Impulse response

Figure shows the impulse responses of a homogeneous VTI medium. The vertical velocity of the medium is 2000 m/s, the anisotropy parameter $\varepsilon$ is 0.4 and the anisotropy parameter $\delta$ 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 $60^\circ$, while the impulse response in Figure (b) is accurate to only $30^{\circ}$.The impulse responses also verify the relative-dispersion-relation error analysis in Figure .