2.5d Downward Continuation Using Data Mapping Theory

Unlike many previous implementations of Kirchhoo-type waveeeld extrapolation (Berryhill, 1979; Bevc, 1995), we propose a procedure that is not only kinematically correct , but dynamically correct in heterogeneous media, in a model-consistent sense. Our approach is to specialize the general,\true-amplitude" data mapping platform of Bleistein & Jaramillo (1997) to the process of downward continuation. We apply stationary phase analysis to this general expression under the assumptions of downward continuation of both common-source and common-receiver geometries. The asymptotic analysis produces a stationary point for each set of input and output locations, and amplitudes that depend on parameters along the ray paths connecting these locations with the stationary point. In general inhomogeneous media , however, a large investment in external ray tracing is required to locate this point and to calculate the associated ray quantities. Alternatively, the procedure may be greatly simpliied when assumptions about the wavespeed distribution can be made, and analytic results can be used in conjunction with, or in place of, ray tracing results. Here we present the form of the ex-trapolation integral for evaluation of amplitudes under the assumption of constant wavespeed, which allows this process to be performed entirely by analytic methods.