LABORATORY RESULTS IN RESISTIVITY LOGGING*

This paper is an experimental extension of the theoretical investigations by Roy (1975) on the relative performances of the Laterolog 7, normal and some other sondes in logging of resistive formations. Only infinitely resistive formations have been simulated and placed in a tank containing tap water (true resistivity 27 Ωm) as electrolyte—representing both the mud column and the adjacent formations. Two sets of laboratory results (Doll 1951, NN 1958, 1969), have been repeated and we find that, for both these sets, the performance of the normal device is by far the superior of the two. In addition, we have studied the effect of varying the spacings A₁A₂, O₁O₂ and AM of Laterolog 7, normal, and two new sondes—Laterolog 4 and modified unipole—for two bore hole diameters in each case. For formation thicknesses less than A₁A₂ or AM, the Laterolog 7 is unsuitable because its response is flat and close to the base-line value. The normal device is more diagnostic, although, in such a case, it registers a trough or a resistivity low even against a resistive formation. For bed thicknesses clearly greater than A₁A₂ or AM, the normal sonde is decidedly superior to Laterolog 7, since its anomalies are sharper and larger. When the formation thickness is equal to or only slightly larger than A₁A₂ or AM, Laterolog 7 is somewhat better as it records a readable positive deflection while the normal does not. However, one must remember that a single run of the conventional resistivity log includes two normals and a lateral at different spacings. Laterolog 4 and modified unipole can in many instances produce better logs than normal, other considerations apart. The results are consistent with our own theoretical predictions and experience in surface resistivity profiling. They do not, however, agree with the prevalent concepts on Laterolog 7 vis-a-vis normal sonde.     

ON SOME RESISTIVITY LOG INTERPRETATION CHARTS*

The paper relates primarily to the borehole and the side bed correction charts for Latero-logs 3 and 7. Versions of some of these charts published by different companies—or even by the same company in different years—exhibit significant variations. Usually, such publications do not contain adequate information on how the charts were constructed and do not explain why discrepancies occur. Because of these reasons, an attempt has been made in this paper to reconstruct the borehole correction chart for Laterolog 7 and the shoulder bed correction charts for Latero-logs 3 and 7. For the latter two, the results found differ substantially from those published earlier. The paper demonstrates how departure (response) curves and correction charts for the lateral and the Laterolog 7 sondes can be computed from those for the normal sonde. An apparent resistivity formula is suggested for Laterolog 7 in which all currents that exist in the ground at the time of measurement and that produce the signal are monitored and used. Response curves and correction charts for Laterolog 7, based on such a formula, are presented as illustrations.     

THEORETICAL AND EXPERIMENTAL INVESTIGATIONS FOR CAVITY RESEARCH WITH GEOELECTRICAL RESISTIVITY METHODS*

The exact localization of subterranean cavities and the determination of their dimensions is very important for the planning of geotechnical and mining activities. It is a complicated geophysical task often at the limit of detection. Nevertheless geophysical investigation is the only alternative to a dense and expensive grid of boreholes. This report tests the usefulness of geoelectrical resistivity methods for cavity detection under some new aspects. The basis for evaluation was a theoretical analysis of different conventional and focussing measuring arrays and of special arrays for a geoelectrical research between two boreholes. The limit of detectability of a cylindrical cavity of defined cross-section and depth was calculated for the different measuring arrays on the basis of computation of the apparent resistivity ρa. Furthermore, the influence of possible errors (current supply of the electrodes and the distance between the electrodes) is discussed for focussed systems. The second part of the article is directed at the behaviour of the apparent resistivity ρa, the disturbing potential δV_d caused by the cavity and the normal potential δV₀ of the measuring array all in relation to a homogeneous earth. Some new results are presented. In the last part of the article theoretical results are compared with some field measurements.     

RESISTIVITY TYPE CURVES OVER OUTCROPPING VERTICAL DYKE—II *

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

Relative performance of focused and unfocused devices in a two-dimensional borehole environment

Borehole direct current (dc) resistivity problems are solved using finite difference method (FDM) primarily to extend the log interpretation in the two-dimensional (2D) domain. Transitional invaded zone, flushed zone, uncontaminated zone, shoulder beds and borehole filled with mud are simulated simultaneously in the model. Linear variation of resistivity is assumed for transitional invaded zone. Normal, lateral and modified laterolog7 (LL7⁴) electrode configuration (discussed in the text) responses were computed using expanding rectangular grid system. LL7⁴ responses with variable geometric factor did show some superiority over the conventional normal and lateral for conductive target beds sandwiched between the resistive beds. For relatively small borehole diameter, all three probes can detect resistive target bed satisfactorily. However, for highly conductive mud both LL7⁴ and normal electrode configuration fail to detect any signal from the target bed. Bypassing effect of the current for LL7⁴ is more than that in normal log. Lateral log shows a signal of conductive invaded zone generated by the conductive mud. Bucking current ratio peaks and the geometric factor peaks in LL7⁴ can detect the bed boundaries.     

