Open AccessThe elastodynamic Green's tensor in an anisotropic half‐space
Author(s) -
BenMenahem A.,
Sena A. G.
Publication year - 1990
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1111/j.1365-246x.1990.tb04475.x
Subject(s) - hankel transform , multipole expansion , wavenumber , isotropy , mathematical analysis , tensor (intrinsic definition) , tensor field , anisotropy , half space , field (mathematics) , space (punctuation) , mathematics , representation (politics) , symmetric tensor , green s , physics , geometry , exact solutions in general relativity , fourier transform , quantum mechanics , pure mathematics , linguistics , philosophy , politics , political science , law
SUMMARY We study the effect of the free surface on waves from buried sources in an elastic half‐space with azimuthal isotropy. The exact Green's tensor is obtained in the form of a Hankel transform over the horizontal wavenumber. The integrals are then evaluated at the far‐field by means of the stationary phase approximation. An alternative representation of the Green's tensor is offered in the form of a hybrid multipole expansion valid also in the near‐field. The variation of the reflection coefficients as a function of the image source angle is presented for various earth models and it is shown that the effect of the anisotropy at the source is more important than its effect on the reflected waves from the free surface.