Next: SplitStep Fourier Approximation
Up: Acoustic waveequation in 3D
Previous: Acoustic waveequation in 3D
Developing an expression for the extrapolation wavenumber requires
isolating one of the wavenumbers in equation 11 (herein
assumed to be coordinate ). Rearranging the results of
expanding equation 11 by introducing indicies i,j=1,2,3
yields,
 

 (12) 
An expression for wavenumber can be obtained by completing the
square,
 
(13) 
 
Isolating wavenumber yields,
 
(14) 
where a_{i} are nonstationary coefficients given by,
 
(15) 
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 14, are
squared such that the familiar Cartesian splitstep Fourier correction is
recovered below.
Next: SplitStep Fourier Approximation
Up: Acoustic waveequation in 3D
Previous: Acoustic waveequation in 3D
Stanford Exploration Project
4/5/2006