2D and 3D resistivity inversion of Schlumberger vertical electrical soundings in Wadi El Natrun,Egypt: A case study

The Wadi El Natrun area is characterized by a very complicated geological and hydrogeological system. 45 vertical electrical soundings (Schlumberger array) were measured in the study area to elucidate the peculiarity of this unique regime, specifically the nature of waterless area. 2D and 3D resistivity inversion based on the finite element technique and regularization method were applied on the data set. 2D and 3D model resolution was investigated through the use of the Depth and Volume of Investigation Indexes. A very good matching was found between the zones of high resistivity, the waterless area, and the non-productive wells. The low resistivity zones (corresponding to Lower Pliocene clay) were also identified. The middle resistivity fresh water aquifer zones were recognized. Available results can assist in the aquifer management by selecting the most productive zone of groundwater.     

3D FD resistivity modelling and sensitivity analyses applied to a highly resistive phonolitic body

A highly resistive phonolitic body near Sainerholz / Westerwald in Germany has been investigated for geological mapping using vertical electrical soundings in a Schlumberger configuration. Because of its explicitly three-dimensional shape, conventional 1D and 2D interpretation techniques are not applicable. Therefore, a new 3D finite-difference forward modelling algorithm has been applied to acquire information about its subsurface structure and to explain the observed data. This investigation focuses on two exposed soundings: one located near the centre of the body and the other close to its rim. For the interpretation, data from electromagnetic measurements on the lateral extension of the body are additionally taken into account as well as geological a priori information. A possible 3D conductivity model is presented and evidence for its validity is discussed using model studies and sensitivity analyses. The latter are carried out using a newly developed 3D FD sensitivity modelling code with which the total subsurface response can be decomposed. This permits the determination of the resolution of model parameters, indicating the contribution of different parts of the model to the overall response. The results emphasize the feasibility of 3D forward modelling in practice.     

THE INFLUENCE OF LATERAL INHOMOGENEITIES ON THE DIPOLE METHODS*

The theory of electrical dipole soundings proved that this method can produce resistivity measurements, which are comparable with those obtained by electrical soundings of the Wenner or Schlumberger type. Their main advantage is the use of short cable lengths, which is important if the depth of penetration should be large. A considerable disadvantage of the dipole method is the great sensitivity to lateral discontinuities. Though these have an influence on the Schlumberger arrangement as well, they can disturb a dipole sounding to such an extent than an interpretation based on a horizontal layer case is no more possible. There are six different dipole arrays, which differ from each other with respect to the angle enclosed by the two dipole orientations-the current dipole AB and the measuring dipole MN. The theoretical comparison of the dipole arrays with the Schlumberger array concerning their sensitivity to lateral discontinuities is a useful basis for the choice of the most suitable configuration. Considering geological subsurface conditions the right choice of a dipole array can give an optimal result, i.e. a dipole sounding for which the sensitivity to lateral discontinuities is as small as possible under the given circumstances.     

Detecting lateral resistivity inhomogeneities with the Schlumberger array

A method of detecting lateral resistivity inhomogeneities with a multi-electrode cable for the Schlumberger array is presented. Using such a cable system, two dipole-dipole soundings are gathered in addition to the Schlumberger sounding at each point. Offset differences calculated from the dipole-dipole data give qualitative information about lateral resistivity inhomogeneities. Results from 1D modelling can give quantitative information about the 2D resistivity distribution since the dipole-dipole soundings are made to either side of the Schlumberger sounding point. Examples from two different locations in Norway are shown. At Reinøya, northern Norway, a dipping layer, confirmed by refraction seismic data, was identified. In a sedimentary basin with a contamination plume at Haslemoen, southern Norway, the method has revealed lateral variations in resistivity. In both cases, the Schlumberger soundings could be fitted with a 1D resistivity model.     

