Elastic waves in nonhomogeneous media under 2D conditions: I. Fundamental solutions

Soil Dynamics and Earthquake Engineering

Volumn 18, Issue 1, 1999, Pages 19-30

  Manolis, George D ^a   Shaw, Richard P ^b   Pavlou, Stavros ^c  

^a ARISTOTLE UNIVERSITY OF THESSALONIKI   (Greece)

^b the State University of New York   (United States)

^c UNIVERSITY OF PATRAS   (Greece)

Author keywords

Fundamental solutions; Nonhomogeneous media; Seismic waves; Wave propagation

Indexed keywords

CONFORMAL MAPPING; DIFFERENTIAL EQUATIONS; EQUATIONS OF MOTION; FOURIER TRANSFORMS; MATHEMATICAL OPERATORS; POISSON RATIO; WAVE PROPAGATION;

EULER EQUATIONS; WAVE DECOMPOSITION;

SEISMIC WAVES;

ELASTIC WAVE; SEISMIC WAVE; WAVE PROPAGATION;

EID: 0033066620     PISSN: 02677261     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0267-7261(98)00038-4     Document Type: Article

References (43)

1. Kennet BLN. Seismic wave propagation in stratified media. Cambridge: Cambridge University Press, 1983.
2. Ewing WM, Jardetzky WS, Press F. Elastic waves in layered media. New York: McGraw-Hill, 1957.
3. Ben Menachem A, Singh SJ. Seismic waves and sources. New York: Springer-Verlag, 1981.
4. Hanyga A, editor. Seismic wave propagation in the earth. Amsterdam: Elsevier, 1985.
5. Brekhovskikh LM, Beyer R. Waves in layered media, 2nd edn. New York: Academic Press, 1980.
6. Graff KF. Wave motion in elastic solids. Colombus, OH: Ohio University Press, 1975.
7. Thomson W. Transmission of elastic waves through a stratified solid medium. Journal of Applied Physics. 21:1950;89-93.
8. Haskell N.A. The dispersion of surface waves in multilayered media. Bulletin Seismological Society of America. 43:1953;17-34.
9. Haskell N.A. Radiation pattern of surface waves from point sources in multi-layered medium. Bulletin Seismological Society of America. 54:1964;337-393.
10. Biot M.A. Continuum dynamics of elastic plates and multilayered solids under initial stress. Journal of Mathematics and Mechanics. 12:1963;793-810.
11. Shaw R.P., Bugl P. Transmission of plane waves through layered linear viscoelastic media. Journal Acoustical Society of America. 46(3):1969;649-654.
12. Kausel E., Roesset J.M. Stiffness matrices for layered soil. Bulletin Seismological Society of America. 71:1981;1743-1761.
13. Bravo M.A., Sanchez-Sesma F., Chavez-Garcia F. Ground motion on stratified alluvial deposits for incident SH waves. Bulletin Seismological Society of America. 78:1988;436-450.
14. Chen JT, Chen LY, Hong HK. Regularization method for deconvolution problems in soil dynamics. In: Brebbia CA, Kim S, Osswald TA, Power H, editors. Boundary elements XVII. Southampton: Computational Mechanics Publications, 1995:351-358.
15. Bonnet G, Heitz JF. Nonlinear seismic response of a soft layer. In: Duma G, editor. Proceedings 10th European Conference on Earthquake Engineering. Rotterdam: Balkema, 1995:361-364.
16. Pires JA. Stochastic seismic response analysis of soft soil sites. In: Kussmaul K, editor. Structural mechanics in reactor technology - 12. London: Elsevier Science Publishers, 1993;M/K:219-224.
17. Safak E. Discrete time analysis of seismic site amplification. Journal of Engineering Mechanics ASCE. 121:1995;801-809.
18. Urratia-Galicia JL, Ruiz SE, Diederich R. Comparison of matrix methods in one-dimensional amplification problems. In: Cakmak AS, Herrera IS, editors. Engineering seismology and site response. Southampton: Computational Mechanics Publications, 1989:89-99.
19. Wang C.Y., Herrmann R.B. A numerical study of P-, SV-, and SH-wave generation in a plane layered medium. Bulletin Seismological Society of America. 70:1980;1015-1036.
