THE QUANTITATIVE ANALYSIS OF FREQUENCY-DOMAIN INDUCED POLARIZATION SOUNDINGS OVER HORIZONTAL BEDS * BY D. PATELLA** and D. SCHIAVONE*** ABSTRACT PATELLA, D., and SCHIAVONE, D., 1976, The Quantitative Analysis of Frequency- Domain Induced Polarization Soundings over Horizontal Beds, Geophysical Prospecting 24, 334-343. Following up our recent study of an indirect procedure for the practical determination of the maximum frequency-effect, defined as fe = I - pm/pdc with pm the resistivity at infinite frequency, we show at first how, through the Laplace transform theory, pm 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 condi- tions, we derive the integral expression of the apparent resistivity at infinite frequency pm,a in the case of a horizontally layered earth. Finally, from the definition of the maxi- mum apparent frequency-effect, analytical expressions of fe, 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. INTRODUCTION In the study of the frequency behaviour of a polarizable medium, the theoretical physical parameter which characterizes the maximum amount of polarization of different geological formations is the so called frequency- effect (fe), defined as (see, for instance Patella and Schiavone 1976) : fe = I- P~/P~ (1) p. and pm, the resistivities at zero and infinite frequency, respectively, are real quantities simply deduced as limiting values of the complex frequency depen- dent resistivity p(k) appearing in the following well known relation (Wait ‘959) : E(io) = p(io) J(i0). (2) * Paper read at the thirty-seventh Meeting of the European Association of Explora- tion Geophysicists in Bergen, June 1975. ** Osservatorio di Geofisica e Fisica Cosmica - University of Bari (Italy). I** Istituto di Geodesia e Geofisica - University of Bari (Italy),