SOME ASPECTS OF INDUCED POLARIZATION (TIME DOMAIN)*

In the first part, the author, recalling the principle of d/c current measurements, shows by means of some examples, different experimental results relative to the induced polarization phenomenon. He presents the case of the negative induced polarization which can be explained by geometric effects. He gives some examples of saturation curves and discusses the problem of the linearity of the I.P. phenomenon. Then he shows some aspects which demonstrate that I.P. decay curves do not always conform to the general law. He concludes by showing the influence of the current electrodes, the position of which, relative to the polarizable bodies, may alter the shape of the I.P. anomalies. In the second part, the author presents different case histories of I.P. mineral surveys where I.P. is compared to other geophysical methods and drilling results.     

AN INTERACTIVE COMPUTER/GRAPHIC-DISPLAY-TERMINAL SYSTEM FOR INTERPRETATION OF RESISTIVITY SOUNDINGS*

A fast computer-procedure giving the apparent resistivity curve as well as the partial derivatives with respect to the layer-parameters is presented. It is based on the linear filter method developed by D. P. Ghosh in 1971. The sampling frequency is 10 points per decade, and 3 decades are covered. The maximum relative error is less than 10^?3, and in most cases orders of magnitude smaller. The computation time on a CDC 6400 for one curve given in 30 points ranges linearly from .17s for a two-layer case to .36s for a ten-layer case. The procedure is used to plot master curves interactively on a graphic display terminal (Tektronix 4010) connected to the CDC 6400. By trial-and-error adjustments a set of layer-parameters is found, giving essentially the measured curve.     

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.     

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.     

COMPARATIVE FIELD PERFORMANCE OF ELECTRODE ARRAYS IN TIME-DOMAIN INDUCED POLARIZATION PROFILING *

Five test profiles in time-domain induced polarization measurements over conducting sulphide and graphite mineralisations were run with the two-electrode, three-electrode, modified unipole, pole-dipole, dipole-dipole, Schlumberger, and Wenner α and β configurations. The results show that, compared to the other electrode systems, the simplest two-electrode array produces the largest anomalies with the smallest of spacings.     

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。     

PROGRESS IN THE DIRECT INTERPRETATION OF RESISTIVITY SOUNDINGS: AN ALGORITHM*

An algorithm is presented for the direct interpretation of resistivity sounding data. The algorithm is based on the method of successive reductions to lower boundary plane of the resistivity transform function. A novel aspect of the algorithm is that error limits are assigned to the initial values of the resistivity transform, and these error limits are carried through in all the subsequent computations. The width of the error range is then used as the basis for assigning weight factors in the final computation of thicknesses and resistivities of the layers. The errors in the resistivity transform derived from the solution given by the algorithm are usually not more than twice as large as those in the original data.     

VERTICAL FREQUENCY EFFECT SOUNDING IN INDUCED POLARIZATION AND GALVANIC RESISTIVITY METHODS *

It has been shown that for a polarizable layer as a transmission medium there is an indirect proportionality between the frequency effect (fe) in induced polarization (IP) and the wave number of the electrical induced field. Making use of this relationship for a two layered earth a polarization transform function has been obtained. Since the mathematical expression for the polarization transform function is the same as that of the resistivity transform function, it is possible to make direct interpretation for IP frequency effect field curves. Thus, AA or QQ type resistivity sequences can be interpreted from induced polarization response of a horizontally stratified earth without resistivity extrema. A depth factor has been defined in order to obtain the true depth using the apparent depth. In this way, some electromagnetic effects between horizontal layers with different polarizabilities can partly be eliminated.     

A NUMERICAL COMPUTATION PROCEDURE FOR THE DIRECT INTERPRETATION OF GEOELECTRICAL SOUNDINGS*

In this paper a numerical method of direct interpretation of geoelectrical soundings is described. It has similarities with already existing direct methods, but owing to its simplicity and, in particular, to the possibility of applying it also without digital computers, it proves useful mostly in the field, where very often an accurate method for the interpretation of multi-layer curves is required. The direct interpretation system splits up into three steps: i) the evaluation of the resistivity transform after application of Hankel's inversion theorem; ii) the determination of the layer distribution after application of Koefoed's recurrent procedure; iii) the control of the solution. Each step is considered and the practical procedures suggested. Finally two field examples are presented and discussed.     

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.     

A MAN/COMPUTER INTERPRETATION SYSTEM FOR RESISTIVITY SOUNDINGS OVER A HORIZONTALLY STRAFIFIED EARTH*

The proposed system works as follows:

• 1 By a trial-and-error procedure using a graphic display terminal a geologically relevant layer sequence with parameters (ρ_j, d_j) is adjusted to yield roughly the measured curve.
• 2 The resulting layer sequence is used as starting model for an iterative least squares procedure with singular value decomposition. Minimization of the sum of the squares of the logarithmic differences between measured and calculated values with respect to the logarithms of the resistivities and thicknesses as parameters linearizes the problem to a great extent, with two important implications:

• a) a considerable increase in speed (the number of iterations goes down), thus making it cheap to achieve the optimum solution;
• b) the confidence surfaces in parameter space are well approximated by the hyper-ellipsoids defined by the eigenvalues and eigenvectors of the normal equations.

Since these are known from the singular value decomposition we do in fact know all possible solutions compatible with the measured curve and the geological concept.

• 3 It is possible to “freeze” any combination of parameters at predetermined values. Thus extra knowledge and/or hypotheses are easily incorporated and can be tested by rerunning step (2). The overall computing time for a practical case is of the order of 10 sec on a CDC 6400.

     

AN INTERPRETATION SYSTEM FOR GEO-ELECTRICAL SOUNDING GRAPHS *

For the two and three layer cases geo-electrical sounding graphs can be rapidly and accurately evaluated by comparing them with an adequate set of standard model graphs. The variety of model graphs required is reasonably limited and the use of a computer is unnecessary for this type of interpretation. For more than three layers a compilation of model graphs is not possible, because the variety of curves required in practice increases immensely. To evaluate a measured graph under these conditions, a model graph is calculated by computer for an approximately calculated resistivity profile which is determined, for example, by means of the auxiliary point methods. This model graph is then compared with the measured curve, and from the deviation between the curves a new resistivity profile is derived, the model graph of which is calculated for another comparison procedure, etc. This type of interpretation, although exact, is very inconvenient and time-consuming, because there is no simple method by which an improved resistivity profile can be derived from the deviations between a model graph and a measured graph. The aim of this paper is, on the one hand, to give a simple interpretation method, suitable for use during field work, for multi-layer geo-electrical sounding graphs, and, on the other hand, to indicate an automatic evaluation procedure based on these principles, suitable for use by digital computer. This interpretation system is based on the resolution of the kernel function of Stefanescu's integral into partial fractions. The system consists of a calculation method for an arbitrary multi-layer case and a highly accurate approximation method for determining those partial fractions which are important for interpretation. The partial fractions are found by fitting three-layer graphs to a measured curve. Using the roots and coefficients of these partial fractions and simple equations derived from the kernel function of Stefanescu's integral, the thicknesses and resistivities of layers may be directly calculated for successively increasing depths. The system also provides a simple method for the approximative construction of model graphs.     

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.     

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。     

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。     

INTERPRETATION GRAPH FOR VERTICAL TABULAR CONDUCTORS IN E.M. IN-LINE DIP-ANGLE MEASUREMENTS*

A graphical interpretation method is presented by which separately the depth and the product of conductivity and thickness of a vertical plate-shaped conducting orebody can be determined. The method is based on the result of model experiments.