Adaptive curvelet-domain primary-multiple separation

Our contribution:

We present a new technique that mitigates the effects of unbalanced amplitudes that vary relatively smoothly along the locations and dips of the predicted multiples. Our approach is complementary to windowed matched-filtering techniques (Verschuur and Berkhout, 1997), which offer limited control over window-to-window variations amongst the estimated matched filters. Our method also avoids relative expensive multiple predictions required by iterative SRME. To offer better control over these variations, errors in the single-window SRME-predicted multiples are modeled by a zero-order pseudo-differential operator, a kind of spatially varying dip filter, which can be well approximated by a diagonal curvelet-domain scaling (Herrmann et al., 2007c). This scaling is estimated from the input data and predicted multiples by a nonlinear optimization procedure, during which smoothness amongst neighboring curvelet coefficients is imposed. This smoothness amongst the curvelet coefficients ensures a scaling that is well-behaved spatially and as a function of the dip. This approach employs the adaptability of curvelets, while the smoothness constraint prevents overfitting of the data, which can lead to a loss of primary energy. Although distinct, our approach is similar to recent work in migration-amplitude recovery, where scaling methods with smoothness constraints have been proposed (Symes, 2007; Guitton, 2004). This letter builds explicitly on a curvelet-based approach to this problem introduced by Herrmann et al. (2007c).

Adaptive curvelet-domain primary-multiple separation