THE QUANTITATIVE INTERPRETATION OF DIPOLE SOUNDINGS BY MEANS OF THE RESISTIVITY TRANSFORM FUNCTION*

In this paper a theorem is demonstrated which allows—after the introduction of a suitable dipole kernel function or dipole resistivity transform function—to write the apparent resistivity function as an Hankel transformable integral expression. As a practical application of the theorem a procedure of quantitative interpretation of dipole soundings is suggested in which the dipole resistivity transform function obtained after inversion of the original dipole apparent resistivity data is used to control the goodness of the set of layering parameters which have been derived with our previous method of transformation of dipole sounding curves into equivalent Schlumberger diagrams.     

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 AUTOMATIC FITTING OF A RESISTIVITY SOUNDING BY A GEOMETRICAL PROGRESSION OF DEPTHS *

The problem of interpretation of geoelectrical resistivity soundings has been studied and a compromise method of interpretation developed. A simple depth sequence of increasing bed thickness is taken and resistivities assigned to the various layers so that a good fit is obtained to the observed apparent resistivity curve. An initial estimate of the resistivities is made by a direct method but the model is then altered to give an improved fit by the indirect method of curve matching. The whole method is computerized and input data to the computer program consists of spacings and apparent resistivities. The method is extremely rapid, about one third of the computation time is devoted to obtaining the resistivity transform by the method of convolution. A normal type of solution, incorporating additional information if necessary, can also be obtained.     

Theoretical study of slope effects in resistivity surveys and applications

When electric soundings are made over an irregular terrain, topographic effects can influence the values of apparent resistivity and lead to erroneous 1D interpretation. A 3D finite-element method has been applied to study the topographical effect of a slope on Schlumberger soundings parallel to the strike. When the resistivity survey is performed at the top of the slope, the apparent resistivity values can be two times higher than in the flat-earth case, depending on the angle (α) and height (H) of the slope, and on the distance (X) between the sounding and the slope top. The results are presented as nondimensional curves which can be used for evaluating topographic anomalies for any value of the parameters α, H and X. It is numerically shown that the topographic effects can be removed from measurements on horizontally layered structures with an irregular earth surface. Real measurements were performed in different geological conditions over an irregular terrain. The correction method based on the nondimensional curves has been applied to the data and has enabled the determination of the correct layered ground configuration using 1D interpretation.     

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.     

DEFINITION AND APPLICATION OF THE FREQUENCY -EFFECT TRANSFORM FUNCTION TO THE INTERPRETATION OF IP SOUNDINGS*

This paper deals with a new method of quantitative interpretation of induced polarization soundings in the frequency-domain. From the general expression of the apparent frequency-effect for soundings carried out on a multi-layered earth the application of Hankel's inversion theorem allows to introduce a new function, called here the “frequency-effect transform”. The new interpretation method consists of two steps: 1) the inversion of field data to obtain the frequency-effect transform graph and 2) the analysis of this graph to derive the layering parameters. The first step is performed by means of a slightly revised version of a simple numerical procedure, previously suggested by the author for the inversion of d.c. resistivity sounding data. The second step is carried out by a complete curve-matching procedure, applied directly on the transform graph. This implies suitable master curves, whose preparation doesn't meet all the mathematical difficulties which are present when preparing master curves of the apparent frequency-effect function.     

A NUMERICAL COMPUTATION PROCEDURE FOR THE DIRECT INTERPRETATION OF GEOELECTRICAL SOUNDINGS*

In this paper a numerical method of direct interpretation of geoelectrical soundings is described. It has similarities with already existing direct methods, but owing to its simplicity and, in particular, to the possibility of applying it also without digital computers, it proves useful mostly in the field, where very often an accurate method for the interpretation of multi-layer curves is required. The direct interpretation system splits up into three steps: i) the evaluation of the resistivity transform after application of Hankel's inversion theorem; ii) the determination of the layer distribution after application of Koefoed's recurrent procedure; iii) the control of the solution. Each step is considered and the practical procedures suggested. Finally two field examples are presented and discussed.     

