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 Biondi, B., and Palacharla, G., 1993, 3D wavefield depth extrapolation by rotated McClellan filters: SEP77, 2736.

 Hale, D., 1991, 3D depth migration via McClellan transformations: Geophysics, 56, 17781785.

 Lu, W.S., and Antoniou, A., 1992, Twodimensional digital filters: Marcel Dekker Inc.

 McClellan, J., and Chan, D., 1977, A 2D FIR filter structure derived from the Chebyshev recursion: IEEE Trans. Circuits Syst., CAS24, 372384.

 Nautiyal, A., Gray, S. H., Whitmore, N. D., and Garing, J. D., 1993, Stability versus accuracy for an explicit wavefield extrapolation operator: Geophysics, 58, 277283.

 Parks, T., and Burrus, C., 1987, Digital filter design: John Wiley and Sons.

 Soubaras, R., 1992, Explicit 3D migration using equiripple polynomial expansion and Laplacian synthesis: 62nd Ann. Internat. Mtg., Soc. Explor. Geophys., Expanded Abstracts, 905908.

APPENDIX A
In this Appendix, I give the Chebyshev recursion formula and
the different approximations to
.
The Chebyshev recursion formula is given by,
 
(9) 
The original McClellan transformation is given by
 
(10) 
The modified McClellan transformation is given by (taken from Hale (1991)),
 
(11) 
where c is chosen, by exactly matching a particular value k along the
diagonal k_{x}=k_{y}. c=0.0255 was used here, which corresponds to k=.
The 2D filter in the xy domain corresponding to the original
McClellan transformation is given by,
1/8 
1/4 
1/8 
1/4 
1/2 
1/4 
1/8 
1/4 
1/8 
The 2D filter in the xy domain corresponding to the modified McClellan
transformation is given by (taken from Hale (1991)),
c/8 
0 
c/4 
0 
c/8 

1/8 
1/4 
1/8 

c/4 
1/4 
(1+c)/2 
1/4 
c/4 

1/8 
1/4 
1/8 

c/8 

c/4 

c/8 
The 2D filters have a quadrantal symmetry, so the number of floating
point operations required for the 2D convolution of the filter with
data is reduced.
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Stanford Exploration Project
11/17/1997