Reflection and transmission of low-frequency spherical waves at gas-liquid interfaces

Abstract

High-frequency asymptotic solutions of the canonical problem of a spherical wave reflection at and transmission through a plane interface are well known. These asymptotics are usually derived using the stationary phase method and its extensions assuming that the distance between the point sound source and a receiver is large compared to the wavelength. The opposite case, where the distance is either of the order of or smaller than the wavelength, is of interest in a number of problems such as radiation of infrasound into the atmosphere by underwater explosions and earthquakes. Available quasi-stationary approximations fail to describe correctly acoustic power flux through the interface. Here, a low-frequency asymptotics of the acoustic field is obtained for gas-liquid interfaces. It is found that the acoustic field transmitted into gas can be approximately represented as a field due to a virtual point source in an unbounded medium. Positions of the virtual sources of the low- and high-frequency transmitted waves are compared. It is found that the bulk of acoustic energy transmission through the interface occurs at epicentral distances of the order of the source depth, regardless of the wavelength.