MORE ON THE LATEROLOG* DEVICE**

Basic Laterolog devices employ a measure-current focusing technique to provide well logs of formation resistivity that feature sharp vertical definition combined with a depth of investigation much improved over those of normals of comparable spacings. To develop the concept of measure-current focusing, a disk-electrode arrangement analogous to a guard-ring capacitor is considered first, leading finally to consideration of a real sonde in a cylindrical borehole. In the latter, auxiliary currents are adjusted to maintain substantially at zero the vertical potential gradients above and below the central measure-current electrode; this has the effect of focusing the measure-current beam. However, prediction of sonde responses on the basis of current patterns can in some cases be misleading. Indeed, for a given Laterolog array, one may use a (reciprocalmode) current pattern radically different from the one defined by the basic (direct-mode) measure-current focusing scheme and still obtain the same resistivity measurement. This feature is illustrated for Laterolog 3 by use of transfer impedances, and demonstrated for certain more general cases using the reciprocity theorem. Comparisons of Laterolog responses across typical thin beds, both non-invaded and invaded, with those of normal devices of a comparable range of spacings illustrate the improved vertical resolution obtained with Laterolog devices. The examples also show the different magnitudes of the auxiliary currents (thenceforth designated “bucking”- or “focusing” currents) used in the direct and reciprocal modes and illustrate how these currents must continuously vary in order to maintain the focused condition as the sonde moves through the bed. Finally, briefly considering possible applications of Laterolog-type arrays in surface prospecting, it is shown that a one-dimensional array laid out on the surface does not provide the same degree of measure-current focusing as is obtained in a borehole. Some improvement is obtained with a combination of two crossed linear arrays. Much more is obtained using a circular array.     

MODEL STUDIES ON SOME ASPECTS OF RESISTIVITY AND MEMBRANE POLARIZATION BEHAVIOUR OVER A LAYERED EARTH*

Electrolytic model tank experiments to study resistivity and time domain induced polarization (IP) response over layered earth models were initiated primarily to facilitate the understanding of field results. Alternate layers of clay and sand (or clay-coated sand) with, in some cases, a surficial layer of water were assembled in the tank and resistivity and IP measurements made for a range of electrode spacings using the Wenner configuration. Graphite and silver-silver chloride electrodes were used as current and potential electrodes respectively. Clay-coated (3% by weight) sand was found to generate stronger polarization than either clay or sand alone. Apparent chargeability m_a was observed to be positive for a nonpolarizable surface layer. For a polarizable surface layer, the sign of IP was controlled by the polarizability, the thickness of the second layer, and the spacing of the electrode spreads. The apparent chargeability m_a can theoretically change sign from positive to negative and vice versa with a gradual increase in electrode spacing, and such negative IP effects were obtained in a few observations. A simultaneous decrease in IP and an increase in resistivity, which is a qualitative diagnostic feature for the occurrence of clean freshwater sand aquifers, could also be generated in the model tank experiment. Combined resistivity and IP soundings were carried out near Fredericton Junction and Tracy, New Brunswick, Canada. Field curves are presented along with the model curves for qualitative comparison and understanding of IP behaviour over a layered earth. Twenty-five out of twenty-seven soundings show only positive apparent chargeabilities, whereas two show chargeability sign changes (positive/negative/positive). The model study gives reason to believe that surface soils and Quaternary gravel boulder deposits near Fredericton Junction are relatively non-polarizable. As an auxiliary experiment, sand and clay were taken in different proportions by weight and mixed thoroughly with water in a cement mixer. The mixtures were then compressed with a suitable die and plunger under 3.6 Pa pressure to prepare cylindrical samples of height 18 cm and diameter 15.5 cm. IP measurements were done on the flat faces using the Wenner configuration with a= 2 cm. Chargeability was found to be negative for 100 and 90% clay mixtures. It reached a positive maximum for an 80% clay-20% sand mixture and then decreased gradually with increasing sand and decreasing clay content.     

