Solution of the Rayleigh eigenproblem in Viscoelastic media

Bulletin of the Seismological Society of America

Volumn 92, Issue 6, 2002, Pages 2297-2309

  Lai, Carlo G ^a   Rix, Glenn J ^a  

^a Studio Geotecnico Italiano   (Italy)

^b GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; ATTENUATION; EIGENVALUES AND EIGENFUNCTIONS; RAYLEIGH SCATTERING; VISCOELASTICITY; WAVE PROPAGATION;

LAYERED MEDIA;

SEISMOLOGY;

ALGORITHM; PHASE VELOCITY; RAYLEIGH WAVE; SEISMOGRAM; VISCOELASTICITY; WAVE PROPAGATION;

EID: 0036704690     PISSN: 00371106     EISSN: None     Source Type: Journal    
DOI: 10.1785/0120010165     Document Type: Article

References (46)

1. Abd-Elall, L., L. Delves, and J. Reid (1970). A numerical method for locating the zeros and poles of a meromorphic function, in P. Rabinowitz (Editor), Numerical Methods for Non Linear Algebraic Equations. Gordon and Breach Science Publishers, London, 47-59.
2. Aki, K., and P. G. Richards (1980). Quantitative Seismology: Theory and Methods, Freeman, New York.
3. Anderson, D., and C. Archambeau (1964). The anelasticity of the earth. J. Geophys. Res., 69, no. 10,2071-2084.
4. Anderson, D., A. Ben-Menahem, and C. Archambeau (1965). Attenuation of seismic energy in the upper mantle, J. Geophys. Res., 70, no. 6, 1441-1448.
5. Båth, M. (1984). Mathematical Aspects of Seismology, Elsevier, Amsterdam.
6. Boore, D. M. (1972). Finite difference methods for seismic wave propagation in heterogeneous materials, in B. Bolt (Editor), Methods in Computational Physics, Academic Press, New York, 11, 1-37.
7. Borcherdt, R. (1971). Inhomogeneous body and surface wave plane waves in a generalized viscoelastic half-space, Ph.D. Thesis, University of California. Berkeley.
8. Borcherdt, R. (1973a). Energy and plane waves in linear viscoelastic media, J. Geophys. Res. 78, no. 14, 2442-2453.
9. Borcherdt, R. (1973b). Rayleigh-type surface wave on a linear viscoelastic half-space, J. Acoust. Soc. Am. 54, no. 6, 1651-1653.
10. Borcherdt, R., and L. Wennerberg (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.
11. Brent, R. (1973). Algorithms for Minimization Without Derivatives. Prentice-Hall, Englewood Cliffs, New Jersey.
12. Buchen, P. (1971). Plane waves in linear viscoelastic media, Geophys. J. R. Astr. Soc. 23, 531-542.
13. Christensen, R. (1971). Theory of Viscoelasticity-An Introduction, Academic Press, New York.
14. Delves, L., and J. Lyness (1967). A numerical method for locating the zeros of an analytic function, Math Comp. 21, 543-560.
15. Electric Power Research Institute (1991). Proceedings: NSF/EPRI workshop on dynamic soil properties and site characterization, technical report NP-7337.
16. Faccioli, E., F. Maggio, A. Quarteroni, and A. Tagliani (1996). Spectral-domain decomposition methods for the solution of acoustic and elastic wave equations, Geophysics 61, 1160-1174.
17. Fung, Y. (1965). Foundations of Solid Mechanics. Prentice-Hall, Englewood Cliffs, New Jersey.
18. Hardin, B., and V. Drnevich (1972). Shear modulus and damping in soils: measurement and parameter effects, J. Soil Mech. Found. Eng. 98, 603-624.
19. Haskell, N. (1953). The dispersion of surface waves on multilayered media. Bull. Seism. Soc. Am. 43, 17-34.
20. Henrici, P. (1974). Applied and Computational Complex Analysis, volume 1, J. Wiley, New York.
21. Herrmann, R. (1994). Computer Programs in Seismology, St. Louis University, St. Louis, Missouri.