Delineation of Near-Surface Structure in the Southern Part of 15th of May City, Cairo, Egypt Using Geological, Geophysical and Geotechnical Techniques

The integration of geological, geophysical, and geotechnical interpretation at the southern part of 15th of May City, have been used to evaluate the subsurface stratigraphy, especially the clay layer which may cause serious danger to construction. Those techniques have been used to delineate the subsurface structures as normal faults, which play a critical role on the stability of buildings. Geological setting of the area has been evaluated through the construction of a geological map from different geological sections and samples obtained from more than 30 observation points. Geophysical tools such as vertical electrical soundings (12 VESs), 2-D dipole–dipole array (7 sections), P-wave shallow seismic refraction (31 profiles) and multiple channel analysis of surface waves (31 MASW profiles) have been carried out to image the subsurface situation. Geotechnical evaluation using 26 boreholes, samples, laboratory tests and geotechnical parameters has been done at the area of interest. The geological setting demonstrates that the city had been constructed on the second and third members of Qurn Formation (Upper Eocene) composed of argillaceous limestone, marl and shale. Two normal faults are passing through the area were observed. The resistivity (VES and dipole–dipole) and seismic (P-waves and MASW) results reflect the presence of the two normal faults cross the study area, affecting the obtained section of marl, clayey marl and limestone layers. The geotechnical information indicate the presence of the normal faults and the existence of clay layer with swelling ability reaching 140%, which may cause cracks in the upper layers and/or subsidence.     

Correlation of vertical electrical sounding and electrical borehole log data for groundwater exploration

We have correlated the longitudinal unit conductance CL obtained from interpreted vertical electrical sounding data with the formation resistivity R_t and the formation resistivity factor F, obtained by carrying out electrical borehole logging. Interpreted geophysical data of eleven soundings and two electrical borehole log records are used for the analysis. The geophysical data used were acquired in a sedimentary basin. The study area is called Lower Maner Basin located in the province of Andhra Pradesh, India. Vertical electrical soundings were carried out using a Schlumberger configuration with half current electrode separation varying from 600–1000 m. For logging the two boreholes, a Widco logger‐model 3200 PLS was used. True formation resistivity R_t was calculated from a resistivity log. Formation resistivity factor F was also calculated at various depths using R_t values. An appreciable inverse relation exists between the correlated parameters. The borehole resistivity R_t and the formation resistivity factor F decrease with the increase in the longitudinal unit conductance CL. We have shown the use of such a relation in computing borehole resistivity R_t and formation resistivity factor F at sites that posses only vertical electrical sounding data, with a fair degree of accuracy. Validation of the correlation is satisfactory. Scope for updating the correlation is discussed. Significance and applications of the relation for exploration of groundwater, namely to update the vertical electrical sounding data interpretation by translating the vertical electrical sounding data into electrical borehole log parameters, to facilitate correlations studies and to estimate the porosity (φ), permeability (K) and water saturation S_w of water bearing zones are discussed.     

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.     

INTERPRETATION OF RESISTIVITY MEASUREMENTS OVER 2D STRUCTURES1

Resistivity measurements were carried out in a survey area in the south of Germany. This area is characterized by complicated subsurface geology. Schlumberger full-arrays and their respective half-arrays were recorded simultaneously. The results obtained by the one-dimensional (1D) interpretation of the full-array measurements were incorrect because of a resistivity discontinuity. This discontinuity, under a relatively thick overburden, could only be located by the half-array soundings. Its exact location and the resistivity distribution in the subsurface were ascertained by comparing the sounding curves with 2D model curves, which are calculated by a finite-difference method.     

