3D impulse response

Figures - compare the impulse responses of our algorithm with those of anisotropic phase shift method. The medium is a homogeneous, tilted TI medium. The symmetry axis of the medium is in the (x,z) plane and is tilted $30^\circ$ from the vertical direction. The P-wave velocity in the direction parallel to the symmetry axis is 2000 m/s. The anisotropy parameters $\varepsilon$ and $\delta$ are 0.4 and 0.2, respectively. The location of the impulse is at x=2000 m and y=2000 m. The travel time for the three impulses are 0.4 s, 0.6 s and 0.8 s, respectively. Figure shows a depth slice of the impulse responses at z=1500 m. Figure (a) is obtained with our algorithm and Figure (b) is obtained with the anisotropic phase-shift method. First, Figure (a) is very similar to (b). Second, the depth slice of the impulse response is not a circle. The wave propagates faster in y than in x direction. Third, the impulse location x=2000 m and y=2000 m is not the center of the impulse response. The impulse response is symmetric along y=2000m, but it is not symmetric along x=2000 m.

 

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Figure 6 Comparison of the anisotropic plane-wave migration of a synthetic dataset by the 19-point filter and the new 5-point filter. (a) The density model. (b) The migration result of the 19-point filter. (c) The migration result of the new 5-point filter.

Figure shows an in-line slice of the impulse responses at y=2000 m. Figure (a) is obtained with our algorithm and Figure (b) is obtained with the anisotropic phase-shift method. Figure shows a cross-line slice of the impulse responses at x=2000 m. Figure (a) is obtained with our algorithm and Figure (b) is obtained with the anisotropic phase-shift method. From Figure and , we can see that the impulse of our algorithm is very close to that of the anisotropic phase-shift method at low-angle energy and is different from the the anisotropic phase-shift method at high-angle energy. Since the medium is homogeneous, the anisotropic phase-shift method is accurate. So our algorithm is accurate for the energy up to $50^{\circ}$ in the impulse response, compared to the anisotropic phase-shift method.