spaced at intervals of a few hundred metres in areas of specific interest. At high frequencies, AMT and CSAMT sites are often even more closely spaced, 50-200 metres being common in commercial surveys. Close spacings are sometimes required simply because of the scale of the geological features under investigation. However even with large scale features it has sometimes been found necessary to separate sites by no more than a few hundred metres because of statics shifts, discussed below. Interpretation now includes 1D, 2D and 3D modelling, and 1D and 2D inversion. The first are relatively commonly done on personal computers, 1D inversion in a few minutes and 2D inversion in a few hours, whereas even a simple 3D forward model 450 K Vozoff may take many hours on a Vax 11/780. Wide use is made of the (crude but trivially simple) 1D Niblett-Bostick transformation. Imaging schemes in time and depth domains are emerging which may be very helpful in complex 2D and 3D situations. MT is increasingly used in conjunction with other data, especially seismic, well logs and active EM. An interesting example is described in w10, but other applications are to be found in the abstracts of the annual SEG and EAEG meetings (e.g., Berkman et at 1983; Young and Lucas 1988).

4. Fields in model

4.1 Fields in a horizontally-layered earth In the following, the familiar ID theory is summarized in order to fix the notation and the jargon used in the remainder of the paper. It is assumed that the magnetic permeability of the earth is P=Po =4n x 10-7H/m and that time variation is as exp(-icot), where angular frequency co = 2nf. It is also assumed that displacement currents can be neglected everywhere in the earth. We use a rectangular coordinate system with positive x northward, y eastward and z positive downward. Then, for example, H z will be the vertical component of H, positive downward, etc. In a uniform or 1D earth the E and H fields are orthogonal and comprise an EM wave diffusing (almost) vertically into the earth, dissipating as it goes. In the uniform earth the fields are related to each other and to the conductivity ~ and frequency co through (Stratton 1941, p. 490)

H = (k/pco)n x E, (1) where k = (1 + = (copa/2)

= I/J,

6 is the skin depth and n is the unit vector pointing vertically downward. Then the ratio E~/Hy at the surface is

E~/Hy = cop/k = (1 - i)(cop/2a) 1/2, (2) showing explicitly the relationships between the conductivity and the measured fields. The same relationship holds for Ey and - Hx. The ratio of Ex to Hy is proportional to x/~, where p = 1/a. If EffHy = Z~y, where Z o is the impedance defined by E~ and Hi, then

Z~y = (cot/k) = (1 - i)(pcop/2) (3) or pxy = Z* yZ y/pco. (4)

The asterisk indicates complex conjugation and Pxy is the resistivity derived from Magnetotellurics: Principles and practice 451

Zxy. The Z u are complex with phase ~b equal to the phase difference between E~ and Hj. pxy can also be written as

= 1___ Ex 2 (4a) Pxy co/z Hy

Units of Z are ohms and those of p are ohm-re. With E. and Hy in 'common' or 'practical' units (mV/km and gammas or nanoteslas, respectively), and using only the moduli, ,, 1 E. 2

Note that p and Z are independent of field strength since the entire system is assumed to be linear. Since both exp ( + icot) and exp (- icot) are used by various practitioners, two different phase ranges are found in the literature. Using the plus sign, ~y is in the first quadrant (0~ to + 90~ and with the minus sign it will be in the fourth quadrant (- 90 ~ to 0~ ~by~ is two quadrants away in each case. In commercial practice, both phases are sometimes found plotted in the range (0 ~ to 90~ Within a uniform earth, the solutions to Maxwell's equations for both E and H are of the form A = Aoexp [i(kz - cot)] = A o exp (- icot) exp (iaz) exp (- az), (5) where Ao is the surface value of the field component. The depth at which the fields have fallen to 1/e of their surface amplitudes is clearly z = t~ = 1/a. As a useful rule of thumb

6~500x/-~-fmetres. (6)

Pa and ~ are constants in the uniform earth model. In a multi-layered model, the fields in the i-th layer are the sum of two terms,

Aiexp(+ kiz ) + Biexp(- kiz), (7) one for the up-going and the other for the down-going energy. The coefficients Ai and B~ in each layer are found by forcing the solutions to satisfy the boundary conditions (e.g. Wait 1962). The results are now apparent resistivity po(f) and phase ~b(f), which are frequency- dependent. A recurrence expression for apparent resistivity and phase in an n-layered medium is

p=(~) = (z~zz)/Icol 2, (8) Im[Z] ~(co) = arctan Re [Z]' Z~+l+ r~, z~(o~) = sjz~+~ + 452 K Vozoff

Tj = w(pj) tanh(whffx//-~j), w = (- ioJ#)*,

S~ = ~ tanh (whffx/~j),

Z n = wx~ n. The subscripts here are layer indices, with j indicating the jth layer, and Zj is the impedance at the top of the jth layer. Two characteristics important to interpretation are as follows. First, given a finite number of layers, phase always returns to the same value (45 ~) as frequency goes to either zero or infinity. This is by contrast with apparent resistivity (which is asymptotic to Pn or Pl) and can be useful in interpreting data from complex areas, as discussed below. Second, as frequency decreases, changes in phase are evident before changes in apparent resistivity; as frequency increases the reverse is true. Hence when interpreting data containing noise, there are benefits to using both apparent resistivity and phase jointly (Vozoff and Jupp 1975). Real and imaginary parts of the impedance are related through the Hilbert transform (Kunetz 1972; Weidelt 1972; Boehl et al 1977; Parker 1983; Clay and Hinich 1981). Hence if apparent resistivity is known accurately, the phase can be derived from it by