TRANSFORMATION OF DIPOLE RESISTIVITY SOUNDING MEASUREMENTS OVER LAYERED EARTH BY LINEAR DIGITAL FILTERING *

The technique of linear digital filtering as developed for the direct interpretation of Schlumberger and Wenner soundings (Ghosh 1971) has been applied here for the derivation of the resistivity transform function from the field dipole measurements as the first step in directly interpreting dipole data. Filter coefficients for this transformation have been worked out for the radial-polar, perpendicular and parallel (30°) arrays of dipole sounding. The procedure combines speed with accuracy.     

MAGNETO-TELLURIC EXPERIMENTS IN NORTHERN FINLAND *

Magneto-telluric experiments were performed in August 1974 in the Muhos Jotnian sedimentary formation and the Koillismaa Precambrian basement complex by the Centre de Recherches Géophysiques, Garchy, and the Department of Geophysics, University of Oulu, employing the “Résistivimètre magnéto-tellurique”, an instrument which permits apparent resistivity values to be observed at eight pre-selected frequencies between 8–1700 Hz. Preliminary soundings were made on the Muhos formation and on its surroundings, after which a magneto-telluric profile was measured involving eleven sites on a line 13 km long extending across the formation. Some further soundings were made at certain sites of known stratigraphy. The resistivity values in the sedimentary formation were found to vary between 10 ωm and 200 ωm, while those in the basement were markedly higher. This resistivity contrast suggests that the method seems to be suitable for delimiting the sedimentary formation. Soundings made on the basement at Koillismaa show apparent resistivity values in the range 1000–20000 ωm. The interpretation of these soundings was in agreement with other, independently obtained geophysical results.     

Airborne VLF measurements and mapping of ground conductivity in Sweden

Airborne VLF data are routinely collected by The Geological Survey of Sweden (SGU) as part of its bedrock mapping programme. In this paper we demonstrate that the novel Tensor VLF technique developed at Uppsala University and SGU can provide useful qualitative and quantitative information about the electrical conductivity distribution in the upper few hundred meters. Single transmitter scalar VLF maps emphasize those conductive structures that have dominant strikes in the direction of the transmitter. The tensor tipper (essentially the vertical magnetic field from currents along the strike direction) calculated from multiple transmitters is dependent only upon the underlying conductivity structure. Transformation of the tipper into the peaker (the horizontal divergence) has proven to enhance the lateral resolution while the transformation to the apparent resistivity can be used to discriminate different rock types. Two case histories from the application of VLF data are presented in this study. Two dimensional structures can be quantitatively modelled by modern inversion methods developed originally for deep electromagnetic MT soundings. Direct inversion of the real and imaginary parts of the tipper provides more quantitative information about the subsurface resistivity distribution.     

Mapping Coastal Aquifers by Joint Inversion of DC and TEM Soundings-Three Case Histories

Electrical and electromagnetic methods are well suited for coastal aquifer studies because of the large contrast in resistivity between fresh water-bearing and salt water-bearing formations. Interpretation models for these aquifers typically contain four layers: a highly resistive unsaturated zone; a surficial fresh water aquifer of intermediate resistivity; an underlying conductive, salt water saturated aquifer; and resistive substratum. Additional layers may be added to allow for variations in lithology within the fresh water and salt water layers. Two methods are evaluated: direct current resistivity and time domain electromagnetic soundings. Use of each method alone produces nonunique solutions for resistivities and/or thicknesses of the different layers. We show that joint inversion of vertical electric and time domain electromagnetic soundings produces a more tightly constrained interpretation model at three test sites than is produced by inversion methods applied to each data set independently.     

