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.     

INDUCED POLARIZATION RESPONSE OF A HORIZONTALLY MULTILAYERED EARTH WITH NO RESISTIVITY CONTRAST*

The induced polarization response of a horizontally multilayered earth with no resistivity contrast can rapidly be calculated on a desk calculator or minicomputer for any electrode array. The formulation is a simple series summation of the products of weighting coefficients and the true induced polarization responses for each of the layers. The coefficients are directly derivable from the corresponding resistivity model. This series approach to IP formulation was originally described by Seigel but has not been treated extensively in the present-day geophysical literature. This method can be applied to either time or frequency domain induced polarization measurements. Once the coefficients are known, apparent induced polarization response can readily be obtained by judicious substitution of known, suspected, or assumed values of the true induced polarization of each layer. Basic formulation is presented for the IP potential coefficients (pole-pole or two array) with no resistivity contrast between the layers. From these coefficients, response of any number of layers for any electrode array can be obtained by suitable differentiation. Some examples of Wenner array for a three-layered earth and dipole-dipole array for a four-layered earth are used to illustrate the application. The results of this technique are valid for many natural situations of modest resistivity contrast. However, they definitely cannot be used if there are highly contrasting resistivity layers present. Such an approach is conceptually simple and is useful for survey planning, checking or setting the “depth-of-penetration”of a given array. For field induced polarization data that fits reasonably well to the no-resistivity-contrast model, this simple approach facilitates quantitative interpretation.     

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.     

THE QUANTITATIVE ANALYSIS OF FREQUENCY-DOMAIN INDUCED POLARIZATION SOUNDINGS OVER HORIZONTAL BEDS*

Following up our recent study of an indirect procedure for the practical determination of the maximum frequency-effect, defined as fe = 1 ? pρ_∞/ρdc with ρ_∞ the resistivity at infinite frequency, we show at first how, through the Laplace transform theory, ρ_∞ can be related to stationary field vectors in the simple form of Ohm's law. Then applying the equation of continuity for stationary currents with a suitable set of boundary conditions, we derive the integral expression of the apparent resistivity at infinite frequency ρ_∞,a in the case of a horizontally layered earth. Finally, from the definition of the maximum apparent frequency-effect, analytical expressions of fe_α are obtained for both Schlumberger and dipole arrays placed on the surface of the multi-layered earth section in the most general situation of vertical changes in induced polarization together with dc resistivity variations not at the same interfaces. Direct interpretation procedures are suggested for obtaining the layering parameters directly from the analysis of the sounding curves.     

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 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 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.     

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.     

INVESTIGATION OF SOME NON-LINEAR PHENOMENA OF INDUCED POLARIZATION USING A PHYSICAL-AND-MATHEMATICAL MODEL*

The electrical behaviour of a polarizable sample formerly studied (Time-Domain) through both the classical and the condenser methods is simulated using the theoretical responses given by a three dimensional physical-and-mathematical model, which has been proposed in a previous paper by one of us on the basis of certain hypotheses. The apparent capacitance responses of the sample are qualitatively simulated in order to tackle the problem under this point of view; moreover, an attempt to obtain a quantitative simulation of experimental data within the limits of the present reliability of the model, using theoretically obtained Model Master Curves characterized by dimensionless parameters, is done. This research is carried out in the frame of a broader study referring to a possible scheme of simulation of the so-called induced ionic polarization, concerning a number of idealized pseudo-reversible, potentially irreversible, non-linear phenomena.     

