FDTD modeling of induced polarization phenomena in transient electromagnetics

• Published in: Geophysical journal international Vol. 209; no. 1; p. ggx023
• Main Authors: Commer, Michael, Petrov, Petr V., Newman, Gregory A.
• Format: Journal Article
• Language: English
• Published: United States Oxford University Press 01-04-2017
• Subjects: Electrical properties; Electromagnetic theory; GEOSCIENCES; Marine electromagnetics; MATHEMATICS AND COMPUTING; Numerical approximations and analysis; Numerical solutions
• ISSN: 0956-540X; 1365-246X
• DOI: 10.1093/gji/ggx023

The finite-difference time-domain scheme is augmented in order to treat the modelling of transient electromagnetic signals containing induced polarization effects from 3-D distributions of polarizable media. Compared to the non-dispersive problem, the discrete dispersive Maxwell system contains costly convolution operators. Key components to our solution for highly digitized model meshes are Debye decomposition and composite memory variables. We revert to the popular Cole-Cole model of dispersion to describe the frequency-dependent behaviour of electrical conductivity. Its inversely Laplace-transformed Debye decomposition results in a series of time convolutions between electric field and exponential decay functions, with the latter reflecting each Debye constituents' individual relaxation time. Finally, these function types in the discrete-time convolution allow for their substitution by memory variables, annihilating the otherwise prohibitive computing demands. Numerical examples demonstrate the efficiency and practicality of our algorithm.