Synthetic examples

The real data examples in this chapter will involve prestack datuming, but to provide insight as to how wave-equation datuming compares to static shift, and for clarity of exposition, I will demonstrate a few concepts using the zero-offset synthetic data from Chapter .

Figure  is a comparison of static shift and wave-equation datuming applied to the same synthetic data displayed in Figure . Although both methods unravel the topographic distortion, the curvature of the diffracted events is substantially different. This difference in curvature is due to the inaccuracy of the static shift; in this situation the assumption of vertical raypaths is invalid.

As mentioned earlier, detrimental effects occur when wave-based processing is applied after an inappropriate static shift. This is illustrated in the top two panels of Figure . In this case, time-migration has been applied after static shift downward in Figure a and after static shift upward in Figure b. In both cases, the static shift has distorted the data so badly that migration fails. A similar failure can be expected for any wave-based process applied to prestack data. In this case, I define wave-based process as any method which is built on the assumption that the data obey the wave equation. This includes methods such as normal-moveout correction (NMO), dip-moveout correction (DMO), NMO stack, prestack migration, and velocity analysis. This may partially explain the common observation that DMO applied to overthrust data often has detrimental effects (Tilander and Mitchel, 1995; Burke and Knapp, 1995).

When the data are extrapolated to the flat datum by wave-equation datuming, the wavefield character of the data are preserved. This is demonstrated in the lower panels of Figure  where the data have been migrated after upward and downward continuation. Accurate images are formed in both cases.

 

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Figure 1 (a) Static shift upward and (b) wave-equation datuming upward . The two processes result in events with differing curvature. Panel b is the same as Figure b and is reproduced here for ease of comparison.

 

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Figure 2 Static shift and wave-equation datuming followed by migration. (a) Static shift downward followed by time migration, and (b) static shift upward followed by time migration. The process of static shift distorts the wavefield so that migration fails. (c) Wave-equation datuming downward followed by time migration, and (d) wave-equation datuming upward followed by time migration. Wave-equation datuming preserves the proper kinematics so that subsequent wave-based processing can be successfully applied. Panels c and d are the same as Figures b and b and are reproduced here for ease of comparison.