Algorithms for the computation of the electromagnetic response of a multilayered, laterally anisotropic sea floor to arbitrary finite sources

Abstract

In a previous paper, we have shown that estimates of both the mean conductivity and the azimuthal anisotropy of the sea floor can be obtained by measuring the diffusion times of an electromagnetic disturbance from a transmitter on the sea floor to a set of receivers located around it. For that seminal study, the model considered was a simple double half‐space, an upper half‐space representing sea water in contact with a lower, more resistive half‐space representing laterally anisotropic crustal material, material for which the electrical conductivity in one horizontal direction x is different from the conductivity in the other two principal directions y and z. A uniform half‐space is rarely a realistic model of the sea floor. We extend the theory here to include the effects of several crustal layers which may have differing conductivity and anisotropy. We develop in two‐dimensional wavenumber domain the general solution of the governing Maxwell equations in terms of two scalar functions, the x‐components of electric and magnetic fields. The theory is valid for any finite source. We show that for static fields, the general solution simplifies greatly and expressions for measured magnetic and electric fields may be obtained through processes of upward and downward recursion and, for the magnetic field, surface integration over layer interfaces. At non‐zero frequencies, when the effect of electromagnetic induction is included in the formulation, the solution is more pedantic because elementary recursion rules could not be found and may not exist. Fundamental solutions for both the perpendicular magnetic and electric components must be written down for each layer and determined simultaneously as the solution of a large set of linear equations. Copyright © 1992, Wiley Blackwell. All rights reserved