TRANSIENTS AND FIELD BEHAVIOUR IN INDUCED POLARIZATION*

This paper deals with electromagnetic fields in the so called “Transient Induced Polarization Technique”. Field equations are integrated in the case of a polarizable sphere inbedded in a sterile overburden. The existence of a remanent polarization vector P which slowly decays once the charging current has been cut off is taken as the initial condition. When the surface between the air and overburden is (as a first step) disregarded, the Laplace transform of the EM fields is given. The integral of the electric field (which is fairly often the result of prospection work) is independent of the various time constants related to electrochemical processes, but it stands as a good measurement of the total electrostatic dipole created by the charging current. We investigate the geometrical circumstances that can bring negative values of I.P. signal. Such negative values can be found in two cases: 1. The discharge currents are. distorted by the ground surface. 2. The I.P. signal is picked up by electrodes inside the polarizable material. The last part is dedicated to an account of experimental work performed on models and of an actual case history. The mathematical derivations are included in an appendix.     

RESISTIVITY PROFILING WITH DIFFERENT ELECTRODE ARRAYS OVER A GRAPHITE DEPOSIT*

Motivated by several papers by Indian colleagues suggesting that a single-pole array is the most favorable one for locating electrically conductive targets in the underground, detailed measurements were carried out with different electrode arrays over a well-known graphite deposit near Pfaffenreuth, Germany. The following arrays were used: (1) Wenner array; (2) single-pole array; (3) half-Wenner array; (4) half-Schlumberger array. Each of the arrays established the location of the main graphite deposit. The half-Schlumberger array turned out to be the most reliable one since it showed details which were only very poorly indicated by the other arrays or not at all. Mathematical modeling of three-dimensional bodies simulating the geological situation for this deposit were carried out. These results show an unexpectedly good correlation with the measured effects.     

FIELD RESULTS WITH DOWNWARD CONTINUATION TECHNIQUE IN INDUCED POLARIZATION PROFILING USING POINT ELECTRODES1

The method of downward continuation is well known to those working in gravity, magnetic, SP and low-frequency electromagnetic exploration. It is demonstrated that the method of continuation can also be usefully employed in the interpretation of induced polarization gradient profiling using point electrodes to determine target depth. The apparent resistance R_a and chargeability M_a measurements obtained with point electrode excitation of the ground have been used to compute the values of (R_a)_l and (M_a)_l that would be obtained with a linear array. Continuation of the apparent polarizability profile thus obtained with the linear array gives a value for the depth of the target which agrees closely with that obtained by the continuation of the SP profile. On the other hand, continuation of the profile of the secondary transient signal (V_S)_L alone, yields a depth of the target which is in agreement with the borehole information. However, it is seen that the secondary transient voltage profiling response splits into two anomalies which fall on either side of the SP and/or (M_a)_l anomaly centre, and does not coincide with that of the latter.     

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.     

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.     

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.     

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.     

TEST OF RECIPROCITY AND SUPERPOSITION IN TIME DOMAIN INDUCED POLARIZATION MEASUREMENTS*

The principles of reciprocity and superposition, which hold in normal resistivity measurements, are sometimes considered to apply also to Induced Polarisation measurements. In this paper, an account is given of experiments designed to test how far such a proposition is justified. The experiments comprise a limited field test and more extensive observations using a tank analogue. Within acceptable limits, both tests showed that these basic theorems are applicable to I.P. potentials provided that these are measured at the same instant after switch off and that identical charging regimes are used. The implications of these findings are discussed.     

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.     

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.     

COMPARISON OF TIME,FREQUENCY, AND PHASE MEASUREMENTS IN INDUCED POLARIZATION*

In comparing the similarity between time, frequency, and phase measurements as used in the induced polarization method of geophysical prospecting, parameters must first be defined and the basis for comparison established. The conditions for mathematical equivalence then follow in a natural sequence. Laboratory measurements are made on a variety of rock samples to indicate the type of comparison and correlation expected from field measurements. Results indicate that frequency domain and phase measurements are equivalent, but two frequency domain measurements are needed to produce the same amount of polarization information as a single phase measurement. Frequency and time domain measurements will be similar but never equivalent due to the basic differences in their respective parameter definitions.     

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.     

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.     

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.     

RESISTIVITY AND INDUCED POLARIZATION RESPONSES OF ARBITRARILY SHAPED 3-D BODIES IN A TWO-LAYERED EARTH*

Numerical computations using the integral equation method are presented for resistivity and IP responses due to arbitrarily shaped 3-dimensional bodies in a layered earth. The unknown surface charge density distribution is expressed as the solution of Fredholm's integral equation of the second kind. Use of moment method (with pulse basis function and point-collocation) yields the matrix equations for the unknowns. The contributions to Green's function are solved (a) analytically for the primary and (b) by convolution for the secondary contributions resulting in a fast algorithm. The further step of computing potential, apparent resistivity, chargeability etc., for any electrode system, is straightforward. Our results show a good agreement with those from finite difference methods and physical tank experiments. The CPU time is only 138 s on a super-minicomputer for an apparent resistivity pseudo-section, even with 96 elementary cells as used for discretization. A large number of models for different geological situations were studied; some are presented here.     

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.     

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.