AN INTEGRAL EQUATION FOR THE GEOELECTRIC RESPONSE OF THIN RESISTIVE BODIES1

Thin sheet-like forms are common target bodies in geoelectric prospecting. Depending on their mineralogy and other factors these bodies may be relatively conductive or relatively resistive with respect to their surroundings. For suitably remote field points (relative to the thickness) these features manifest themselves geoelectrically in terms of their conductivity-thickness product for relatively conductive bodies or in terms of their resistivity-thickness product for resistive forms. While the case of a conductive sheet has received some attention in the geophysical literature, resistive sheets have been largely ignored. Accordingly an efficient technique to model the geoelectric responses of a resistive lamina is presented here. The technique involves representing the lamina in terms of a distribution of normally directed current dipole moment whose density is shown to satisfy an inhomogeneous Fredholm integral equation of the second kind. The technique is rigorously tested in a 2D environment and is shown to produce reliable and suitably accurate results. An application of the method is presented in which the apparent resistivity and chargeability responses measured with a gradient array over a dipping resistive ribbon are computed. These are compared with the responses observed over a relatively conductive ribbon in the same orientation.     

RESISTIVITY TYPE CURVES OVER OUTCROPPING VERTICAL DYKE—II *

The theoretical horizontal resistivity profiles Over an outcropping vertical dyke with two-electrode and Schlumberger electrode systems are discussed. The two-electrode array seems very useful in locating the highly conducting thick or thin vein, while the Schlumberger (gradient) array is suited to detect the conducting vein of low and moderately high resistivity contrast and as well as the resistive vein of all widths and resistivity contrasts. Besides, the inline gradient array has a distinction of establishing a clue to evaluate the resistivity contrast of the vein.     

RESISTIVITY AND IP MODELING OF THE THREE-ARRAY DOWN-HOLE PROSPECTING TECHNIQUE*

The resistivity and induced polarization responses due to a number of IP targets for a down-hole three-array have been calculated numerically. The IP targets are approximated by triangle-faceted polyhedra; number and size of the facets are limited by the numerical procedure. Despite this limitation a number of profiles have been obtained for a sphere, lens, prolate spheroid and thin dipping slab. The profiles obtained do not differentiate between the shapes of the IP targets, but depend upon the vertical extent of the target within the search-radius of the borehole. The type curves produced could be of use for preliminary interpretation and in the field for planning the next stages of a geophysical survey. The lateral and vertical search radii of the borehole are increased by the use of such an array. For the bodies used it is estimated that the search radii are extended by 2.0 dipole units.     

RESISTIVITY TYPE CURVES OVER OUTCROPPING VERTICAL DYKE—I *

The theoretical horizontal resistivity profiles over an outcropping vertical dyke for various parameters-electrode spacing, vein-width and resistivity contrast—with inline alpha, beta and gamma-Wenner electrode systems are described. The resistivity profiles present a most bewildering variety of shapes as compared to those in resistivity soundings. The analysis of type curves suggests suitable electrode configuration for detection of wide, moderately wide, and thin veins. The negative apparent resistivity values on the gamma anomalies for resistive vein over certain vein-widths of higher positive values of resistivity reflection factor contradict the concept of apparent resistivity hitherto held.     

IN-LOOP PULSE EM RESPONSE OF A STRATIFIED EARTH*

The in-loop pulse electromagnetic response of a stratified earth has been expressed in terms of an apparent resistivity- time plot using the PEM response over a homogeneous half-space which is typically unipolar with monotonic decay. This half-space response characteristic provides a unique relationship between Crone PEM channel amplitude and the apparent half-space resistivity. The possibility to resolve a thin intermediate conductive and resistive layer with the in-loop PEM system has been investigated. The system is well in shallow geoelectric mapping.     

Three-dimensional tomography using high-power induced polarization with the similar central gradient array

Induced polarization (IP) 3D tomography with the similar central gradient array combines IP sounding and IP profiling to retrieve 3D resistivity and polarization data rapidly. The method is characterized by high spatial resolution and large probing depth. We discuss data acquisition and 3D IP imaging procedures using the central gradient array with variable electrode distances. A 3D geoelectric model was constructed and then numerically modeled. The data modeling results suggest that this method can capture the features of real geoelectric models. The method was applied to a polymetallic mine in Gansu Province. The results suggest that IP 3D tomography captures the distribution of resistivity and polarization of subsurface media, delineating the extension of abrupt interfaces, and identifies mineralization.     

