Optimum weighted stack for multiple suppression

In water deeper than about 300 m, common midpoint stack is moderately effective at suppressing multiple reflections. The stacking process acts as a low-pass multiple filter, rejecting, to some extent, frequencies greater than the reciprocal of the multiple's residual moveout on the farthest offset trace. A weighted stack can often be even more effective at attenuating multiples, if the weights are chosen such that the multiple filter response has low amplitudes at those frequencies where the multiple is strong. A least-squares technique is developed to determine optimum weights, based on the multiple's frequency content, the water depth, the primary velocity, and on a stabilization factor equivalent to white noise in deconvolution filter design. To be truly optimum, the weights must vary both spatially, to account for water-depth changes, and temporally, to account for sediment velocity changes and mute patterns; but the filter responses are not very sensitive to the input parameters and need to be redesigned only infrequently. The superiority of weighted stacks to uniform stacks is demonstrated by application to three deep-water examples. In all cases, weighted stacks attenuate multiples more effectively than do conventional uniform stacks.