FOCUSSED ELECTRICAL RESISTIVITY ARRAYS: SOME THEORETICAL AND PRACTICAL EXPERIMENTS*

The “Laterolog 7′’and the “Microlaterolog’ have been studied theoretically for the case of a conducting halfspace containing a single overburden, using a technique based on the method of images. The results have shown these focussed arrays to be more sensitive to the lower medium (i.e., having greater depth of investigation) than unfocussed ones of the same dimensions, when the “correct’ geometric factor is used. The geometric factor of a focussed electrode array is somewhat involved, and is explained with reference to an ideal focussed array; such an array would pass a measuring current of constant intensity into a fixed geometrical shape of conducting material, irrespective of any layering or any other heterogenities that may be present, using auxiliary current sources of variable magnitude. This concept of a constant amount of current flowing in a beam of fixed geometry and current density, is the basis of focussed arrays, and it is shown that the geometric factor, used to calculate the apparent resistivity, is the one derived when considering the homogeneous case. The value of the constant measuring current, alone, is used to convert the measured potential difference into a resistance, the ratio between this value and the combined intensities of the auxiliary current sources, for the homogeneous case, being incorporated into the geometric factor. Surprisingly good agreement was found between the theoretical models and practical experiments using a focussing seabed resistivity probe which is a substantial modification of the “Microlaterolog”. Both show similar deviations from the ideal case which are explained in terms of refraction at the overburden interface. All experiments indicated that focussed arrays have a greater depth of investigation than similar unfocussed ones for a single overburden, whether it be resistive or conductive.     

ZERO—PHASE FORWARD FILTERS FOR RESISTIVITY SOUNDING*

Forward filters to transform the apparent resistivity function over a layered half-space into the resistivity transform have been derived for a number of sample intervals. The filters have no apparent Gibbs' oscillations and hence require no phase shift. In addition, the end points of the filter were modified to compensate for truncation. The filters were tested on simulated ascending and descending two-layer cases. As expected, “dense” filters with sample spacing of In (10)/6 or smaller performed very well. However, even “sparse” filters with spacing of In (10)/2 and a total of nine coefficients have peak errors of less than 5% for p₁:p₂ ratios of 10^–6 to 10⁶. If a peak error of 5.5% is acceptable, then an even sparser filter with only seven coefficients at a spacing of 3 In (10)/5 may be used.     

Evaluation of electric parameters of anisotropic sandy-shaly Miocene formations on the basis of resistivity logs

In this paper, electrical properties of an anisotropic rock formation are discussed. Electrical anisotropy parameters, i.e., horizontal resistivity, R _H , and vertical resistivity, R _V , and anisotropy coefficient in the sandyshaly Miocene formation, are determined on the basis of induction logs and laterologs. Graphs of R _V = f(R _H ) calculated for different resistivities of sandstones and shales and variable volumes of those two components allow us to conclude about the correctness of the applied method for determining the resistivity parameters of autochthonous Miocene formations.     

Depth of detection of buried resistive targets with some electrode arrays in electrical prospecting

Assuming the minimum detectable anomaly to be 10%, depths of detection of a 2D vertical resistive sheet of thickness t are found to be 4.0t, 3.0t, 4.0t and 4.0t with Wenner, two-electrode, three-electrode and dipole-dipole (β-Wenner) arrays, respectively, when the array spread is in-line. On the other hand, the depths of detection obtained with a broadside spread of the arrays right over the sheet are much less and are correspondingly 2.5t, 2.0t, 2.5t and 2.5t. An increase in the depth extent W of the sheet from 10t to 20t does not increase its depth of detection with the arrays. The depths of detection of an infinitely resistive horizontal cylinder of radius R are respectively 1.5R, 1.8R, 2.0R and 2.0R with the above-listed arrays when the array spread is in-line. With broadside spread of any of the arrays, the depth of detection is seen to be 2.5R. In the case of a spherical target of radius R, the detection depths of any of the arrays are found to be small and to vary between 0.8R and 1.1R. Comparatively, the detection depths of resistive targets are much lower than those of conductive targets of the same size and shape, with any electrode array. Among all the arrays studied, the two-electrode array performs worst in the detection of resistive targets while it performs best in detecting conducting targets of limited lateral extent. In the case of a spherical target, either resistive or conductive, there is no distinct change in its detection depth with array.     