Image processing of 2D resistivity data for imaging faults

A methodology to locate automatically limits or boundaries between different geological bodies in 2D electrical tomography is proposed, using a crest line extraction process in gradient images. This method is applied on several synthetic models and on field data set acquired on three experimental sites during the European project PALEOSIS where trenches were dug. The results presented in this work are valid for electrical tomographies data collected with a Wenner-alpha array and computed with an l₁ norm (blocky inversion) as optimization method. For the synthetic cases, three geometric contexts are modelled: a vertical and a dipping fault juxtaposing two different geological formations and a step-like structure. A superficial layer can cover each geological structure. In these three situations, the method locates the synthetic faults and layer boundaries, and determines fault displacement but with several limitations. The estimated fault positions correlate exactly with the synthetic ones if a conductive (or no superficial) layer overlies the studied structure. When a resistive layer with a thickness of 6 m covers the model, faults are positioned with a maximum error of 1 m. Moreover, when a resistive and/or a thick top layer is present, the resolution significantly decreases for the fault displacement estimation (error up to 150%). The tests with the synthetic models for surveys using the Wenner-alpha array indicate that the proposed methodology is best suited to vertical and horizontal contacts. Application of the methodology to real data sets shows that a lateral resistivity contrast of 1:5–1:10 leads to exact faults location. A fault contact with a resistivity contrast of 1:0.75 and overlaid by a resistive layer with a thickness of 1 m gives an error location ranging from 1 to 3 m. Moreover, no result is obtained for a contact with very low contrasts (∼1:0.85) overlaid by a resistive soil. The method shows poor results when vertical gradients are greater than horizontal ones. This kind of image processing technique should be systematically used for improving the objectiveness of tomography interpretation when looking for limits between geological objects.     

INTERPRETATION OF TRANSIENT EM COMMON-LOOP ANOMALIES BY RESPONSE CHARACTERISTICS*

Theoretically exact type curves for a semi-infinite thin conductor are presented for various dip, angles, depth of burial and conductance. The study shows that the common-loop response shape is sensitive to small changes in conductor dip, but is affected more subtly by comparable strike variations. For large sheet conductors a decrease in the strike angle results in a broadening but unlike that for a finite plate there is no reduction in peak amplitude. For dipping conductors, response asymmetry and the direction and magnitude of peak amplitude displacement can be used to assess the disposition and quality of the conductor. A generalized interpretation scheme is proposed, based on dimensionless response characteristics and normalized decay curves, to facilitate the rapid in-field determination of conductor dip, conductance and depth of burial, for any time regime.     

THEORETICAL TRANSIENT EM RESPONSE CURVES OVER A THIN DIPPING DYKE IN FREE SPACE–SEPARATED INLINE LOOP CONFIGURATION*

Theoretically exact type curves are presented to show the effect on response shape of changing dip, strike, transmitter-receiver separation, depth of burial and target conductance. Relatively small dip variations produce a marked asymmetry in response shape. For steeply dipping conductors, strike can be determined from the cross-over width of the anomaly. The curves illustrate the dynamic character of the transient process, and suggest how the spatial disposition and quality of large sheet conductors might be inferred from the extent of peak-amplitude displacement with time, and rate of eddy-current diffusion. A generalized interpretation scheme is proposed based on dimensionless response characteristics which will facilitate the rapid determination of conductor dip, conductance and depth of burial for any time regime.     

Physical Modeling Results on Modified Pseudo-depth Sections in Exploration of Highly Resistive Targets – II

-- This work extends the results that Apparao et al. (1997a) obtained for a vertical resistive sheet to the case of inclined resistive sheet models for different electrode arrays. It is found that the depth of investigation (DI) remains the same as that for the vertical target. Using this DI, modified pseudo-depth sections have been constructed over sheet models at different inclinations. It is noted that, for the Wenner array, the maximum anomaly contours fall directly over the target cross section. For dipole-dipole and three-electrode arrays, these contours fall on the up-dip side of the dipping target, with the maximum anomaly contour matching the depth level of the top of the target. It is also observed that the target cross section is at a distance of about 0.33L (L/3) from the maximum anomaly value/contour position for the three-electrode array and 0.25L (L/4) for the dipole-dipole system. These features are identifiable in the individual profiles and may help field geophysicists in the recognition and location of dipping target bodies.     

