Stationarity transformation of multiples to improve the performance of predictive deconvolution

Abstract

Predictive deconvolution is a very effective multiple attenuator for zero‐offset data and for nonzero offset data acquired in water depths less than 100 m. However, predictive deconvolution’s efficacy degrades rapidly with offset, a degradation that correlates highly with nonstationarity of the primary‐to‐multiple traveltime separation. For model data, predictive deconvolution’s performance degrades by a factor of two when the multiple period changes by only 5 ms (20% of the seismic wavelet’s dominant period) within the deconvolution gate. For two‐thirds of the model‐data offsets, the change in primary‐multiple separation on each trace exceeds 40% of the dominant period, and deconvolution is completely ineffective at removing multiples. We develop a stationarity transform, which is a moveout operation or a time‐variable time shift that can be applied separately to each trace. The stationarity transform stabilizes the traveltime separation between primary and first‐order multiple, based upon the assumptions of hyperbolic moveout, layer‐cake geology, and Dix multiple velocities. After applying the stationarity transform to a model data set consisting of primaries and first‐order multiples only, predictive deconvolution suppresses multiples at the theoretical suppression limit for all offsets. Furthermore, predictive deconvolution is equally effective for low‐frequency and high‐frequency wavelets. When the data set is made more realistic by including higher‐order multiples, predictive deconvolution’s ability to suppress multiple reflections degrades only slightly with offset. Stationarity transformation also improves predictive deconvolution’s multiple suppression on a real data set. Because the real data set is from a region where the water depth is shallower than 100 m, predictive deconvolution suppresses multiples effectively on the near‐ and middle‐offset traces, even without stationarity transformation. However, on the farthest offsets, stationarity transformation improves the efficacy of predictive deconvolution significantly.