~btf) = -~rc+f n folnfP,(f')~~-~,]f,i=-fz, df' (9) where P l is the high frequency asymptotic value of po(f). Qualitatively, if p. is plotted on a log-log scale, its phase is proportional to the slope of the curve, but from a baseline at - 45 ~ A convienient but crude approximation which avoids the integration is

~b(f)~ _4[1 + 0logp,(f)]~logf_]' (9a) but it should be used with caution since it can easily be in error by 10-15 ~ (Weidelt 1972). Other definitions of apparent resistivity are possible and sometimes even desirable. Spies and Eggers (1986) point out the somewhat arbitrary nature of the traditional definition, and discuss several alternatives including Kunetz' time-domain definition. Some of these do not show the undershoot/overshoot behaviour associated with the usual definition, which is advantageous in intuitive evaluation of 1D results.

4.2 Anisotropic and inhomogeneous media Virtually all rocks are anisotropic, often on several scales. For example, any layered sequence is anisotropic since currents will flow more easily in the plane of the layering than across it. On a finer scale, any laminated rock in which the lamina have differing resistivities will be anisotropic. The effect of anisotropy within the middle layer of a three-layer medium is shown in Vozoff (1972, figure 16), while Abramovici (1974) presents the theory for such media. A folded sequence will be more conductive along strike then across it. In general, it is not possible to observe small scale anisotropy Magnetotellurics: Principles and practice 453 except in the laboratory. Surface measurements can only detect an effective anisotropy due to large-scale organization. The term heterogeneous here refers to media in which conductivity varies with position in two or three directions (2D or 3D). In principle, Maxwelrs equations are solved in the same way for 2D and 3D as for 1D. In practice, there are very few 2D or 3D configurations for which simple analytical solutions such as eqs (5) and (7) have been found, and the equations must be solved by approximate numerical methods (e.g., Hohmann 1988). Qualitatively, several complications arise as we progress from 1D to 2D to 3D. In the 1D case E/H is independent of the direction of the coordinate axes and of position. As a consequence, if H is linearly polarized, E is always at right angles to H. In the 2D and 3D cases E is generally not perpendicular to H, and the ratio depends on both the coordinate directions and position. In the 1D case there is no vertical magnetic field component, whereas an H~ can be induced in both of the other cases. Thus both the fields and their interpretation become more interesting. The mechanisms of these changes can be explained as follows. In the 1D case, current flow is always parallel to conductivity boundaries. The main change physically as we go to 2D models is that current can now cross boundaries. When this occurs, the boundary condition that j, be continuous forces E, to change at the boundary, since E, = j J0.. (The subscript n here indicates the component normal to the boundary.) The change in E, occurs bec.ause a charge distribution is set upon the boundary and sustained by the current. At a contact between 0.t and 0.2 it is easily shown that El,n/E2.n=0.1/0.2, and the charge density is Jn(0.2--O"1)" Geometrically the situation is analogous to the electrostatic case. The charge sets up its own (time-varying, secondary) electric field which adds vectorially to the primary field, so that patterns of current flow and magnetic fields are altered. This is responsible for the effects mentioned above. These effects can be conveniently visualized in the 2D case, the simplest example being the outcropping vertical contact. There, Maxwelrs equations in rectangular coordinates separate into two independent modes, one for E along strike (TE, or H perpendicular to strike) and the other for H along strike (TM, or E perpendicular to strike). This is shown by orienting one of the rectangular coordinates along strike direction and solving by separation of variables. Then the partial derivatives wrt strike are set equal to zero and two independent sets of equations remain. If the x axis is the strike direction, the separated equations are (Swift 1971)

aE,/~y -- ~Ey/@z = i#o~ H~, dHx/@z = 0.Ey, ~Hx/~y = -- 0.Ez, (lOa) for TM (H along strike), and

tgHJt3y - tgHy/t~z = 0.Ex, O Ex/ Oz = igoJ Hy, (10b)