THE USE OF FILTERED BESSEL FUNCTIONS IN DIRECT INTERPRETATION OF GEOELECTRICAL SOUNDINGS *

We start from the Hankel transform of Stefanescu's integral written in the convolutionintegral form suggested by Ghosh (1971). In this way it is possible to obtain the kernel function by the linear electric filter theory. Ghosh worked out the sets of filter coefficients in frequency domain and showed the very low content of high frequencies of apparent resistivity curves. Vertical soundings in the field measure a series of apparent resistivity values at a constant increment Δx of the logarithm of electrode spacing. Without loss of information we obtain the filter coefficient series by digital convolution of the Bessel function of exponential argument with sine function of the appropriate argument. With a series of forty-one values we obtain the kernel functions from the resistivity curves to an accuracy of better than 0.5%. With the digital method it is possible to calculate easily the filter coefficients for any electrode arrangement and any cut-off frequency.     

A 3D resistivity model derived from the transient electromagnetic data observed on the Araba fault,Jordan

72 inloop transient electromagnetic soundings were carried out on two 2 km long profiles perpendicular and two 1 km and two 500 m long profiles parallel to the strike direction of the Araba fault in Jordan which is the southern part of the Dead Sea transform fault indicating the boundary between the African and Arabian continental plates. The distance between the stations was on average 50 m.The late time apparent resistivities derived from the induced voltages show clear differences between the stations located at the eastern and at the western part of the Araba fault. The fault appears as a boundary between the resistive western (ca. 100 Ωm) and the conductive eastern part (ca. 10 Ωm) of the survey area. On profiles parallel to the strike late time apparent resistivities were almost constant as well in the time dependence as in lateral extension at different stations, indicating a 2D resistivity structure of the investigated area.After having been processed, the data were interpreted by conventional 1D Occam and Marquardt inversion. The study using 2D synthetic model data showed, however, that 1D inversions of stations close to the fault resulted in fictitious layers in the subsurface thus producing large interpretation errors. Therefore, the data were interpreted by a 2D forward resistivity modeling which was then extended to a 3D resistivity model. This 3D model explains satisfactorily the time dependences of the observed transients at nearly all stations.     

A simple direct interpretation method for an electrical sounding carried out over an inclined interface

Summary The potential field due to a point electrode, above an inclined interface, has been given in the form of a multiple integral, involving modified Bessel functions of the second kind (Skalskaya [9]²). From this formula it is only possible to derive formulae, from which type curves may be computed, for a limited number of cases. By considering the asymptotic expansion of the Hankel transform of this potential function, it is possible to derive results which will permit the complete interpretation of a Schlumberger sounding, carried out in the direction of strike; for an arbitrary angle of dip of the contact. The method of interpretation is suitable for use on a digital computer and has been found to give rapid and reliable results.     

Lateral and topographic effects in geoelectric soundings

Several two-dimensional structures are modelled for vertical electrical soundings in arrays parallel and perpendicular to the strike of the structure. The models are a horst and a graben within a three-layer medium, a cliff over two layers, and heterogeneities around the electrodes. Apparent resistivity curves are shown for different model parameters and different distances to the two-dimensional structures. Some of the features on the shape of these curves are inflections that may be misinterpreted as fictitious layers, of slopes greater than 45°; some features are simply anomalous peaks. One-dimensional interpretation of a two-dimensional graben model has been performed, in order to show typical errors when 2D structures are interpreted as one-dimensional. A real case corresponding to a landfill near Barcelona and showing strong lateral and topographic effects is presented. This represents combined effects of the above theoretical 2D models.     

COMPUTATION OF THE ELECTRIC POTENTIAL IN THREE-DIMENSIONAL STRUCTURES*

A method has been developed for computation of the electrical DC potential of an arbitrary three-dimensional resistivity structure using a finite difference method. The threedimensionality is necessary for interpretation of geoelectrical soundings with controlled point sources over a laterally inhomogeneous medium. Lateral inhomogeneities should be considered in resistivity soundings with large layouts. The results obtained with the described method permit a more realistic representation of geological features. The resolution of the method is determined by the number of elements in the resistivity network. The problem of core memory space has been resolved by using random access disc files. The results computed using a Fortran program are in good agreement with analytically obtained solutions.     

