Radiation and attenuation of waves in a random medium

Abstract

A theoretical analysis of the wave field radiated by a point source in a weakly inhomogeneous one-dimensional random medium is presented. The analysis is based on a perturbation technique and includes all single- and double-scattering terms, as well as some scattering terms of higher order. Approximate expressions, valid when the absorption of the medium is small, are obtained for the mean intensity (i.e., the mean square of the modulus of the complex wave amplitude) and the mean energy flux of the wave as a function of propagation range. These expressions show that, as a consequence of backscattering by the random inhomogeneities of the medium, the mean intensity and mean energy flux decrease more rapidly with range than would be the case in the absence of randomness. This more rapid rate of decrease with range can be interpreted as an excess attenuation of the wave as a result of the randomness of the medium. It is also found that the mean radiated power is altered slightly by the randomness of the medium. The excess-attenuation results are found to be consistent with observations.