3Ex/3y = - i/~oJHz for TE (E along strike)polarization. Analytical solutions are known in the TM mode 454 K Vozoff for two models: the outcropping vertical contact and the outcropping vertical dyke (d'Erceville and Kunetz 1962; Rankin 1962). From these considerations it is seen that, in any 2D model, if the magnetic field is linearly polarized along strike (TM), the induced electric field only has a component across strike. By the same token, if H is across strike then E is parallel to strike (TE). In the TE case, a vertical magnetic field component arises near a lateral conductivity change. This is due to the fact that current densities and electric fields vary across such a change, and from the z component of V x E = - ~B/~t, ~Ey/Ox - dE JOy = - dBJdt. H, goes to zero with distance from the lateral change. A magnetic field in an arbitary direction will induce both E~ and Ey components. These will have different phases, so a linearly polarized H will generally give rise to an elliptically polarized E. Thus for the 2D contact described above, the following behaviour pattern results. At large distances (compared to skin depth) on either side of the contact, Zxy =EJHy and Zy~ = Ey/H~ are both asymptotic to the 1D value for the location. On crossing the contact, the TE components (Ex, Hy and Zxy) vary smoothly with position, whereas the TM components (Ey and Zyx) change abruptly. In detail, for the TM mode Hx has only a small change which occurs smoothly, but Ey overshoots, rising as it approaches the contact from the resistive side and falling as it approaches from the conductive side. In the TE mode, Ex changes smoothly and monotonically, while H~ also varies smoothly but has a small maximum near the contact. H, peaks near the contact and goes to zero within a few skindepths on either side. An overburden smooths all of these transition features. Many 2D model programs and algorithms are available, in the public domain literature and commercially. They include finite difference, finite element and integral equation methods (eg. Jones and Price 1971a, 1971b; Madden 1971; Swift 1971; Brewitt-Taylor and Weaver 1976; Travis and Chave 1986; Wannamaker et al 1986). Hohmann (1988) provides a current review of the state-of-the-art, for both 2D and 3D modelling. In the 3D case, there is always some surface exposed to charge accumulation. Since by definition the surfaces are localized, there is generally no direction in which linearly polarized H results in only a linearly polarized, perpendicular E. Thus the convenient mode separation of the 2D case does not occur. Instead, a linearly polarized magnetic field in any direction will induce an elliptically polarized E field, complicating modelling and interpretation. The interpretation problem is approached through an eigenanalysis of Z. Directional information now appears in terms of pairs of ellipses, or eigenstates, which are combinations of the orthogonal components of E or H. As in the 2D case, these have the property of giving simplified (diagonal or antidiagonal) impedance elements(Eggers 1982; LaTorraca et al 1986; Yee and Paulson 1987). This topic is further discussed below. The physics of 3D models is discussed by Park et al (1983), Wannamaker et al (1984b) and Park (1985), among others. From Park (1985), 3D responses can be described as a combination of three effects: vertical current gathering, horizontal current gathering and local induction (figure 7). Charge accumulates on the surfaces through which current is gathered. The importance of each of the three effects at any MT site depends on shape, depth, conductivities and frequency. At low frequencies, local induction is proportional to frequency but gathering becomes independent of Magnetotellurics: Principles and practice 455

f f

f I / / 11

'~.~176

.." -- . ".. :

- .. : "

V V

Local induction -- Horizontal Current Gathering ...... Vertical Current Gathering

Figure 7. Currents in a 3D body immersed in a conductive halfspace. (from Park 1985). frequency (Park 1985; West and Edwards 1985) so that they can in principle be distinguished. To deal with the complications in E-H relationships which are found in real data, Cantwell (1960) and Rokitiansky (1961) showed that, by assuming linearity, the relationships between E and H at each frequency could be written systematically as:

Ex = Z~xHx + Z,,yH r, E r = Zr~Hx + Zyr Hy.

In the now familiar matrix notation this is

E~ Zxx Zxr H~

or E = ZH, again at each frequency. The importance of this formulation is that, on physical grounds, the terms Z o must be independent of fluctuations in signal intensity, in the same way as apparent resistivity in the 1D case. However the equations again assume that E is due entirely to H. Noise in either one will generally not appear in the other, or else it will appear in a way which is not directly related to the assumed physical model, so the 'true' value of Z will be obscured. Most of the data processing described below was developed to improve the estimates of Z by statistical means, to minimise the damage done by noise. 456 K Vozoff

It is evident that Z simplifies in the 1D and 2D cases In the former, Zxx and Zyy are zero, Zyx = (0- Zxy, andz;) Z = - Zxy

In 2D, if one of the coordinate directions is (or is rotated to be) along strike,

0 Z~y '

otherwise all four terms are non-zero. Fields and tensors can always be mathematically rotated through angle 0 clockwise to another coordinate system by E' = RE, H' = RI-I, and Z'= RZIi T, where

cos0 sin0'~ R-- -sin0 cos0,]

and R T is the transpose of R. Cevallos (1986) demonstrated that Z is actually a pseudotensor rather than a true tensor, which explains some of the problems which have been encountered with its manipulation. He defined a true tensor ~ by

E = .~(H x n). (12)

The elements Z 0 of Z are related to (k~, the elements of .~, by (11 = Zxy, (12 = - Z~,x, (21 = Zyy and (22 = -Zyx. Thus

- Z~X

Alternatively, another true tensor can be defined by (E x n) = q/H..~ is diagonal for 1D and 2D models (in the principal axes). Further, combinations of ~ with its complex conjugate transpose (~.~) are hermitian. The attraction of this to interpretation is that it gives real (rather than complex) directions. In a layered medium containing a 3D body, Wannamaker et al (1984b) obtain the following basic relationships between incident and total fields:

E h = [I + PIE i (14) and ns = E1 + QZ,]H,, (15)

where Zt is the impedance of the layered medium without the body, P and Q are scattering tensors, I is a 2 x 2 identity matrix, and the subscripts h and i indicate horizontal components and incident fields, respectively. Then

Z = [I + P]ZI[I + QZt]- 1, (16) where Z is the complete impedance tensor. For a conductive 3D inlier at frequencies low enough that the skin depth within it is larger than the body, then P and Q become real constants, independent of frequency, MagnetoteUurics: Principles and practice 457 and QZ~ vanishes (as Z,) as frequency goes to zero. In that case Z becomes Z - [I + P]Z,, (17) giving for the four unrotated apparent resistivities P~x = PtP2~y pxy = pa(1 + Pxx) 2, Pyx = pl(1 + P,)~, and p, = pzP~. (18) Pz is the apparent resistivity at that frequency for the unperturbed layered medium. The coefficients ofpt in eqs (18) are always positive, so that the Pu are always positive. The off-diagonal terms can be larger or smaller than p~, depending on position, etc. This is a very helpful insight for dealing with the so-called 'statics' problem, amongst others. Tippers are known to behave systematically differently in 3D areas than 2D areas: they persist to lower frequencies, but are smaller. This is predicted in Ting and Hohmann (1981) and Wannamaker et al (1984a, b). An important consequence of these features of 3D responses in regard to routine MT interpretation is that, if one simply applies 1D inversion to apparent resistivity curve Pu, the resulting layer resistivities will be too large (small) by a factor Po/P~ and thicknesses will be too large (small) by a factor (pu/p,)~.. It is also clear that in the 2D case, inversion of the TE mode will give a better estimate of the underlying layered section than will TM.

