2.5-D wave equations and high‐frequency asymptotics

The need for modeling 3-D seismic data in a 2-D setting has motivated investigators to create so‐called 2.5-D modeling methods. One such method proposed by Liner involves the use of an approximate 2.5-D wave operator for constant‐density media. The traveltimes and amplitudes predicted by high‐frequency asymptotic ray series (WKBJ) analysis of the Liner 2.5-D wave equation match those predicted by Bleistein’s 2.5-D ray‐theoretic development in constant wavespeed media. However, high‐frequency analysis indicates that the Liner 2.5-D variable wavespeed equation will have a maximum amplitude error of ±35% in a linear c(z) model where the wavespeed doubles or halves from the beginning to the end of a raypath. These amplitudes are comparable to those produced by converting 2-D data to 2.5-D using correction factors of the type proposed by Emersoy and Oristaglio and Deregowski and Brown, with the exception being that the Liner equation lacks the half derivative waveform correction present in these operators. An alternate method of constructing 2.5-D wave operators based on the WKBJ analysis is proposed. This method permits variable density (acoustic) 2.5-D wave operators to be derived.