Rune Mittet

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

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.

A two-step approach to depth migration of low frequency electromagnetic data.

Summary In order to migrate electromagnetic data from a low frequency controlled source, 3D electromagnetic Green functions should be used since the near-field effects may be large. Imaging principles of the correlation type do not have sufficient depth sensitivity to be used in a one-pass migration step. Depth sensitivity is increased if a non-local operator is introduced in the imaging condition. This operator accounts for the lateral propagation of the EM field in the high resistivity reservoir. The non-local operator depends on two parameters related to the resistivity and thickness of an assumed resistivity anomaly. These parameters can be estimated from a limited set of forward modeling operations.