MULTIPLE SUBTRACTION USING A HYBRID LEAST-SQUARES FILTERING, NON-LINEAR WEIGHTING AND COMPLEX CURVELET DOMAIN APPROACH

The study of de-multiple methods is a very important task in seismic data processing. For the typical prediction-subtraction methods, predicted multiples usually are never perfect and need adaption. However, considering the absence of orthogonality between predicted multiples and the primaries in the data, standard matching or subtraction methods often do not provide satisfactory results. To resolve this issue, primary/multiple separation via the curvelet domain has been introduced. However, the threshold methods based on the real curvelet transform (RCT) are sensitive to event positioning errors. In case of a slight event mispositioning, the amplitude of the RCT's coefficients change dramatically. For that reason, a primary and multiple separation scheme based on least-squares (LS) matching and complex curvelet transform (CCT) is introduced in this paper. Firstly, the LS matching method is applied to do a rough amplitude matching and global time shift correction, then an optimal problem can be built and solved to correct the residual misfit in the CCT domain by taking advantage of the amplitude shift invariance property of the CCT. In addition, a non-linear primary protection masking process preserves most primaries during the process. Validation of this hybrid procedure on synthetic and field data shows that the primaries can be correctly recovered from the original data.