Parabolic Wave Equation Approximations in Heterogenous Media

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Abstract
The properties of different variants of parabolic approximations of scalar wave equations are analyzed. These equations are of general form which includes those used in seismology, underwater acoustics and other applications. A new version of the parabolic approximation is derived for heterogeneous media. It has optimal properties with respect to wave reflection at material interfaces. The amplitudes of the reflected and transmitted waves depend continuously on the interface. Existence, uniqueness and energy estimates are proved.