The amplitude calculation requires that the slowness models are smooth. I apply the algorithm to compute the amplitudes for a medium having a velocity function that increases linearly with depth. The velocity gradient is 1.5 1/sec. Figure shows the amplitudes computed for a line source having an isotropic radiation pattern. The computed amplitudes for a point source having an isotropic radiation pattern are shown in Figure . Comparing these two figures, we see that for a point source, the amplitudes decay faster than for a line source. Both figures show that large errors appear in a narrow region just below the source position. These errors are due to the approximation of using constant velocity cells in polar coordinates. To solve this problem, I have proposed a new approach called the local paraxial ray method (Zhang, 1991). I expect that the local paraxial ray method can handle the amplitude calculation for slowness models containing reasonably large contrasts.

Figure 5

Figure 6

12/18/1997