Adaptive curvelet-domain primary-multiple separation

Primary-multiple separation by curvelet-domain thresholding

Because of the curvelet's sparsity and parameterization (by position, scale and dip) primaries and multiples naturally separate in this domain. This property explains the success of threshold-based primary-multiple separation. According to the latest development in threshold-based primary-multiple separation (Saab et al., 2007; Wang et al., 2007), the estimated primaries are given by

$${\widetilde{\mathbf{s}}}_1= \big(\mathbf{p},\mathbf{t}\big),$$ (6)

with the operator Bayes$\big(\cdot,\cdot\big)$ denoting primary estimation by our iterative Bayesian separation scheme (detailed in Saab et al., 2007), which uses the total data and a curvelet-domain threshold vector, $\mathbf{t}$ , as input and which produces the estimated primaries, ${\widetilde{\mathbf{s}}}_1$ . This curvelet-domain threshold is given by the absolute values of the (scaled) predicted multiples. Equation 6 is an instance of a non-adaptive curvelet-domain primary-multiple procedure, which as reported in the literature (Herrmann et al., 2007b,d; Saab et al., 2007; Wang et al., 2007), has successfully been applied to synthetic- and real-data examples.

Adaptive curvelet-domain primary-multiple separation