RESISTIVITY TYPE CURVES OVER OUTCROPPING VERTICAL DYKE—I *

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

3D laterolog array sonde design and response simulation

A new three-dimensional laterolog array sonde (3D-LS) is presented. The 3DLS is based on existing high-resolution laterolog array and azimuthal resistivity imaging sondes with radial, longitudinal, and circumferential detection abilities. Six investigation modes are designed using the 3D finite-element method and different investigation depths are simulated based on the pseudo-geometrical factor of the six modes. The invasion profile is described using multi-array radial logs. From the analysis of the pseudo-geometrical factor, the investigation depth of the 3D-LS is about 1.5 m for conductive invasion, which is close to that of the dual laterolog tool but greater than that of the highly integrated azimuthal laterolog sonde. The vertical and azimuthal resolution is also analyzed with the same method. The 3DLS can detect low-resistivity anomalies of 0.5 m thickness and 15° around the borehole for infinitely thick formations. This study lays the foundation for more work on 3D laterolog array sonde for evaluating low-resistivity anomalies.     

Magnetic instabilities in rapidly rotating spherical geometries II. more realistic fields and resistive instabilities

Abstract

Magnetic instabilities play an important role in the understanding of the dynamics of the Earth's fluid core. In this paper we continue our study of the linear stability of an electrically conducting fluid in a rapidly rotating, rigid, electrically insulating spherical geometry in the presence of a toroidal basic state, comprising magnetic field B_MB _O(r, θ)1ø and flow U_MU _O(r, θ)1ø The magnetostrophic approximation is employed to numerically analyse the two classes of instability which are likely to be relevant to the Earth. These are the field gradient (or ideal) instability, which requires strong field gradients and strong fields, and the resistive instability, dependent on finite resistivity and the presence of a zero in the basic state B _O(r,θ). Based on a local analysis and numerical results in a cylindrical geometry we have established the existence of the field gradient instability in a spherical geometry for very simple basic states in the first paper of this series. Here, we extend the calculations to more realistic basic states in order to obtain a comprehensive understanding of the field gradient mode. Having achieved this we turn our attention to the resistive instability. Its presence in a spherical model is confirmed by the numerical calculations for a variety of basic states. The purpose of these investigations is not just to find out which basic states can become unstable but also to provide a quantitative measure as to how strong the field must become before instability occurs. The strength of the magnetic field is measured by the Elsasser number; its critical value _c describing the state of marginal stability. For the basic states which we have studied we find _c 200–1000 for the field gradient mode, whereas for the resistive modes _c 50–160. For the field gradient instability, _c increases rapidly with the azimuthal wavenumber m whereas in the resistive case there is no such pronounced difference for modes corresponding to different values of m. The above values of _c indicate that both types of instability, ideal and resistive, are of relevance to the parameter regime found inside the Earth. For the resistive mode, as is increased from _c, we find a shortening lengthscale in the direction along the contour B_O = 0. Such an effect was not observable in simpler (for example, cylindrical) models.     

Geoelectrical structure and hydrogeological investigations of the southern Rif Cordillera (Morocco)

An electrical prospecting survey is conducted in the Rharb basin, a semi‐arid region in the southern part of the Rifean Cordillera (Morocco) to delineate characteristics of the aquifer and the groundwater affected by the marine intrusion related to Atlantic Ocean. Analysis and interpretations of electrical soundings, bi‐logarithmic diagrams and the geoelectrical sections highlight a monolayer aquifer in the southern part, a multilayer system in the northern part of the Rharb basin and lenticular semi‐permeable formations. Several electrical layers have been deduced from the analysis of bi‐logarithmic diagrams: resistant superficial level (R₀), conducting superficial level (C₀), resistant level (R), intermediary resistant level (R′), conducting level (Cp) and intermediary layer of resistivity (AT). Spatial distribution of the resistivity deduced from the interpretation of apparent resistivity maps (AB = 400 and 1000 m) and the decreasing of resistivity values (35–10 Ωm), in particular in the coastal zone show that this heterogeneity is related to several anomalies identified in the coastal area, which result from hydraulic and geological processes: (i) heterogeneous hydraulic conductivity in particular in the southern part of the Rharb; (ii) lateral facies and synsedimentary faulting and (iii) the relationship between the electrical conductivity and chloride concentration of groundwater shows that salinity is the most important factor controlling resistivity. The distribution of fresh/salt‐water zones and their variations in space along geoelectrical sections are established through converting subsurface depth‐resistivity models. Copyright © 2010 John Wiley & Sons, Ltd.     