ON THE EFFECTS OF THICKNESS OF THE HALF-PLANE MODEL IN HLEM INDUCTION PROSPECTING OVER SULPHIDE DYKES IN A HIGHLY RESISTIVE MEDIUM1

In the quantitative data interpretation for HLEM induction prospecting, a vertical half-plane model in an insulating medium is widely employed. For this assumption to be valid, the steeply dipping massive sulphide dykes must have large strike lengths and depth extents, but small thickness. We report investigations, using the laboratory scale-modelling method, on the response variation of large vertical conductors as the thickness is varied. We conclude that a steeply dipping large dyke can be approximated by a half-plane model only if its thickness is less than half the skin depth. An inductively thick conductor produces larger amplitudes and relatively higher quadrature compared to a thin conductor, even if both have the same induction number.     

A SOLUTION OF THE DIPPING INTERFACE PROBLEM USING THE SQUARE ARRAY RESISTIVITY TECHNIQUE*

Apparent resistivity measurements with the square array technique in the vicinity of a dipping interface have the advantage over collinear array methods that they are less dependent on orientation of the array. In order to exploit this, existing potential solutions for the dipping interface problem have been adapted for the computation of apparent resistivities over such a feature using a square array. Comprehensive interpretation techniques covering this problem are given and the limitations imposed by residual array orientation effects are discussed.     

A new method for geoelectrical investigations underwater1

A new electrical method is proposed for determining the apparent resistivity of multi-earth layers located underwater. The method is based on direct current geoelectric sounding principles. A layered earth model is used to simulate the stratigraphic target. The measurement array is of pole-pole type; it is located underwater and is orientated vertically. This particular electrode configuration is very useful when conventional electrical methods cannot be used, especially if the water depth becomes very important. The calculated apparent resistivity shows a substantial quality increase in the measured signal caused by the underwater targets, from which little or no response is measured using conventional surface electrode methods. In practice, however, different factors such as water stratification, underwater streams or meteorological conditions complicate the interpretation of the field results. A case study is presented, where field surveys carried out on Lake Geneva were interpreted using the calculated apparent resistivity master-curves.     

An audiomagnetotelluric study of the Meugueur-Meugueur ring structure, Aïr, Niger: ring dyke or cone sheet?

Three radial audiomagnetotelluric (AMT) sounding profiles were carried out across the narrow, 65-km diameter troctolitic Meugueur-Meugueur ring structure, central Aïr, Niger, to study its electrical configuration; one profile extended across the bedrock into the large Ofoud complex situated slightly off geographical centre within the ring. Apparent resistivity data from 27 sites ranged from isotropic to strongly anisotropic. In nearly all soundings, one- and two-dimensional modelling indicated the presence of a major zone of low resistivity (60–600 Ωm), about 200 m thick, dipping steeply inwards at an angle of 65–80° and extending to a depth of at least 2–5 km. This layer, overlain and underlain by rocks of higher resistivities in excess of 5000 Ωm, is taken to be the outer contact. A highly resistive body, about 200 m in width, dipping inwards to a depth of at least 4 km is taken to be the Meugueur-Meugueur intrusion, which is thus interpreted to be a cone sheet.     

Upper crustal electrical resistivity structures in the vicinity of the Çatalca Fault, Istanbul, Turkey by magnetotelluric data

A magnetotelluric survey was performed at the Çatalca Region, west of Istanbul, Turkey with the aim of investigating geoelectrical properties of the upper crust near the Çatalca Fault and its vicinity. Broadband magnetotelluric data were collected at nine sites along a single southwest-northeast profile to image the electrical resistivity structure from surface to the 5 km depth. The dimensionality of the data was examined through tensor decompositions and highly two-dimensional behavior of the data is shown. Following the tensor decompositions, two-dimensional inversions were carried out where E-polarization, B-polarization and tipper data were utilized to construct electrical resistivity models. The results of the inversions suggest: a) the Çatalca Fault extends from surface to 5 km depth as a conductive zone dipping to southwest; b) the thickness of the sedimentary cover is increasing from SW to NE to 700 m with low resistivity values between 1–100 Ωm; c) the crystalline basement below the sedimentary unit is very resistive and varies between 2000–100000 Ωm; d) a SW-dipping resistivity boundary in the northeastern part of our profile may represent the West Black Sea Fault.     

