Asymptotic phase errors in parabolic approximations to the one-way Helmholtz equation

Journal of the Acoustical Society of America

Volumn 99, Issue 3, 1996, Pages 1405-1413

  Tappert, F D ^a   Brown, Michael G ^a  

^a UNIVERSITY OF MIAMI   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ACOUSTICS; ALGORITHM; ARTICLE; FOURIER ANALYSIS; MATHEMATICAL ANALYSIS; MODEL; PRIORITY JOURNAL; SEA;

EID: 0029867510     PISSN: 00014966     EISSN: None     Source Type: Journal    
DOI: 10.1121/1.414719     Document Type: Article

References (16)

1. F. D. Tappert, "The parabolic approximation method," in Wave Propagation and Underwater Acoustics, Lecture Notes in Physics, Vol. 70, edited by J. B. Keller and J. S. Papadakis (Springer-Verlag, New York, 1977), Chap. V, pp. 224-287.
2. M. G. Brown, "A Maslov-Chapman wavefield representation for wide angle one-way propagation," Geophys. J. Int. 116, 513-526 (1994).
3. F. D. Tappert and R. H. Hardin, "Computer simulation of long-range ocean acoustic propagation using the parabolic equation method," in Proceedings of the 8th International Congress on Acoustics (Goldcrest, London, 1974), Vol. 2, p. 452.
4. L. Nghiem-Phu and F. D. Tappert, "Modeling of reciprocity in the time domain using the parabolic equation method," J. Acoust. Soc. Am. 78, 164-171 (1985).
5. F. D. Tappert, J. L. Spiesberger, and L. Boden, "New full-wave approximation for ocean acoustic travel time predictions," J. Acoust. Soc. Am. 97, 2771-2782 (1995).
6. F. D. Tappert and D. Lee, "A range refraction parabolic equation," J. Acoust. Soc. Am. 76, 1797-1803 (1984).
7. I. W. Schurman, W. L. Siegmann, and M. J. Jacobson, "An energy conserving parabolic equation incorporating range refraction," J. Acoust. Soc. Am. 89, 134-144 (1991).
8. D. J. Thomson and N. R. Chapman, "A wide angle split step algorithm for the parabolic equation," J. Acoust. Soc. Am. 74, 1848-1854 (1983).
9. D. H. Berman, E. B. Wright, and R. N. Baer, "An optimal PE-type wave equation," J. Acoust. Soc. Am. 86, 228-233 (1989).
10. A. Tolstoy, D. H. Berman, and E. R. Franchi, "Ray theory versus the parabolic equation in a long-range ducted environment," J. Acoust. Soc. Am. 78, 176-189 (1985).
11. L. M. Brekhovskikh and O. A. Godin, Acoustics of Layered Media II (Springer-Verlag, Berlin, 1992), footnote, p. 321.
12. W. H. Munk, "Sound channel in an exponentially stratified ocean, with application to SOFAR," J. Acoust. Soc. Am. 55, 220-226 (1974).
13. K. B. Smith, M. G. Brown, and F. D. Tappert, "Ray chaos in underwater acoustics," J. Acoust. Soc. Am. 91, 1939-1949 (1992).
14. M. D. Collins, "A split-step Padé solution for the parabolic equation method," J. Acoust. Soc. Am. 93, 1736-1742 (1993).
15. J. F. Claerbout, Fundamentals of Geophysical Data Processing With Applications (McGraw-Hill, New York, 1976), p. 198.
16. D. Yevick and D. J. Thomson, "Split-step/finite-difference and split-step/ Lanczos algorithms for solving alternative higher-order parabolic equations," J. Acoust. Soc. Am. 96, 396-405 (1994).