CENTRAL FREQUENCY SOUNDING IN SHALLOW ENGINEERING AND HYDRO-GEOLOGICAL PROBLEMS*

The paper deals with the early stages of development of a convenient form of electromagnetic induction method of sounding referred to as ‘Central Frequency Sounding’ and abbreviated as CFS. The method is introduced as a rapid and useful technique for investigation of shallow engineering and hydro-geological problems. Sets of theoretical two-layer master curves, suitable for interpretation of field data involving measurement of the vertical magnetic component of the field induced at the center of a loop placed on a two-layer earth, have been presented. The approximate but reasonably accurate solutions for a two-layer earth of any arbitrary resistivity contrast have been considered for the purpose and expressed in a form suitable for computation. The computed results have been presented in sets of curves useful for interpretation of field data.     

Electrical Struture of the Crust in Manas Earthquake Area,Xinjiang,China

Magnetotelluric sounding data obtalned recently in Manas earthquake area were processed. Inthe result, curves of apparent resistivity, impedance Phase, skewness and optimum rotationangle versus period and the real magnetic induction vectors were obtained. Then the data ofall measuring points were interpreted by 2D automatic inversion. The result indicates thatalong the sounding profile the shallow crust can be divided into 5 segments and the deep crustcan be divided into 3 segments, with faults or deep-seated fault zones as the contactboundaries between them. The sedimentary cover along the profile extents down to depthabout 12 km in maximum and a low-resistivity body exists in the crust in southern section ofthe profile. The interpretation results are well consistent with geological and othergeophysical data. The Manas M7. 7 earthquake occurred near a contact zone where theelectrical structure of the crust sharply changes.     

Results of Crust and Mantle Soundings in Central and Northern Europe in the 21st Century (Review)

The first decade of 21st century is characterized by the appearance of new approaches to deep induction soundings. The theory of magnetovariation and magnetotelluric soundings was generalised or corrected. Spatial derivatives of response functions (induction arrows) were obtained for the ultra-long periods. New phenomena have been detected by this method: secular variations of the Earth’s apparent resistivity and the rapid changes of induction arrows over the last 50 years. The first one can be correlated with the number of earthquakes, and the second one–with geomagnetic jerks in Central Europe. The extensive studies of geoelectrical structure of the crust and mantle were realized in the frame of a series of international projects. New information about geoelectrical structures of the crust in Northern Europe and Ukraine was obtained by deep electromagnetic soundings involving controlled powerful sources. An influence of the crust magnetic permeability on the deep sounding results was confirmed.     

Validation of joint inversion of direct current and electromagnetic measurements

One of the ways to improve the information content of a set of field data is that of combining the interpretation of disparate data sets. Electromagnetic and direct current resistivity methods suffer from inherent equivalence problem. Application of joint inversion for these measurements can overcome the problem of equivalence very well. In the present work, synthetic data from vertical electrical sounding (VES) and horizontal coplanar low-frequency induction sounding (EMHD) are inverted individually and jointly over different types of 1D earth structures. Global optimization with Monte Carlo Multistart algorithm was used in the calculations. The results obtained from the inversions of synthetic data indicate that the joint inversion significantly improves the solution reducing the ambiguity of the models.     

On the influence of DC railway noise on variation data from Belsk and Lviv geomagnetic observatories

Geomagnetic variation data from the observatories in Belsk (BEL, Poland) and Lviv (LVV, Ukraine) significantly suffer from disturbances caused by direct current (DC) electric railways. The aim of this study is to quantify the impact of these disturbances on quantities derived from such data, as the K index of magnetic activity and the induction arrow used in the geomagnetic deep sounding method to indicate lateral contrasts of electric conductivity in the solid earth. Therefore, undisturbed data have been reconstructed by means of a frequency-domain transfer function that relates the horizontal magnetic field components of the observatory to the ones synchronously recorded at a noise-free reference station. The comparison of the K index derived from original and reconstructed data shows an increase of quiet time segments by 29% for LVV and by 14% for BEL due to our noise removal procedure. Furthermore, the distribution of the corrected K indices agrees well with the one from the Niemegk observatory in Germany.     

