TRANSIENT MARINE ELECTROMAGNETICS - THE 2.5-D FORWARD PROBLEM

Marine controlled-source electromagnetic experiments are designed to m easure the electrical conductivity of the sea-floor. The apparatus con sists of a transmitter, typically an electric current dipole, and a se ries of remote receivers. Variations in the current through the dipole cause correlated variations in the electric and magnetic fields at th e receivers. The signals contain information about the electrical cond uctivity of the crustal rocks. Electrical conductivity is related to s uch critical physical parameters as porosity, temperature, composition , fluid content and texture. Many interesting sea-floor structures, su ch as the mid-ocean ridge or the continental margin, may be approximat ed by a 2-D model. There is a defined local horizontal strike directio n and the conductivity along strike is approximately constant. We inve stigate the response of an arbitrary 2-D structure to an artificial, c ompact source deployed on or near the sea-floor, a case commonly descr ibed 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 alon g-strike spatial Fourier domains. Two coupled linear-differential equa tions 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 drama tically improved by exploiting the known rate of convergence towards t he exact solution with systematic doubling of node density. Responses in the space-time domain are recovered by a combination of inverse Lap lace and Fourier transforms. We selected the Gaver-Stehfest algorithm to compute the inverse Laplace transform because it requires the evalu ation of responses at only a small number of real values of the Laplac e variable s, eliminating the need for any complex arithmetic. The out put from the software we present here are fields on the sea-floor that result from a sudden increase in current through an electric-dipole t ransmitter, transient step responses. Computed transient responses are checked for accuracy against the analytic solution for a double half- space model and equivalent numerical solutions for an appropriate test structure. Two practical applications of the algorithm are demonstrat ed. First, it has been suggested that the traveltimes of signals betwe en 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-oce an ridge segment is modelled in detail. The diffusion of signals throu gh the structure and their distortion by the conductive axial magma ch amber and the near-surface zones of hydrothermal fluid circulation are presented as a sequence of snapshots. The geometry and physical prope rties of the magma chamber and the subsurface hydrothermal circulation , kev components of all proposed geological models of ocean crust form ation, may be constrained. The perturbations of the signal on the sea- floor are measurable and diagnostic of the presence of these conductor s.