INDUCED POLARIZATION,A METHOD TO STUDY WATER-COLLECTING PROPERTIES OF ROCKS*

During the last decade many hypotheses were suggested to explain the phenomenon of induced electrical polarization in ionic conductive media. The most reliable of these is Fredricksberg's. Fredricksberg (1962) supposed that the pore spaces of a rock is composed of successively narrow (active zones) and wide (inactive zones). He simulated these pore spaces by a synthetic material that has an extremely high resistance. The pore spaces were generally in tube forms which exhibited some constrictions. He saturated these tubes with an electrolyte of a given concentration. An electric current was passed through this model. He observed an induced polarization voltage after current interruption. He attributed the formation of this voltage to a concentration gradient which took place due to the presence of excess charges in the active zones. Fredricksberg introduced a parameter (9) which described the relation among the lengths and cross sectional areas of the wide zones, the number of ions within each zone after current interruption with the recorded polarizability. The aim of this work is to correlate Fredricksberg's parameter with a parameter determined for natural rocks and to show experimentally the validity of this hypothesis when applying for some varieties of sandstones and volcanic rocks. The new parameter will help to evaluate a relationship between the polarizability and the water-collecting properties of rocks. Herein, we used the tortuosity T of sandstone samples instead of the parameter φ which was used by Fredricksberg to represent the pore geometry within his model (tortuosity of the passes within the model). It was shown that both φ and T have the same relationship with the polarizability ν of the rock samples and if φ or T have very low or very high values the polarizability ν tends to its minimum value, i.e. the curve representing the relation between ν and T has a maximum point corresponding to an intermediate value of T. This result supports Fredricksberg's hypothesis and confirm his results on synthetic models. For volcanic rocks the formation factor F was used since it was difficult to determine the porosity of the samples and consequently to calculate the tortuosity T as for sandstone samples. Experimental results confirm those obtained from sandstone. The grain constituents of sandstone samples were represented on equilateral triangle and the magnitude of induced polarization ν of each sample was deduced and represented on this triangle. Equipolarizability values ν drawn on this triangle showed that TJ will increase as the silty fractions of the rock increase, where the center of this triangle (represents minimum porosity) has polarizability less than 0.25%. An attempt was made to determine the coefficient of anisotropy of volcanic rock samples using the induced polarization method. For this reason the polarizability was deduced by measuring the induced polarization voltage for two perpendicular directions in a fractured cubes of andesitic basalt samples the coefficient of anisotropy was found to be equal 1.18.     

激发极化法基础理论研究——确定二次极化电流的新方法

本文提出一种通过测磁场确定面极化和体极化介质中二次极化电流的新方法.它与以往测电场的方法有所不同.当时域单向长脉冲激发电流通过面极化和体极化介质时,便在其表面和内部产生激发极化效应.在通电时间内和断电后的放电过程中,若极化介质内产生了二次极化电流,它必将在周围产生二次磁场.我们通过观测二次磁场可靠地确定了介质中二次电流的存在与否和量值大小以及矢量方向等重要内容.本文除给出一些实验结果外,还给出了实例.多年来,国内、外学者对体极化介质中二次极化电流的存在问题是有争议的,本文对此给出了具有充分说服力的实验结果,有利于统一这方面的认识.     

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.     

激发极化法基础理论研究——确定二次极化电流的新方法

本文提出一种通过测磁场确定面极化和体极化介质中二次极化电流的新方法.它与以往测电场的方法有所不同.当时域单向长脉冲激发电流通过面极化和体极化介质时,便在其表面和内部产生激发极化效应.在通电时间内和断电后的放电过程中,若极化介质内产生了二次极化电流,它必将在周围产生二次磁场.我们通过观测二次磁场可靠地确定了介质中二次电流的存在与否和量值大小以及矢量方向等重要内容.本文除给出一些实验结果外,还给出了实例.多年来,国内、外学者对体极化介质中二次极化电流的存在问题是有争议的,本文对此给出了具有充分说服力的实验结果,有利于统一这方面的认识.     

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.     

磁激电方法技术试验研究

激电法是矿产勘查的主要方法技术,其中应用最多的是电激电法,但电激电法在接地条件困难区(倒石堆、沙漠、戈壁、永久冻土)难以发挥效果,为了发展不接地的磁激电技术,在对磁激电法的基本原理、方法技术、数据处理等方面进行研究的基础上,开展了磁激电法与电激电法的对比试验,并对试验结果进行了分析。     

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.     

体极化介质激发极化法理论研究

本文首先根据实验结果和对体极化介质激发极化机理的分析,并由极化率的定义出发,采用与以往不同的方法,提出等效电阻率概念。其次,根据位场的叠加原理,给出在稳定电流场中二次极化场欧姆定律的微分形式。然后,根据电量不灭定律,提出稳定电流场中二次极化电流密度法向分量连续的边界条件式。最后,给出几种典型条件下的理论计算结果。