2.5d Downward Continuation Using Data Mapping Theory (corrected)

Data mapping is a procedure for transforming seismic or acoustic data collected with one set of source/receiver locations and wavespeed model, to data equivalent to that collected in a diierent source/receiver connguration and wavespeed model. A major application of this general process is downward continuation of the waveeeld, or wave-equation datuming. Unlike many previous implementations of the downward continuation process, this study proposes a procedure that is not only kinematically correct, but also dynamically correct in heterogeneous media, at least in a model-consistent sense. Here the general,\true-amplitude" data mapping platform of Bleistein & Jara-millo (1997) is specialized to the process of downward continuation of receivers given a common source, and to downward continuation of sources given a common receiver. This is done by stationary phase analysis of the general data mapping integral, as specialized to the downward continuation problem for common-source or 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 this stationary point with the source and receiver locations. In general heterogeneous media, a large investment in external ray tracing is required to locate this point and calculate the associated ray quantities. The procedure may be greatly simpliied, however, when assumptions about the wavespeed structure of the medium can be made, and analytic results can be used in conjunction with, or in place of, ray tracing results.