Transient marine electromagnetics: the 2.5-D forward problem

Abstract

Marine controlled-source electromagnetic experiments are designed to measure the electrical conductivity of the sea-floor. The apparatus consists of a transmitter, typically an electric current dipole, and a series of remote receivers. Variations in the current through the dipole cause correlated variations in the electric and magnetic fields at the receivers. The signals contain information about the electrical conductivity of the crustal rocks. Electrical conductivity is related to such critical physical parameters as porosity, temperature, composition, fluid content and texture. Many interesting sea-floor structures, such as the mid-ocean ridge or the continental margin, may be approximated by a 2-D model. There is a defined local horizontal strike direction and the conductivity along strike is approximately constant. We investigate the response of an arbitrary 2-D structure to an artificial, compact source deployed on or near the sea-floor, a case commonly described as having 2.5 dimensions. Our aim is to improve the design of sea-going experiments and provide a tool for the interpretation of data. We transform the governing Maxwell equations into the Laplace and along-strike spatial Fourier domains. Two coupled linear-differential equations result whose dependent variables are the along-strike components of the electric and magnetic fields. The equations are solved by the finite element method. The accuracy of the numerical solution is dramatically improved by exploiting the known rate of convergence towards the exact solution with systematic doubling of node density. Responses in the space-time domain are recovered by a combination of inverse Laplace and Fourier transforms. We selected the Gaver-Stehfest algorithm to compute the inverse Laplace transform because it requires the evaluation of iespnses at vniy a small number of real values of the Laplace variable s, eliminating the need for any complex arithmetic. The output from the software we present here are fields on the sea-floor that result from a sudden increase in current through an electric-dipole transmitter, transient step responses. Computed transient responses are checked for accuracy against the analytic solution for a double half-space model and equivalent numerical solutioiis for an appropriate test structure. Two practical applications of the aigorithm are demonstrated. First, it has been suggested that the traveltimes of signals between a transmitter and a receiver array towed along the sea-floor may be rapidly inverted for variations in sea-floor conductivity, a type of tomography. We verify that the traveltime method works effectively for vertical structures. Second, the response of a fast-spreading mid-ocean ridge segment is modelled in detail. The diffusion of signals through the structure and their distortion by the conductive axial magma chamber and the near-surface zones of hydrothermal fluid circulation are presented as a sequence of snapshots. The geometry and physical properties of the magma chamber and the subsurface hydrothermal circulation, key components of all proposed geological models of ocean crust formation, may be constrained. The perturbations of the signal on the sea-floor are measurable and diagnostic of the presence of these conductors.