Summary

Primaries (signal) and multiples (noise) exhibit often different kinematics and amplitudes (i.e., patterns) in time and space. Multidimensional prediction-error filters (PEFs) approximate these patterns to separate noise and signal in a least-square sense. These filters are time-space variant to handle the non-stationarity of multi-offset seismic data. PEFs for the primaries and multiples are estimated from pattern models. In an ideal case where accurate pattern models of both noise and signal exist, the pattern-based method recovers the primaries while preserving their amplitudes. In the more general case, the pattern model of the multiples is obtained by using the data as prediction operators. The pattern model of the primaries is obtained by convolving the noise PEFs with the input data. In this situation, 3-D PEFs are preferred to separate (in prestack data) the multiples properly and to preserve the primaries. Comparisons of the proposed method with adaptive subtraction with a $\ell^2$ norm demonstrate that for a given multiple model, the pattern-based approach attenuates the multiples and recovers the primaries generally better. In addition, tests on a 2-D line from the Gulf of Mexico demonstrate that the proposed technique copes fairly well with modeling inadequacies present in the multiple prediction.