Multiple subtraction using an expanded multichannel matching filter

An expanded multichannel matching (EMCM) filter is proposed for the adaptive subtraction in seismic multiple attenuation. For a normal multichannel matching filter where an original seismic trace is matched by a group of multiple-model traces, the lateral coherency of adjacent traces is likely to be exploited to discriminate the overlapped multiple and primary reflections. In the proposed EMCM filter, a seismic trace is matched by not only a group of the ordinary multiple-model traces but also their adjoints generated mathematically. The adjoints of a multiple-model trace include its first derivative, its Hilbert transform, and the derivative of the Hilbert transform. The convolutional coefficients associated with the normal multichannel filter can be represented as a 2D operator in the time-space domain. This 2D operator is expanded with an additional spatial dimension in the EMCM filter to improve the robustness of the adaptive subtraction. The multiple-model traces are generated using moveout equations to afford efficiency in the multiple attenuation application.