20. Cagniard L. Reflection and refraction of progressive seismic waves, English Translation. New York: McGraw-Hill, 1962.
21. Hudson J.A. A quantitative evaluation of seismic signals at teleseismic distances - II. Body waves and surface waves from an extended source. Geophysics Journal. 18:1969;353-370.
22. Umek A, Strukelj A. Green's function for layered halfspace. In: Cakmak AS, editor. Ground motion and engineering seismology. Amsterdam: Elsevier, 1987:339-345.
23. Apsel R.J., Luco J.E. On the Green's function for the layered halfspace. Part II. Bulletin Seismological Society of America. 73:1983;931-951.
24. Pai D.M. Wave propagation in inhomogeneous media: a planewave layer interaction method. Wave Motion. 13:1991;205-209.
25. Mikhailenko B.G. Numerical experiments in seismic investigations. Journal of Geophysics. 58:1985;101-124.
26. Mikhailenko BG. Synthetic seismograms for complex three dimensional geometries using an analytical-numerical technique. Geophysics Journal Royal Astronomical Society 1984;79:963-986.
27. Gazdag J. Numerical convective schemes based on accurate computation of space derivatives. Journal Computational Physics. 13:1971;100-113.
28. Acharya H.K. Field due to a point source in an inhomogeneous elastic medium. Journal Acoustical Society of America. 50:1971;172-175.
29. Hook J.F. Separation of the vector wave equation of elasticity for inhomogeneous materials. Journal Acoustical Society of America. 33:1961;302-313.
30. Alverson R.C., Gair F.C., Hook J.F. Uncoupled equations of motion in nonhomogeneous elastic media. Bulletin Seismological Society of America. 53:1963;1023-1030.
31. Gupta R.N. Reflection of elastic waves from a linear transition layer. Bulletin Seismological Society of America. 56:1966;511-526.
32. Payton R.G. Elastic wave propagation in a nonhomogeneous rod. Quarterly Journal of Mechanics and Applied Mathematics. 19:1966;83-91.
33. Karal F.C., Keller J.B. Elastic wave propagation in homogeneous and inhomogeneous media. Journal Acoustical Society of America. 31:1959;694-705.
34. Manolis G.D., Shaw R.P. Green's function for the vector wave equation in a mildly heterogeneous continuum. Wave Motion. 24:1996;59-83.
35. Shaw RP, Manolis GD. Two dimensional acoustic waves in a heterogeneous medium using conformal mapping and dependent variable transformations. In: Proceedings of Third International Conference on Computational Acoustics, Newark, July 14-17, 1997 (to appear).
36. Churchill RV, Brown JW, Verhey RH. Complex variables and applications. New York: McGraw-Hill, 1974.
37. Greenberg MD. Application of Green's functions in science and engineering. Englewood Cliffs: Prentice-Hall, 1970.
38. Sternberg E., Eubanks R.A. On the concept of concentrated loads and an extension of the uniqueness theorem in the linear theory of elasticity. Journal of Rational Mechanics and Analysis. 6:1955;34-50.
39. Gradsteyn IS, Ryzhik IM. Tables of integrals, series and products. New York: Academic Press, 1980.
40. Shaw RP, Manolis GD. Elastic waves in one-dimensionally layered heterogeneous soil media. In: Kausel E, Manolis GD, editors. Wave motion problems in earthquake engineering. Southampton: Computational Mechanics Publications, Southampton, 1998 (to appear).
41. Braun M. Differential equations and their applications. Berlin: Springer, 1975.
42. Manolis G.D., Shaw R.P. Fundamental solutions to Helmholtz's equation for inhomogeneous media by a first-order differential equation system. Soil Dynamics Earthquake Engineering. 16:1997;81-94.
43. Press WH, Flannery BP, Teukolsky SA, Vetterling WT. Numerical recipes (Fortran Version). Cambridge: Cambridge University Press, 1989.