Design of two-dimensional FIR digital filters by using the singular-value decomposition

1990 ◽  
Vol 37 (1) ◽  
pp. 35-46 ◽  
Author(s):  
W.-S. Lu ◽  
H.-P. Wang ◽  
A. Antoniou
Keyword(s):  
Singular Value Decomposition ◽  
Digital Filters ◽  
Singular Value ◽  
Two Dimensional ◽  
Fir Digital Filters ◽  
Value Decomposition

Implementation of 2D explicit depth extrapolation FIR digital filters for 3D seismic volumes using singular value decomposition

Geophysics ◽  
2010 ◽  
Vol 75 (1) ◽  
pp. V1-V12 ◽  
Author(s):  
Wail A. Mousa ◽  
Said Boussakta ◽  
Desmond C. McLernon ◽  
Mirko Van der Baan
Keyword(s):  
Singular Value Decomposition ◽  
Impulse Response ◽  
Digital Filters ◽  
Finite Impulse Response ◽  
Fir Filter ◽  
Singular Value ◽  
3D Seismic ◽  
Fir Digital Filters ◽  
Value Decomposition ◽  
Seismic Volumes

We propose a new scheme for implementing predesigned 2D complex-valued wavefield extrapolation finite impulse response (FIR) digital filters, which are used for extrapolating 3D seismic wavefields. The implementation is based on singular value decomposition (SVD) of quadrantally symmetric 2D FIR filters (extrapolators). To simplify the SVD computations for such a filter impulse response structure, we apply a special matrix transformation on the extrapolation FIR filter impulse responses where we guarantee the retention of their wavenumber phase response. Unlike the existing 2D FIR filter implementation methods that are used for this geophysical application such as the McClellan transformation or its improved version, this implementation via SVD results in perfect circularly symmetrical magnitude and phase wavenumber responses. In this paper, we also demonstrate that the SVD method can save (depending on the filter size) more than 23% of the number of multiplications per output sample and approximately 62% of the number of additions per output sample when compared to direct implementation with quadrantal symmetry via true 2D convolution. Finally, an application to extrapolation of a seismic impulse is shown to prove our theoretical conclusions.

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