Analysis of the geomagnetic induction tensor

The geomagnetic induction tensor is a means of summarizing the response of the earth at a given observing site to a geomagnetic variation source field. In this paper the characteristics of the tensor elements are examined, both generally and for the special cases of one-dimensional and two-dimensional geologic structure. The first-order model is taken of uniform source fields originating external to a semi-infinite half-space. Graphical ways of presenting the information contained in an induction tensor are explored, including ellipses of rotation, polar diagrams, and diagrams analogous to the Mohr circles of elasticity theory. Criteria to distinguish “two-dimensional” data from “three-dimensional” data are established. The advantages of simultaneously recording “normal” and “anomalous” variations are demonstrated in terms of the extra tensor elements which may then be estimated. The most practical way of presenting information from many stations on a map may be by drawing, for each site, arrows which summarize the response in the vertical field and quadrics which summarize the response in the horizontal field.     

NUMERICAL MODELLING OF STANDARD AND CONTINUOUS VERTICAL ELECTRICAL SOUNDINGS1

Analytical solutions of vertical electrical soundings (VES) have mostly been applied to groundwater exploration and monitoring groundwater quality on terrains of fairly simple geology and geomorphology on which the electrode arrays are symmetrical (e.g. Schlumberger or Wenner configurations). The sounding interpretation assumes flat topography and horizontally stratified layers. Any deviations from these simple situations may be impossible to interpret analytically. The recently developed GEA-58 geoelectrical instrument can make continuous soundings along a profile with any colinear electrode configuration. This paper describes the use of finite-difference and finite-element methods to model complex earth resistivity distributions in 2D, in order to calculate apparent resistivity responses to any colinear current electrode distribution in terrains in which the earth resistivities do not vary along the strike. The numerical model results for simple situations are compared with the analytical solutions. In addition, a pseudo-depth section of apparent resistivities measured in the field with the GEA-58 is compared with the numerical solution of a real complex resistivity distribution along a cross-section. The model results show excellent agreement with the corresponding analytical and experimental data.     

TRAITEMENT AUTOMATIQUE DES SONDAGES ELECTRIQUES AUTOMATIC PROCESSING OF ELECTRICAL SOUNDINGS*

I. Introduction In this section the problem is stated, its physical and mathematical difficulties are indicated, and the way the authors try to overcome them are briefly outlined. Made up of a few measurements of limited accuracy, an electrical sounding does not define a unique solution for the variation of the earth resistivities, even in the case of an isotropic horizontal layering. Interpretation (i.e. the determination of the true resistivities and thicknesses of the ground-layers) requires, therefore, additional information drawn from various more or less reliable geological or other geophysical sources. The introduction of such information into an automatic processing is rather difficult; hence the authors developped a two-stage procedure:

• a) the field measurements are automatically processed, without loss of information, into more easily usable data;
• b) some additional information is then introduced, permitting the determination of several geologically conceivable solutions.

