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Reflection and refraction of acoustic waves at poroelastic ocean bed

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Abstract

Ocean bottom is considered as a plane interface between non-viscous liquid and anisotropic dissipative poroelastic solid. The dissipation comes from the viscosity of pore-fluid as well as the anelasticity of the porous frame. Biot’s theory is used to derive a system of modified Christoffel equations for the propagation of plane harmonic waves in a porous medium. The non-trivial solution of this system is ensured by a determinantal equation. This equation is solved into a polynomial equation of degree eight, whose roots represent the vertical slowness values for the waves propagating upward and downward in a porous medium. The eight, numerically obtained, slowness values are identified with the four waves propagating towards (or away from) the boundary in the porous medium. Incidence of acoustic wave through the liquid at the interface results in its reflection and the refraction of four attenuating waves in the poroelastic medium. The energy partition among the reflected and refracted waves is calculated at the interface. Conservation of energy is obtained except in the case of partially opened surface pores of the porous medium. Energy refracted to the dissipative porous medium is expressed through an energy matrix. The four diagonal elements of this matrix represent the energy shares of the four inhomogeneous waves and the sum of all the off-diagonal elements of this matrix represents the interaction energy. Few significant results are extracted from the observations in the numerical examples studied. These results represent the effect of anisotropic symmetries, anelasticity, wave-frequency, opening, configuration and flow-impedance of pores, on the energy shares of reflected and refracted waves.

References

  1. Ainslie, M. A. and P. W. Burns, Energy-conserving reflection and transmission coefficients for a solid-solid boundary, J. Acoust. Soc. Am., 98, 2836–2840, 1995.

  2. Albert, D. G., A comparison between wave propagation in water-saturated and air-saturated porous materials, J. Appl. Phys., 73, 28–36, 1993.

  3. Badiey, M., L. Jaya, and A. H.-D. Cheng, Propagator matrix for plane wave reflection from inhomogeneous anisotropic poroelastic seafloor, J. Comput. Acoust., 2, 11–27, 1994.

  4. Biot, M. A., The theory of propagation of elastic waves in a fluid-saturated porous solid, I. Low-frequency range, II. Higher frequency range, J. Acoust. Soc. Am., 28, 168–191, 1956.

  5. Biot, M. A., Mechanics of deformation and acoustic propagation in porous media, J. Appl. Phys., 33, 1482–1498, 1962a.

  6. Biot, M. A., Generalized theory of acoustic propagation in porous dissipative media, J. Acoust. Soc. Am., 34, 1254–1264, 1962b.

  7. Borcherdt, R. D., Reflection and refraction of type-II S waves in elastic and inelastic media, Bull. Seism. Soc. Am., 67, 43–67, 1977.

  8. Buckingham, M. J., Theory of acoustic attenuation, dispersion and pulse propagation in unconsolidated granular materials including marine sediments, J. Acoust. Soc. Am., 102, 2579–2596, 1997.

  9. Buckingham, M. J., Theory of compressional and shear waves in fluid like marine sediments, J. Acoust. Soc. Am., 103, 288–299, 1998.

  10. Buckingham, M. J., Theory of compressional and transverse wave propagation in consolidated porous media, J. Acoust. Soc. Am., 106, 575–587, 1999.

  11. Buckingham, M. J., Wave propagation, stress relaxation, and grain-to-grain shearing in saturated, unconsolidated marine sediments, J. Acoust. Soc. Am., 108, 2796–2815, 2000.

  12. Carcione, J. M., Wave Fields in Real Media: Wave Propagation in Anisotropic, Anelastic and Porous Media, Pergamon, Amsterdam, 2001.

  13. Chotiras, N. P., D. E. Smith, and J. N. Piper, Refraction and scattering into a sandy ocean sediment in 30–40 kHz band, IEEE J. Oceanic Engng. 27, 362–375, 2007.

  14. Collins, M. D., J. F. Lingevitch, and W. L. Siegmann, Wave propagation in poro-acoustic media, Wave Motion, 25, 265–272, 1997.

  15. Crampin, S., Suggestions for a consistent terminology for seismic anisotropy, Geophys. Prospect., 37, 753–770, 1989.

  16. Crampin, S., The fracture criticality of crustal rocks, Geophys. J. Int., 118, 428–438, 1994.

  17. de la Cruz, V., J. Hube, and T. J. T. Spanos, Reflection and transmission of seismic waves at the boundaries of porous media, Wave Motion, 16, 323–338, 1992.

  18. Denneman, A. I. M., G. G. Drijkoningen, D. M. J. Smeulders, and K. Wapenar, Reflection and transmission of waves at a fluid/porous medium interface, Geophys., 67, 282–291, 2002.

