NUMERICAL INTERPRETATION OF RESISTIVITY SOUNDINGS OVER HORIZONTAL BEDS*

The digital computer technique described for interpreting resistivity soundings over a horizontally stratified earth requires two steps. First, the kernel function is evaluated numerically from the inverse Hankel transform of the observed apparent resistivity curve. Special attention is given to the inversion of resistivity data recorded over a section with a resistant basement. The second step consists in the least-squares estimation of layer resistivities and thicknesses from the kernel function. For the case of S or T-equivalent beds only one layer-parameter can be obtained, either the longitudinal conductance, or the transverse resistance respectively. Two examples given in the paper show that a wide tolerance is permitted for Choosing the starting values of the layering parameters in the successive approximation procedure. Another important feature for practical applications is good convergence of the iterations. The method is probably best suited for interpreting profiles of electrical soundings with the purpose of mapping approximately horizontal interfaces at depth.     

磁激发极化法中水平圆柱体的一些研究结果

本文简要介绍导电柱体在全空间和半空间的均匀电流场中形成的异常电流磁场理论,给出了正、反演理论公式;计算出了磁电阻率法和磁激发极化法理论剖面曲线;得到了相应的模型实验结果以及在浸染型铜矿上的野外试验结果。这些资料证明了所建立的理论。     

磁激发极化法中水平圆柱体的一些研究结果

本文简要介绍导电柱体在全空间和半空间的均匀电流场中形成的异常电流磁场理论,给出了正、反演理论公式;计算出了磁电阻率法和磁激发极化法理论剖面曲线;得到了相应的模型实验结果以及在浸染型铜矿上的野外试验结果。这些资料证明了所建立的理论。     

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.     

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 INDUCED POLARIZATION RESPONSE OF A THIN HIGHLY-CONDUCTIVE ORE BODY*

Consider a lamina of ore of thickness 2t whose electrical resistivity p₂ is much smaller than the resistivity p₁ of the surrounding host rock. The induced polarization response of such an ore body is investigated under the assumption that it arises from the variation of p₂ with the frequency of measurement. Let p2l and p2h be the resistivities of the ore-body for the low and high frequencies of measurement and L a length of the order of the distance between the transmitting electrodes. A theory is developed under the assumptions that each of the quantities t/L, p2l/p1, p2h/p1, Lp2l/2tp1, and Lp2h/tp1 is small. The main conclusion is that the frequency effect parameter P is given approximately by P=cL(p2l ? p2h)/2tp1, where the constant c is independent of t, p2l, p2h, and p1. Thus for a family of similar ore bodies having differing values of t, P will be the larger the smaller t. Detailed results are given for a semi-infinite submerged dipping dyke and the two dimensional Wenner array.     

THE ASSOCIATION OF RESISTIVITY SOUNDINGS*

A simple measure, the association parameter, is proposed for directly comparing the results of two electrical soundings. The use of this measure to classify field results and to gain some insight into geological structure before extensive depth interpretation is discussed. In particular it is shown that when used with soundings conducted using the tripotential technique the combined use of association parameter arid lateral inhomogeneity index can allow structural patterns to be discerned where otherwise they might be obscured. Possible extension of the technique is considered.     

PHYSICAL AND COMPUTER MODELING OF INDUCED POLARIZATION *

The Laboratory of Geophysics of the University of Arizona was presented with an exploration problem by Falconbridge, Ltd. of Canada. Massive mineralized hemispherical “pods” are in the vicinity of a tuff layer of high conductivity and induced polarization response, covered by large thicknesses of resistive volcanics. The initial approach was to utilize electrolytic tank modeling. The extreme resistivity and IP contrasts proved to be difficult to recreate. Two dimensional modeling was attempted next with conductive paper, using copper and silver paint for anomalous masses. This method also proved inadequate. Finally, mathematical equations were solved which could model any arbitrary anomalous body in any steady state electrical field. Plane waves as well as point current sources producing non-plane waves are possible. Finite difference equations were derived for the non-linear partial differential equations under consideration. The equations were solved using a digital computer. Initially, the boundary conditions had to be satisfied at the boundaries of resistivity changes, severely restricting possible geometric shapes for anomalous bodies. The final and successful solution was to apply numerical techniques to obtain solutions of equations which require only that the relative resistivities through the area be specified. The Falconbridge problem and its solution are analyzed.     

