FAST AUTOMATIC PROCESSING OF RESISTIVITY SOUNDINGS*

The difficulty to use master curves as well as classical techniques for the determination of layer distribution (e_i, ρ_i) from a resistivity sounding arises when the presumed number of layers exceeds five or six. The principle of the method proposed here is based on the identification of the resistivity transform. This principle was recently underlined by many authors. The resistivity transform can be easily derived from the experimental data by the application of Ghosh's linear filter, and another method for deriving the filter coefficientes is suggested. For a given theoretical resistivity transform corresponding to a given distribution of layers (thicknesses and resistivities) various criteria that measure the difference between this theoretical resistivity transform and an experimental one derived by the application of Ghosh's filter are given. A discussion of these criteria from a physical as well as a mathematical point of view follows. The proposed method is then exposed; it is based on a gradient method. The type of gradient method used is defined and justified physically as well as with numerical examples of identified master curves. The practical use for the method and experimental confrontation of identified field curves with drill holes are given. The cost as well as memory occupation and time of execution of the program on CDC 7600 computer is estimated.     

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

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

NEW WAYS FOR THE INTERPRETATION OF GEOELECTRICAL RESISTIVITY MEASUREMENTS IN THE SEARCH FOR AND DELIMITATION OF AQUIFERS

Abstract

Geoelectric resistivity measurements by means of direct current for solving hydrogeological problems have become increasingly significant in recent years. Measurements on the surface according to the four-point-method (SCHLUMBERGER or WENNER arrangement) result in so-called “apparent” resistivities ? α as a function of the electrode distance L. The evaluation of these measuring data, here in form of sounding graphs ? α(L/2), consists of the determination of true resistivities as a function of the depth z. Since a direct computation of ? (z) from α (L/2) is not possible in practice, theoretically computed master curves constitute the essential auxiliary means for the evaluation.

New simplified calculation techniques allow to establish accurately computed master curves for an underground consisting of more than three layers. By means of such standard graphs special problems of hydrogeology can quantitatively be solved by applying geoelectrical methods. The procedure is demonstrated on hand of complicated cases of aquifers devided into several storeys.     

RESISTIVITY SOUNDING ON A MULTILAYERED EARTH CONTAINING TRANSITION LAYERS*

For curves over a horizontally stratified earth where any of the layers has a conductivity variation proportional to (1 +β·z)^N, where β and N are arbitrary constants and z is the depth to the layer, expressions for apparent resistivity for Wenner and Schlumberger sounding are derived. No assumption has been made about the continuity of conductivity at the interface. It is shown that most of the previous investigations in this connection can be regarded as particular cases of the present study.     

ELECTRICAL SOUNDING OF A HALF SPACE WHOSE RESISTIVITY OR ITS INVERSE FUNCTION VARIES LINEARLY WITH DEPTH*

The solution for the potential distribution about a point source of current placed at the surface of a continuous half-space is obtained for two cases: (1) the resistivity increases linearly with depth; (2) the conductivity increases linearly with depth. In each case, an expression for the apparent resistivity is established and master curves are presented for both the Wenner and the Schlumberger configurations. The results can be used in the interpretation of electrical sounding data in specified geologic situations. Furthermore, they may be used as a first step in the development of solutions for the more complex electric sounding problems.     

THE USE OF TWO-ELECTRODE AND SCHLUMBERGER FILTERS FOR COMPUTING RESISTIVITY AND EM SOUNDING CURVES*

Different sets of filter coefficients for the linear filter technique for the computations of resistivity and EM sounding curves are evaluated for several electrode and coil configurations. Instead of this procedure, the two-electrode filter can be used for computations of Wenner, Schlumberger, and dipole—dipole apparent resistivity model curves by defining convolutional expressions which contain the new input functions in terms of the resistivity transform function. Similarly, the Schlumberger filter performs the computations of dipole—dipole apparent resistivity model curves. The Wenner, Schlumberger, and dipole—dipole filter functions are defined in terms of the two-electrode filter using the new convolutional expressions. A relationship between the Schlumberger and dipole—dipole filter functions is given. The above arguments are adopted for the computations of EM sounding curves. It is shown that the EM filter for the horizontal coplanar loop system (which is identical to the two-electrode filter) performs the computations of the mutual coupling ratios for perpendicular, vertical coplanar, and vertical coaxial loop systems. In the same way, the Schlumberger filter can be used to compute vertical coaxial sounding curves. The corresponding input functions are defined in terms of the EM kernel for all convolutional expressions presented. After these considerations, integral expressions of the mutual coupling ratios involving zero-order Bessel function are derived. The mutual coupling ratio for the vertical coaxial loop system is given in the same form as the mutual coupling ratio for the vertical coplanar loop system.     

