This paper gives a unified treatment of electromagnetic ͑EM͒ field decomposition into upgoing and downgoing components for conductive and nonconductive media, where the electromagnetic data are measured on a plane in which the electric permittivity, magnetic permeability, and electrical conductivity are known constants with respect to space and time. Above and below the plane of measurement, the medium can be arbitrarily inhomogeneous and anisotropic.In particular, the proposed decomposition theory applies to marine EM, low-frequency data acquired for hydrocarbon mapping where the upgoing components of the recorded field guided and refracted from the reservoir, that are of interest for the interpretation. The direct-source field, the refracted airwave induced by the source, the reflected field from the sea surface, and most magnetotelluric noise traveling downward just below the seabed are field components that are considered to be noise in electromagnetic measurements.The viability and validity of the decomposition method is demonstrated using modeled and real marine EM data, also termed seabed logging ͑SBL͒ data. The synthetic data are simulated in a model that is fairly representative of the geologic area where the real SBL were collected. The results from the synthetic data study therefore are used to assist in the interpretation of the real data from an area with 320-m water depth above a known gas province offshore Norway. The effect of the airwave is seen clearly in measured data. After field decomposition just below the seabed, the upgoing component of the recorded electric field has almost linear phase, indicating that most of the effect of the airwave component has been removed.

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.

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