An apparent-resistivity concept for low-frequency electromagnetic sounding techniques

Apparent resistivity is a useful concept for initial quickscan interpretation and quality checks in the field, because it represents the resistivity properties of the subsurface better than the raw data. For frequency‐domain soundings several apparent‐resistivity definitions exist. One definition uses an asymptote for the field of a magnetic dipole in a homogeneous half‐space and is useful only for low induction numbers. Another definition uses only the amplitude information of the total magnetic field, although this results in a non‐unique apparent resistivity. To overcome this non‐uniqueness, a complex derivation using two different source–receiver configurations and several magnetic field values for different frequencies or different offsets is derived in another definition. Using the latter theory, in practice, this means that a wide range of measurements have to be carried out, while commercial systems are not able to measure this wide range. In this paper, an apparent‐resistivity concept is applied beyond the low‐induction zone, for which the use of different source–receiver configurations is not needed. This apparent‐resistivity concept was formerly used to interpret the electromagnetic transients that are associated with the turn‐off of the transmitter current. The concept uses both amplitude and phase information and can be applied for a wide range of frequencies and offsets, resulting in a unique apparent resistivity for each individual (offset, frequency) combination. It is based on the projection of the electromagnetic field data on to the curve of the field of a magnetic dipole on a homogeneous half‐space and implemented using a non‐linear optimization scheme. This results in a fast and efficient estimation of apparent resistivity versus frequency or offset for electromagnetic sounding, and also gives a new perspective on electromagnetic profiling. Numerical results and two case studies are presented. In each case study the results are found to be comparable with those from other existing exploration systems, such as EM31 and EM34. They are obtained with a slight increase of effort in the field but contain more information, especially about the vertical resistivity distribution of the subsurface.     

Combined straightforward inversion of resistivity and induced polarization (time-domain) sounding data

It is proposed that the Straightforward Inversion Scheme (SIS) developed by the authors for 1D inversion of resistivity sounding and magneto-telluric sounding data can also be used in similar fashion for time-domain induced polarization sounding data. The necessary formulations based on dynamic dipole theory are presented. It is shown that by using induced polarization potential, measured at the instant when steady state current is switched off, an equation can be developed for apparent ‘chargeability–resistivity’ which is similar to the one for apparent resistivity. The two data sets of apparent resistivity and apparent chargeability–resistivity can be inverted in a combined manner, using SIS for a common uniform thickness layer earth model to estimate the respective subsurface distributions of resistivity and chargeability–resistivity. The quotient of the two profiles will give the sought after chargeability profile. A brief outline of SIS is provided for completeness. Three theoretical models are included to confirm the efficacy of SIS software by inverting only the synthetic resistivity sounding data. Then one synthetic data set based on a geological model and three field data sets (combination of resistivity and IP soundings) from diverse geological and geographical regions are included as validation of the proposal. It is hoped that the proposed scheme would complement the resistivity interpretation with special reference to shaly sand formations.     

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.     

Deep electromagnetic sounding of the lithosphere in the eastern Baltic (fennoscandian) shield with high-power controlled sources and industrial power transmission lines (FENICS experiment)

The paper addresses the technique and the first results of a unique experiment on the deep tensor frequency electromagnetic sounding, the Fennoscandian Electrical conductivity from results of sounding with Natural and Controlled Sources (FENICS). In the experiment, Energy-1 and Energy-2 generators with power of up to 200 kW and two mutually orthogonal industrial 109- and 120-km-long power transmission lines were used. The sounding frequency range was 0.1–200 Hz. The signals were measured in the Kola-Karelian region, in Finland, on Svalbard, and in Ukraine at distances up to 2150 km from the source. The parameters of electric conductivity in the lithosphere are studied down to depths on the order of 50–70 km. A strong lateral homogeneity (the one-dimensionality) of a geoelectric section of the Earth’s crust is revealed below depths of 10–15 km. At the same time, a region with reduced transverse crustal resistivity spread over about 80 000 square kilometers is identified within the depth interval from 20 to 40 km. On the southeast the contour of the anomaly borders the zone of deepening of the Moho boundary down to 60 km in Central Finland. The results are compared with the AMT-MT sounding data and a geodynamic interpretation of the obtained information is carried out.     

Some geoelectrical investigations for potential groundwater zones in part of Azamgarh area of U.P.

