NUMERICAL VISCOSITY CONSIDERATIONS FOR THE MONOCHROMATIC 45-DEGREE EQUATION
, by Larry Morley
An analysis of a class of positive real, viscous, 45-degree extrapolation operators shows that the customary
procedure of transforming the frequency w to w + ie does not give an operator with very desirable attenuation
properties. Much better dip filtering characteristics can be realized in the evanescent part of F-K space by
damping only the higher order terms in the 45 degree expansion for the exact dispersion relation. As a bonus,
it turns out that an operator constructed in this manner has less phase distortion everywhere in the passband
for typical values of the viscosity parameters.
From a practical standpoint this means that 45 degree migration is best carried out by incorporating viscous
terms directly in the migration operator. This no-cost option gives better results than premultiplying the
input dataset by exponential gain before doing a pure all pass migration.
STANFORD