Data Subset for S-R Migration

The original dataset contains 6,764,207 traces (about 44 GB). Choosing a small, meaningful, ``complete'' subset of data for source-receiver migration, however, is not trivial, because the geometry of acquisition makes the offset distribution of adjacent CMPs in both inline and crossline directions different. This is illustrated in Figure  which shows the offset distribution inline for a few adjacent CMPs. Only every fourth CMP the offset distribution repeats. Although not shown, the situation in the crossline direction is worse. There are 20 different crossline offsets (from -475 to 475 m), but for any CMP line taken at a fixed crossline position, all traces correspond to the same crossline offset.

The input to the source-receiver migration algorithm is a regular 5-D cube

$$D(t,\mathbf{m},\mathbf{h}),$$

where $\mathbf{m}$ is the vector of surface position, $\mathbf{h}$ is the vector of surface offsets and t is the traveltime. In order to create such a cube, even for a small dataset, a large number of null traces need to be inserted. For example, for a 4 by 4 kms of full-fold CMP data we will have: 51200 CMPs (at 12.5 by 25 m) each with 240 inline offsets (100 to 6075 m offsets at 25 m sampling) and 20 crossline offsets (-475 to 475 m offsets at 25 m sampling) for a total of 440 million traces!. Since each trace has 1751 samples (7 seconds at 4 ms sampling interval), this means a dataset of almost 800 GB.

 

sketch3
Figure 6 Schematic showing the unequal offset distribution of adjacent CMPs in the inline direction. The stars represent the receivers and the small circles represent the CMP positions. The table on bottom left side lists the offset distribution of a few traces corresponding to four arbitrary adjacent CMPs numbered 1 to 4 as indicated by the arrows. Notice that the adjacent CMPs have different offset distribution.

In order to make a more manageable dataset, further data reduction is necessary. Here we are particularly interested in the effect of crossline dip in the moveout of the multiples after migration, therefore we chose to subsample the data in the inline coordinates only. We subsampled the inline CMP axis such that every other CMP was discarded. This has the advantage of not only halving the number of CMPs but also halving the number of inline offsets as can be seen in Figure  since now the inline offset interval is 50 m rather than 25 m. We also subsampled the time axis to 16 ms, which required that the data be filtered to a maximum frequency of 32 Hz even though the original wavelet had frequencies up to about 60 Hz as shown in Figure . This is appropriate in this case because vertical resolution is not critical for our purposes. Finally, we limited the inline offsets to 4000 m which sacrifices the steeper flanks of the moveout of the multiples as shown in Figure . With these reductions, the dataset size becomes about 70 GB after some padding in all spatial directions to avoid or at least lessen migration artifacts.

Figure  shows a near offset cube of the five-dimensional selected dataset. Notice that there are only six crossline CMPs for a given inline CMP location, corresponding to the six sail lines, and there is no data redundancy in the crossline direction. Similarly, only every other inline CMP position has a trace with a given crossline CMP location because of the dual shot geometry. Panel (a) of Figure  shows the inline and distribution of offsets for an inline CMP section taken at crossline CMP position 2212.5 and crossline offset of -12.5 m. Here again we note the on-off pattern of the offset distribution due to the dual shot source as indicated in the sketch in Figure . Similarly, panel (b) of Figure  shows the distribution of crossline offsets for a CMP section in the crossline direction taken at inline CMP location 8400 and inline offset of 100 m.

 

zoff1
Figure 7 Near offset cube (50 m offset inline and -12.5 offset crossline) of the selected dataset.

 

inline-xline
Figure 8 Left panel: inline distribution of offsets for an inline CMP section taken at crossline CMP location 2212.5 and at -12.5 m crossline offset. Right panel: crossline distribution of offsets for a crossline CMP section taken at inline CMP location 8400 and at 100 m inline offset.