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.     

DIPOLE-DIPOLE DEEP GEOELECTRIC SOUNDINGS OVER GEOLOGICAL STRUCTURES*

Alfano L. 1980, Dipole-Dipole Deep Geodectric Soundings over Geological Structures, Geophysical Prospecting 28, 283–296. The dipole-dipole array is used for deep vertical geoelectric soundings for practical reasons. However, the data obtained are often too scattered and the quality is lower than that of a Schlumberger sounding. The mathematical transform from these fields data to the corresponding Schlumberger ones is needed. It is demonstrated that for more general underground structures different from plane parallel stratifications, only the continuous polar dipole-dipole array permits a general and reliable transform of this type. It follows that any other dipole-dipole array, (for instance the azimuthal, equatorial, parallel, perpendicular, etc.), are useless over complex structures, or in the presence of irregularities on the ground surface.     

INDUCED POLARIZATION RESPONSE OF A POLARIZABLE INHOMOGENEOUS SPHERE *

Expressions for the I. P. activity coefficient for an inhomogeneous sphere with the conductivity increasing/decreasing from the core towards the periphery according to a power law have been derived. In certain geometrical situations of the electrode configurations a negative I. P. signal is obtained. The negative I. P. may be understood as due to modifications in the discharge current from the polarized medium during the discharge process. The results of the investigation may be useful for more accurate interpretation of I. P. anomalies due to isometric inhomogeneous bodies.     

CONTOUR MAP PRESENTATION OF DIPOLE-DIPOLE INDUCED POLARIZATION DATA*

Dipole-dipole induced polarization (IP) data are displayed typically as multi-level profiles, or as contours on vertical sectional plots referred to as pseudo-sections. The dipole-dipole array tends to yield IP anomalies in which the most anomalous values are displaced laterally from the source body. The data patterns are fairly interpretable on pseudo-sections or on multi-level profiles but are sufficiently complex to discourage the contouring of the data in plan. A method was developed for the presentation of dipole-dipole IP data on a contour map. The method consists of a simple averaging of data which can be performed manually if desired. It yields a single output value per station which reflects all levels of the pseudo-section, and is suitable for contouring in plan. The advantage of the technique is that it provides a quantitative picture of IP anomalies in their background or regional setting.     

AN APPROACH TO THE IDENTIFICATION OF FINE SEDIMENTS BY INDUCED POLARIZATION LABORATORY MEASUREMENTS*

Time-domain-induced polarization (IP) laboratory measurements were performed on about 200 fine sediment samples with varying water content. The results permitted an analysis of IP properties of clays, loams, silts, and sands. Particular emphasis has been given to the analysis of the chargeability m as a function of lithotype and the water content. By analyzing decay curves, a new parameter was identified. It is a statistically specific characteristic of the lithotype and is independent of the water content. Therefore, it provides a diagnostic parameter for lithotype identification. In association with the values of chargeability and electrical resistivity, this parameter permits a reliable evaluation of water content and yields useful information about the porosity and permeability of the lithotype.     

激发极化法的“饱和效应”问题

西格尔（H.O.Seigel）从理论计算得到导电颗粒含量为25％的极化球体有最大异常,因此认为:激发极化法只宜于寻找中等浸染程度的矿体,对于含量很高的矿体或良导致密型矿体,激发极化法是不行的。据称这种“饱和效应”的理论得到野外结果的证实。 本文根据我国激发极化法在良导致密型矿体上大都能获得明显视极化率异常的事实,说明西格尔的“饱和效应”理论与事实不符。本文认为良导致密型极化体不存在“饱和效应”问题,激发极化法对它们的勘探也是有效的。可能由于西格尔把低含量理论公式,不计条件地推导到高含量、甚至良导矿体,因此他的结论是错误的。本文最后讨论了电阻率因素对浸染型球体视极化率强度的影响。     