22. Hille, E. (1973). Analytic Function Theory, Second edition, volume 1, Chelsea, New York.
23. Ishibashi, I., and X. Zhang (1993). Unified dynamic shear moduli and damping ratios of sand and clay, Soils Found. 33, no. 1. 182-191.
24. Ishihara, K. (1996). Soil Behaviour in Earthquake Geotechnics, Oxford Science Publications, Oxford, U.K.
25. Kausel, E., and J. M. Roesset (1981). Stiffness matrices for layered soils, Bull. Seism. Soc. Am. 71, no. 6, 1743-1761.
26. Keilis-Borok, V. (1989). Seismic Surface Waves in a Laterally Inhomogeneous Earth, Kluwer. Dordrecht, Netherlands.
27. Kennett, B. (1983). Seismic Wave Propagation in Stratified Media, Cambridge University Press, Cambridge, U.K.
28. Lai, C. G. (1998). Simultaneous inversion of Rayleigh phase velocity and attenuation for near-surface site characterization. Ph.D. thesis. Georgia Institute of Technology.
29. Lee, W., and S. Solomon (1978). Simultaneous inversion of surface wave phase velocity and attenuation: Love waves in western North America, J. Geophys. Res. 83, 3389-3400.
30. Lo Presti, D., S. Shibuya, and G. Rix (1999). Innovation in soil testing, in M. Jamiolkowski, R. Lancellotta, and D. Lo Presti, (Editors), Pre-Failure Deformation Characteristics of Geomaterials, Balkema, Rotterdam.
31. Manolis, G., and D. Beskos (1988). Boundary Element Methods in Elastodynamics, Unwin Hyman, London.
32. Mitchell, B. J. (1975). Regional Rayleigh wave attenuation in North America. J. Geophys. Res. 80, 4904-4916.
33. Mokhtar, T. A., R. B. Herrmann, and D. R. Russell (1988). Seismic velocity and q-model for the shallow structure of the arabian shield from short-period rayleigh waves. Geophysics 53, 1379-1387.
34. Pipkin, A. (1986). Lectures on Viscoelasticity Theory, Second edition, Springer-Verlag, Berlin.
35. Press, F. and J. Healy (1957). Absorption of Rayleigh waves in low-loss media, J. Appl. Phys. 28, no. 11, 1323-1325.
36. Press, W., S. Teukolsky, W. Vetterling, and B. Flannery (1992). Numerical Recipes-The Art of Scientific Computing, Second edition, Cambridge University Press, Cambridge UK.
37. Read, W. (1950). Stress analysis for compressible viscoelastic materials, in J. Appl. Phys. 21.
38. Rix, G., C. Lai, and A. Spang (2000). In situ measurement of damping ratio using surface waves. J. Geotech. Geoenviron. Eng. 126, no. 5, 472-480.
39. Schwab, F., and L. Knopoff (1971). Surface waves on multilayered anelastic media, Bull. Seism. Soc. Am. 61, no. 4, 893-912.
40. Schwab, F., and L. Knopoff (1972). Fast surface wave and free-mode computations, in B. Bolt (Editor), Methods in Computational Physics, Academic Press, New York, Vol. 11, 87-180.
41. Shibuya, S., T., Mitachi, F. Fukuda, and T. Degoshi (1995). Strain rate effects on shear modulus and damping of normally consolidated clay. Geotech. Test. J. 18, 365-375.
42. Silva, W. (1978). Inversion of Love-wave data for velocity and anelasticity using exact kernels. Geophys. J. R. Astr. Soc. 55, 363-371.
43. Takeuchi, H., and M. Saito (1972). Seismic surface waves, in B. Bolt, (Editor), Methods in Computational Physics, Academic Press, New York, Vol. 11, 217-295.
44. Thomson, W. (1950). Transmission of elastic waves through a stratified solid medium. J. Appl. Phys. 21, 89-93.
45. Vucetic, M. (1994). Cyclic threshold shear strains in soils. J. Geotech. Eng. 120, 2208-2228.
46. Vucetic, M., and R. Dobry (1991). Effect of soil plasticity on cyclic response. J. Geotech. Eng. 117, 89-107.