Asymmetric Doppler Amplitudes in the Surface Scatter Channel

The generation of asymmetric doppler side bands in scatter channels in which the transmitter and receiver are at different depths has been demonstrated in several recent papers. (E. Y. Harper and F. M. Labianca, J. Acoust, Soc. Am. 57, 1044-1051 (1975) and 58, 349-364 (1975)). In these papers the wave equation was solved by using a perturbation procedure. In the present paper a similar result is obtained by using a modified Fresnel expansion of the Kirchoff integral. The resulting expansion, which is correct to third order but contains only terms up to second order is then easily manipulated by standard methods. The ratio of side band amplitudes can be found by solving a fairly simple algebraic equation, and the general features of the result appear to be qualitatively similar to those observed in the earlier studies. (Author)