High-order finite-difference simulations of marine CSEM surveys using a correspondence principle for wave and diffusion fields

Abstract

The computer time required to solve a typical 3D marine controlled-source electromagnetic surveying (CSEM) simulation can be reduced by more than one order of magnitude by transforming low-frequency Maxwell equations in the quasi-static or diffusive limit to a hyperbolic set of partial differential equations that give a representation of electromagnetic fields in a fictitious wave domain. The dispersion and stability analysis can be made equivalent to that of other types of wave simulation problems such as seismic acoustic and elastic modeling. Second-order to eighth-order spatial derivative operators are implemented for flexibility. Fourth-order and sixth-order methods are the most numerically efficient implementations for this particular scheme. An implementation with high-order operators requires that both electric and magnetic fields are extrapolated simultaneously into the air layer. The stability condition given for high-order staggered-derivative operators here should be equally valid for seismic-wave simulation. The bandwidth of recovered fields in the diffusive domain is independent of the bandwidth of the fields in the fictitious wave domain. The fields in the fictitious wave domain do not represent observable fields. Propagation paths and interaction/reflection amplitudes are not altered by the transform from the fictitious wave domain to the diffusive frequency domain; however, the transform contains an exponential decay factor that damps down late arrivals in the fictitious wave domain. The propagation paths that contribute most to the diffusive domain fields are airwave (shallow water) plus typically postcritical events such as refracted and guided waves. The transform from the diffusive frequency domain to the fictitious wave domain is an ill-posed problem. The transform is nonunique. This gives a large degree of freedom in postulating temporal waveforms for boundary conditions in the fictitious wave domain that reproduce correct diffusive frequency-domain fields.

Resolution of Full Waveform Inversion Using Controlled-source Electromagnetic Method

“…In that situation, the stability condition used in the conventional finite-difference time-domain (FDTD) algorithm needs a very small time steps. To overcome this problem, Mittet (2010) proposed FDTD solution in a fictitious time domain. The three dimensional time-domain Maxwell equation is transformed in the fictitious time domain using the equation,…”

“…For forward simulation, fictitious time domain method is employed to calculate electromagnetic fields by finite-differential timedomain (FDTD) method (Mittet, 2010). For inversion simulation, a full waveform inversion method is employed using synthetic data.…”

Three-dimensional electromagnetic responses of disk-shaped hydrocarbon reservoir in marine sediments

“…Many three-dimensional (3D) frequency-domain and time-domain EM models have been developed Um and Alumbaugh, 2007;Sasaki and Meju, 2009;Mittet, 2010). They are based on the finite difference method, and its main attraction is an apparent simplicity of its numerical implementation.…”

Simulation of Electromagnetic Diffusion in Anisotropic Media

“…Further research is necessary to verify if the present algorithm can be used with an electricmagnetic formulation of Maxwell's equations, where derivatives of the material properties are avoided [9,36]. A promising approach can be to solve a fictitious hyperbolic representation of the electromagnetic equations [20,22].…”