POSTSTACK DATUMING

Poststack and prestack datuming, and various migration schemes, all take surface recorded data as containing subsurface primary reflections only. This means that the surface can be regarded as an absorbing boundary when recording the seismic wavefields. In poststack finite-difference reverse-time migration (McMechan, 1983), these surface recorded wavefields are taken as boundary conditions for running the two-way wave equation backward in time. The wavefield at time t=0 is the subsurface reflectivity image, according to the imaging principle. The recorded wavefields can also be taken as the boundary condition for running the two-way wave equation forward or backward in time in a thin strip containing the two datums. The desired wavefields are the history wavefields at the output datum, with the four sides designed as absorbing boundaries. The wave equation runs forward in time (beginning from the minimum time) if one is extrapolating from a lower datum to a higher datum, and backward in time (from the maximum time) if one is extrapolating from a higher datum to a lower datum, because the actual earth wavefields expand up from the subsurface. The theory and results of datuming by the Kirchhoff-method can be found in Berryhill (1979, 1984) and Shtivelman and Canning (1988). Here I do the datuming by solving the two-way acoustic wave equation by the finite-difference method. Even though any recursive wavefield extrapolation method can be applied to accomplish datuming, I have chosen this particular method because it is more accurate and can honor arbitrary velocity models. The following sections describe upward and downward datuming with increasing degrees of complexity. The results show that a traveltime trajectory distorted by irregular recording topography can be corrected by datuming to a planar datum, either upward or downward.