Abstract
A new technique is explained to study the propagation of inhomogeneous waves in a general anisotropic medium. The harmonic plane waves are considered in a viscoelastic anisotropic medium. The complex slowness vector is decomposed into propagation vector and attenuation vector for the given directions of propagation and attenuation of waves in an unbounded medium. The attenuation is further separated into the contributions from homogeneous and inhomogeneous waves. A non-dimensional inhomogeneity parameter is defined to represent the deviation of an inhomogeneous wave from its homogeneous version. Such a partition of slowness vector of a plane wave is obtained with the help of an algebraic method for solving a cubic equation and a numerical method for solving a real transcendental equation. Derived specifications enable to study the 3D propagation of inhomogeneous plane waves in a viscoelastic medium of arbitrary anisotropy. The whole procedure is wave-specific and obtains the propagation characteristics for each of the three inhomogeneous waves in the anisotropic medium. Numerical examples analyze the variations in propagation characteristics of each of the three waves with propagation direction and inhomogeneity strength.
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References
Crampin S.: The fracture criticality of crustal rocks. Geophys. J. Int. 118, 428–438 (1994)
Borcherdt R.D.: Reflection and refraction of type-II S waves in elastic and anelastic media. Bull. Seism. Soc. Am. 67, 43–67 (1977)
Borcherdt R.D.: Reflection–refraction of general P and type-I S waves in elastic and anelastic solids. Geophys. J. R. Astron. Soc. 70, 621–638 (1982)
Carcione J.M., Cavallini F.: Forbidden directions for inhomogeneous pure shear waves in dissipative anisotropic media. Geophysics 60, 522–530 (1995)
Carcione J.M., Cavallini F.: Attenuation and quality factor surfaces in anisotropic viscoelastic media. Mech. Mater. 19, 311–327 (1995)
Carcione J.M., Helle H.B., Zhao T.: Effects of attenuation and anisotropy on reflection amplitude versus offset. Geophysics 63, 1652–1658 (1998)
Crampin S.: A review of wave motion in anisotropic and cracked elastic media. Wave Motion 3, 343–391 (1981)
Shuvalov A.L.: On the theory of plane inhomogeneous waves in anisotropic elastic media. Wave Motion 34, 401–429 (2001)
Cerveny V., Psencik I.: Plane waves in viscoelastic anisotropic media-I. Theory Geophys. J. Int. 161, 197–212 (2005)
Krebes E.S.: The viscoelastic reflection/transmission problem: two special cases. Bull. Seism. Soc. Am. 73, 1673–1683 (1983)
Borcherdt R.D., Wennerberg L.: General P and type-I S and type-II S waves in anelastic solids: inhomogeneous wave fields in low-loss solids. Bull. Seism. Soc. Am. 75, 1729–1763 (1985)
Carcione J.M.: Wave Fields in Real Media: Wave Propagation in Anisotropic, Anelastic and Porous Media. Pergamon, Amsterdam (2001)
Krebes E.S., Lee L.H.T.: Inhomogeneous plane waves and cylindrical waves in anisotropic anelastic media. J. Geophys. Res. 99, 23899–23919 (1994)
Sharma M.D.: Propagation of inhomogeneous plane waves in dissipative anisotropic poroelastic solids. Geophys. J. Int. 163, 981–990 (2005)
Musgrave M.J.P.: Crystal Acoustics. Holden Day, San Francisco (1970)
Auld B.A.: Acoustic Fields and Waves in Solids. Wiley, New York (1973)
Rasolofosaon P.N.J., Zinszner B.E.: Comparison between permeability anisotropy and elasticity anisotropy of reservoir rocks. Geophysics 67, 230–240 (2002)
Sharma M.D.: Group velocity along a general direction in a general anisotropic medium. Int. J. Solids Struct. 39, 3277–3288 (2002)
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Sharma, M.D. Propagation of inhomogeneous plane waves in anisotropic viscoelastic media. Acta Mech 200, 145–154 (2008). https://doi.org/10.1007/s00707-008-0034-6
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DOI: https://doi.org/10.1007/s00707-008-0034-6