In contrast to primaries in the original dataset, pseudo-primaries can illuminate different areas at different angles. They contain subsurface information that primaries do not. Because of recording geometries, it is often difficult to obtain near-offset data, as well as far-offset data. Pseudo-primaries created from multiples can help fill these acquisition holes.
Figure 2 illustrates how missing near-offset traces are recovered in the pseudo-primary dataset. In Figure 2a, near offsets are missing when the source is at xp. In Figure 2b, the primary reflection is recorded at xp and the multiple reflection is recorded at xm for the shot at xs. By cross-correlating the traces at xp and xm in Figure 2b, we obtain the pseudo-primary trace, whose shot and receiver locations are xp and xm, respectively. So the near-offset missing trace is recovered in the pseudo-primaries.
Figure 3 illustrates how missing far-offsets are recovered by the pseudo-primary dataset in some special cases. Using reciprocity, we can obtain the negative-offset data by mirroring sources and receivers. In Figure 3a, the primary reflection with a source at xp and receiver at xm is outside the acquisition spread. In Figure 3b, a primary reflection is recorded at xp and a multiple reflection is recorded at xm for the shot at xs. Both xp and xm are within the acquisition spread. By cross-correlating the traces at xp and xm in Figure 3b, we obtain a trace of the pseudo-primaries, whose shot and receiver locations are xp and xm, respectively. So the far-offset missing trace is recovered with pseudo-primaries. Note that to recover the far-offset trace, as is illustrated in Figure 3, we need a steeply dipping reflector.
We now illustrate our technique on the Sigsbee2B dataset. Figure 4 shows four shot gathers with a source at 50,000 ft: (a) the original dataset (primaries + multiples) with near and far offsets removed, (b) the surface-related multiples with near and far offsets removed, (c) the original dataset (primaries + multiples) with full offsets, and (d) the pseudo-primary dataset.
We mirrored the sources and receivers to get negative offsets. To demonstrate that pseudo-primaries can interpolate data inside the acquisition holes, we removed the offsets that are less than 2,000 ft and greater than 20,000 ft from the original dataset and the surface-related multiples, which are illustrated in Figure 4a and 4b. Figure 4d shows the pseudo-primary shot gather obtained by cross-correlating the original dataset with the multiple dataset without near and far offsets. Comparing the original shot gather in Figure 4c (no mute) with the pseudo-primary shot gather in Figure 4d, we conclude that the pseudo-primary shot gather is very similar to the original shot gather. Note that some artifacts and noisy events appear in the pseudo-primary gather. The noise arises during the cross-correlation of unpaired events at different surface locations. It might be better handled by the method of Berkhout and Verschuur (2003). The near-offset data are recovered very well in the pseudo-primary gather. For far offsets, notice that the event in the oval of Figure 4c, which is removed in Figure 4a, is recovered in Figure 4d. We think that this far-offset event is recovered in the pseudo-primary gather due to the presence of two large canyons with steeply dipping walls on the salt body (Figure 1), similar to the structure illustrated in Figure 3. Note that more shots would help to recover more events at far offsets in Figure 4d.
Figure 5 compares the original zero-offset dataset with the pseudo-primary zero-offset dataset. Same as Figure 4, the pseudo-primary dataset is generated by cross-correlating the original dataset with the multiple dataset without near and far offsets. These two zero-offset datasets have similar structures.