On the determination of the apparent frequency-effect in the frequency-domain induced polarization method

Abstract

In the variable-frequency technique of the Induced Polarization (IP) method, the frequency-effect parameter, defined as: ƒ e = (ρ dc − ρ ∞) ρ dc , cannot actually be directly obtained since the resistivity ρ ∞ at infinite frequency cannot be measured. Thus some indirect procedures are needed to evaluate ƒ e . We propose a possible solution through the study of the correlation between frequency-domain and transient IP measurements, based on the application of the Laplace transform theory. From this a simple integral relation between the complex frequency-dependent resistivity and the time-dependent chargeability is at first obtained. Then the analysis of the properties of IP transients, which indicates that the chargeability can be expressed as a sum of n exponential decay terms with different initial amplitudes A j , allows to obtain an explicit form of the complex frequency-dependent resistivity, from which it follows that the frequency-effect is simply the sum of the coefficients A j . This result allows to calculate ƒ e in several different ways; the simplest consists in the measurements of the real or in-phase component of the complex resistivity at a discrete number of frequencies of the applied current.