Computing rough surface Doppler effects on broadband pulse propagation using a split-step Fourier parabolic equation model

Abstract

The current interest in broadband pulse propagation in shallow water is increasing with the need for improved active sonar systems and the growth of applications utilizing underwater acoustic communications. Such shallow-water propagation is dominated by boundary interactions. If the ocean surface is rough on the scale of the acoustic wavelength, considerable scattering can occur that can significantly influence the coherent propagation. Because the rough ocean surface is also evolving dynamically, such scattering can introduce Doppler shifting and spreading of the acoustic pulse spectrum. Following the method of F. D. Tappert and L. Nghiem-Phu [J. Acoust. Soc. Am. Suppl. 1 77, S101 (1985)], an exact formulation for scattering from a rough surface is introduced into the Monterey-Miami Parabolic Equation Model [JCA 9, 243–285 (2001)]. An algorithm is then developed for computing the solution of pulse propagation as the rough surface evolves dynamically. The result can be shown to produce the proper spatial scattering as well as introduce the correct Doppler shifts from the dynamic surface. A simple sinusoidal rough surface interface will be employed to test the algorithm followed by a more complex, realistic rough ocean interface. Spatial and temporal properties of the scattered field will be examined and discussed.