Magnetic interpretation of pairs of sheets and their equivalence to dykes

Magnetic anomaly profiles over two thin sheets separated by a small distance resemble those of dykes andvice versa. Interpretation of anomalies over a pair of sheets based on the magnetic properties of dykes predicts a dyke whose centre lies midway between the positions of the sheets. The dyke, on the other hand, is magnetically equivalent to a pair of sheets, both lying at the same depth and having the same magnetization.The magnetic anomalies due to a pair of sheets can be interpreted by framing linear equations between the anomalies and their distances measured from an arbitrary reference. Application of this method to anomalies of dipping sheets with a finite depth extent is indicated.     

STATISTICAL EVALUATION OF MT AND AMT METHODS APPLIED TO A BASALT-COVERED AREA IN SOUTHEASTERN ANATOLIA,TURKEY*

The efficacy of the magnetotelluric and audiomagnetotelluric (MT/AMT) methods for detailing the structure of a hypothetical geological section is investigated by using the singular value decomposition (SVD) technique. The section is representative of southeastern Turkey, which is mostly covered by basalt and is a prime area for oil exploration. One of the geological units, the Germav shale at a depth of 600 m, is a problem layer for electromagnetic surveys because of its very low resistivity (on average 3 Ωm) and highly variable thickness across the area (200–900 m). In the MT frequency range (0.0004–40 Hz) its total conductance—or, since its resistivity is known from resistivity log information, its thickness—is the best resolved model parameter. The total depth to the Germav shale and the resistivity of the Cambrian/Precambrian basement are the marginally resolved parameters. In the AMT frequency range (4–10000 Hz) the resistivity of the surface basalt layer strongly affects the resolution of the other, less important, model parameters which are the total depth to the Germav shale and the total conductance of the Germav shale. The errors in the measurements determine the number of model parameters resolvable, and are also important for interpretation of the geological model parameters to within a desired accuracy. It is shown that statistical evaluation of the MT and/or AMT interpretations by using an SVD factorization of the sensitivity matrix can be helpful to define the importance of some particular stage of the interpretation, and also provides a priori knowledge to plan a proposed survey. Arrangements of MT and AMT observations, together with some Schlumberger resistivity soundings, on a large grid will certainly provide three-dimensional detailed information of the deep geoelectric structure of the area.     

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.     

TIME-DOMAIN ELECTROMAGNETIC SOUNDING—COMPUTATION OF MULTI-LAYER RESPONSE AND THE PROBLEM OF EQUIVALENCE IN INTERPRETATION*

Computations of the time-domain electromagnetic response of a multi-layered earth have been carried out for different source-receiver coil systems. The primary excitation is a train of half-sinusoidal waveforms of alternating polarity. The conversion into the time-domain involves Fourier series summation of the matched complex mutual coupling ratios of the layered earth models computed by a digital linear filter method. As an example, the response of a perpendicular coil system on the ground surface for two source-receiver separations has been presented for a five-layer earth model. This has been compared with the responses of homogeneous, two-layer, three-layer, and four-layer models. Next, the investigations have been extended to study the problems of equivalence of three-layer models, the intermediate layer of which is either conductive or resistive. For an intermediate conductive layer (H-type), the studies show that in the early portion of the signal the interpretation of a true three-layer earth is possible to some extent, whereas the ambiguity due to equivalence persists in the late samples. On the other hand, for an intermediate resistive layer (K-type), the three-layer earth and its equivalent model cannot be distinguished from each other over the entire sampling period. On the basis of a computational approach, equivalence has been empirically established as √h/ρ=constant for H-type earth-sections, and as h²ρ=constant for K-type earth sections, where h and ρ are respectively the thickness and resistivity of the intermediate layer.     

GEOELECTRICAL SURVEYS OF DIPPING STRUCTURES1

Among resistivity methods, models containing two dipping discontinuity surfaces with a conductive medium between them have been considered in this study. The theoretical apparent resistivity curves obtained for such models were calculated using Alfano's integral equation for various dip angles of planes at different array distances from the contacts. The results obtained showed that it is possible to achieve the dip values of the discontinuities under particular conditions, but ambiguities cannot be ruled out.