Investigating changes of electrical characteristics of the saturated zone affected by hazardous organic waste

The Picillo Farm, EPA Superfund Site, in western Rhode Island was an unauthorized disposal site of hazardous organic chemicals. Predominantly organic contaminants have entered an aquifer comprised of layered glacial deposits and fractured bedrock and spread past the site boundaries with groundwater flow. Hydraulic conductivities in the glacial deposits range over two orders of magnitude and fractures and faults in the granitic bedrock further complicate the spreading of contaminants. Monitoring wells delineate two plumes that extend towards a fault-controlled valley with lakes and wetlands; one to the northwest and the other to the southwest. In this investigation we studied the electrical characteristics of both plumes.One dimensional Schlumberger depth soundings were conducted along several profile lines over the plumes and compared to those over non-contaminated sections of the site. With regard to the southwestern plume, high formation factors (ratio of bulk layer to pore water resistivity) between 12 and 45 were observed compared to values between 2.5 and 7.7 measured over the non-contaminated sections. Also, high values (> 5) of vertical electrical anisotropy (ratio of geoelectrically determined depth to high resistivity bedrock to drilled depth to bedrock) were measured over the contaminated part of the site. These values are extremely high compared to other non-contaminated sites (range: 2 to 3) in glacial stream channels of southern Rhode Island. Geoelectric measurements were affected by lateral effects. However, the consistency of high formation factors (11 to 35) and high vertical anisotropies (3 to 5) over the southwestern plume in comparison to low formation factors (3 to 8) and vertical anisotropies (1 to 1.5) over non-contaminated sites represents a marked difference between both sites. Overall, the Schlumberger depth soundings are less susceptible to near-surface lateral inhomogeneities than expected from other geoelectrical methods. Also, the disadvantage of a 1D interpretation was compensated by estimating resistivity and thickness ranges within the concept of non-uniqueness using the Dar Zarrouk parameters (Maillet, R., 1947. The fundamental equations of electrical prospecting. Geophysics, 12(4): 529–556.).The results over the northwestern plume, i.e. an area with higher contaminant concentration than the southwestern plume, were mixed and showed no consistent trends. Predominantly reducing conditions, as indicated by the presence of soluble ferric (FeII) iron hydroxides in ground water samples, increased the electrical conductivity. This is believed to have compensated the effect of high formation factors on the bulk saturated layer resistivity within the affected area.     

GEOELECTRICAL MODEL CALCULATIONS FOR TWO-DIMENSIONAL RESISTIVITY DISTRIBUTIONS*

For the calculation of geoelectrical model curves for a two-dimensional resistivity distribution, the potential equation is transformed by means of a Fourier cosine transform into a two-dimensional Helmholtz equation containing the separation parameter λ. The numerical solution of this equation for different values of λ for an irregular grid is obtained using the method of finite differences combined with the method of overrelaxation. The method by which derivatives are replaced by finite differences turned out to be very important, especially for high resistivity contrasts. After testing several methods designed to deal with any type of resistivity distribution, a method of discretization similar to that used by Brewitt—Taylor and Weaver (1976) for magnetotelluric modeling for H polarization was found the best. Examples are given of model curves for Schlumberger soundings over a vertical fault covered by overburden. The incorrect use of horizontal-layer models leads to erroneous interpretations that are more complex than the real subsurface situations.     

Geophysical surveys in Parvati valley geothermal field, Kullu, India

Direct current resistivity surveys and shallow temperature measurements were carried out for geothermal exploration in a part of Parvati valley, goethermal field, Himachal Pradesh, India. At a few places, the Schlumberger soundings pointed to the presence of a relatively low-resistivity shallow layer, which probably represents fractured and jointed quartzite, saturated with hot/cold water. Wenner resistivity profiles indicate the presence of some possible shallow subsurface lateral hot water channels across the valley at Manikaran. Shallow temperature measurements show a good subsurface thermal anomaly near the confluence of the rivers Brahmaganga and Parvati. The results of the survey, together with other available geodata, suggest that an anomalous heat source does not lie beneath the study area.It is postulated that the meteoric water, originating at high elevations after heating as a result of circulation at depth, emerges at the surface in the Parvati valley as hot springs, after mixing in various proportions with near surface cold waters.     

