Acoustic field in a shallow, stratified ocean with a poro-elastic seabed

ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik

Volumn 77, Issue 9, 1997, Pages 677-688

  Gilbert, R P ^a   Lin, Z ^a  

^a UNIVERSITY OF DELAWARE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 21744439071     PISSN: 00442267     EISSN: 15214001     Source Type: Journal    
DOI: 10.1002/zamm.19970770907     Document Type: Article

References (26)

1. AHLUWALIA, D.; KELLER, J.: Exact and asymptotic rep representations of the sound field in a stratified ocean. Wave propagation and underwater acoustics. Lecture Notes in Physics 70. Springer, Berlin 1977.
2. BEEBE, J. H.; MCDANIEL, S. T.; RUBANO, L. A.: Shallow-water transmission loss prediction using the Biot sediment model. J. Acoust. Soc. Am. 71 (1982) 6, 1417-1426.
3. BIOT, M. A.: Theory of propagation of elastic waves in a fluid-saturated porous solid. I. Lower frequency range. II. Higher frequency range. J. Acoust. Soc. Am. 28 (1950) 2, 168-178, 179-191.
4. BIOT, M. A.: Mechanics of deformation and acoustic propagation in porous media. Jour. Applied Physics 33 (1962), 1482-1498.
5. BUCHANAN, J.; GILBERT, R.: Transmission loss in the far field over a seabed with a rigid substrate assuming the Biot sediment model. Jour. Computational Acoustics 4 (1966) 1, 29-54.
6. BURRIDGE, R.; KELLER, J. B.: Poroelasticity equations derived from micro-structure. J. Acoust. Soc. Amer. 70 (1981), 1140-1146.
7. COLLINS, M. D.: Higher-order and elastic parabolic equations for wave propagation in the ocean. In: LEE, D.; CAKMAK, A.; VICHNEVETSKY, R. (Eds.), Computational acoustics. Vol. 3. Elsevier Science Publishers 1990.
8. COLLINS, M. D.: Higher-order Padé approximations for accurate and stable elastic parabolic equations with application to interface wave propagation. J. Acoust. Soc. Am. 89 (1991), 1050-1057.
9. DERSKI, W.: Equations of Mottin for a fluid-saturated porous solid. Bull. Motion. Pol. Sci., Sér., Sci. Techn. 26 (1978), 11-16.
10. EHLERS, W.; KUBIK, J.: On finite dynamic equations for fluid-saturated porous media. Acta Mechanica 105 (1994), 101-117.
11. GELFAND, I. M.; LEVITAN, B. M.: On the determination of a differential equation from its spectral function. Amer. Math. Soc. Trans., Ser. 2 I (1955), 253-304.
12. GILBERT, R. P.; LIN, Z. Y.: Acoustic wave in the shallow ocean with a layer of elastic sediment. Acustica (to appear).
13. GILBERT, R. P.; XU, Y.: Starting fields and far fields in ocean acoustics. Wave Motion 11 (1989), 507-524.
14. GILBERT, R. P.; XU, Y.: Dense sets and the projection theorem for acoustic harmonic waves in homogeneous finite depth oceans. Math. Methods Appl. Scis. 12 (1989), 69-76.
15. GILBERT, R. P.; XU, Y.: The propagation problem and far-field patterns in a stratified finite-depth ocean. Math. Methods in the Appl. Sciences 12 (1990), 199-208.
16. GILBERT, R. P.; XU, Y.: Generalized Herglotz functions and inverse scattering problems in finite depth oceans. Inverse problems, SIAM, 1992.
17. GREENE, R. R.: A high-angle one-way wave equation for seismic wave propagation along rough and sloping interfaces. J. Acoust. Soc. Am. 77 (1985), 1991-1998.
18. HAMILTON, E. L.: Geoacoustic modeling of the sea floor. J. Acoust. Soc. Am. 68 (1980) 5, 1313-1340.
19. HOLLAND, C. W.; BRUNSON, B. A.: The Biot-Stoll model: An experimental assessment. J. Acoust. Soc. Am. 84 (1988) 4, 1437-1443.
20. GRAFF, KARL F.: Wave motion in elastic solids. Ohio State University Press 1975, p. 285.
21. KOWALSKI, S. J.: Comparison of Biot equations of motion for fluid-saturated porous solid with those of Derski. Bull. Acad. Pol. Sci., Ser. Sci. Techn. 27 (1979), 455-461.
22. LÉVY, T.: Propagation des ondes dans un mileux poreaux saturé de fluide. C.R. Acad. Sci. Paris A 286 (1978), 289-292.
23. SANCHEZ-PALENCIA, E.: Non-homogeneous media and vibration theory. Lecture Notes in Physics, Springer, Berlin 1980.
24. STOLL, R. D.: Acoustic waves in saturated sediments. In: HAMPTON, L. (Ed.), Physics of sound in marine sediments. Plenum, New York 1974.
25. STOLL, R. D.; BRYAN, G. M.: Wave attenuation in saturated sediments. J. Acoust. Soc. Am. 47 (1970) 5, 1440-1447.
26. XU, Y.: An injective far-field pattern operator and inverse scattering problem in a finite depth ocean. Proceedings of the Edinburgh Mathematical Society 34 (1991), 295-311.