Seismic data acquired in areas with irregular topography introduce a numerical problem for migration algorithms that are based on depth extrapolation. Since numerically efficient migration schemes are usually based on depth extrapolation algorithms that allow the extrapolation of a wavefield from a flat surface to another flat surface, datuming is required prior to migration. Datuming is a method of processing for extrapolation of a known wavefield at a specified datum of arbitrary shape to another specified datum, also of arbitrary shape. For small differences in elevation and slow velocity variations between the input datum and the output datum, static shifting is a sufficiently accurate datum correction procedure. However, for significant differences in elevations and a more complicated velocity model, the accuracy of the static solution may prove to be insufficient, and a more exact method should be used.
Berryhill presented a wave equation datuming scheme for poststack and prestack data using the Kirchhoff integral method. Following his work, various forms of the Kirchhoff integral solution to the wave equation have been used by different authors for migration Shtivelman and Canning (1988); Wiggins (1984) and for layer replacement Berryhill (1986); Yilmaz and Lucas (1986).
This appendix presents a datuming scheme that can be used with any depth extrapolation scheme such as the phase-shiftG (1978), split-step Stoffa and Fokkema (1990), and finite-difference methods Claerbout (1985).