Example 2: A more realistic synthetic

We next apply non-stationary PEF's to the synthetic dataset described by Sava and Guitton (2003). The model is designed to resemble a typical Gulf of Mexico subsalt problem.

Each angle gather is processed separately, but the same parameters are used for all gathers. A typical gather is shown in Figure a. For the noise PEF estimation we again use the multiple model estimated with the PRT approach (Figure b), and for the signal PEF we use a laterally smoothed version (Figure d) of the primary model estimated from the PRT approach (Figure c). The smoothing is accomplished by averaging across 8 traces in each direction from a given trace, and helps to weaken or remove the remaining multiple energy. This improves the ability of the signal PEF's to accurately represent the pattern of the signal. The primary model estimated by the PEF approach is shown in Figure f, with the corresponding multiple model in Figure e. The result is clearly a much better separation of the multiples from the primaries in the angle domain.

 

CIG_BP_nice
Figure 2 (a) Input data- one angle gather from the synthetic. (b) Multiple model estimated with PRT approach. (c) Primary model estimated from PRT approach. (d) Signal model used for PEF estimation (smoothed version of (c)). (e) Multiple model estimated with PEF approach. (f) Primary model estimated with PEF approach.

A comparison of common-angle gathers (Figure ) highlights the effectiveness of the non-stationary PEF approach. Figure a shows a window of the raw data at an angle of 15 degrees. Figure b shows the corresponding PRT result, with improved resolution of the deeper reflectors. And Figure c shows the PEF result, with considerable improvement over the PRT result, particularly of the reflector at 19 kft.

 

BP_CA
Figure 3 Common-angle gathers, at an angle of 15 degrees. (a) Raw data. (b) PRT result. (c) PEF result, with improved clarity of reflectors at 15 kft and 19 kft.

The real test of effectiveness, of course, is a comparison of the stacked results. A final stack of the raw data is shown in Figure a, the PRT result in Figure b, and the final PEF stack is shown in Figure c. The PEF result shows improvement in the clarity of reflectors in the lower part of the record.

 

BP_stack
Figure 4 Stacked images. (a) Stack of raw data. (b) Stack of PRT result. (c) Stack of PEF result. Note improved clarity of reflector at depth of 19 kft.

We chose the smoothed PRT result as the model for estimation of the signal PEF after testing several options. The PRT primary model contains sufficient multiple energy that the PEF estimation is impacted significantly, and the final estimated signal contains considerable multiple energy as well. The use of ${\bf Nd}$presents similar limitations and similar problems with the final result, due to the inability of the noise PEF ${\bf N}$ to completely remove the multiple energy. The smoothed version of the PRT primary model is the most effective model that we tested. The smoothing helps to remove a considerable amount of the remaining multiple energy and generally cleans up the model so that the PEF estimation is a simpler problem. This smoothing would not be a wise choice as a processing step on raw data, but it is acceptable for cleaning up the PEF-estimation model and results in PEF's that are well-suited to task of separating primaries from multiples in this case.