Adaptive Multiple Subtraction Based on an Accelerating Iterative Curvelet Thresholding Method.

Abstract

In the seismic exploration, recorded data contain primaries and multiples, where primaries, as signals of interest, can be used to image the subsurface geology. Surface-related multiple elimination (SRME), one important class of multiple attenuation algorithms, operates in two stages, multiple prediction and subtraction. Due to the phase and amplitude errors in the predicted multiples, adaptive multiple subtraction (AMS) is the key step of SRME. The main challenge of this technique resides in removing multiples without distorting primaries. The curvelet-based AMS methods, which exploit the sparsity of primary and multiple in curvelet domain and the misfit between the original and estimated signals in data domain, have shown outstanding performances in real seismic data processing. These methods are realized by using the iterative curvelet thresholding (ICT), which has heavy computation burden since it includes two forward/inverse curvelet transform (CuT) pairs in each iteration. To ameliorate the computational cost, we propose an accelerating ICT method by exploiting the misfit between the original and estimated signals in curvelet domain directly. Since the proposed method only needs do one forward/inverse CuT pair, it is faster than the traditional ICT method. Considering that the error of the predicted multiple is frequency-dependent, we furthermore introduce the joint constraints within different frequency bands to stabilize and improve the multiple attenuation. Synthetic and field examples demonstrate that the proposed method outperforms the traditional ICT method. In addition, the proposed method has shown to be suitable for refining other AMS methods' results, yielding a SNR improvement of 0.5-2.8 dB.