激发极化法的“饱和效应”问题

西格尔（H.O.Seigel）从理论计算得到导电颗粒含量为25％的极化球体有最大异常,因此认为:激发极化法只宜于寻找中等浸染程度的矿体,对于含量很高的矿体或良导致密型矿体,激发极化法是不行的。据称这种“饱和效应”的理论得到野外结果的证实。 本文根据我国激发极化法在良导致密型矿体上大都能获得明显视极化率异常的事实,说明西格尔的“饱和效应”理论与事实不符。本文认为良导致密型极化体不存在“饱和效应”问题,激发极化法对它们的勘探也是有效的。可能由于西格尔把低含量理论公式,不计条件地推导到高含量、甚至良导矿体,因此他的结论是错误的。本文最后讨论了电阻率因素对浸染型球体视极化率强度的影响。     

INDUCED POLARIZATION IN ELECTROMAGNETIC INDUCTIVE SCHEMES*

Using homogeneous full-space and half-space models, we show that induced-polarization properties of the medium influence the inductive coupling between two circuits. It is suggested that existing methods to interpret electromagnetic sounding data should be viewed with caution if the electro-chemical dispersion is not taken into account.     

A LABORATORY INVESTIGATION OF THE INDUCED POLARIZATION OF THE TRIASSIC SHERWOOD SANDSTONE OF LANCASHIRE AND ITS HYDROGEOLOGICAL APPLICATIONS*

The time-domain induced polarization (IP) of saturated Sherwood Sandstone correlates significantly with the intergranular permeability and the matrix conductivity but only at low electrolyte concentrations (< 500 p.p.m. NaCl). An increase in the magnitude of sandstone IP with increase in the valence of the electrolyte cation is pronounced but occurs only at intermediate concentrations, i.e., between 100 and 2500 p.p.m. Surface IP and resistivity depth sounding measurements, supplemented by data from laboratory measurements, can be used to estimate the groundwater conductivity and hence the salinity in a moderate to strongly saline sandstone aquifer.     

A SIMPLE DERIVATION OF SEIGEL'S TIME DOMAIN INDUCED POLARIZATION FORMULA *

It is advantageous to postulate the phenomenological equivalence of chargeability with a slight increase in resistivities rather than a similar reduction in the conductivities. Substitution of these increments in the expression for the total differential of apparent resistivity leads directly to Seigel's formula. Included also are (i) an equally simple demonstration that, for a homogeneously chargeable ground with arbitrary resistivity distribution, the apparent chargeability m_a, equals the true homogeneous value m, and (ii) a direct derivation of the completely general resistivity relation where the symbols have the usual meanings.     

A NEW PARAMETER FOR THE INTERPRETATION OF INDUCED POLARIZATION FIELD PROSPECTING (time-domain) *

In a previous paper it has been shown that we can relate the transient IP electric field E_p , existing in a rock after a step wave of polarizing current, with the steady-state current density J_ss during the current step wave as follows: E_p =ρ' J_ss . This relation may be interpreted as a generalized Ohm's law, valid in linear cases, in which ρ’(fictitious resistivity) is defined as the product of the true resistivity ρ with the chargeability m. Supposing E _p=— grad U_p and applying the divergence condition div J_ss = o, one can, for a layered earth, obtain a general expression for the depolarization potential U_p as a solution of Laplace's equation ?²U_p= o. Since the mathematical procedure for the solution of this last equation is identical to that used in resistivity problems, we propose now the introduction of an apparent fictitious resistivity ρ'_a (defined as the product of the apparent resistivity ρ_a with the apparent chargeability m_a) as a new parameter for the interpretations of IP soundings carried out over layered structures with a common electrode array. The most general expression of ρ'_a as a function of the electrode distance turns out to be mathematically identical to the general expression of ρ'_a. Therefore it is possible to interpret a ρ'_a field curve using the same standard graphs for resistivity prospecting with the usual method of complete curve matching. In this manner a great deal of work is saved since there is no need to construct proper m_a graphs for the interpretation of IP soundings, as it has been done up to now. Finally some field examples are reported.     

ON THE INTERPRETATION OF RESISTIVITY SOUNDINGS BY THE LEAST-SQUARES METHOD*

An interactive least-squares method for the interpretation of VES curves was proposed by Johansen (1977). The method permits one to select some parameters (thicknesses and/or resistivities of individual layers) and to change the rest in such a way that the interpreted model approaches the measured data. This note suggests a modification of Johansen's method, in which not only the individual parameters can be selected but also linear combinations of parameters—in particular, the sum of thicknesses of several layers.