Energy flux in viscoelastic anisotropic media

Geophysical Journal International

Volumn 166, Issue 3, 2006, Pages 1299-1317

  Červený, Vlastislav ^a   Pšenčík, Ivan ^b  

^a CHARLES UNIVERSITY   (Czech Republic)

^b GEOPHYSICAL INSTITUTE   (Czech Republic)

Author keywords

Attenuation vector; Energy flux; Energy velocity vector; Inhomogeneous plane waves; propagation vector; viscoelastic anisotropic media

Indexed keywords

ALGORITHM; ANISOTROPIC MEDIUM; ENERGY FLUX; VISCOELASTICITY;

EID: 33747613104     PISSN: 0956540X     EISSN: 1365246X     Source Type: Journal    
DOI: 10.1111/j.1365-246X.2006.03057.x     Document Type: Article

References (49)

1. Ainslie, M.A. & Burns, P.W., 1995. Energy conserving reflection and transmission coefficients for a solid-solid boundary, J. acoust. Soc. Am., 98, 2836-2840.
2. Aki, K. & Richards, P.G., 1980. Quantitative Seismology, Freeman, San Francisco, California.
3. Auld, B.A., 1973. Acoustic Fields and Waves in Solids, Wiley, New York.
4. Borcherdt, R.D., 1973. Energy and plane waves in linear viscoelastic media, J. geophys.Res., 78, 2442-2533.
5. Borcherdt, R.D. & Wennerberg, L., 1985. General P, 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.
6. Boulanger, P., 1998. Energy flux for damped inhomogeneous plane waves in viscoelastic fluids, Wave Motion, 28, 215-225.
7. Boulanger, P. & Hayes, M., 2000. Special inhomogeneous waves in cubic elastic materials, ZAMP, 51, 1031-1038.
8. Brokešová, J. & Červený, V., 1998. Inhomogeneous plane waves in dissipative isotropic and anisotropic media. Reflection/transmission coefficients, in Seismic waves in complex 3-D structures, Report 7, pp. 57-146. Charles University, Faculty of Mathematics and Physics, Dept. of Geophysics, Praha. (Available online at 'http://sw3d.mff.cuni.cz'.)
9. Buchen, P.W., 1971. Plane waves in linear viscoelastic media, Geophys. J.R. astr. Soc., 23, 531-542.
10. Burridge, R., 1976. Some Mathematical Topics in Seismology, Courant Inst. of Math. Sci., New York Univ., New York.
11. Carcione, J.M., 1994. Wavefronts in dissipative anisotropic media, Geophysics, 59, 644-657.
12. Carcione, J.M., 1995. Constitutive model and wave equation for linear, viscoelastic, anisotropic media, Mech. Mat., 19, 311-327.
13. Carcione, J.M., 1997a. Reflection and refraction of anti-plane shear waves at a plane boundary between viscoelastic anisotropic media, Proc. R. Soc. Lond., A, 453, 919-942.
14. Carcione, J.M., 1997b. Reflection and transmission of qP-qS plane waves at a plane boundary between viscoelastic transversely isotropic media, Geophys. J. Int., 129, 669-680.
15. Carcione, J.M., 2001. Wave Fields in Real Media: Wave Propagation in Anisotropic, Anelastic and Porous Media, Pergamon, Amsterdam.
16. Carcione, J.M. & Cavallini, F., 1993. Energy balance and fundamental relations in anisotropic-viscoelastic media, Wave Motion, 18, 11-20.
17. Carcione, J.M. & Cavallini, F., 1995. Forbidden directions for inhomogeneous pure shear waves in dissipative anisotropic media, Geophysics, 60, 522-530.
18. Carcione, J.M., Helbig, K. & Helle, H.B., 2003. Effects of pressure and saturating fluid on wave velocity and attenuation of anisotropic rocks, Int. J. Rock Mech. Min. Sci., 40, 389-403.
19. Caviglia, G. & Morro, A., 1992. Inhomogeneous Waves in Solids and Fluids, World Scientific, Singapore.
20. Caviglia, G. & Morro, A., 1999. Existence and uniqueness in the reflection-transmission problem, Q.J. Mech. Appl. Math., 52, 543-564.
21. Červený, V., 2001a. Seismic Ray Theory, Cambridge Univ. Press, Cambridge.
22. Červený, V., 2001b. Energy flux of time-harmonic waves in anisotropic dissipative media, in Seismic waves in complex 3-D structures, Report 11, pp. 301-314, Charles University, Faculty of Mathematics and Physics, Dept. of Geophysics, Praha. (Available online at 'http://sw3d.mff.cuni.cz') pp. 301-314, Charles University, Faculty of Mathematics and Physics, Dept. of Geophysics, Praha.