ELECTRICAL SOUNDING OF A HALF-SPACE WITH A MONOTONIC CONTINUOUS VARIATION OF THE RESISTIVITY WITH DEPTH*

The interpretation of electrical sounding data for a subsurface with monotonic continuous variation of the resistivity with depth is becoming increasingly necessary. The contribution of this article is the derivation of the solution for the Wenner and the Schlumberger apparent resistivity functions for a resistivity varying as a real power of a linear positive function of the depth. The interpretation of sounding data in these cases can be used to estimate the variation of the porosity or the salt content of the pore water with depth.     

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.     

THE INTERPRETATION OF THE VERTICAL FAULT PROBLEM IN GEOELECTRICS USING HANKEL INTEGRAL*

It is shown how to interpret, without curve-matching, Schlumberger resistivity soundings carried out with the array parallel to the surface trace of a vertical boundary plane separating two media with different resistivities (the vertical fault problem). To this end, it is demonstrated that the apparent resistivity function can be expressed as an Hankel-transformable integral that allows to invert the apparent resistivity curve into an associated resistivity transform curve. The study of the asymptotical properties of this function and of some mathematical properties of a related reduced transform function allows to realize a simple procedure for deriving the parameters of the model. In practice, this procedure consists in fitting a straight-line to a semi-logarithmic plot of the reduced transform function and in evaluating the intercept along the vertical axis and the slope.     

Neogene aquifer properties specified through the interpretation of electrical sounding data,Salamiyeh region,central Syria

Twenty‐nine Schlumberger electrical soundings were carried out in the Salamiyeh region in Syria using a maximum current electrode separation of 1 km. Three soundings were made at existing boreholes for comparison. Aquifer parameters of hydraulic conductivity and transmissivity were obtained by analysing pumping test data from the existing boreholes. An empirical relationship between hydraulic conductivity determined from the pumping test and both resistivity and thickness of the Neogene aquifer has been established for these boreholes in order to calculate the geophysical hydraulic conductivity. A close agreement has been obtained between the computed hydraulic conductivity and that determined from the pumping test. The relationship established has, therefore, been generalized in the study area in order to evaluate hydraulic conductivity and transmissivity at all the points where geoelectrical measurements have been carried out. This generalization allows one to derive maps of the hydraulic conductivity and transmissivity in the study area based on geoelectrical measurements. These maps are important in future modelling processes oriented towards better exploitation of the aquifers. Copyright © 2006 John Wiley & Sons, Ltd.     

USE OF ELECTRICAL RESISTIVITY METHODS FOR THE STUDY OF COAL SEAMS IN PARTS OF THE RANIGANJ COALFIELD (INDIA)*

The surface resistivity method has been used to study a few exposed coal seams located in the northwestern part of the Raniganj Coalfield (belonging to the Damodar Valley Gondwana basin), India. Different electrode configurations, viz., Wenner, two-electrode and half-Schlumberger, have been used with different electrode spacings in horizontal profiling. The vertical distribution of resistivity has been studied using Schlumberger configuration at different locations along the profile. Laboratory studies of resistivity (at partial to full water saturation conditions) and porosity of different coal, shaly sandstone and sandstone samples of the survey area had already been carried out before the field survey. The results indicated the presence of a good resistivity contrast between the coal seams and the surrounding formations. The field results did not bear this out: the resistivity responses of the coal formations on the profiles and sounding curves are not as clear as one would expect for such high contents. The Wenner profiles show a broad resistivity anomaly over the coal seams. Two-electrode profiles are less noisy than Wenner profiles. Sharp peaks have been observed over the coal seams. The half-Schlumberger configuration seems the best: all the coal seams and their edges can be accurately outlined on the resistivity curves. Borehole data close to the profile have been used for correlating the field results. There is good agreement with vertical electrical soundings.     

