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Developing an expression for the extrapolation wavenumber requires
isolating one of the wavenumbers in equation 25 (herein
assumed to be coordinate ). Rearranging the results of
expanding equation 25 by introducing indicies i,j=1,2,3
yields
 

 (26) 
An expression for wavenumber can be obtained by completing the
square
 
(27) 
 
Isolating wavenumber yields
 
(28) 
where a_{i} are nonstationary coefficients given by
 
(29) 
Note that the coefficients contain a mixture of m^{ij} and g^{ij}
terms, and that positive definite terms, a_{4}, a_{5}, a_{6} and a_{10}
in equation 28are squared, such that the familiar Cartesian splitstep Fourier correction is recovered.
For general 2D situations, the coefficients in equation 29 reduce to
 
(30) 
while a strictly orthogonal 2D mesh leads to the following coefficients
 
(31) 
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Stanford Exploration Project
1/16/2007