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

## 2pUW5. Accuracy of parabolic approximations for travel time.

**F. D. Tappert
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M. G. Brown

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