Gaussian beam migration

Lewei Mo

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ABSTRACT

This paper reports on my use of Gaussian beam wave propagation theory to downward continue all the frequency components of individual surface recorded wavefield traces (point sources) into the subsurface. According to the Huygens secondary point source principle, the surface recorded wavefields can be regarded as a series of point sources. The theory of Gaussian beam wave propagation asserts that asymptotic high frequency wavefield components propagate along rays, of which the wavefronts are parabolas and the amplitude profiles overriding the ray paths are Gaussian functions decaying away from the central ray paths. With my method, Gaussian beam wave propagation is implemented in the space-frequency domain. Poststack and prestack common-shot profile migration are accomplished by applying the corresponding imaging condition to the downward continued Gaussian beam wavefields in the frequency domain. The surface seismograms are migrated separately, and the migration process finishes by summing the contributions of all surface recorded traces to obtain the subsurface reflectivity image. This migration scheme combines the advantages of complete wave equation migration and ray tracing based migration. Tests with synthetic data show that the Gaussian beams evaluated along only seventeen rays from each surface seismogram location can image a fairly complex velocity and reflectivity model.