23. Červený, V., 2004. Inhomogeneous harmonic plane waves in viscoelastic anisotropic media, Stud. Geophys. Geod., 48, 167-186.
24. Červený, V. & Pšenčík, I., 2005a. Plane waves in viscoelastic anisotropic media. I. Theory, Geophys. J. Int., 161, 197-212.
25. Červený, V. & Pšenčík, I., 2005b. Plane waves in viscoelastic anisotropic media II. Numerical examples, Geophys. J. Int., 161, 213-229..
26. Declercq, N.F., Briers, R., Degrieck, J. & Leroy, O., 2005. The history and properties of ultrasonic inhomogeneous waves, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, 52, 775-791.
27. Deschamps, M., 1990. Réflexion-réfraction de l'onde plane hétérogène: Repartition de l'énergie, J. Acoust., 3, 251-261.
28. Deschamps, M. & Assouline, P., 2000. Attenuation along the Poynting vector direction of inhomogeneous plane waves in absorbing and anisotropic solids, Acustica, 86, 295-302.
29. Deschamps, M. & Poncelet, O., 2002. Inhomogeneous plane wave and the most energetic complex ray, Ultrasonics, 40, 293-296.
30. Deschamps, M., Poirée, B. & Poncelet, O., 1997. Energy velocity of complex harmonic plane waves in viscous fluids, Wave Motion, 25, 51-60.
31. Fedorov, F.I., 1968. Theory of Elastic Waves in Crystals, Plenum, New York.
32. Frazer, L.N. & Fryer, G.J., 1989. Useful properties of the system matrix for a homogeneous anisotropic visco-elastic solid, Geophys. J., 97, 173-177.
33. Gajewski, D. & Pšenčík, I., 1987. Computation of high-frequency seismic wavefileds in 3-D laterally inhomogeneous anisotropic media, Geophys. J. R. astr. Soc., 91, 383-411.
34. Hanyga, A., 1999. Asymptotic theory of wave propagation in viscoporoelastic media, in Theoretical and Computational Acoustics '97, pp. 429-448. eds Teng, Y.-C., Shang, E.-C., Pao, Y.-H., Schulz, M.H. & Pierce, A.D., World Scientific, Singapore.
35. Hanyga, A. & Seredyńska, M., 1999. Thermodynamics and asymptotic theory of wave propagation in viscoporous media, in Theoretical and Computational Acoustics, Vol. 97, pp. 449-456. eds Teng, Y.-C., Shang, E.-C., Pao, Y.-H., Schulz, M.H. & Pierce, A.D., World Scientific, Singapore.
36. Hayes, M., 1980. Energy flux for trains of inhomogeneous plane waves, Proc. R. Soc. Lond., A, 370, 417-429.
37. Helbig, K., 1994. Foundations of Anisotropy for Exploration Seismics, Pergamon, Oxford.
38. Jakobsen, M., Johansen, T.A. & McCann, C., 2003. The acoustic signature of fluid flow in complex porous media, J. appl. Geophys. 54, 219-246.
39. Krebes, E.S., 1983. Discrepancies in energy calculations for inhomogeneous waves, Geophys. J. R. astr. Soc., 75, 839-846.
40. Krebes, E.S. & Le, L.H.T., 1994. Inhomogeneous plane waves and cylindrical waves in anisotropic anelastic media, J. geophys. Res., 99 (B12), 23899-23919.
41. Leroy, O., Quentin, G. & Clayes, J.M., 1988. Energy conservation for inhomogeneous plane waves, J. acoust. Soc. Am., 84, 374-378.
42. Mann, J.A., Tichy, I. & Romano, A.J., 1987. Instantaneous and time-averaged energy transfer in acoustic fields, J. acoust. Soc. Am., 82, 17-29.
43. Richards, P., 1984. On wavefronts and interfaces in anelastic media. Bull. seism. Soc. Am., 74, 2157-2165.
44. Scott, N.H., 1997. Energy flux and dissipation of inhomogeneous plane wave forms in Kelvin-Voigt viscoelasticity, Int. J. Engng Sci., 35, 561-572.
45. Shuvalov, A.L., 2001. On the theory of plane inhomogeneous waves in anisotropic elastic media, Wave Motion, 34, 401-429.
46. Shuvalov, A.L. & Scott, N.H., 1999. On the properties of homogeneous viscoelastic waves. Q. J. Mech. Appl. Math., 52, 405-417.
47. Shuvalov, A.L. & Scott, N.H., 2000. On singular features of acoustic wave propagation in weakly dissipative anisotropic thermoviscoelasticity, Acta Mechanica, 140, 1-15.
48. Thomson, C.J., 1996a. Notes on Rmatrix, a program to find the seismic plane-wave response of a stack of anisotropic layers, Queen's University, Dept. of Geol. Sci., Kingston.
49. Thomson, C.J., 1996b. Notes on waves in layered media to accompany program Rmatrix, Queen's Univ., Dept. of Geol. Sci., Kingston.