The final interpretation remains with the geophysicist who has to adjust the results of the processing to all the specific conditions of his actual problem. II. Principles of the procedure In this section the fundamental idea of the procedure is given as well as an outline of its successive stages. Since the early thirties, geophysicists have been working on direct methods of interpreting E.S. related to a tabular ground (sequence of parallel, homogeneous, isotropic layers of thicknesses h_i and resistivities ρ_i). They generally started by calculating the Stefanesco (or a similar) kernel function, from the integral equation of the apparent resistivity: where r is the distance between the current source and the observation point, S₀ the Stefanesco function, ρ(z) the resistivity as a function of the depth z, J₁ the Bessel function of order 1 and λ the integration variable. Thicknesses and resistivities had then to be deduced from S₀ step by step. Unfortunately, it is difficult to perform automatically this type of procedure due to the rapid accumulation of the errors which originate in the experimental data that may lead to physically impossible results (e.g. negative thicknesses or resistivities) (II. 1). The authors start from a different integral representation of the apparent resistivity: where K₁ is the modified Bessel function of order I. Using dimensionless variables t = r/2h₀ and y(t)=ζ (r)/ρ₁ and subdividing the earth into layers of equal thicknesses h₀ (highest common factor of the thicknesses h_i), ø becomes an even periodic function (period 2π) and the integral takes the form: The advantage of this representation is due to the fact that its kernel ø (function of the resistivities of the layers), if positive or null, always yields a sequence of positive resistivities for all values of θ and thus a solution which is surely convenient physically, if not geologically (II.3). Besides, it can be proved that ø(θ) is the Fourier transform of the sequence of the electric images of the current source in the successive interfaces (II.4). Thus, the main steps of the procedure are: a) determination of a non-negative periodic, even function ø(θ) which satisfies in the best way the integral equation of apparent resistivity for the points where measurements were made; b) a Fourier transform gives the electric images from which, c) the resistivities are obtained. This sequence of resistivities is called the “comprehensive solution”; it includes all the information contained in the original E.S. diagram, even if its too great detail has no practical significance. Simplification of the comprehensive solution leads to geologically conceivable distributions (h, ρ) called “particular solutions”. The smoothing is carried out through the Dar-Zarrouk curve (Maillet 1947) which shows the variations of parameters (transverse resistance R_i= h_i.ρ_i–as function of the longitudinal conductance C_i=h_i/ρ_i) well suited to reflect the laws of electrical prospecting (principles of equivalence and suppression). Comprehensive and particular solutions help the geophysicist in making the final interpretation (II.5). III. Computing methods In this section the mathematical operations involved in processing the data are outlined. The function ø(θ) is given by an integral equation; but taking into account the small number and the limited accuracy of the measurements, the determination of ø(θ) is performed by minimising the mean square of the weighted relative differences between the measured and the calculated apparent resistivities: minimum with inequalities as constraints: where t_l are the values of t for the sequence of measured resistivities and p_l are the weights chosen according to their estimated accuracy. When the integral in the above expression is conveniently replaced by a finite sum, the problem of minimization becomes one known as quadratic programming. Moreover, the geophysicist may, if it is considered to be necessary, impose that the automatic solution keep close to a given distribution (h, ρ) (resulting for instance from a preliminary interpretation). If φ(θ) is the ø-function corresponding to the fixed distribution, the quantity to minimize takes the form: where: The images are then calculated by Fourier transformation (III.2) and the resistivities are derived from the images through an algorithm almost identical to a procedure used in seismic prospecting (determination of the transmission coefficients) (III.3). As for the presentation of the results, resorting to the Dar-Zarrouk curve permits: a) to get a diagram somewhat similar to the E.S. curve (bilogarithmic scales coordinates: cumulative R and C) that is an already “smoothed” diagram where deeper layers show up less than superficial ones and b) to simplify the comprehensive solution. In fact, in arithmetic scales (R versus C) the Dar-Zarrouk curve consists of a many-sided polygonal contour which múst be replaced by an “equivalent” contour having a smaller number of sides. Though manually possible, this operation is automatically performed and additional constraints (e.g. geological information concerning thicknesses and resistivities) can be introduced at this stage. At present, the constraint used is the number of layers (III.4). Each solution (comprehensive and particular) is checked against the original data by calculating the E.S. diagrams corresponding to the distributions (thickness, resistivity) proposed. If the discrepancies are too large, the process is resumed (III.5). IV. Examples Several examples illustrate the procedure (IV). The first ones concern calculated E.S. diagrams, i.e. curves devoid of experimental errors and corresponding to a known distribution of resistivities and thicknesses (IV. 1). Example I shows how an E.S. curve is sampled. Several distributions (thickness, resistivity) were found: one is similar to, others differ from, the original one, although all E.S. diagrams are alike and characteristic parameters (transverse resistance of resistive layers and longitudinal conductance of conductive layers) are well determined. Additional informations must be introduced by the interpreter to remove the indeterminacy (IV.1.1). Examples 2 and 3 illustrate the principles of equivalence and suppression and give an idea of the sensitivity of the process, which seems accurate enough to make a correct distinction between calculated E.S. whose difference is less than what might be considered as significant in field curves (IV. 1.2 and IV. 1.3). The following example (number 4) concerns a multy-layer case which cannot be correctly approximated by a much smaller number of layers. It indicates that the result of the processing reflects correctly the trend of the changes in resistivity with depth but that, without additional information, several equally satisfactory solutions can be obtained (IV. 1.4). A second series of examples illustrates how the process behaves in presence of different kinds of errors on the original data (IV.2). A few anomalous points inserted into a series of accurate values of resistivities cause no problem, since the automatic processing practically replaces the wrong values (example 5) by what they should be had the E.S. diagram not been wilfully disturbed (IV.2.1). However, the procedure becomes less able to make a correct distinction, as the number of erroneous points increases. Weights must then be introduced, in order to determine the tolerance acceptable at each point as a function of its supposed accuracy. Example 6 shows how the weighting system used works (IV.2.2). The foregoing examples concern E.S. which include anomalous points that might have been caused by erroneous measurements. Geological effects (dipping layers for instance) while continuing to give smooth curves might introduce anomalous curvatures in an E.S. Example 7 indicates that in such a case the automatic processing gives distributions (thicknesses, resistivities) whose E.S. diagrams differ from the original curve only where curvatures exceed the limit corresponding to a horizontal stratification (IV.2.3). Numerous field diagrams have been processed (IV. 3). A first case (example 8) illustrates the various stages of the operation, chiefly the sampling of the E.S. (choice of the left cross, the weights and the resistivity of the substratum) and the selection of a solution, adapted from the automatic results (IV.3.1). The following examples (Nrs 9 and 10) show that electrical prospecting for deep seated layers can be usefully guided by the automatic processing of the E.S., even when difficult field conditions give original curves of low accuracy. A bore-hole proved the automatic solution proposed for E.S. no 10, slightly modified by the interpreter, to be correct.     

