Adaptive multiple subtraction using independent component analysis

Adaptive multiple subtraction is a critical and challenging procedure for the widely used surface-related multiple attenuation (SRMA) techniques. In this paper, I present an adaptive multiple subtraction algorithm based on independent component analysis (ICA). The method expresses the problem of adaptive multiple subtraction as a blind source separation (BSS) problem with two mixtures (the seismic data and the predicted multiple) of two or more sources (primaries and multiples). By taking advantage of the sparse property of the seismic data, the method adopts a geometric ICA method to recover the mixing matrix and a linear programming technique to recover the sources when more than two sources are included. The major advantage of the proposed method is that it does not require that the multiples and primaries in the data be orthogonal to each other; that is, the method can perform adaptive multiple subtraction when multiples and primaries have overlap. Furthermore, by expressing the problem of adaptive multiple subtraction as an underdetermined BSS model (more sources with less mixtures), the method can separate the primaries and the multiples when there is time delay and amplitude inconsistency between the true and the predicted multiples. The proposed method is demonstrated on several synthetic datasets generated by simple convolution and finite-difference modeling.