Summary

In this chapter, I develop a method to match estimates of primaries and multiples to data containing both. The method works with prestack or poststack data in either data space or image space and addresses the issue of cross-talk (leakage) between the estimates of the primaries and the estimates multiples. I pose the problem as a non-linear optimization in which non-stationary filters are computed in micro-patches to simultaneously match the estimates of the primaries and the multiples to the data, in a least-squares sense. I apply the method iteratively by updating the estimates of the primaries and the multiples after the least-squares solution is found. Only a few of these iterations are needed. The computer cost is a negligible fraction of the cost of computing the estimate of the multiples with convolutional methods such as SRME. I show, with several synthetic and real data examples, that the matched estimates of both primaries and multiples have little cross-talk. I also apply the method to the separation of spatially-aliased ground-roll and body waves and show that most residual ground-roll contaminating the estimate of the body waves can be eliminated. This method is applied in chapter 6 to adaptively match and subtract the multiple estimate from a 3D real dataset from the Gulf of Mexico.