  19. Deresiewicz, H. and R. Skalak, On uniqueness in dynamic Poroelasticity, Bull. Seismol. Soc. Am., 53, 793–799, 1963.

  20. Gurevich, B., Elastic properties of saturated porous rocks with aligned fractures, J. Appl. Geophys., 54, 203–218, 2003.

  21. Johnson, D. L., J. Koplik, and R. Dashen, Theory of dynamic permeability and tortuosity in fluid-saturated porous media, J. Fluid Mech., 176, 379–402, 1987.

  22. Kohler, W. E., A one-dimensional randomly stratified model of ocean sediments, Wave Motion, 10, 421–441, 1988.

  23. Kuo, E. Y. T., Acoustic wave scattering from two solid boundaries at the ocean bottom: Reflection loss, IEEE J. Oceanic Eng., 17, 159–170, 1992.

  24. Lin, C.-H., V. M. Lee, and M. D. Trifunac, The reflection of plane waves in a poroelastic half-space saturated with inviscid fluid, Soil Dyn. Earthquake, 25, 206–223, 2006.

  25. Liu, J. Y., C. F. Huang, and S. W. Shyue, Effect of seabed properties on acoustic wave fields in a seismo-acoustic ocean waveguide, Ocean Eng., 28, 1437–1459, 2001.

  26. Potel, C. and F. J. de Belleval, Propagation in an anisotropic periodically multilayered medium, J. Acoust. Soc. Am., 93, 2669–2677, 1993.

  27. Rasolofosaon, P. N. J. and B. E. Zinszner, Comparison between permeability anisotropy and elasticity anisotropy of reservoir rocks, Geophys., 67, 230–240, 2002.

  28. Schmitt, D. P., Acoustic multipole logging in transversely isotropic poroelastic formations, J. Acoust. Soc. Am., 86, 2397–2421, 1989.

  29. Sharma, M. D., Three-dimensional wave propagation in a general anisotropic poroelastic medium: phase velocity, group velocity and polarisation, Geophys. J. Int., 156, 329–344, 2004a.

  30. Sharma, M. D., 3-D wave propagation in a general anisotropic poroelastic medium: reflection and refraction at an interface with fluid, Geophys. J. Int., 157, 947–958, 2004b.

  31. Sharma, M. D., Propagation of inhomogeneous plane waves in dissipative anisotropic poroelastic solids, Geophys. J. Int., 163, 981–990, 2005.

  32. Sharma, M. D., Propagation of harmonic plane waves in a general anisotropic porous solid, Geophys. J. Int., 2007 (in press).

  33. Sharma, M. D. and M. L. Gogna, Wave propagation in anisotropic liquid-saturated porous solids, J. Acoust. Soc. Am., 89, 1068–1073, 1991.

  34. Stoll, R. D., Acoustic waves in saturated sediment, in Physics of sound in Marine Sediments, edited by L. Hampton, 19–39, Plenum, New York, 1974.

  35. Stoll, R. D., Acoustic waves in Ocean sediments, Geophys., 42, 715–725, 1977.

  36. Stoll, R. D., Experimental studies of attenuation in sediments, J. Acoust. Soc. Am., 66, 1152–1160, 1979.

  37. Stoll, R. D., Theoretical aspects of sound transmissions in sediments, J. Acoust. Soc. Am., 68, 1341–1350, 1980.

  38. Stoll, R. D. and G. M. Bryan, Wave attenuation in saturated sediments, J. Acoust. Soc. Am., 47, 1440–1447, 1970.

  39. Stoll, R. D. and T.-K. Kan, Reflection of acoustic waves at a water-sediment interface, J. Acoust. Soc. Am., 70, 149–156, 1981.

  40. Vashishth, A. K. and P. Khurana, Rayleigh modes in anisotropic, heterogeneous poroelastic layers, J. Seismol., 9, 431–448, 2005.

  41. Yang, J., Importance of flow condition on seismic waves at a saturated porous solid boundary, J. Sound Vib., 221, 391–413, 1999.

  42. Yamamoto, T., Acoustic propagation in the ocean with a poro-elastic bottom, J. Acoust. Soc. Am., 73, 1587–1596, 1983.

  43. Yamamoto, T., Acoustic scattering in the ocean from velocity and density fluctuations in the sediments, J. Acoust. Soc. Am., 99, 866–879, 1996.

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Correspondence to A. K. Vashishth.

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Vashishth, A.K., Sharma, M.D. Reflection and refraction of acoustic waves at poroelastic ocean bed. Earth Planet Sp 61, 675–687 (2009) doi:10.1186/BF03353176

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Key words

  • Poroelasticity
  • anisotropy
  • ocean-bottom
  • reflection
  • refraction
  • acoustic