Wave Propagation in a Medium with Random, Spheroidal Inhomogeneities

Abstract

An acoustic or electromagnetic wave propagating in a material medium experiences fluctuations in amplitude and phase that can be attributed in part to scattering from inhomogeneities due to variations in the refractive index of the transmission medium. Since such “patches of inhomogeneity” are often regarded as lenticular in shape, it is the purpose of this paper to extend, for both plane and spherical sound waves, contemporary wave-fluctuation theory (based on a Gaussian correlation function for refractive index) to include the circumstance of spheroidal inhomogeneities. Mean-square amplitude and phase fluctuations are considered for acoustic waves propagating in a statistically isotropic medium in which random deviations of the refractive index are small. Large-scale inhomogeneities of arbitrary spheroidal shape are treated, and the influence of transmitter-to-receiver range, acoustic wavelength, and “patch” dimensions on variations in wave amplitude and phase is derived for this general case. Particular attention is given the high-frequency ray limit (Bergmann region) and the low-frequency (Fraunhofer diffraction) region. The significant effects on wave fluctuations of both spherical and nonspherical inhomogeneities are compared for plane and spherical acoustic waves.