5. Data processing and analysis

Under normal conditions neither E nor H is polarized linearly, and the data contain signal plus noise over a very broad range of frequencies. To extract the conductivity information fro~ the observed data it is first necessary to separate the frequencies and then to statistically determine relationships (apparent resistivities, impedances) amongst field components at each frequency. Once this has been done then the conductivity structure can be determined (at least in principle) by comparison with models. Time domain processing is discussed below. Conversion from time to frequency domain is generally done by Fast Fourier Transformation (FFT) after preliminary removal of mean and linear trends, and windowing to avoid transient effects from the ends of the data sets (Bendat and Piersol 1971). Data are usually collected in several broad, overlapping frequency bands, each of which can be treated in the same way. Wight et al (1977) and Wight and Bostick (1980) developed an efficient technique, called cascade decimation, for continuous data collection and processing. By low-pass filtering and decimation, all of the data collected in this procedure contribute to the results over their entire spectrum. Provision can be made to deemphasize data segments containing noise contamination (Pelton, pets. comm.). MT data quality improved spectacularly as a result of two developments, digital recording in the early 1960s, and the remote reference (RR) method (Gamble et al 458 K Vozoff

1979a). In the latter, in addition to the duster of three magnetometers and two pairs of electrodes at the site of interest, another orthogonal pair of components is simultaneously collected at a site near by. In principle, the signals will be common but the noises will be different, so that the remote (reference) signals are used for synchronous detection. This has made vast improvement in the quality of the results in the many cases where noise is of the same order of size as the signal. ,In extreme cases, where noise is either negligible or far greater than signal, the RR approach is unable to improve results. Young et af (1988) show examples of results obtained by conventional processing and by RR. These indicate slightly greater scatter in the single site results, but a certain amount of preselection and editing took place before publication. Certainly the differences in the original papers from Berkeley are more pronounced. An important property of the RR procedure is that it also provides estimates of the noise spectrum in each channel (Gamble et al 1979b). This makes it possible to estimate the noise in each of the impedance elements at each frequency, which is useful in providing confidence limits on the parameters of inversion models. Of course there is a cost involved in RR operation, due to the extra acquisition and processing required. This is minimized by maintaining a reference pair for a complete survey, where this is possible. Another approach has been to deploy several complete (5-channel) systems recording simultaneously in an area, with synchronized timing. Then any one can be used as a reference for any other. Bostick (pers. comm., 1986) suggested the use of the order of a dozen sets of equipment in this way, with telemetric recording at a single location. Other commercial contractors frequently collect data at several sites at a time. The question of noise correlation-distance arises when a pair of sites are too near each other. Goubau et al (1984) obtained results showing that a few tens of meters separation can be enough to provide an independent noise environment. However it would seem that this distance must depend on the nature of the noise and of the equipment. For example, SQUIDs and induction coils might be expected to have different sensitivities to microseisms. Newer 'robust' methods for spectral analysis of geomagnetic data have been described by Chave et al (1987) and by Egbert and Booker (1986), among others. These methods are adaptive, in that their detailed operation depends on the data and thus tends to be iterative and slower than conventional procedures. Robust methods might be expected to improve results because 'real' MT data almost never satisfy the statistical assumptions of Gaussian distribution and stationarity upon which normal spectral analysis is based. Sutarno (pers. comm., 1988) is completing a study of the application of these and related methods to long MT recordings from both 'normal' and very noisy sites. With noisy s~gie-site data he found that it is possible to do as well by robust processing of very noisy single-site data as by using a RR, but at the cost of considerably more data processing.

6. Tensor manipulation for 3D sites

Proper manipulation of the impedance tensor from a geologically complex site can make the difference between credible and incredible results. This is because apparent resistivities and phases must be smoothly varying functions of frequency whose behaviour is rigidly constrained by the physics of the method. One major problem Ma#netotellurics: Principles and practice 459 has been the application to data from 3D environments of tensor manipulation methods appropriate only for 2D data. In particular, the use of simple rotation to 'optimum directions' is a 2D concept whose application to 3D data has been justified only in 'almost-2D' conditions (Jones and Vozoff 1978). However, the practice has been to routinely apply 2D rotation to all data as a step in the interpretation process, with results that are sometimes less than satisfying. Indicators of three-dimensionality are well-known. They include widely varying apparent resistivity and phase curves, non-zero tensor skew, the absence of a definite minimum in tensor ellipticity, and the difficulty of relating results of 1D or 2D analyses to a sensible geological model. Impedance skew and ellipticity are defined from

Zx~ + Zyr = cl, (19) Z~y - Zyx = c2, (20) and Z,,xZ,, - Zx, Zy~, = c3. (21)

