In Chapter , I apply the Kirchhoff datuming operator to land data to help ameliorate the effects of rugged topography. I compare the results of wave-equation datuming to statics and show that redatuming and regridding with the Kirchhoff datuming operator results in a superior stacked section and migrated image.
Seismic imaging algorithms are generally applied to data which is redatumed to a planar surface. In regions of mild topography where the near-surface velocity is much slower than the subsurface velocity, a static shift is adequate for the transformation. However, when the necessary shift increases in magnitude and when the near surface velocity is comparable to the subsurface velocity, the static approximation becomes inadequate. Under these circumstances, a static shift distorts the wavefield and degrades the velocity analysis and imaging. In this case it is necessary to propagate the wavefield numerically to some level datum. This wave-equation datuming process may be used to ``flood'' the topography by filling it with a replacement velocity and upward continuing the data through it.
Unlike redatuming with static shifts, wave-equation redatuming removes the distortions caused by topography in a manner consistent with wavefield propagation. This insures that subsequent processing steps which assume hyperbolic form, or even more complicated trajectories consistent with wave propagation, can be accurately applied.
For example, Figure shows a shot gather from the Canadian foothills before and after wave-equation datuming. After wave-equation datuming the distorting effects of the topography are removed and the reflection events have laterally continuous trajectories consistent with wave propagation. The datuming operation also serves to regrid the data onto a uniformly sampled output mesh, fill in the shot gap, and attenuate steep-dip noise.