GEOTHERMAL PROSPECTING BY GEOELECTRIC SOUNDINGS IN NE GREECE*

In total 77 direct current resistivity soundings were carried out during a geothermal exploration survey of the Genisea, NE Greece, geothermal field. The data revealed a high electrical conductivity zone at the center of the investigated area and suggested that an anomalous heat source lay beneath the study area. This was confirmed by subsequent drilling data. Temperature measurements, from 11 boreholes, were used for the construction of isotherms that correlated very closely with the geoelectric data.     

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.     

THE QUANTITATIVE ANALYSIS OF FREQUENCY-DOMAIN INDUCED POLARIZATION SOUNDINGS OVER HORIZONTAL BEDS*

Following up our recent study of an indirect procedure for the practical determination of the maximum frequency-effect, defined as fe = 1 ? pρ_∞/ρdc with ρ_∞ the resistivity at infinite frequency, we show at first how, through the Laplace transform theory, ρ_∞ can be related to stationary field vectors in the simple form of Ohm's law. Then applying the equation of continuity for stationary currents with a suitable set of boundary conditions, we derive the integral expression of the apparent resistivity at infinite frequency ρ_∞,a in the case of a horizontally layered earth. Finally, from the definition of the maximum apparent frequency-effect, analytical expressions of fe_α are obtained for both Schlumberger and dipole arrays placed on the surface of the multi-layered earth section in the most general situation of vertical changes in induced polarization together with dc resistivity variations not at the same interfaces. Direct interpretation procedures are suggested for obtaining the layering parameters directly from the analysis of the sounding curves.     

DIRECT INTERPRETATION OF RESISTIVITY DATA OVER TWO-DIMENSIONAL STRUCTURES*

A direct interpretation scheme is developed which is capable of determining most of the geological features of a ground which can be assumed to be two dimensional in structure. This scheme extends the earlier work of Pekeris (1940) and Koefoed (1968) to the case where the basal layer of a ground is undulating. It also has a limited use for finding the parameters of a dipping dyke in the lower medium. Though the top and dip of the dyke can be determined, this is not true for the thickness.     

GEOELECTRIC AXIAL DIPOLE SOUNDING CURVES FOR A CLASS OF TWO-DIMENSIONAL EARTH STRUCTURES*

With the aim of studying the behaviour of geoelectric axial dipole vertical soundings over complex geology, a systematic theoretical approach is presented for a class of earth structures characterized by horizontal and vertical parallel boundary planes. The two-dimensional cylindrical bodies of infinite length and rectangular cross-section are constrained to have resistivities satisfying Alfano's condition at every intersection line of the graticule, in order to adopt the image-point theory. A detailed analysis is performed for models with any number of horizontal boundaries and two vertical discontinuities. The apparent resistivity formulas are obtained and selected apparent resistivity curves are drawn for different parameter combinations and various directions of the sounding expansion axis. The class under consideration contains as a particular case the HVC model elaborated in Alpin's monograph, where only a small collection of master curves is available for the axial array. The reconstruction of those curves by the present formulation shows the existence of large discrepancies. A test based on the transformation to equivalent half-Schlumberger sounding curves supports the conclusion that an unidentified error must exist in some part of the theoretical approach of the Russian researchers. Finally, some field sounding curves based on geothermal and volcanological surveys are presented and interpreted by complete curve matching, essentially to show the applicability of the theoretical solutions.     

A MAN/COMPUTER INTERPRETATION SYSTEM FOR RESISTIVITY SOUNDINGS OVER A HORIZONTALLY STRAFIFIED EARTH*

The proposed system works as follows:

• 1 By a trial-and-error procedure using a graphic display terminal a geologically relevant layer sequence with parameters (ρ_j, d_j) is adjusted to yield roughly the measured curve.
• 2 The resulting layer sequence is used as starting model for an iterative least squares procedure with singular value decomposition. Minimization of the sum of the squares of the logarithmic differences between measured and calculated values with respect to the logarithms of the resistivities and thicknesses as parameters linearizes the problem to a great extent, with two important implications:

• a) a considerable increase in speed (the number of iterations goes down), thus making it cheap to achieve the optimum solution;
• b) the confidence surfaces in parameter space are well approximated by the hyper-ellipsoids defined by the eigenvalues and eigenvectors of the normal equations.

Since these are known from the singular value decomposition we do in fact know all possible solutions compatible with the measured curve and the geological concept.

• 3 It is possible to “freeze” any combination of parameters at predetermined values. Thus extra knowledge and/or hypotheses are easily incorporated and can be tested by rerunning step (2). The overall computing time for a practical case is of the order of 10 sec on a CDC 6400.