The ratio cl/c2 is the skew (or skewness), ~. ct will be zero in (noise-free) 1D and 2D models. Ellipticity,

[3(0) = Zx~(O) - Z,y(0) (22) z~,(o) + z,~(0) is zero (for noise-free data) in the 1D case, and in the 2D case when the x or y axis is along strike. In the search for an effective 3D analysis there is currently under way an active debate on the information content of the impedance tensor. It is well known that, in the 1D case, Z, = Zji = 0 and Z~j = -Z~i. Since Pa and phase are related through the Hilbert transform, that impedance contains only a single real function of frequency. Likewise, in the 2D case the tensor contains two independent complex elements plus direction, a real constant. It is probable that modulus and phase of each element are also related through Hilbert transforms in this case, so that the two functions are real and there are only two independent functions and a constant (Fischer and Schnegg 1980). In 3D environments, the 2 x 2 tensors could in principle contain up to eight (four complex) independent functions. The statics models of w considered by Wannamaker et al (1984), Zhang et al (1986) and Groom and Bailey (1988), are perturbed 1D or 2D cases; the low frequency assumption leads to simplifications in the relationships between the phases of tensor elements, so that the full complexity never develops. What about the general 3D case? In discussing the conventional treatment, Eggers (1982) states that it yields ~ parameters. He believes there should be eight, and that the set is incomplete. Yee and Paulson's (1987) canonical eigenvalue decomposition of Z (actually of the hermitian form Z* Z), which is the most recent word on the subject, is said to yield eight real parameters. These are a major and minor impedance, each with a phase, and a pair of directions, (one for E, one for H), each again with its phase. However, elsewhere Yee and Paulson (pers. comm.~ 1986) conclude that the same dispersion relations which apply in the 1D and 2D cases also hold for the 3D case. Papoulis (1962, Chap. 10) leads to the same conclusion. Despite new developments in graphics hardware and software, the need 460 K Vozoff to present and use eight parameters in interpretation would present a real practical problem if it had to be done at every site. Even four parameters are awkward to digest. This question remains to be investigated through application to both real and model data. In any case, it appears to me that more use must be made of the spatial information in conjunction with detailed spectral impedances.

7. Inversion and interpretation

Interpretation here means eventually attaching geological labels to the results of the geophysical measurements. Inversion may be used in the process, to get numerical models which match the results. As experience has accumulated, interpretation has developed in both quantitative and qualitative directions. I noted at the outset that the most critical need is the ability to relate MT results to geological 'realities': mineralogical composition, porosity and permeability, fabric and fracture characteristics, temperature, etc. The aim is to minimize the number of holes that must be drilled for exploration and development. Our abilities are improving, but they still have a very long way to go: at present we are still struggling with the most basic geometric problems. Qualitative interpretation usually begins with a comparison of the MT results and any independent information--geology, well logs, seismic, gravity or magnetics. This is done either site by site (1D basis), or on a 2D basis in which the locations and directions of profiles are selected from the available data. Niblett-Bostick (N-B) transformation (Niblett and Sayn-Wittgenstein 1960; Bostick 1977; Jones 1983) is often done at this stage because of its simplicity. In many cases this is all that is required because the problem consists of testing some simple hypothesis, for example, "the section at site A correlates with that at site B". N-B results are (or should be) confirmed by quantitative inversion. However the main features of the geological section can often be seen in the N-B transformation. Instead of the two quantities Pxy and Pyx, some interpreters use a single function such as Pd = (1/o~/z)[ZxxZ,- ZxyZy~l, or Pays= (Pxy + py~)/2. These give single sections which are less prone to scatter than individual Po (e.g. Ranganayaki 1984). Interpretation of more complex 2D and 3D structure is usually best begun qualitatively as well. Correlation between sites can often be seen in po and phase, as well as in the N-B curves. The emerging picture is frequently reinforced by continuity in the pattern of conventional rotation directions and tippers, so that the plan of a structure can be mapped with considerable confidence. The asymptotic behaviour of 3D models with frequency, discussed above, can also be applied at this stage to confirm the main features of the model. One shortcut to quantitative interpretation is to begin with simple 3D plate models, as was done by Flores-Luna (1986). The results can then be elaborated with more complex bodies or used to start an inversion. If large sums of money are to be spent on drilling a target, whether on the basis of MT, seismic, gravity or any other data, it is common sense first to apply quantitative techniques to the interpretation of those data. This may consist of forward modelling or of inversion. There have been a great many publications on MT inversion over the past 10 years, to the point where it is difficult to summarize or generalize them. A good general review is badly wanted at the present time. Magnetotellurics: Principles and practice 461