Summary The results of some electrical sounding measurements have been used for defining potential groundwater zones in part of Azamgarh district of Uttar Pradesh, India. The area covered is a part of gangetic alluvial tract. Aquifers consist of lenticular sand masses distributed within the alluvium. The ideal geoelectrical conditions, generally desired for the interpretation of resistivity curves, lack in the area. Among the number of layers encountered in lithologs, only a few are delineated by quantitative interpretation of the sounding data. A study of the total transverse resistance and longitudinal conductance for a particular depth of the alluvial column has helped in defining potential groundwater zones.     

Automated 1D interpretation of resistivity soundings by simultaneous use of the direct and iterative methods*

Noise contamination of measured data greatly affects the final results of inversion. Three types of noise source — random and systematic errors and the uncertainties due to the inadequacy of the mathematical model in representing the actual physical conditions — are discussed in the framework of resistivity sounding data. Two methods are proposed for describing these uncertainties. The first possibility is to smooth the measured data by a combination of simple fitting functions that satisfies the ‘1D smoothness’ criteria and consequently simulates the behaviour of a 1D Schlumberger apparent resistivity curve. The second method is to derive weight coefficients from the differences between the measured and the smoothed data sets. Both methods are carried out under the control of the interpreter. The relative merits and drawbacks of the direct and iterative interpretation methods used for the estimation of the parameters of the layered earth model are summarized. Two variants of the combination of these methods are presented to obtain more powerful and automatic interpretation schemes. In the sequential interpretation, an initial guess supplied by the direct method is improved by the iterative method to obtain a reasonable fit between the measured data and the model response. In the simultaneous interpretation, the successive application of the direct and iterative methods is carried out, starting from the first branch of the apparent resistivity curve. The operation is then shifted to subsequent branches that represent the deeper parts of the geoelectric section. This is similar to the data acquisition applied in direct current sounding in which the depth penetration is increased by expanding the current electrode spacings. The proposed sequential and simultaneous interpretation algorithms require minimum aids and efforts of the interpreter.     

Deep resistivity structure of the Dikili-Bergama region, west Anatolia, revealed by two- dimensional inversion of vertical electrical sounding data

Within the framework of the National Marine Geological and Geophysical Program, we re‐examined deep vertical electrical sounding (VES) data. The data, measured in 1968 by the General Directorate of Mineral Research and Exploration (MTA) of Turkey with the aim of exploring the deep resistivity structure of the Dikili–Bergama region, focus on the geothermal potential. The geoelectrical resistivity survey was conducted using a Schlumberger array with a maximum electrode half‐spacing of 4.5 km. The two‐dimensional (2D) inversion was utilized to interpret the VES data that were collected along 15‐ to 30‐km profiles. The 2D resistivity–depth cross‐sections obtained show very low resistivity values near the Dikili and Kaynarca hot springs. The 2D inversion results also indicate the presence of fault zones striking nearly N–S and E–W, and fault‐bounded graben‐horst structures that show promising potential for geothermal field resources. The 2D gravity model, which is in good agreement with the density variation of the region, supports the resistivity structure revealed by 2D inversion. The lithology information obtained from the borehole near Kaynarca also confirms the results of the resistivity interpretation and the density model.     

MATRIX METHOD FOR THE TRANSFORMATION OF RESISTIVITY SOUNDING DATA OF ONE ELECTRODE CONFIGURATION TO THAT OF ANOTHER CONFIGURATION1

Matrix equations are derived to transform the resistivity sounding data obtained in one type of a four-electrode array to the corresponding resistivity sounding data that would be obtained using a different four-electrode array. These expressions are based primarily on recent work in which we have established a linear relation between the apparent resistivity and the kernel function by using a powerful exponential approximation for the kernel function. It is shown that the resistivity sounding data of two different four-electrode arrays have a linear relation through an essentially non-singular matrix operator and, as such, one is derivable from the other for a one-dimensional model and it can also be extended to two-dimensions. Some numerical examples considering synthetic data are presented which demonstrates the efficiency of the method in such transformations. Two published field examples are also considered for transformation giving a reliable 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.     

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.     

