Implementation of 3-D wavefield extrapolation using singular value decomposition

In this paper, we propose a new scheme for implementing predesigned two-dimensional (2-D) complex-valued explicit depth migration finite impulse response (FIR) digital filters, which are used for three-dimensional (3-D) migration. The implementation is based on Singular Value Decomposition (SVD) of such quadrantal symmetrical 2-D FIR filters. In order to simplify the SVD computations for such impulse response structure, we apply a special matrix transformation on the migration FIR filters where we guarantee the retention of their wavenumber phase response. Unlike the existing explicit depth implementation methods, this implementation via SVD results in perfect circularly symmetrical responses. It also saves 53.3% of the total implementation cost per output sample when compared to direct implementation with symmetry via true 2-D convolution.