Narrow- and wide-angle parabolic equations with arbitrary variations in the sound speed and medium velocity

Acoustic wave propagation in inhomogeneous media such as the atmosphere and ocean can be efficiently modelled with parabolic equations. This presentation overviews recently derived narrow- and wide-angle parabolic equations for sound propagation in motionless and moving media, along with algorithms for their numerical implementation. These parabolic equations preserve the phase of the sound wave and are valid for arbitrary variations in the sound speed and arbitrary (subsonic) Mach number of the medium velocity. Within the ranges of their applicability, the parabolic equations considered exactly describe sound propagation in stratified moving media. These features are particularly important for long-range multipath sound propagation when the phase increments along different arrivals should be calculated accurately. Despite their generality, the narrow- and wide-angle parabolic equations are relatively simple. Moreover, they can be efficiently solved with available Crank-Nicholson numerical techniques. Example calculations are provided that demonstrate the numerical implementation of the narrow- and wide-angle parabolic equations and their accuracy as compared to parabolic equations based on the effective sound speed approximation.