Given a possible model based on geology or other information or concepts, it can be used in two different ways. First, it can be used to construct a computer model whose response can then be compared with that observed. Alternatively, it may be the basis for inversion, which usually requires an initial model followed by iterative refinement. Inversion is widely available for 1D models, is in limited availability for 2D, and is not yet generally available for 3D models because of the large computing requirements. The two related benefits of inversion which are not easily available through forward modelling are statistical confidence limits on the results, and an appreciation of the uniqueness of the model. They are linked to the scatter in impedance estimates (and hence to signal/noise in the raw field data) and to the complexity of the model (Jupp and Vozoff 1975; Larsen 1981; Raiche et al 1985). I will deal first with 1D inversion. Roughly speaking, the publications tend to come in one of two varieties: simple and useful but specific, or elegant and instructive but very general. The former are usually overdetermined cases, consisting of small numbers of layers and many data points. Conductivities and thicknesses are found such that the response fits the observed data to within the measurement errors, as estimated from RR processing or from scatter in the data. The problem is linearized by taking a starting model which is assumed to be close to the 'correct' solution. Its response is compared to that observed, and adjustments are made to each of the parameters based only on the first partial derivatives of response w.r.t, each of the parameters. The significant change from the approach of 30 years ago is the use of an approximate generalized inverse instead of the direct inverse, for stability. This is obtained through the Marquardt method (Menke 1984) or by a modified Marquardt approach using singular value decomposition (SVD), as in Jupp and Vozoff (1975). The generalized inverse also provides direct means of estimating probable error bounds (or confidence limits) on the resulting parameters, using observed data variances and the structure of the parameter space (Jupp and Vozoff 1975, p 971). The more elegant publications have tended to treat models in which resistivity is a continuous function of depth or has many layers. The problem is underdetermined, i.e. there are more unknowns than data, and solutions tend to be obtained by linear programming, or by direct construction (e.g. Weidelt 1972; Oldenburg 1979; Parker 1983; Coen et al 1983). Other controls on layer parameters are then required to stabilize the resulting profiles. It is well known that the MT inversion problem is poorly conditioned, in that a small change in the data can lead to a very large change in some of the parameters output by the inversion. Changes in these poorly resolved parameters must be controlled during inversion or else results can diverge catastrophically on account of the nonlinearity of the forward problem. This is especially critical to the success of the underdetermined approaches, in which there are many more layers than data. It can be controlled by maintaining the number of layers small enough that conductivity changes smoothly between them, or by arbitrarily forcing a spline on the conductivities. Constable et al (1987) force the conductivity to have minimum roughness, which they define as the integral over depth of the first or second derivative of log(a(z)) wrt z. The same problem exists in the overdetermined case, where there is always a temptation to add 'just one more layer'. Raiche et al (1985) suggest a statistical measure, the average predicted residual error (APRE) to indicate the optimum number of layers for a given data set. The properties of 1D solutions--conditions for their existence, methods of 462 K Vozoff constrained and unconstrained construction, and assessment of resulting profiles (including error bounds and uniqueness)--are very well documented, largely in the 'elegant' class of papers. Oldenburg (1984) presents a comprehensive review of the Backus-Gilbert approach. Parker (1983) explores the limits on the information extractable from MT data alone, while Vozoff and Jupp (1975) illustrate the benefits of formal joint inversion of MT with other kinds of measurements. For example, the Parker paper shows that the models having the best possible fit to a finite number of accurate data values are completely unacceptable geologically. Such pathological results are avoided by applying constraints in the form of data independent of the MT. Inversion to 2D models has also been developed for both the continuous and discontinuous cases, usually utilizing the same principles and often the same code as for 1D. Our own 2D inversion (Jupp and Vozoff 1977) combines the SVD code developed for our 1D inversion (Jupp and Vozoff 1975) with Madden's (1971) 2D finite difference forward model program. (The same SVD code is being used in a wide variety of problems, as for example the transient EM inversion explained in detail in Raiche et al 1985). This had the disadvantage that the geometry was fixed: resistivities changed during inversion but the blocks could not. More recently, Cerv and Pek (1981) and Pek (1987) developed the extension in which block boundaries are also permitted to change, and Travis and Chave (1986) demonstrated moving finite elements in response to current density gradients. The latter was intended for transient EM modelling. Finally the work of Rodi and his associates must be mentioned. In Rodi et al (1983) and Jiracek et al (1987), use is made of a 2D linear inversion scheme in which conductivity is described by an optimally smooth function which is fitted to TE and TM data in an 11 sense. Modelling is by finite elements. The suitability of smooth models depends on the geological context. In 1972 Kunetz published a fundamental paper on time domain processing and interpretation for the 1D problem. There he set up the problem for what has come to be called a 'Goupillaud medium' and showed the parallels to both the seismic reflection and the DC resistivity problems in 1D. Since then a number of papers have been published in which this broad approach is applied to theoretical and/or observational MT data in 1D (Whittall and Oldenburg 1986; Wang et al 1986; Liu et al 1987) and 2D (Lee et al 1987; Levy et al 1988). The formal solution to the 1D MT problem consists of an upgoing and a downgoing field in each layer, reflecting at each interface, exactly as in the acoustic problem, but differs in that MT 'wavelets' are absorbed in each transition. Kunetz showed that the MT case can be set up as a formal convolution problem, so long as absorption is included. The reflection coefficients depend on the conductivity contrasts, so if the first layer resistivity is known, both the reflection coefficients and the absorption coefficients depend only on the resistivity contrasts in succeeding layers. The inverse problem consists of estimating reflection coefficients from the surface impedance. Kunetz demonstrates how impedance can be estimated in the time domain, but points out the difficulty of doing so over a broad enough time range from uniformly-samplexi data. Frequency domain impedances must usually be estimated over 4-5 frequency decades to define a meaningful range of depths. Presumably a time domain response would also have to be determined over several decades of time, raising problems of both data acquisition and dynamic range. The first problem might be overcome using Magnetotellurics: Principles and practice 463 techniques like Wight and Bostick's (1981) cascade decimation. It is less clear whether dynamic range is easily dealt with. Zhdanov and Frenkel (1983) demonstrate downward continuation in time domain of E and H separately for discrete 2D bodies in a conductive halfspace. In fact, in each of the publications noted (except Zhdanov and Frenkel, for which few computational details are given, but which appears to be time domain) the responses are estimated from spectral functions, which are then transformed to reflection coeffcient sereies. The computing involved appears to be as lengthy as that in conventional inversion, although the results may be presented in terms of reflection coefficients at interfaces rather than resistivities between the interfaces. However conversion between the two presentations is trivial and conventionally inverted results could easily be shown in the same way. It appears to me that, if there is an advantage in this pseudoseismic approach, it will be in computationally cheaper and more robust (if possibly less accurate) images of 3D and complex 2D structure. The results might then be compared with those from conventional inversion, or used as starting models for such inversion, in the same way as the N-B transformation, but for a wider range of structural complexity. Wang and I are presently investigating this possibility, with models and with real data.

