Abstract:

A hybrid treatment for wide-angle paraxial propagation that includes effects of both sediment dispersion and weak nonlinearity has been developed. A Fourier transform approach is used to combine effects of refraction, diffraction, and sediment dispersion in the frequency domain, and nonlinear effects in the time domain. A nonlinear wide-angle time-domain equation developed recently is first split into linear and nonlinear component equations. The linear equation is decomposed into its discrete frequency-domain counterparts. Sediment attenuation and dispersion are incorporated using a complex wave number along with a frequency-dependent formula for phase velocity to satisfy causality. The numerical implementation consists of first decomposing a broadband source into its frequency components and propagating them over a range step using a wide-angle PE. Fourier synthesis is used to reconstruct the signal, which is then corrected to account for nonlinear effects in the time domain. Numerical examples illustrating the effects of dispersion and nonlinearity on shallow-water wide-angle propagation will be presented and compared with available results. [Work supported by ONR.]