COMBINED SOUNDING-PROFILING RESISTIVITY MEASUREMENTS WITH THE THREE-ELECTRODE ARRAYS*

A combination of DC-resistivity sounding and profiling measurements can be used to obtain the maximum information about distribution of resistivities in the earth. Combined sounding-profiling measurements with the AMN, MNB arrays are considered. The resistivity data from such measurements can be presented as: (a) normal sounding curves, (b) combined sounding-profiling curves, (c) profiling curves, (d) pseudo-sections, or as transformations obtained by the so-called gradient processing, to emphasize the influence of the target objects. The examples chosen from numerical modeling and field tests show the efficiency of measurements with three-electrode arrays to accurately locate thin conductors and contacts of lithological units of different resistivities. An interpreted cross-section is compared with the results of other geophysical measurements (VLF-R, dipole EM, Δ, IP) showing good correlation.     

The effect of the electrical anisotropy on the response of helicopter-borne frequency-domain electromagnetic systems

Helicopter electromagnetic (HEM) systems are commonly used for conductivity mapping and the data are often interpreted using an isotropic horizontally layered earth model. However, in regions with distinct dipping stratification, it is useful to extend the model to a layered earth with general anisotropy by assigning each layer a symmetrical 3 × 3 resistivity tensor. The electromagnetic (EM) field is represented by two scalar potentials, which describe the poloidal and toroidal parts of the magnetic field. Via a 2D Fourier transform, we obtain two coupled ordinary differential equations in the vertical coordinate. To stabilize the numerical calculation, the wavenumber domain is divided into two parts associated with small and large wavenumbers. The EM field for small wavenumbers is continued from layer to layer with the continuity conditions. For large wavenumbers, the EM field behaves like a DC field and therefore cannot be sensed by airborne EM systems. Thus, the contribution from the large wavenumbers is simply ignored. The magnetic fields are calculated for the vertical coaxial (VCX), horizontal coplanar (HCP) and vertical coplanar (VCP) coil configurations for a helicopter EM system. The apparent resistivities defined from the VCX, VCP and HCP coil responses, when plotted in polar coordinates, clearly identify the principal anisotropic axes of an anisotropic earth. The field example from the Edwards Aquifer recharge area in Texas confirms that the polar plots of the apparent resistivities identify the principal anisotropic axes that coincide well with the direction of the underground structures.     

