Extra-wide-angle parabolic equation for wave propagation in inhomogeneous media

Abstract

To describe wave propagation at large angles with respect to a nominal direction, wide-angle parabolic equations (WAPEs) have been widely used in atmospheric and ocean acoustics, geophysics, electromagnetic wave propagation, and other fields of physics. This paper considers an application of an extra-wide-angle parabolic equation (EWAPE) for such problems. For small variations of the refractive index of a medium, the EWAPE describes wave propagation up to 90 deg with respect to the nominal direction and is more general than the WAPEs used in the literature. The EWAPE can be written in an integral form or as a pseudo-differential equation and may be solved by a split-step spectral algorithm or the Padé series expansions of the pseudo-differential operators. The EWAPE is also generalized to large variations in the refractive index, sound propagation above an impedance boundary, and a moving medium with small or large Mach numbers. For sound propagation in a moving medium, the EWAPE enables derivation of new WAPEs which are accurate and simpler to implement than those currently available in the literature. Numerical examples illustrating the application of these new WAPEs to sound propagation in a moving atmosphere are presented.