     

THE ASSOCIATION OF RESISTIVITY SOUNDINGS*

A simple measure, the association parameter, is proposed for directly comparing the results of two electrical soundings. The use of this measure to classify field results and to gain some insight into geological structure before extensive depth interpretation is discussed. In particular it is shown that when used with soundings conducted using the tripotential technique the combined use of association parameter arid lateral inhomogeneity index can allow structural patterns to be discerned where otherwise they might be obscured. Possible extension of the technique is considered.     

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.     

GEOELECTRIC MODELS IN ENGINEERING GEOPHYSICS*

Man's engineering activities are concentrated on the uppermost part of the earth's crust which is called engineering-geologic zone. This zone is characterized by a significant spatialtemporal variation of the physical properties status of rocks, and saturating waters. This variation determines the specificity of geophysical and, particularly, geoelectrical investigations. Planning of geoelectric investigations in the engineering-geologic zone and their subsequent interpretation requires a priori) geologic-geophysical information on the main peculiarities of the engineering-geologic and hydrogeologic conditions in the region under investigation. This information serves as a basis for the creation of an initial geoelectric model of the section. Following field investigations the model is used in interpretation. Formalization of this a priori) model can be achieved by the solution of direct geoelectric problems. An additional geologic-geophysical information realized in the model of the medium allows to diminish the effect of the “principle of equivalence” by introducing flexible limitations in the section's parameters. Further geophysical observations as well as the correlations between geophysical and engineering-geologic parameters of the section permit the following step in the specification of the geolectric model and its approximation to the real medium. Next correction of this model is made upon accumulation of additional information. The solution of inverse problems with the utilization of computer programs permits specification of the model in the general iterational cycle of interpretation.     

DIRECT INTERPRETATION OF TWO-ELECTRODE RESISTIVITY SOUNDINGS *

This paper describes the procedure for interpreting the apparent resistivity data measured with the two-electrode array directly with the help of kernel function. The calculation of kernel function from the observed resistivity curve is done by the method of decomposition. In the method of decomposition the resistivity curve is approximated by a sum of certain functions, whose choice is only restricted by the requirement that the contribution to the kernel function corresponding to them should be easily computable. A few such functions are classified. These, and the standard curves for corresponding kernel functions obtained by utilising an integral expression for two-electrode array expressing the kernel explicitly in terms of the apparent resistivity functions, are plotted on log-log scale. The determination of layer parameters, that is, the layer resistivities and thicknesses from the kernel function can be carried out by a method proposed by Pekeris (1940).     

CONTOUR MAP PRESENTATION OF DIPOLE-DIPOLE INDUCED POLARIZATION DATA*

Dipole-dipole induced polarization (IP) data are displayed typically as multi-level profiles, or as contours on vertical sectional plots referred to as pseudo-sections. The dipole-dipole array tends to yield IP anomalies in which the most anomalous values are displaced laterally from the source body. The data patterns are fairly interpretable on pseudo-sections or on multi-level profiles but are sufficiently complex to discourage the contouring of the data in plan. A method was developed for the presentation of dipole-dipole IP data on a contour map. The method consists of a simple averaging of data which can be performed manually if desired. It yields a single output value per station which reflects all levels of the pseudo-section, and is suitable for contouring in plan. The advantage of the technique is that it provides a quantitative picture of IP anomalies in their background or regional setting.     

A GENERAL TECHNIQUE FOR THE DIRECT INTERPRETATION OF RESISTIVITY DATA OVER TWO-DIMENSIONAL STRUCTURES*

The indirect method of interpreting resistivity data is capable only of limited success because of the difficulty of calculating type curves for complex structures. Consequently a need arises for a direct method of interpretation for complex generalized structures. Such a technique for the direct interpretation of apparent resistivity data, obtained by electrical soundings carried out over two-dimensional structures, has been developed from an examination of the Hankel transform of such data. The method is based on the observation that the asymptotic expansion of the Hankel transform is critically dependent upon the minimum distance between the measuring device and the surface of discontinuity in resistivity. The variation in the across strike direction may be mapped by a sequence of depth soundings made parallel to each other and separated in the across strike direction.     

EFFECT OF VERTICAL CONTACT ON WENNER RESISTIVITY SOUNDINGS*

The allowance for the influence of a vertical contact is evaluated on Wenner resistivity sounding curves, which are graphically constructed on bilogarithmic paper over simple composite earth models consisting of a vertical contact separating two- or three layered earth on one side and a homogeneous medium on the other side. The error incurred in the graphical constructions is explored. Finally, the use of these graphically constructed sounding curves is shown in the interpretation of two Wenner field soundings measured in a complex geologic area.     