Computation of apparent resistivity profiles from VLF-EM data using linear filtering1

A simple filter is developed which transforms VLF-EM real magnetic field transfer functions into apparent resistivities. It is based on the relationship between the horizontal derivative of the surface electric field and the vertical magnetic field at the surface of a two-dimensional earth model. The performance of this simple autoregressive filter is tested for modelled and real survey data. The technique yields profiles of apparent resistivity very similar, both in magnitude and in wavelength, to those which would have been obtained using VLF-EM resistivity measurements or d.c. resistivity profiling. This low-pass filter has the advantage of reducing high-wavenumber noise in the data; therefore only the major features of the VLF-EM profile are displayed.     

INDUCED POLARIZATION RESPONSE OF A HORIZONTALLY MULTILAYERED EARTH WITH NO RESISTIVITY CONTRAST*

The induced polarization response of a horizontally multilayered earth with no resistivity contrast can rapidly be calculated on a desk calculator or minicomputer for any electrode array. The formulation is a simple series summation of the products of weighting coefficients and the true induced polarization responses for each of the layers. The coefficients are directly derivable from the corresponding resistivity model. This series approach to IP formulation was originally described by Seigel but has not been treated extensively in the present-day geophysical literature. This method can be applied to either time or frequency domain induced polarization measurements. Once the coefficients are known, apparent induced polarization response can readily be obtained by judicious substitution of known, suspected, or assumed values of the true induced polarization of each layer. Basic formulation is presented for the IP potential coefficients (pole-pole or two array) with no resistivity contrast between the layers. From these coefficients, response of any number of layers for any electrode array can be obtained by suitable differentiation. Some examples of Wenner array for a three-layered earth and dipole-dipole array for a four-layered earth are used to illustrate the application. The results of this technique are valid for many natural situations of modest resistivity contrast. However, they definitely cannot be used if there are highly contrasting resistivity layers present. Such an approach is conceptually simple and is useful for survey planning, checking or setting the “depth-of-penetration”of a given array. For field induced polarization data that fits reasonably well to the no-resistivity-contrast model, this simple approach facilitates quantitative interpretation.     

二维大地电磁各向异性参数对视电阻率的影响研究

大地电磁法是广泛应用于深部地质结构探测、油气和矿产资源勘查等领域的一种地球物理方法.电性各向异性对电磁观测数据有很大影响,但介质各向异性参数对不同模式视电阻率的影响还较少有较为系统的研究.本文基于Maxwell方程组,推导了二维大地电磁场在任意各向异性介质中电场和磁场相互耦合的变分方程,结合有限单元法及并行计算编写了二维大地电磁任意各向异性正演程序,采用三角形网格剖分.验证程序正确性后,以倾斜板状体作为模型来研究三个主轴电阻率及三个旋转欧拉角和四种模式的视电阻率之间的关系.结果表明,主轴各向异性时,xy模式视电阻率几乎只受x方向电阻率影响,yx模式视电阻率主要受y方向电阻率影响,但同时也受z方向电阻率一定影响;三个欧拉角中只有倾角不为零时,yx模式视电阻率受倾角大小的影响较大,xy模式视电阻率几乎不受倾角的影响;只有走向角不为零时,四种模式的视电阻率同时受x、y两个主轴电阻率和走向角的大小的影响.     

