## Acoustic and elastodynamic 3D Green's functions for isotropic media
with a weak velocity gradient

**Vaclav Vavrycuk**
### Summary

Approximate analytical formulae for complete acoustic and elastodynamic
3D Green's functions in isotropic media with a weak and constant velocity
gradient are presented. The formulae were derived by analytical calculation
of higher-order approximations of the ray series. The ray series of
the acoustic Green's function consists of only one non-zero term, the ray
series of the elastodynamic Green's function consists of three non-zero terms
including the zeroth-order term. Since the ray series is finite for both
the Green's functions, the formulae are complete and valid in the whole
frequency range. The formulae are approximate because we assumed a weak
velocity gradient and used the first-order perturbation theory. Moreover,
the formulae are valid only in a limited region around a point source.
A wavefield generated by an explosive point source, and the elastostatic
Green's function have also been derived.

### Whole paper

The reprint is available in
PDF (223 kB).

*Wave Motion*, **31** (2000), 223-236.

SW3D
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