The split-step Fourier method is developed and applied to migrating stacked seismic data in two and three dimensions. This migration method, which is implemented in both the frequency-wavenumber and frequency-space domains, takes into account laterally varying velocity by defining a reference slowness (reciprocal of velocity) as the mean slowness in the migration interval and a perturbation term that is spatially varying. The mean slowness defines a reference vertical wavenumber which is used in the frequency-wavenumber domain to downward continue the data across a depth interval as in constant-velocity phase-shift migration. The perturbation term is used to define a 'source' contribution that is taken into account by the application of a second phase shift in the frequency-space domain. Since the method does not include the effects of second and higher order spatial derivatives of the slowness field, the method theoretically is accurate only when there are no rapid lateral slowness variations combined with steep angles of propagation. However, synthetic and real examples indicate that good results are obtained for realistic geologic structures.

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