Impulse response tests

The performance of an extrapolation operator can be verified by its impulse response. Figures - are the impulse responses of the qP-wave in the same medium using three different methods. The symmetry axis of the medium is tilted $30^{\circ}$ from the vertical direction. The qP- and qSV-wave velocities in the direction parallel to the symmetry axis are 2000 m/s and 1100 m/s, respectively. The anisotropic parameters $\varepsilon$ and $\delta$ are 0.4 and 0.2, respectively. The impulse location is at 4000 m.

Figure is the impulse response of isotropic phase-shift with an anisotropic correction operator. Figure is the impulse response of isotropic FFD with an anisotropic correction operator. The reference velocity for the FFD is 1500 m/s. We use 39 points for the explicit correction operator in Figures and . Since the medium is homogeneous, we can also extrapolate the wavefield with anisotropic phase-shift (equation (5)). Figure is the impulse response of anisotropic phase-shift. Comparing Figures , and , the impulse response of the isotropic operator with an anisotropic correction operator is the same as that of the anisotropic phase-shift method for propagating angles up to almost $80^{\circ}$.It is different from anisotropic phase-shift for higher angles because the explicit correction operator is not same as the one for anisotropic phase-shift for wavenumbers close to the evanescent area.