Adaptive curvelet-domain primary-multiple separation

Abstract

In many exploration areas, successful separation of primaries and multiples greatly determines the quality of seismic imaging. Despite major advances made by surface-related multiple elimination ͑SRME͒, amplitude errors in the predicted multiples remain a problem. When these errors vary for each type of multiple in different ways ͑as a function of offset, time, and dip͒, they pose a serious challenge for conventional least-squares matching and for the recently introduced separation by curvelet-domain thresholding. We propose a data-adaptive method that corrects amplitude errors, which vary smoothly as a function of location, scale ͑fre-quency band͒, and angle. With this method, the amplitudes can be corrected by an elementwise curvelet-domain scaling of the predicted multiples. We show that this scaling leads to successful estimation of primaries, despite amplitude, sign, timing, and phase errors in the predicted multiples. Our results on synthetic and real data show distinct improvements over conventional least-squares matching in terms of better suppression of multiple energy and high-frequency clutter and better recovery of estimated primaries.

Groundroll prediction by interferometry and separation by curvelet‐domain matched filtering

“…Each of these steps is important and the performance of both steps are interrelated, e.g., the separation by the Bayesian algorithm will be unsuccessful when the predictions are over fitted. Even in cases where the predictions are reasonable, e.g., during multiple removal, Herrmann et al (2008b) showed that significant improvements can be made by exploiting curvelet-domain adaptation and sparsity. Our findings in this paper are similar, event though the removal of groundroll is more difficult because of the large amplitudes and dispersive behavior of groundroll.…”

“…According to Herrmann et al (2007), this curvelet-domain matched filter is based on the following assumptions : (i) the stationary difference is removed by a global (Fourier) matching procedure, which corresponds to removal of the source/receiver directivity during primary-multiple separation (Herrmann et al, 2008b), and (ii) the remaining non-stationary difference is assumed to vary smoothly in phase space-i.e., the amplitude mismatches are assumed to vary smoothly as a function of position and dip along coherent wavefronts.…”

“…This operator, some sort of position and dip-dependent filter, can be approximated by a positive scaling in the curvelet domain (Herrmann et al, 2008b):…”

Curvelet‐domain matched filtering

“…Even though there is less of a direct link between the actual physics and this forward model, successful application of this approximation, where the differences between these two wavefield components are assumed to vary smoothly in phase space, has shown excellent results (Herrmann et al, 2008b).…”

“…In this paper, we propose a method correcting for these nonstationary effects by making the following assumptions: (i) the stationary difference is removed by a global matching procedure, which corresponds to removal of the source/receiver directivity during primary-multiple separation (Herrmann et al, 2008b) or to making the migration operator zero-order during migration (see Herrmann et al, 2008a, and another contribution by the authors to the proceedings of this conference), and (ii) the remaining non-stationary difference is assumed to vary smoothly in phase space-i.e., the amplitude mismatches are assumed to vary smoothly as a function of position and dip along coherent wavefronts.…”