The effect of irregular acquisition topography is that it distorts seismic data. This is a serious problem in mountainous regions where there is extreme topographic relief along seismic lines. Wave-equation extrapolation provides a useful method of transforming data to a planar datum and then determining the near-surface velocity structure. This eliminates the distortion caused by the topography and allows standard processing methods such as velocity analysis, DMO, and migration to be applied.
Shtivelman and Canning 1988 show how data can be continued through known velocity structures using an asymptotic form of the Kirchhoff integral equation. McMechan and Chen 1990 implicitly include effects due to topography and near-surface velocity variation in prestack migration. In order for these methods to work, the near-surface velocity must be known. The more general situation I outlined in a previous report 1992 is one for which the near-surface velocity structure is unknown. In this situation I propose upward continuing the data to some planar datum above the topography with some fictitious extrapolation velocity. This should unravel the distortions caused by the irregular acquisition topography and allow standard imaging techniques to be applied to the data.
The proposed method is similar to wave-equation datuming applied to marine data to compensate for irregular water-bottom topography Berryhill (1979, 1984, 1986); Yilmaz and Lucas (1986). In the marine case, the data are downward continued to the water-bottom with the water velocity, and then upward continued with the water-bottom velocity. This removes the distortions due to the irregular water-bottom.
Land data is much like the marine data which has been continued to the water-bottom. I propose that the land data be extrapolated upward to some flat datum with an appropriate velocity. Once the data have been extrapolated to the flat datum, standard velocity analysis methods may be used to determine the near-surface velocity. Processing and imaging can be performed at the new datum or the data can be downward continued to some lower datum.
In this paper I present the implementation of a Kirchhoff datuming algorithm and apply it to real marine data and to synthetic land data. This paper presents the new concept that Kirchhoff datuming can be cast as conjugate pairs for upward and downward continuation. This property is exploited by Zhang and Claerbout 1992 as the basis for an interpolation algorithm. Ji and Claerbout 1992 and Popovici 1992 consider the conjugacy of Fourier domain wave-equation datuming.
I analyze the effect of irregular topography on zero-offset and pre-stack data. Forward models are generated by Kirchhoff modeling and migrated by Kirchhoff migration. Static shift is shown to be inappropriate but wave-equation datuming followed by migration produces a good image. Wave-equation datuming provides a way of extrapolating a distorted wavefield to a planar datum without knowledge of the near surface velocity structure. Once the data is at the planar datum, the velocity structure can be determined.