8. Statics effects

As experience has been gained in the field, it has become increasingly clear that apparent resistivity curves are sometimes shifted vertically from their values expected on the basis of independent information. For example, in a simple, horizontally layered location Pxr may be identical to pyx except for a vertical shift, although the two phase curves are the same (after the 180~ shift). Where well logs or other conductivity data are available, it can sometimes be dearly demonstrated that one or both of the curves are displaced. This is clearly analogous to the static time shifts of , hence the name. The physics of this specific effect has been discussed by Berdichevsky and Dmitriev (1976), Wannamaker et al (1984b), Sternberg et al (1985) and Zonge and Hughes (1989), among others. It is most evident in CSAMT data because of the short station spacings commonly used. As noted above, the effect arises on account of very local, shallow inhomogeneities which locally perturb the E field without significantly disturbing H. By definition, a static shift is frequency-independent and is not seen in phase. Hence the source region must be both superficial and very shallow in extent (much less than a skin depth). Such regions naturally occur in a variety of sizes, and the larger ones will depart from the ideal at the highest recorded frequencies. In principle they can be identified and interpreted from the data, possibly with the helt~ of more closely spaced stations. Figure 8 illustrates the effect diagrammatically. The source region can obviously be either 2D or 3D. In 2D we would expect statics to be much smaller for the TE mode than for TM, since currents do not cross conductivity boundaries in the TE case. Equations (14)-(18) from Wannamaker et a l (1984b) demonstrate that these 3D features alter apparent resistivity by real tensor coefficients, independent of frequency. A few numerical models of statics problems have been published (Berdichevsky and Dmitriev 1976:, Zhang et al 1987; Groom and Bailey 1988). The second deals with a thin overburden overlying a uniform basement. Both overburden and basement 464 K Vozoff

/.-.---- P$> Pl /////~/_ .- o~ < Pl / I .gE

period (sec)

i

Pl Pz :> Pl Figure 8. Statics shifts due to a superficial inhomogeniety of resistivity p,. The central curve is asymptotic to p~ at short period and to P2 at long period. (after Sternberg et al 1985). are transversely isotropic, but have different impedances and principal directions. This represents a shield area with a regional 'grain' covered by a thin layer whose grain is in another direction. The analysis shows that the relationships amongst the Z u are particularly simple if measurement axes coincide with one of the principal conductivity axes. The other two references deal with small 3D bodies in regional 1D (Berdichevsky and Dmitriev 1976) or 2D (Groom and Biley 1988) environments. In the former, the models consist of vertical elliptical cylinders within a thin conductive layer, overlying a two-layer basement. The upper layer is an insulator and the lower has infinite conductivity. Results, in terms of real scalar distortion coefficients, are computed on the principal axes of the cylinders. The Groom and Bailey paper approximates the static effect of a small superficial hemisphere in a 2D regional environment. In contrast to the first work, fields and impedances are computed along several directions through the hemisphere. On lines through the centre of the hemisphere parallel to one of the regional axes, the impedances are found to have been shifted by real scalars, in accordance with the Berdichevsky- Dmitrie~' results. Off those axes, however, a real tensor is required to relate the results to those with the hemisphere absent. This agrees with the results of Wannamaker et al (1984b) mentioned above. A variety of methods have been used to overcome static offsets (Warner et al 1983; Sternberg et al 1982, 1985; Andrieux and Wightman 1984; Wightman and Andrieux 1984; Prieto et al 1984). These include the use of independent, external information such as electrical well logs, or DC, EM or seismic survey results. More common approaches involve spatial averaging at some frequency or frequencies, sometimes Magnetotellurics: Principles and practice 465 over distances comparable to skin depth (Bostick 1986; Sternberg et al 1982, 1985). As noted above, the structure of the impedance tensor may in some situations give a direct clue to the structural nature of the conditions which cause the statics effects.

