3D shot-profile migration in ellipsoidal coordinates

Impulse Response Tests

We conducted impulse response tests on a 500 x 400 x 400 mesh in a homogeneous medium with slowness $s=0.0005$ s/m. The initial wavefield consisted of three smoothed point sources at $t=[0.5,0.75,1]$ seconds. Using this experimental setup, we expect the impulse responses to consist of three hemispherical surfaces of radii $r=[1000, 1500, 2000]$ meters. We used the narrow-azimuth coordinate system pictured in figure 1.

Figure 4's upper and lower panels show the inline and crossline responses, respectively. To illustrate the accuracy of the approach, we overlaid three lines showing the analytical results. Note that the impulse responses are limited at high angles both by the coordinate system boundaries and by the 50 sample cosine-taper function applied at the edges. Figure 5 shows the 1300 m depth slice. The symmetric response indicates that the Li filter has accounted for the numerical anisotropy from the numerical splitting.

CrossIn
Figure 4. Ellipsoidal coordinate impulse response cross sections through the 3D image volume for the narrow-azimuth ellipsoidal coordinate system defined in figure 1. Top panel: Inline response. Bottom panel: Crossline response. [CR]

Depth1300 Figure 5. Image volume depth slice taken at 1300m. Note the circular symmetry of the impulse response and the stronger inline amplitudes relative to the crossline. [CR]

3D shot-profile migration in ellipsoidal coordinates