Realization of 2-D Seismic Migration FIR Digital Filters for 3-D Seismic Volumes via Singular Value Decomposition

In this paper, we propose a new scheme for realizing predesigned two-dimensional (2-D) complex-valued seismic migration FIR digital filters, which are used for migrating three-dimensional (3-D) seismic volumes. The realization 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 filter impulse responses where we guarantee the retention of their wavenumber phase response. Unlike the existing realization methods which are used for this geophysical application, this realization via SVD results in perfect circularly symmetrical magnitude and phase wavenumber responses. It also saves 23.08% of the number of multiplications per output sample as well as 61.54% of the number of additions per output sample when compared to direct implementation with symmetry via true 2-D convolution