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Figure shows the impulse responses of a homogeneous VTI medium.
The vertical velocity of the medium
is 2000 m/s, the anisotropy parameter is 0.4 and the anisotropy parameter
is 0.2. The travel-time of the impulse is 2 seconds. Figure (a) is the impulse response of
the optimized implicit finite-difference operator, Figure (b) is the impulse response of
the finite-difference operator by Taylor-series analysis suggested by Ristow and Ruhl (1997),
and Figure (c) is the impulse response of the phase-shift
operator, using equation (3) as the dispersion relation. Comparing these three impulse
responses, we can see that the impulse response of the optimized implicit finite-difference operator (Figure (a) ) is
more accurate than the impulse response from Taylor-series analysis (Figure (b)).
The impulse response in Figure (a) is accurate to , while the impulse
response in Figure (b) is accurate to only .The impulse responses also verify the relative-dispersion-relation error analysis in Figure .

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Stanford Exploration Project

4/5/2006