This paper traces the early development of the induced polarization method, starting with field observations by Conrad Schlumberger in a mining region in France, about 1913. Starting about 1929 he introduced this technique into hydrocarbon borehole logging in the USSR, and this resulted in further development in eastern and western Europe.

The dynamic response characterizing the induced-polarization (IP) phenomenon is modelled by a nonlinear diffusion equation (Burger's equation) supplemented by relevant initial and boundary values. The analysis of the model yields a voltage step response and an impedance curve in the frequency domain which agree qualitatively with experimental measurements. Curve fits based on the model have been made in the case of electrochemical cell measurements. The diffusion coefficients estimated by means of these curves are of the same order of magnitude as those calculated using experimental measurements. The normalized transient with these diffusion coefficients agrees with observations, but probably has a shorter discharge time. We have also carried out a comparison with predictions obtained from a linear, finite diffusion layer model, thus showing that for most practical situations the nonlinear term modelling the migration effect can be neglected

The following two theorems are proved and discussed: 1. (1) the open-circuit potential difference between two electrodes M,N when steady current is passing through electrodes A,B is equal to that between A and B if the same current is passed through M,N for any arbitrary conductivity distribution in the ground provided only the ground is a linear medium;2. (2) the complex electromotive force developed in a receiver circuit R of small dimensions, due to alternating current flowing in a transmitter circuit T of small dimensions is exactly equal to the complex e.m.f. in T if the same current is flowing in circuit R, no matter how arbitrary the distribution of conductivity, magnetic permeability and dielectric permittivity in the ground, provided only the ground is a linear medium.A linear medium is one in which the current density, magnetic flux density and electric displacement are linear functions of electric and magnetic field intensities. The more general form of the second theorem when the dimensions of the circuits are not small is proved first and the special case of (2) derived from it.

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.

Anyone who compares the present thoroughly revised and enlarged edition of this book with the three previous ones, the first of which was published in 1962, may well ask whether the principles of applied geophysics have become more numerous during the last 25 years or so. Such is not the case and the much larger size of the present edition is due to the principles' having been explained in greater detail than heretofore. There are major and minor alterations, additions and emendations, too numerous to be listed here, throughout the book but I would like to draw attention specifically to some of them. The chapter on seismic methods is now far more extensive than before and so are also the chapters on electric and electromagnetic methods. There is also a separate chapter on well logging in oil fields giving the essential ideas. Considering the virtual plethora of available books on seismic methods and on well logging I have not thought it necessary to extend these chapters further. This has enabled me to keep the book to a reasonable length and at the same time retain its fairly comprehensive character. Other features of the present edition are solved examples in the text and the problems at the end of all principal chapters. Answers and hints to the latter are given at the end of the book.