Perturbative corrections to acoustic Doppler backscattering I. Ocean surface gravity waves

Perturbative corrections to the Doppler backscattering spectrum using Rayleigh-Rice perturbation theory are examined. For comparison with recent results regarding the validity of perturbation theory in the static limit, calculations using Pierson-Moskowitz and modified Toba spectra to describe the wave height distribution are performed. The order [kh]⁴ interference term acts to lower the weight associated with the lowest-order delta function peaks at the “Bragg frequencies” for backscattering. Another term of the same order spreads the spectrum away from these delta peaks.