9. Source effects and CSAMT

On present knowledge of current distributions in the magnetosphere and ionosphere, it is expected that impedances might at times depart from their plane wave values near the magnetic equator and at subauroral latitudes (Vozoff 1991). Research remains to be done on this possibility. Otherwise, it is now generally accepted (on the basis of a report written by Madden and Nelson in 1964 but unpublished Until 1986) that MT fields at frequencies less than 0.1-1.0Hz can be assumed to be planar, It is likewise established that above 1 Hz, where fields are due to electrical storms, impedances can be severely altered by the proximity of the storm (Vozoff 1989). Source regions should be more than 3-5 skin depths away for comfort: if the storm can be seen it is too close to use. Because of problems with signal/noise ratio between 0.1 and 10 Hz, the use of an artificial source is now well established as the Controlled Source Audio Frequency MT (CSAMT) method. However if the source is too near, the E/H ratios from a CSAMT transmitter can also be very different from those obtained from remote storms. In such cases the impedance depends on the kind of source (loop or grounded wire), its orientation, and its distance in skin depths. Among other complications there is no single obvious plotting position for interpretation, since both transmitter and receiver positions are involved in the result. Because skin depth decreases with increasing conductivity and frequency, the impedance may well depend on transmitter location at low frequencies but approach the plane wave value at high frequencies. An effort is made in CSAMT surveys to get the transmitter as far from the survey positions as possible, consistent with adequate field strength, so as to take advantage of the simplicity of interpretation for plane wave source fields. However this aim conflicts with the desire in commercial surveys for rapid coverage, and compensation of CSAMT results for transmitter effects is an ongoing problem (Yamashita et ai 1985; Zonge et al 1986; Maclnnes and Wait 1988; Zonge and Hughes 1989). It is not yet clear whether the particular problem of even a thin resistive zone beneath a conductive overburden can be resolved on the basis of CSAMT data alone.

10. The resistive layer problem

Resistive layers can also pose a problem for conventional MT, when it is desired to resolve their resistivity quantitatively. It is well known that MT is able to resolve the thickness of resistive layers but is unable to resolve their resistivity unless the layer is very thick. This is because little current is induced in such layers and the magnetic fields pass through almost unaware of their presence. In certain exploration applications it is important to be able to map porosity variations in resistive units, especially carbonates in which 40% of the world's oil is found. Resistivities in the lower crust are likewise poorly known. Galvanic methods are known to have better resolving power than EM methods for such problems, but 466 K Vozoff most examples are beyond the depth capability of DC resistivity measurements. It is worth pointing out that a medium scale transient EM measurement using a galvanic source has been successfully applied to the exploration problem. Based on a suggestion by Eadie (1981), Vozoff et al (1985) used a l'5km wire, driven by a 50 ampere square wave current and grounded at each end, to generate, measure and jointly invert E and H fields at distances to 15km. In a survey carried out in the Canning Basin of northwestern Australia, resistivity variations were successfully mapped in a thick carbonate zone of interest at 2-5 km depth. Similar results have been obtained recently in Europe (Strack, pers. comm.). The technique, known as LOTEM, was shown to be most effective when used in conjunction with other information, especially seismic, well logs and MT. Until very recently the interpretation and modelling were done purely on a 1D basis, since the discrete source requires computing expenditure substantially greater than that for MT. However Newman, Strack and others at the University of Cologne (Pers. comm., 1988) are using Newman's 3D model program (Gunderson et al 1986) with our 1D inversion program to study the effects of discrete bodies on our procedure. Computing demands are indeed substantial. Further experience with this method is being acquired in several parts of the world, including India, at the present time.

11. Case histories

Results from surveys having a wide variety of objectives have been published in recent years. Predictably, many excellent sets of results have not appeared because of commercial considerations. Those which are published tend to come from research and/or governmental groups. Some significant regional MT results are those of Stanley (1982), Stanley et al (1985), Maidens and Paulson (1988), Jiracek et al (1983, 1987), Young and Repasky (1986), Rasmussen et al (1987), Young and Lucas (1988), and Ritz and Vassal (1986), whereas regional AMT results are shown in Hoover et al (1976), Strangway et al (1980), Benderitter and Gerard (1984), Ballestracci (1982) and Mabey et al (1978). Lakanen (1986) shows results of detailed (scalar) AMT results in mineral exploration in a shield environment. Many brief case histories appearing in the extended abstracts of the annual SEG meetings have never been published, and the SEG reprints volume on MT (Vozoff 1986) includes a section of case histories. On reading these it is clear that important results can be obtained in surveys, even with less than ideal data quality. This is particularly noticeable in the AMT examples where the equipment has tended to be fairly primitive but the measurements have been rapid. What has been lacking in the quality has been made up by the quantity of data. However this philosophy is not recommended since one might very well end up with a large quantity of useless data. The quality of MT data has been uniformly better, but of course data collection is much slower. The advent of tensor AMT systems has considerably improved those results (Vozoff 1989).

12. Conclusions

The past 10 years have seen necessary improvements in our ability to collect, process and interpret magnetotellurics in complex 3D structural environments. These Magnetotellurics: Principles and practice 467

improvements have also made it possible to detect some of the more subtle features associated with simpler conditions, such as stratigraphic petroleum traps, where necessary. At the same time the capabilities of the method have become more familiar to a wider range of earth scientists, and they are now recognising situations where it can usefully be employed. MT has become a standard component of many large scale national and international projects, in Europe, North America and Asia. We are seeing a great growth in the use of MT in direct conjunction with other geological and geophysical data, often for joint quantitative inversion. Two major needs at this stage are a better understanding of the factors governing conduction beyond the range reached by drilling (> 10 km), and considerably more experience with the new tools for tensor analysis and interpretation. In the more immediately achievable category, a broad general review of inversion which includes the multidimensional and the recent time and depth-domain work would be very valuable. At this stage, many of the academic and commercial results obtained over the past 15 years should also bereevaluated, to take advantage of the improved methodology and new insights which are reviewed here.

References

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