TRANSFORMATION OF DIPOLE SOUNDINGS OBTAINED ALONG A CROOKED LINE *

Data collected in a dipole-dipole sounding along a crooked line can be transformed to form an approximately equivalent Schlumberger sounding, using a simple matrix inversion technique. The equivalent curve can be interpreted using rapid interpretation methods.     

ON THE PROPERTIES OF THE RECIPROCAL GEOELECTRIC SECTION*

The interpretation of vertical electrical sounding data can be facilitated by the application of the reciprocal geoelectric section. If an apparent resistivity field curve has a descending right end, the apparent resistivity curve of the reciprocal geoelectric section can be obtained by the application of linear filter theory; from this the total transverse resistance of the geoelectric section can be calculated without having to interpret the field curve. In addition, Orellana's auxiliary point method can now be extended to interpret three and four layer apparent resistivity curves of all types. This paper summarizes the properties of the resistivity transform curve, the apparent resistivity curve, and the apparent resistivity curve of the reciprocal geoelectric section, with several new applications.     

ON THE INTERPRETATION OF RESISTIVITY SOUNDINGS BY THE LEAST-SQUARES METHOD*

An interactive least-squares method for the interpretation of VES curves was proposed by Johansen (1977). The method permits one to select some parameters (thicknesses and/or resistivities of individual layers) and to change the rest in such a way that the interpreted model approaches the measured data. This note suggests a modification of Johansen's method, in which not only the individual parameters can be selected but also linear combinations of parameters—in particular, the sum of thicknesses of several layers.     

GEOELECTRIC INVESTIGATIONS OF A FAULT SYSTEM IN QUATERNARY DEPOSITS*

Geoelectric soundings were used to investigate the younger fault activity (Middle and Early Pleistocene) of the southwestern fault margin area of the Central Graben (and extension of the Rhine Graben) in the southern Netherlands and northern Belgium. Some effects of this fault activity can still be observed in the present geomorphology and hydrography. Investigations have been concentrated on the uppermost 20–30 m, consisting mainly of Middle and Early Pleistocene fluviatile deposits. Marshy clays and loams are most conductive. They alternate with large sand beds and gravelly gully infillings, characterized by high specific resistivities. Problems in the interpretation of the geoelectric data, caused by the variability of the deposits, are partially solved by in-situ resistivity measurements (“mini-electric” measurements). In spite of the lithologic inhomogeneity, a few marker horizons allow the geologic structure to be determined. Some new tectonic boundaries have been traced. The movements along the faults during the Quaternary are very small (less than 10 m). Therefore, the network of soundings has to be very dense and a very intensive analysis of the soundings is necessary. The results also have a hydrogeologic significance. This project illustrates the possibility of locating small tectonic structures in relatively inhomogeneous deposits by a detailed and carefully designed geoelectric survey.     

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.     

唐山大震区深部构造的初步研究

本文介绍利用地震转换波测深法研究1976年7.8级唐山大震区深部构造的某些结果,得出了沿两条测线的深部构造剖面图。发现在极震区的数十公里的范围内,地壳和上地幔具有异常结构,在地壳中部比震区外围多出一个中间层位,埋深约12-20km,地壳上部界面向上挠曲,而莫霍面和上地幔顶部界面却强烈地向下挠曲,引起了震区岩石圈厚度的加大,在震区存在深浅不等的深部断裂。深部构造与震源分布的对比表明,唐山主震和绝大多数余震均分布在壳内中间层之上,有的甚至就分布在壳内中间层的上、下界面附近。转换波测深结果表明,本区地壳上地幔中强烈的升降差异运动可能是唐山大震的重要促发因素。     

唐山大震区深部构造的初步研究

本文介绍利用地震转换波测深法研究1976年7.8级唐山大震区深部构造的某些结果,得出了沿两条测线的深部构造剖面图。发现在极震区的数十公里的范围内,地壳和上地幔具有异常结构,在地壳中部比震区外围多出一个中间层位,埋深约12—20km,地壳上部界面向上挠曲,而莫霍面和上地幔顶部界面却强烈地向下挠曲,引起了震区岩石圈厚度的加大,在震区存在深浅不等的深部断裂。深部构造与震源分布的对比表明,唐山主震和绝大多数余震均分布在壳内中间层之上,有的甚至就分布在壳内中间层的上、下界面附近。转换波测深结果表明,本区地壳上地幔中强烈的升降差异运动可能是唐山大震的重要促发因素。