Analytical solutions in differential form for the m-nth moment equations of waves in inhomogeneous random media

Abstract

The series solutions of the m-nth moment equations are given in differential form for wave propagation in inhomogeneous random media when the small angle scattering approximation is valid. Three kinds of random media models are considered. In the first model, the material parameter in the medium fluctuates inhomogeneously in the direction of propagation and homogeneously in the direction transverse to the propagation path. In the second model, the fluctuation of the material parameter is homogeneous in the direction of the wave path and inhomogeneous in the direction transverse to the propagation path. In the third model, a monochromatic wave propagates in a medium and the statistical parameter of the medium varies both in longitudinal direction and transverse direction. In the first two cases, the solutions of the equations can be used to derive various moments of the wave with different wave numbers in different points. In the third case, the solutions can be used to study the moments of a monochromatic wave. The series solutions in differential form have some advantages over the series solutions in multiple convolution integral form in the study of certain problems related to the wave propagating in multiple scattering media.