COMPARATIVE ANALYSIS OF TIME DOMAIN AND FREQUENCY DOMAIN IN THE INDUCED POLARIZATION PROSPECTING METHOD*

The polarization content of a medium, in both the time and frequency domains, can be described by parameters which differ in inherent physical meaning and their practical significance. For real situations, general expressions for the apparent parameters, previously determined for both domains, exist for the general case of soundings on a horizontally multi-layered earth. The comparative analysis of these expressions, here restricted to the simple case of a two-layered earth, shows that the theoretical sounding curves of the frequency-domain are different from those of the time-domain. In particular, for every resistivity or chargeability contrasts examined, the apparent frequency-effect curve lies always over the corresponding apparent chargeability curve, but both curves reach the same asymptotical values for shortest and largest spacings. The important conclusions which can be drawn from this result is that both techniques are suitable to investigate subsoil polarizability anomalies. However, from a practical point of view, it is more convenient to adopt the frequency-domain technique when the polarizability increases with depth, while, on the contrary, the time-domain technique is more efficacious when the polarizability decreases with depth.     

THE THIN-LAYER PROBLEM IN GEOELECTRICAL PROSPECTING *

For a thin highly-conducting layer with given longitudinal conductance the recurrence formulae for an n-fold horizontally stratified subsoil are established for d.c. resistivity and magnetotelluric soundings. Similarly, a thin low conductivity layer with given transverse resistance is treated in the d.c. case and a non-conducting intermediate bed in magnetotellurics. Model curves for a thin high- or low-conductivity intermediate layer in the three-layer case have been carried out, which may serve as an extension of the well-known three-layer diagrams for a Schlumberger configuration. The corresponding model curves in magnetotellurics are given. By numerical comparison of these curves with real three-layer curves some diagrams have been developed to show the allowed thicknesses of the intermediate layer in the Schlumberger case and in the case of magnetotelluric sounding.     

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.     

STUDYING THE INTERCONNECTION OF GROUND AND SURFACE WATERS IN REPRESENTATIVE BASINS UNDER THE PROGRAMME OF THE INTERNATIONAL HYDROLOGICAL DECADE

Abstract

Four geoelectrical soundings were measured with a combination of Schlumberger and azimuthal or equatorial dipole electrode arrays on a Carboniferous limestone basin of the Condroz area, Belgium. The measuring technique is briefly outlined as well as the interpretation procedure, which follows a closed-loop scheme with control of calculated model curves. Some general problems of interpretation of geoelectrical sounding curves are tackled, as far as they have a practical bearing on the treatment of Condroz soundings.

The problem of determining the very high resistivity of limestone is approached through ARCHIE's formula, an empirical relation between the bulk rock resistivity, the porosity and the electrolyte resistivity. An evaluation of the latter two parameters, combined with electrical horizontal conductance measurements directly made on resistivity sounding curves, offers a possibility for fast determination of the total water storage in a limestone aquifer. Such storage determinations could be applied whenever an aquifer shows up as a conductive layer interbedded between two highly resistant layers (e.g. nonsaturated limestone and compact, non-fractured limestone).     