PROGRESS IN THE DIRECT INTERPRETATION OF RESISTIVITY SOUNDINGS: AN ALGORITHM*

An algorithm is presented for the direct interpretation of resistivity sounding data. The algorithm is based on the method of successive reductions to lower boundary plane of the resistivity transform function. A novel aspect of the algorithm is that error limits are assigned to the initial values of the resistivity transform, and these error limits are carried through in all the subsequent computations. The width of the error range is then used as the basis for assigning weight factors in the final computation of thicknesses and resistivities of the layers. The errors in the resistivity transform derived from the solution given by the algorithm are usually not more than twice as large as those in the original data.     

2D modelling of resistivity and magnetotelluric data from the Belvedere Spinello salt mine,Italy1

The Belvedere Spinello salt mine is located in the Catanzaro Province of Calabria in Southern Italy. An extensive mining program has caused the development of Underground cavities filled with brine and the migration of this brine has been of great environmental concern to the mine owners. This paper presents the results of a multidimensional interpretation of a two-phase resistivity and magnetotelluric (MT) survey that was performed in an attempt to determine the complex conductivity structure of the mine area and to gain information on brine development and migration pathways. Key resistivity soundings were interpreted using a 2.5D algorithm based on the Polozhii decomposition method. The MT data were interpreted using a 2D finite-element code. A conductivity model was developed, integrating available geological and drill-hole information. The interpretation of the MT data, collected five years after the acquisition of the resistivity data, shows a conductive feature of depth that is not resolved in the resistivity interpretation. This feature has been interpreted as a thick brine zone that has developed as a result of mining during the interval between the resistivity and the MT measurements.     

Exploration of the extension of two lava tubes,faults and dikes using very low frequency-electromagnetic technique in NE Jordan

The very low frequency-electromagnetic (VLF-EM) technique was used to delineate two sub-parallel lava tubes, faults and dikes in Umm El-Quttein area, NE Jordan. The investigation of the lava tubes was conducted through 22 VLF-EM profiles across lava strike; the length of profiles ranged from 700 to 1700 m. The lava tubes outcrop at two sites: Azzam cave and Al-Howa tunnel, characterized by slightly weathered basalt, columnar joints and fissure zones; qualitative interpretation of Fraser and Karous-Hjelt maps differentiate those zones as linear, elongated and circular anomalous zones. The 2-D tipper inversion of VLF-EM data and resistivity imaging had the potential to screen out three anomalous zones of likely resistivity contrast: the lava tube body with resistivity over 2500 Θ·m, the fractured zones with resistivity less than 500 Θ·m, and the host vesicular basalt with resistivity of 1500 Θ·m. The strike of lava tubes varied from SW to NE direction with depth less than 20 m and width from 10 to 30 m.     

The theory of the continuous wavelet transform in the interpretation of potential fields: a review

We consider the use of the continuous wavelet transform in the interpretation of potential field data. We report its development since the publication of the first paper by Moreau et al . in 1997. Basically, it consists in the interpretation in the upward continued domain since dilation of the wavelet transform is the upward continuation altitude. Thus within a range of altitudes, the wavelet transform of the noise is decreased faster than the wavelet transform of the potential field caused by underground sources; this means that the signal-to-noise ratio is much better than those involved in other enhancing methods (e.g., Euler deconvolution, gradient analysis, or the analytic signals). Similarly to the Euler deconvolution, its first target parameters were the source positions and shape. The method has then been developed to estimate size and directions of extended sources (e.g., faults and dikes of finite dimensions) and also the magnetization direction in the case of magnetic data. Latest developments show that when combined with a Radon transform, the continuous wavelet transform can help in the automatic detection of elongated structures in 3D, simultaneously to the estimation of their strike direction, shape and depth. Several applications to real case studies have been shown before; however for clarity's sake in the present paper, only synthetic cases have been reproduced to clearly sum up the development of the methodology.