Abstract
It is illustrated that IP phenomena in rocks can be described using conductivity dispersion models deduced as solutions to a 2nd-order linear differential equation describing the motion of a charged particle immersed in an external electrical field. Five dispersion laws are discussed, namely: the non-resonant positive IP model, which leads to the classical Debye-type dispersion law and by extension to the Cole-Cole model, largely used in current practice; the non-resonant negative IP model, which allows negative chargeability values, known in metals at high frequencies, to be explained as an intrinsic physical property of earth materials in specific field cases; the resonant flat, positive or negative IP models, which can explain the presence of peak effects at specific frequencies superimposed on flat, positive or negative dispersion spectra.
Highlights
Electric dispersion in rocks is the phenomenology on which the Frequency-Domain (FD) Induced Polarization (IP) geophysical survey method is based
Five dispersion laws have been discussed, namely: 1) the non-resonant positive IP model, which leads to the classical Debye dispersion law and by extension to the Cole-Cole law, largely used in current practice; 2) the non-resonant negative IP model, which introduces the possibility of explaining negative chargeability values, known in metals at high frequencies, as an intrinsic physical effect in some earth materials; 3) the resonant flat, positive or negative
IP models, which explain the presence of peak effects at specific frequencies superimposed on flat, positive or negative dispersion spectra
Summary
Electric dispersion in rocks is the phenomenology on which the Frequency-Domain (FD) Induced Polarization (IP) geophysical survey method is based. Many empirical models have been proposed to explain IP effects in rocks. Where ω is the angular frequency, i is the imaginary unit, q and m2 represent the electric charge and the mass of the carrier, m0 is an elastic-like coefficient accounting for recall effects, m1 is a friction-like coefficient accounting for dissipative effects due, e.g., to collisions, and R(ω) is the FT of the trajectory of the charge carrier. Assuming for simplicity that the dispersive material contains only one species of charge carriers, indicating with K the number of charge carriers per unit of volume, the following expression for the dispersive conductivity function σ(w), called admittivity (Stoyer, 1976), has. It is equivalent to the Lorentz dispersion formula obtained as solution to the 2nd-order ordinary differential equation of harmonic oscillation (Balanis, 1989)
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