DC resistivity methods for determining resistivity in the earth's crust

The use of Schlumberger and dipole arrays for crustal-scale resistivity soundings is considered. Advantages and disadvantages of the two methods are described. The depth to which resistivity may be determined from field measurements is discussed as well as the determination from the sounding curves of various parameters associated with layered structure. The interpretation of experimental data using reference curves as well as two approaches used in computer assisted interpretation are discussed.     

A Bayesian trans-dimensional approach for the fusion of multiple geophysical datasets

We propose a Bayesian fusion approach to integrate multiple geophysical datasets with different coverage and sensitivity. The fusion strategy is based on the capability of various geophysical methods to provide enough resolution to identify either subsurface material parameters or subsurface structure, or both. We focus on electrical resistivity as the target material parameter and electrical resistivity tomography (ERT), electromagnetic induction (EMI), and ground penetrating radar (GPR) as the set of geophysical methods. However, extending the approach to different sets of geophysical parameters and methods is straightforward. Different geophysical datasets are entered into a trans-dimensional Markov chain Monte Carlo (McMC) search-based joint inversion algorithm. The trans-dimensional property of the McMC algorithm allows dynamic parameterisation of the model space, which in turn helps to avoid bias of the post-inversion results towards a particular model. Given that we are attempting to develop an approach that has practical potential, we discretize the subsurface into an array of one-dimensional earth-models. Accordingly, the ERT data that are collected by using two-dimensional acquisition geometry are re-casted to a set of equivalent vertical electric soundings. Different data are inverted either individually or jointly to estimate one-dimensional subsurface models at discrete locations. We use Shannon's information measure to quantify the information obtained from the inversion of different combinations of geophysical datasets. Information from multiple methods is brought together via introducing joint likelihood function and/or constraining the prior information. A Bayesian maximum entropy approach is used for spatial fusion of spatially dispersed estimated one-dimensional models and mapping of the target parameter. We illustrate the approach with a synthetic dataset and then apply it to a field dataset. We show that the proposed fusion strategy is successful not only in enhancing the subsurface information but also as a survey design tool to identify the appropriate combination of the geophysical tools and show whether application of an individual method for further investigation of a specific site is beneficial.     

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.     

A multiscale electrical survey of a lateritic soil system in the rain forest of Cameroon

Resistivity investigations were carried out on an elementary watershed in SW Cameroon, firstly to assess the applicability of direct-current (DC) resistivity methods to solve various pedological problems in intertropical regions, and subsequently to determine the relationships between electrical resistivities and pedological properties of lateritic soil systems. The survey included measurements in pits with a small Wenner fixed-spacing array (SWA), vertical electrical soundings (VES) and vertical electrical “quick soundings” (VEQS) both using the Schlumberger configuration. The VES data were interpreted using a conventional multilayer inversion program to obtain best-fit models. Constraints to the interpretation of these data were provided by SWA and pedological information from existing observation pits. The results of the interpretation reveal five distinct geoelectrical layers overlying a resistive bedrock. The first is a thin organo-mineral upper layer with low resistivities in the range 250–450 Ωm. The second layer corresponds to micro-aggregated clayey materials and is more resistive (1300–1800 Ωm). The third represents the main part of ferruginous materials and is even more resistive (2000–4500 Ωm). The fourth corresponds to unsaturated saprolite and the last to saturated saprolite (ground water) with resistivities ranging from 800 to 1500 Ωm and from 150 to 250 Ωm, respectively. Estimates of soil volumes for the entire study area were obtained from VEQS interpretations. Most of the soil cover corresponds to saprolite (74%, being saturated by ground water), while topsoil and ferruginous materials represent 14 and 12%, respectively. Finally, geophysical results based upon 1-D inversion provide a satisfactory approximation of the various lateritic components' 3-D geometry over the watershed. The study provides original quantitative results concerning the behaviour of intertropical soil systems as well as some geomorphological keys for soil mapping at a regional scale.