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In the ideal solution, evanescent components corresponding to the real
eigenvalues would be eliminated, whereas components corresponding to the
imaginary eigenvalues would be unaltered. Unfortunately, in the general
case this requires the separation of evanescent components through a
costly matrix diagonalization. A method for eliminating the evanescent
components without the matrix diagonalization and without severely affecting
the nonevanescent components is therefore required.
A scheme proposed in Kosloff and Kessler (1987) included use of
a spatially variant, high-cut filter to *P* and after each step of the propagation of the solution. The high-cut wavenumber
*k*_{cut} at each point of application was based on the criterion
, where *c*_{max} denotes the highest
velocity in a taper region surrounding the point of application.

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Stanford Exploration Project

1/13/1998