AN INTERPRETATION THEORY FOR INDUCED POLARIZATION VERTICAL SOUNDINGS (TIME-DOMAIN)*

In this paper it is shown how one may obtain a generalized Ohm's law which relates the induced polarization electric field to the steady-state current density through the introduction of a fictitious resistivity defined as the product of the chargeability and the resistivity of a given medium. The potential generated by the induced polarization is calculated at any point in a layered earth by the same procedure as used for calculating the potential due to a point source of direct current. On the basis of the definition of the apparent chargeability m_a, the expressions of m_a for different stratigraphie situations are obtained, provided the IP measurements are carried out on surface with an appropriate AMNB array. These expressions may be used to plot master curves for IP vertical soundings. Finally some field experiments over sedimentary formations and the quantitative interpretation procedure are reported.     

江苏地电阻率预测指标研究

结合地电阻率的前兆机理和实际观测结果,给出构造活动作用下地电阻率的两类前兆异常变化:一是与观测场地周围应力场变化相关的长趋势变化;二是与震源岩石裂隙破裂相关的大幅下降变化。针对地电阻率的两类前兆异常变化,以江苏5个地电阻率场地的历史观测数据为例,采用一年窗长的归一化速率进行分析,提出将归一化速率值的二倍方差作为地电阻率的异常指标,并对预测指标进行R值检验,得到R=0.513,对应R0=0. 277,R/R0=1. 9,预测结果较理想。     

DC GEOELECTRIC SOUNDING TO DETERMINE WATER CONTENT IN THE SALT MINE ASSE (FRG)*

In the course of investigations concerning disposal of radioactive waste, DC-geoelectric soundings were performed in the salt mine Asse in 1982. The survey resulted in the determination of resistivities of various salt formations. A comparison of various resistivities obtained in salt formations in the mine shows that it is possible to estimate the content of free water in salt using Archie's equation. The significant result of this survey is that salt formations in the mine can be divided into two categories according to their resistivities: 1. Salt with resistivity between 10⁷ and 10⁸Ωm (particularly Na2Sp and Na3β). The particularly pure halitic formations are to be found within this resistivity range. 2. Salt with resistivity between 10³ and 10⁵Ωm (Na2Tl, K2, transition salt). The salt formations with thin layers of anhydrite and a high content of hygroscopic salts are classified in the paper.     

DIGITAL LINEAR FILTER FOR COMPUTING TYPE CURVES FOR THE TWO-ELECTRODE SYSTEM OF RESISTIVITY SOUNDING*

In this paper a technique for computing type curves for the two-electrode resistivity soundings is presented. It is shown that the apparent resistivity due to the system can be represented by a convolution integral. Thus, it is possible to apply the principle of digital linear filtering and compute the desired type-curves. The filter function required for the purpose is found to be identical with that used to compute the EM sounding curves for the two coplanar horizontal loop system. It is further shown that from the two-electrode apparent-resistivity expression one can easily derive the apparent resistivities for other configurations. A comparison of depths of investigation for various systems reveals that the two-electrode system has greater depth of investigation than other conventional systems. This is also supported by the field example presented in the end, which illustrates the relative performance of the two-electrode system vis-a-vis the Wenner system.     

SEISMIC AND ELECTRICAL PROPERTIES OF UNCONSOLIDATED PERMAFROST1

A model has been developed to relate the velocities of acoustic waves V_p and V_s in unconsolidated permafrost to the porosity and extent of freezing of the interstitial water. The permafrost is idealized as an assemblage of spherical quartz grains embedded in a matrix composed of spherical inclusions of water in ice. The wave-scattering theory of Kuster and Toksoz is used to determine the effective elastic moduli, and hence the acoustic velocities. The model predicts V_p and V_s to be decreasing functions of both the porosity and the water-to-ice ratio. The theory has been applied to laboratory measurements of V_p and V_s in 31 permafrost samples from the North American Arctic. Although no direct measurements were made of the extent of freezing in these samples, the data are consistent with the predictions of the model. Electrical resistivity measurements on the permafrost samples have demonstrated their essentially resistive behaviour. The ratio of resistivity of permafrost in its frozen state to that in its unfrozen state has been related to the extent of freezing in the samples. Electromagnetic and seismic reflection surveys can be used together in areas of permafrost: firstly an EM survey to determine the extent of freezing and then the acoustic velocity model to predict the velocities in the permafrost. The necessary transit time corrections can thus be made on seismic reflection records to compensate for the presence of permafrost.