In this paper, we propose an adaptive implementation for separating multiples from primary events in seismic data and subsequently removing the embedded multiples from noisy seismic data using the curvelet transform. Because of the sparseness of the curvelet coefficients of seismic data, the optimization problem is formularized by incorporating L1- and L2-norms, based on the framework of Bayesian Probability Maximization. Iterative soft-thresholding can be used for solving the above optimization problem. By making use of least-square matching filtering, we precondition the multiple models to match the actual multiples in the seismic data prior to the separation step. Moreover, in order to meet the challenges faced by various types of data complications, we develop a frequency regularized adaptive curvelet domain separation approach. This flexibility overcomes the varying effectiveness of separation methods for different frequency bands in responding to the noise and model inaccuracy control. Accordingly, the high adaptability of this extension leads to its higher separation fidelity than existing curvelet domain separation implementations. We demonstrate the applications of our approach on synthetic and field data examples by comparing them with the results from the conventional least-square separation method.


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