Surface multiple attenuation via eigenvalue decomposition

摘要

A marine seismic signal is transformed from time domain into frequency domain and represented by matrix D. The marine data signal is truncated in time, transformed into the frequency domain and represented by matrix DT. Eigenvalue decomposition DT=Sx LAMBDA xS-1 of matrix DT is computed. Matrix product DxS is computed and saved in memory. Matrix inverse S-1 is computed and saved in memory. An initial estimate of the source wavelet w is made. Source wavelet w is computed by iterating the steps of computing diagonal matrix [I-w-1 LAMBDA ], computing matrix inverse [I-w-1 LAMBDA ]-1, retrieving matrix product DxS and matrix inverse S-1 from memory, and minimizing the total energy in matrix product [DxS] [I-w-1 LAMBDA ]-1 S-1. Primary matrix P representing the wavefield free of surface multiples is computed by inserting computed value for w into the expression [DxS] [I-w-1 LAMBDA ]-1S-1. Primary matrix P is inverse transformed from frequency domain into time domain.