Determining transition reaches between torrents and downstream rivers using a valley morphology index in a mountainous landscape

Dividing rivers into homogeneous reaches is key for river processes and watershed management. In contrast to downstream fluvially dominated rivers, upstream debris-flow dominated torrents have steeper channel slopes and smaller valley width/depth ratios. Investigating transition reaches between torrents and fluvially dominated rivers, not only explores the structure of the landscape, but also contributes to hazard management. This study proposed a valley morphology index combining two variables, channel slope and valley width/depth ratio, to determine transition reaches between torrents and rivers. The methodology was applied to 41 mountain streams in Taiwan using a Geographic Information System (GIS)-based topographic analysis. Plots of valley width/depth ratio versus channel slope were used to determine boundary values of the valley morphology index (I_v) separating torrents from rivers. The plots showed that about 80% of the river basins present “L-shaped” curves, which indicate sharp decreases in slope for upstream sections and dramatic increases of valley width/depth ratio for downstream sections. Results further demonstrated an average value of I_v 0.0047 across the study sites. Spatial comparison between geographic regions indicated that transition reaches in eastern rivers tend to occur lower in the drainage basin due, in part, to higher terrain. Local factors, such as tributary confluences and landslides promote the transition from torrents to fluvially dominated rivers. Satellite images verified that the approach correctly identified transition reaches, suggesting that it may provide a useful reference for river management.     

用激发极化测深估算激发体深度的一个实用方法

与电阻率测深相似,激发极化测深(以下简称ВП_(вэз))也能用来确定矿体的埋藏深度。由于岩石矿物激发极化特性比较稳定,在金属矿床上用激发极化测深来确定矿体埋藏深度,比电阻率测深要优越得多。但由于目前还没有一套系统量板,而且除了几种比较简单的情况以外,理论公式的推导问题也还未全部解决。     

A compact representation of magnetotelluric responses for two-layer models

In this paper the locations where ρ_app = ρ₁ and ? = π/4 and where these parameters reach an extreme value in two-layer magnetotelluric (MT) sounding curves are summarized in an extremely compact form. The key parameters over two-layer models with conductivities σ₁, σ₂ and upper layer thickness h are the real S and α, where S is the conductivity contrast and α is the distance between the observation site and the conductivity interface, normalized to the half skindepth in the first layer. If the impedance components, various resistivity definitions ( ρ_{Re Z}, ρ_{Im Z} and ρ_|Z|, based on different parts of the complex impedance Z ) and the magnetotelluric phase ? are derived as a function of S and α, then the conditions for the apparent resistivity ρ_app and the phase ? are that they either satisfy ρ_app = ρ₁ and ? = π/4 or attain extreme values which can be given in terms of simple algebraic equations between S and α. All equations are valid for observation sites at any depth 0 ≤ z ≤ h in the first layer. The set of equations, presented in a tabular form, may make it possible to determine a layer boundary from the short period part of the sounding curves, in particular the ρ_{Re Z} and the ?_MT curves.     

Effect of coupling noise on the interpretation of results of electromagnetic horizontal sounding and modeling

The time variation of a source of alternating current produces an electromagnetic coupling between the transmitting and receiving systems in induced electrical polarization and resistivity surveys that employ horizontal electrical sounding. The coupling alters, sometimes significantly, the resistivity and chargeability values and, consequently, compromises the interpretation of the data. This work develops the analysis of this coupling on the time domain for both a homogeneous Earth and an Earth constituted of several homogeneous horizontal layers. Based on the results, it evaluates the theoretical variation of the voltage and compares it to observed data of an induced electrical polarization and resistivity survey with horizontal electrical sounding. The comparative study of the voltage decay curves assesses the contribution of the electromagnetic coupling to the values of the chargeability and apparent resistivity as a function of the bipole length and the period of the source current. Besides that, the respective pseudosections have delineated the horizontal and vertical variations of those two electrical properties, providing the interpretation of the geoelectrical section. This research is important for the oil industry because it may furnish information that help to: (i) define the structure of the sedimentary strata; (ii) estimate the clay content of the sandstones; and (iii) detect the possible presence of metallic sulphide halos at fractured zones of the sediments above the oil reservoir. It may be adapted to analysis of EM coupling in both resistive and induced electric well logs.     