NUMERICAL INTERPRETATION OF RESISTIVITY SOUNDINGS OVER HORIZONTAL BEDS*

The digital computer technique described for interpreting resistivity soundings over a horizontally stratified earth requires two steps. First, the kernel function is evaluated numerically from the inverse Hankel transform of the observed apparent resistivity curve. Special attention is given to the inversion of resistivity data recorded over a section with a resistant basement. The second step consists in the least-squares estimation of layer resistivities and thicknesses from the kernel function. For the case of S or T-equivalent beds only one layer-parameter can be obtained, either the longitudinal conductance, or the transverse resistance respectively. Two examples given in the paper show that a wide tolerance is permitted for Choosing the starting values of the layering parameters in the successive approximation procedure. Another important feature for practical applications is good convergence of the iterations. The method is probably best suited for interpreting profiles of electrical soundings with the purpose of mapping approximately horizontal interfaces at depth.     

Interpretation of ground VLF-EM data in terms of inclined sheet-like conductor models

The response of two-dimensional, inclined, sheet-like conductors with, low conductance values to plane wave electromagnetic fields in the very low frequency (VLF) range has been evaluated by using a numerical technique. The conductance values of the conductors considered are appropriate for those produced by water and/or clay-filled fracture and shear zones in the Precambrian crystalline rocks of the Canadian Shield. The surrounding host rock was assumed to be, resistive with resistivities in the 1–10 k.m range to reflect the high resistivities over the shield areas. No overburden was assumed in this analysis.The results of the computations are presented in the form of characteristic interpretation diagrams to interpret ground VLF data in the field, where facilities for direct numerical modelling may not be available. A method for interpreting ground VLF data using such characteristic diagrams has been proposed in this paper which requires a prior knowledge of the host rock resistivity and the inclination of the conductor. These two parameters may be derived from a VLF resistivity survey and from appropriate filtering of the VLF tilt angle response. The interpretation method was applied to a ground VLF anomaly obtained at a research site near Atikokan in NW Ontario, which yielded an interpretation compatible with information from geological mapping.Geological Survey of Canada Contribution No. 51888.     

RESISTIVITY ANALYSIS FOR PLANE-LAYER HALF-SPACE MODELS WITH BURIED CURRENT SOURCES*

Boundary-value problems in steady-state current flow were solved numerically for one and two layers over a half-space. Solutions were obtained for layers of various resistivities where one of the current sources was placed below the surface and the second kept at some finite distance from the drill hole. When a fixed surface dipole receiving pair was used, it was found that as the buried source approached a conductive region, quite good determinations of the depth to the conductor could be made, hence reducing the possibility of extended drilling in “dry” holes resulting from poor surface data and/or interpretation. Numerous models were generated to find the optimum positioning of the two current electrodes for different field situations of this type. It was also found that by placing a current source in the conductive region, better resolution of the lateral extent of a possible ore zone could be obtained, due both to the more rapid convergence of the apparent resistivity to the resistivity of the conductor, and the fact that a smaller separation in the receiving dipole could be used. Numerous analog models were constructed to verify the digital results. Surface and down-hole resistivity field data are compared to show the strength of this technique in delineating structure.     

FAST AUTOMATIC PROCESSING OF RESISTIVITY SOUNDINGS*

The difficulty to use master curves as well as classical techniques for the determination of layer distribution (e_i, ρ_i) from a resistivity sounding arises when the presumed number of layers exceeds five or six. The principle of the method proposed here is based on the identification of the resistivity transform. This principle was recently underlined by many authors. The resistivity transform can be easily derived from the experimental data by the application of Ghosh's linear filter, and another method for deriving the filter coefficientes is suggested. For a given theoretical resistivity transform corresponding to a given distribution of layers (thicknesses and resistivities) various criteria that measure the difference between this theoretical resistivity transform and an experimental one derived by the application of Ghosh's filter are given. A discussion of these criteria from a physical as well as a mathematical point of view follows. The proposed method is then exposed; it is based on a gradient method. The type of gradient method used is defined and justified physically as well as with numerical examples of identified master curves. The practical use for the method and experimental confrontation of identified field curves with drill holes are given. The cost as well as memory occupation and time of execution of the program on CDC 7600 computer is estimated.     

