High-fidelity adaptive curvelet domain primary-multiple separation
Xiang Wu, Barry Hung · First Break · 2015
In this paper, we propose an adaptive scheme for primary-multiple separation whereby the multiples are first estimated from the seismic data and then removed using the curvelet transform. Because of the sparseness of seismic data in the curvelet domain, the primary-multiple separation problem is formulated by incorporating L1- and L2-norms, based on the framework of the Bayesian Probability Maximization theory. An iterative soft-thresholding method is used for solving the optimization problem. Prior to removal, the predicted multiples are preconditioned to match the actual multiples in the seismic data by least-squares matched filtering. We show that such an adaptive implementation is more robust and has a superior performance to the conventional least-squares method for attenuating multiples. To improve the effectiveness of primary-multiple separation for complex data, we develop a frequency-regularized adaptive curvelet domain separation approach. The method is optimized for different frequencies to improve attenuation in the presence of noise and in areas where multiple models are less accurate (e.g. narrowing of frequency bandwidth due to the convolution process in SRME). Accordingly, this extension provides more flexibility and leads to higher separation fidelity than its original form. We demonstrate the application of our approach on synthetic and field data. The results obtained from our approaches show significant improvement over those obtained from conventional least-squares methods.