CONCLUSIONS

This paper presents a new algorithm for calculating the Green's function of first arrivals in two dimensions using asymptotic ray approximation. The traveltimes and amplitudes associated with the approximate Green's function are computed on a regular grid using a finite difference scheme. This algorithm is efficient and stable. Examples with different types of slowness models show that for the traveltime calculation, the algorithm can handle very sharply-contrasted slowness models, and for the amplitude calculation, the algorithm requires the slowness models to smooth. I expect that the algorithm and its extension to 3-D will be useful in Kirchhoff prestack depth migration and in traveltime tomographic inversion. I also plan to apply this algorithm to the conversion of migrated time sections to depth sections and to residual depth migration.