Hostname: page-component-848d4c4894-wzw2p Total loading time: 0 Render date: 2024-05-01T13:16:52.637Z Has data issue: false hasContentIssue false
  • English
  • Français

The elastodynamic Green's tensor for the 2D half-space

Published online by Cambridge University Press:  17 February 2009

Peter W. Buchen
Peter W. Buchen
Affiliation:
Department of Applied Mathematics, University of Sydney, N.S.W., Australia, 2006
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

An exact algebraic representation for the 2D elastodynamic Green's tensor is derived. A new displacement potential decomposition is employed which yields, in conjunction with the Pekeris–Cagniard–de Hoop method, the exact representation. The first motions of the major arrivals are evaluated in terms of their polarizations, radiation patterns, geometrical spreading and wave-front singularities. The tensorial components of the Rayleigh wave on the free surface are found and solutions for dipolar line source discussed. We also investigate diffracted phases first noticed by Lapwood in his 1949 paper [13].

Type
Research Article
Information
The ANZIAM Journal , Volume 20 , Issue 4 , December 1978 , pp. 385 - 400
Copyright
Copyright © Australian Mathematical Society 1978

References

[1]Ben-Menahem, A. and Vered, M., “Extension and interpretation of the Cagniard–Pekeris method for dislocation sources”, Bull. Seism. Soc. Amer. 63 (1973), 1611–1636.Google Scholar
[2]Burridge, R. and Knopoff, L., “Body force equivalents for seismic dislocations”, Bull. Seism. Soc. Amer. 54 (1964), 1875–1888.Google Scholar
[3]Burridge, R., Lapwood, E. R. and Knopoff, L., “First motions from seismic sources near a free surface”, Bull. Seism. Soc. Amer. 54 (1964), 1889–1913.CrossRefGoogle Scholar
[4]Cagniard, L., Reflexion et refraction des ondes seismiques progressives (1939). English translation by Flinn, E. A. and Dix, C. J. (McGraw-Hill, International Series in the Earth Sciences, 1962).Google Scholar
[5]de Hoop, A. T., “A modification of Cagniard's method for solving seismic pulse problems”, Appl. Sci. Res., B 8 (1962), 349–356.CrossRefGoogle Scholar
[6]Eason, G., Fulton, J. and Sneddon, I. N., “The generation of waves in an infinite elastic solid by variable body forces”, Phil. Trans., A 248 (1956), 576–607.Google Scholar
[7]Garnir, H. G., “Propagation de l'onde émise par une source ponctuelle et instantanée dans un dioptre plan”, Bull. Soc. Roy. Sci. Liège 3/4 (1953), 85–100/148–162.Google Scholar
[8]Garvin, W. W., “Exact transient solution of the buried line source problem”, Proc. Roy. Soc. Lond., A 234 (1956), 528–541.Google Scholar
[9]Gilbert, F. and Knopoff, L., “The directivity problem for a buried line source”, Geophys. 26 (1961), 626–634.CrossRefGoogle Scholar
[10]Johnson, L. R., “Green's function for Lamb's problem”, Geophys. J. R. Astr. Soc. 37 (1974), 99–131.CrossRefGoogle Scholar
[11]King, D. W., Haddon, R. A. W. and Husebye, E. S., “Precursors to PP”, Phys. Earth Planet. Ints. 10 (1975), 103–127.Google Scholar
[12]Lamb, H., “On the propagation of tremors over the surface of an elastic solid”, Phil. Trans. A 203 (1904), 1–42.Google Scholar
[13]Lapwood, E. R., “The disturbance due to a line source in a semi-infinite medium”, Phil. Trans A 242 (1949), 63–100.Google Scholar
[14]Nankano, H., “On Rayleigh waves”, Jap. J. Asir. Geophys. 2 (1925), 233–326.Google Scholar
[15]Pekeris, C. L., “The seismic surface pulse”, Proc. Nat. Acad. Sci. 41 (1955), 469–480.Google Scholar
[16]Pekeris, C. L., “The seismic buried pulse”, Proc. Nat. Acad. Sci. 41 (1955), 629–639.CrossRefGoogle ScholarPubMed