A MODIFIED GEOELECTRICAL PROCEDURE USING POLARDIPOLE ARRAYS—AN EXAMPLE OF APPLICATION TO DEEP EXPLORATION *

Dipole soundings are more sensitive to noise caused by lateral and superficial inhomogeneities than Schlumberger soundings. However, the former are preferable for deep explorations in view of the relatively short cables required. The simple solution of carrying out the field work by means of dipole spreads, and to transform the dipole resistivity diagrams into Schlumberger ones by means of proper formulae would be valid only for smooth and regular curves; but often, owing to the presence of lateral noises, the dipole data show a considerable scatter. For such cases a “continuous dipole sounding” method is proposed for which all successive dipoles are contiguous, so that all parts of the profiles are covered and interpolation is not necessary. Obviously the moving dipoles have lengths proportional to their distances, so that they appear equal in the usual bilogarithmic scale. It follows that only polar-dipole arrays may be used. The transition from a dipole to the corresponding Schlumberger apparent resistivity diagram requires an integration constant which is not unequivocally determined. Therefore, the solution is not unique, but all possible derived Schlumberger diagrams have a common part. Similarly, they have some common interpretative results, which may be referred to the original dipole diagram obtained in the field. A special measurement technique is required since the dipole-dipole voltages to be determined are noticeably smaller than the Schlumberger ones. This is true also because dipole soundings are used for great depths and for long distances between the two dipoles.     

地电阻率变化与孕震过程研究

在分析唐山７．８级地震前后地电阻率异常变化特征的基础上，研究地电阻率异常量△ρ／ρ０与应变的关系，给出了地电阻率异常量△ρｓ／ρ０对应变ε的转换关系式；分析和研究地电阻率异常发展，演变特征与地震孕震，发生过程的联系及其前兆异常标志。     

A DIGITAL LINEAR FILTER FOR RESISTIVITY SOUNDING WITH A GENERALIZED ELECTRODE ARRAY*

This paper presents a digital linear filter which maps composite resistivity transforms to apparent resistivities for any four—electrode array over a horizontally layered earth. A filter is provided for each of three sampling rates; the choice of filter will depend on resistivity contrasts and computational facilities. Two methods of filter design are compared. The Wiener-Hopf least-squares method is preferable for low sampling rate filters. The Fourier transform method is more successful in producing a filter with a high sampling rate which can handle resistivity contrasts of 100 000: 1.     

Regional induction studies: A review of methods and results

The geomagnetic skin-effect is specified by setting three length scales in relation to each other: L₁ for the overhead source. L₂ for the lateral non-uniformity of the subsurface conductor, L₃ for the depth of penetration of a quasi-uniform transient field into this conductor. Relations for the skin-effect of a quasi-uniform source in layered conductors are generalized to include sources of any given geometry by introducing response kernels as functions of frequency and distance. They show that only those non-uniformities of the source which occur within a distance comparable to L₃ from the point of observation are significant. The skin-effect of a quasi-uniform source in a laterally non-uniform earth is expressed by linear transfer functions for the surface impedance and the surface ratio of vertical/horizontal magnetic variations. In the case of elongated structures and E-polarisation of the source, a modified apparent resistivity is defined which as a function of depth and distance gives a first orientation about the internal distribution of conductivity. The skin-effect of a non-uniform source in a non-uniform earth is considered for stationary and “running” sources. Recent observations on the sea floor and on islands indicate a deep-seated change of conductivity at the continent—ocean transition, bringing high conductivity close to the surface, a feature which may not prevail, however, over the full width of the ocean. There is increasingly reliable evidence for high conductivities (0.02 to 0.1 micro ^?1 m^?1) at subcrustal or even at crustal depth beneath certain parts of the continents, in some cases without obvious correlation to geological structure.     

