(1) |

With higher order multiples the trend in this table continues. This produces similar results to cross-correlating primaries with a multiple model Shan and Guitton (2004), as the additional correlation of the primaries on one term is already taking place with the identical primaries on the other term of the autocorrelation.

Input 1 Input 2 Output first-order multiples first-order multiples zero-lag second-order multiples second-order multples zero-lag first-order multiples primaries pseudo-primaries second-order multiples first-order multiples pseudo-primaries second-order multiples primaries pseudo-first-order multiples

Pseudo-primaries generated in this fashion contain subsurface information that would not be recorded with a non-zero minimum offset. One example of this is a first-order multiple that reflects at the free surface within the recording array, resulting in near offsets being recorded when that wave returns to the surface. This is shown in Figures and , where Figure is a cube of the input Sigsbee2B shots (including the negative offsets predicted by reciprocity) but with offsets less than 2000 feet removed, and Figure is the corresponding cube of pseudo-primaries for the same area. Put briefly, the source coverage of the pseudo-primary data is much greater than that of the input data because all receivers in the original data become sources for the pseudo-primaries.

Figure 1

Figure 2

Figure contains a lot of near-offset information present in the pseudo-primaries that is not present in the recorded primaries. However, simply replacing the missing near offsets of the primaries with the corresponding pseudo-primaries would not yield a satisfactory result due to the crosstalk and noise in the pseudo-primaries.

Figure 3

The crosstalk in the pseudoprimaries is largely a function of the number of shots that are summed over in the input data. Figure shows the shot on the right panel of Figure , but without the summing over shots in equation 1 where instead of summing over shots each shot is plotted along the front face of the cube. It shows how the stacking procedure greatly increases the signal-to-noise ratio.

5/6/2007