GRADIENT ARRAY PROFILES OVER THIN RESISTIVE VEINS1

Furness , P. 1993. Gradient Array Profiles over thin resistive veins. Geophysical Prospecting 41 , 113–130. Gradient array geoelectric surveys are commonly used to explore for buried sheet-like targets. It is demonstrated that under certain circumstances the responses of such features can become practically equivalent for a range of models differing considerably in resistivity and thickness. This is the dual of the familiar equivalence phenomenon associated with thin beds in geoelectric sounding operations. Hence the geoelectric response profiles over thin dipping resistive veins are conveniently studied by considering equivalent forms with vanishing thickness and infinite resistivity but with the same resistivity-thickness product. The effects of varying the dip, depth of burial, depth extent and resistivity–thickness product of such features on the gradient array response profiles are investigated by means of a series of numerical experiments. These demonstrate several effects of significance to survey design and data interpretation. In particular it is found that while the resistivity–thickness product influences the amplitude of the response profiles it has little effect on their form. A similar behaviour is found to be exhibited by veins with extended depth extent when the dip is varied. A complete quantitative interpretation of gradient array profiles over thin dipping resistive veins is thus only possible for veins of limited depth extent. For veins with an extended depth dimension, the data is ambiguous (in a practical sense) in terms of the dip and the resistivity–thickness product. Here, the interpretation can only be expected to deduce the horizontal and vertical locations of the vein apex.     

TRANSFORMATION OF DIPOLAR,WENNER AND TWO-ELECTRODE CURVES TO SCHLUMBERGER APPARENT RESISTIVITY SOUNDING CURVES*

A simple mathematical technique based on regressional analysis allows the transformation of dipolar, Wenner and two-electrode apparent resistivity sounding curves to Schlumberger ones. The algorithm is suitable for a programmable pocket calculator and the accuracy is very high. This has been demonstrated by comparing Schlumberger master curves with transformations of master curves for the other configurations for the same model.     

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.     

A NUMERICAL METHOD TO COMPUTE THE RESISTIVITY TRANSFORM FROM WENNER SOUNDING DATA*

A numerical technique to compute the resistivity transform directly from the observed Wenner sounding data has been developed. In principle, the procedure is based on a decomposition method and consists of two steps: the first step determines a function that approximates the apparent resistivity data and the second step transforms this function into the corresponding kernel by an analytical operation. The proposed method is tested on some theoretical master curves. A high degree of precision is achieved with very little computer time. The applicability is shown on two field examples.     

A deep geophysical study in the Baikal region

Experimental data show that in East Siberia resistivity curves, irrespective of their trends, are affected by galvanic (local) distortions. The preliminary step of the magnetotelluric data processing is to obtain a steady shape of resistivity curves reflecting a true deep section. For this purpose statistical averaging and different criteria of impedance rejecting were used. The available MTS curves were normalized by level to the global magnetovariation curves. Two-dimensional modelling was performed from several sublatitudinal profiles crossing the Baikal rift zone. Three-dimensional models based on two-dimensional modelling and on induction vector distribution have been computed via programs of M. N. Yudin. Following other researchers, two conductive layers are distinguished: i) the mid- and low crustal and ii) the mantle one, with the layer surface uplifted from 100–110 km depth in the southern Baikal rift zone to 60–70 km northeastwards along the eastern Baikal coast. The top of this layer seems to correspond to the asthenospheric roof. The asthenosphere deepening in southern BRZ is likely to be related to a decrease in the asthenospheric bulge width and an increase in the rate of lithospheric thickening with mantle degasing. The origin and evolution of the Baikal rift is considered, proceeding from the model of passive rifting with regard to a long-existing lithospheric inhomogeneity between the Siberian platform and the Sayan-Baikal folded area.     

FREQUENCY ELECTROMAGNETIC SOUNDING USING A VERTICAL MAGNETIC DIPOLE*

A horizontal transmitter loop (vertical magnetic dipole) is used for frequency electromagnetic (FEM) soundings. The frequency ranges from approximately 6 Hz to about 4000 Hz. The vertical and radial magnetic field components are measured for 20 frequencies per decade several hundred meters from the transmitter loop. A very small bandwidth is selected for amplification using a reference signal. An Apple computer is used for data acquisition. A computer program for Marquardt inversion optimizes the parameters for the n-layer case: the resistivities and thicknesses of individual beds and a correction factor for the primary magnetic field. Interpretation of each component individually yields practically the same parameters. Examples from the field are given with interpretation; comparison with dc resistivity measurements is provided. The ratio of vertical/radial magnetic field components vs. frequency can be transformed simply into apparent resistivity vs. apparent depth. This can be done in the field to obtain an estimation of the depth of the layer boundaries. FEM results are compared with Schlumberger d.c. sounding obtained at the same site.