双感应测井资料的快速近似迭代反演

本文给出一种双感应资料快速近似迭代反演技术. 首先建立Fréchet导数的快速算法,保证在反演过程中能够同时获得测井响应相对于地层电阻率和层界面的偏导数,并给出用规范化处理与奇异值分解技术进行迭代反演的具体过程. 为了对理论模拟和井场实际资料进行反演,利用综合分层技术从双感应曲线中提取层界面初始位置和地层电阻率初值,通过单独迭代反演中感应资料,修改层界面和地层电阻率实现中感应资料的最佳拟合,得到探测深度相对较浅的地层电阻率,然后固定层界面位置,再迭代反演深感应资料,得到另一组探测深度相对较深的地层电阻率. 理论和实际资料处理结果证明,两个不同探测深度的电阻率反演结果的相对大小能够准确地反映地层真实的侵入特征.此外,由于深感应仪器具有较深的探测深度,不论在高侵或低侵地层上,深感应反演结果与地层原状电阻率的差异大大小于视电阻率的差异,所以利用反演结果也能得到更好的地层原状电阻率的估计值.     

THE DISPERSION RELATION, OF EARTH''S ELECTROMAGNETIC RESPONSE FUNCTIONS AND THE JOINT INVERSION OF DATA

On the basis of the dispersion relations of MT field, the necessity and applied prospects of the joint inversions using a pair of MT response functions which are correlative with the dispersion relations, are infered. A filter coefficient algorithm is made, with which the corresponding impedance phase data can be estimated using a set of apparent resistivities. The tests for the observed MT data show that when comparing the impedance phase estimated using the dispersion relation with the ob served phase, it can be checked whether the dispersion relation between observed apparent resistivity and phase data is satisfied or not, and that the use of the phase data corrected using the dispersion relation in the joint inversion is advantageous to obtain more confident results. It is shown that joint inversions are more advantageous than single parameter inversions, and that in the most case the joint inversion using the apparent resistivities of impedance real and imaginary parts is more advantageous than the jointinversion using the normal apparent resistivity and impedance phase. The existence of the dipersion relations between the ratio apparent resistivity and corresponding impedance phase of the orthogonal electric and magnetic field horizontal Components in the frequency EM sounding with horizontal electric dipole(FEMS) are discussed, the better effect of the joint inversion using the pair of EM response functions is obtained. The problems on the one-dimensional joint inversion for the MT and FEMS apparent resistivities, for which the observed frequency bands partly overlape each other, are studied. It is shown that this joint inversion is applicable and effective:the joint inversions of the practical data for two kinds of EM methods at two sites give the results well corresponding to the drilling data. The simulated MT inversions for the data of two kinds of EM methods are made, and more confident results also are obtained.     

水平分层大地的交流视电阻率

本文给出了水平分层大地视电阻率的一种改进的定义,在这种改进了的视电阻率的远区曲线中,假极值效应有所压低,曲线的起伏度变得比原来的大,视电阻率的值也较接近于地层的真实电阻率.这些特性对于作出正确的判断都是有利的.     

THEORETICAL RESISTIVITY SOUNDING RESULTS OVER A TRANSITION LAYER MODEL *

An earth model with a transition layer (anisotropic inhomogeneous) is considered. The inhomogeneity in σ_v (vertical conductivity) of the transition layer is represented by a power law variation. Expressions for potential distribution in the upper layer, transition layer and bottom layer are obtained by solving appropriate differential equation for each layer. By utilizing the boundary conditions, expressions of apparent resistivity for Wenner and Schlumberger configurations are derived. Numerical analysis is performed for linear and quadratic variation of σ_v. The results are presented in the form of theoretical apparent resistivity curves for both configurations. Negative apparent resistivities are the interesting feature of this analysis.