DISCUSSION OF RESULTS

Figure 3 shows the impulse response of prestack slant stack migration with PSPI, with p=.00021 s/m, v₁(z)=1500+0.5z m/s at y=0 m, and v₂(z)=2500+0.5z m/s at y=2560 m. The skewed impulse responses are caused by the velocity variations in depth and in lateral variation.

To test the accuracy of the PSPI operator, I used v₁(z)=1500 m/s at y=0 m and v₂(z)=2500 m/s at y=2560 m to simulate the response of v=2000 m/s at y=1280 m. Figure 4 shows these two impulse responses together. The impulse response with a wider aperture is from the PSPI, and the other is the response with v=2000 m/s. The bottom of the responses coincide very well, even with the velocity discrepancy. By increasing the velocity discrepancy, we get Figure 5, with v₁(z)=1000 m/s and v₂(z)=3000 m/s. The bottom of the responses are no longer coincident, and the discrepancy gets worse as the depth increases.

 

fig3
Figure 5 The superposition of the impulse response of v=2000 m/s and v₁(z)=1000 m/s at y=0 m and of v₂(z)=3000 m/s at y=2560 m with PSPI.