Two-dimensional, regularised inversion of VLF data

Very low frequency electromagnetic (EM) methods using VLF transmitters have found many applications in subsurface geophysical investigations. Surface measurements involving both the vertical component of the magnetic field (VLF-EM or VLF-Z) and of the apparent resistivity (VLF-R) are increasingly common. Although extensive VLF data sets have been successfully used for mapping purposes, modelling and interpretation techniques which asess the third (i.e. depth) dimension appear limited.Given a profile of VLF-R measurements the main purpose of the present study is to demonstrate an automatic method for the construction of a resistivity cross-section. The technique used is one of a new generation of regularised inversion methods. These techniques attempt to overcome the problem of equivalence/non-uniqueness in EM sounding data by constructing the resistivity distribution with the minimum amount of structure that fits the data.VLF data represent a special case of plane-wave EM sounding in that they conform, in practice, to a single-frequency technique. This fact imposes a limitation in the amount of vertical resolution that we can expect using such data. In the case of two-dimensional modelling and inversion, resolution through the cross-section is a resultant attribute from both vertical and lateral resistivity gradients within the subsurface. In order to provide insight into the practical application of regularised inversion techniques to VLF data, both synthetic and field examples are considered. Both sets of examples are primarily concerned with VLF data applied to near-surface fault mapping where the main aim is to assess the location, dip and depth extent of conductive subsurface features.     

Use of VFSA for resolution, sensitivity and uncertainty analysis in 1D DC resistivity and IP inversion

We present results from the resolution and sensitivity analysis of 1D DC resistivity and IP sounding data using a non-linear inversion. The inversion scheme uses a theoretically correct Metropolis–Gibbs' sampling technique and an approximate method using numerous models sampled by a global optimization algorithm called very fast simulated annealing (VFSA). VFSA has recently been found to be computationally efficient in several geophysical parameter estimation problems. Unlike conventional simulated annealing (SA), in VFSA the perturbations are generated from the model parameters according to a Cauchy-like distribution whose shape changes with each iteration. This results in an algorithm that converges much faster than a standard SA. In the course of finding the optimal solution, VFSA samples several models from the search space. All these models can be used to obtain estimates of uncertainty in the derived solution. This method makes no assumptions about the shape of an a posteriori probability density function in the model space. Here, we carry out a VFSA-based sensitivity analysis with several synthetic and field sounding data sets for resistivity and IP. The resolution capability of the VFSA algorithm as seen from the sensitivity analysis is satisfactory. The interpretation of VES and IP sounding data by VFSA, incorporating resolution, sensitivity and uncertainty of layer parameters, would generally be more useful than the conventional best-fit techniques.     

GEOELECTRICAL MODELS INVOLVING LAYERS WITH A LINEAR CHANGE IN RESISTIVITY AND THEIR USE IN THE INVESTIGATION OF CLAY DEPOSITS*

A model has been set up for the interpretation of geoelectrical sounding data for certain kinds of clay deposits containing gradually varying amounts of sand. The model assumes that in the so-called gradient layer, resistivity varies linearly with depth. Model calculations show how such a layer can be replaced by two homogeneous layers. An inversion procedure using the Marquardt algorithm has been developed for the interpretation of sounding data obtained with the Schlumberger array; it assumes a gradient layer beneath several covering layers. The procedure is demonstrated on two clay deposits. A comparison is made between the newly developed interpretation, the traditional approach using model curves, and computerized inversion for a homogeneous layer model.     

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.     

Inversion of DC resistivity data using neural networks

The inversion of geoelectrical resistivity data is a difficult task due to its non-linear nature. In this work, the neural network (NN) approach is studied to solve both 1D and 2D resistivity inverse problems. The efficiency of a widespread, supervised training network, the back-propagation technique and its applicability to the resistivity problem, is investigated. Several NN paradigms have been tried on a basis of trial-and-error for two types of data set. In the 1D problem, the batch back-propagation paradigm was efficient while another paradigm, called resilient propagation, was used in the 2D problem. The network was trained with synthetic examples and tested on another set of synthetic data as well as on the field data. The neural network gave a result highly correlated with that of conventional serial algorithms. It proved to be a fast, accurate and objective method for depth and resistivity estimation of both 1D and 2D DC resistivity data. The main advantage of using NN for resistivity inversion is that once the network has been trained it can perform the inversion of any vertical electrical sounding data set very rapidly.