Phase‐field imaging: The electromagnetic equivalent of seismic migration

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Abstract
An alternative approach to the interpretation of electromagnetic (EM) data is to downward continue the observations to construct a two‐dimensional resistivity image of the medium that produced them. The downward continuation can be done in a straightforward manner by drawing a parallel between the EM and acoustic wave equations. With appropriate approximations and identification of specific terms that are equivalent and with transformation from an initial‐value problem to a boundary‐value problem, EM data can be imaged using any of the methods originally developed for migration of seismic data. The method we chose here is Claerbout’s one‐way, finite‐difference, wave‐equation migration. The algorithm is implemented in the frequency domain. Independent images of relative reflectivity are obtained by processing E and H pseudosections separately; the best estimate of the actual reflector position is the region of coincidence of the two images. The same approach can be used in reverse for modeling the EM responses of two‐dimensional resistivity distributions. The main assumptions are direct analogies of the assumptions involved in state‐of‐the‐art seismic processing: details of EM reflectivity contained in the data wave fields are separable from the estimated background conductivity through which the wave field is downward continued, and there are no multiple reflections. Thus, the main restriction is that the resistivity variation be sufficiently small. The concept of imaging resistivity, as a function of position, is shown to be feasible and a direct analogy of seismic migration.

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