Interface reflection of spherical acoustic waves in the first- and second-order rational parabolic approximations and their artifacts

The accuracy of the first- and second-order rational parabolic approximations of the vertical slowness and the nature of the artifacts associated with them in the space-time solutions to the acoustic wave equations in a fluid medium are investigated. In particular, the reflection of an impulsive, point-source generated, spherical wave against the boundary with a medium with a higher wave speed is analyzed. From the space-time Green's functions in the relevant two-media configuration, evaluated with the aid of the modified Cagniard method, it is found that, instead of generating the real, physical head wave, the approximations generate artificial head-wavelike arrivals. The analysis makes explicit in which regions of space and in which time interval the artifacts show up and of what nature they are. Numerical results are presented. 28 refs., 15 figs