ASA 129th Meeting - Washington, DC - 1995 May 30 .. Jun 06

2pUW5. Accuracy of parabolic approximations for travel time.

F. D. Tappert

M. G. Brown

Appl. Marine Phys., Univ. Miami, RSMAS, 4600 Rickenbacker Cswy., Miami, FL 33149

Many different full-wave parabolic approximations are analyzed with regard to the accuracy of their travel time predictions by considering the geometrical acoustic (ray tracing) limit. The two small parameters are (epsilon)=(1-n[sup 2])/2 and (mu)=p[sup 2]/2, where n is the depth and range-dependent index of refraction and p is a scaled ray grazing angle. By expanding the exact and approximate Hamiltonian and Langrangian functions in powers of (epsilon) and (mu), which tend to have the same order of magnitude, it is found that among the class of parabolic approximations that can be implemented with the efficient ``split-step Fourier'' algorithm only the recently developed c[sub 0]-insensitive approximation [Tappert et al., J. Acoust. Soc. Am., to be published] has full second-order accuracy. The highly touted ``modified log'' parabolic approximation of Berman et al. [ 228--233 (1989)] has only first-order accuracy, the same as the ``standard'' parabolic approximation, and furthermore it has a second-order bias toward times that are too early. Numerical calculations confirm and quantify these results. [Work supported by ONR.]