## Elastodynamic and elastostatic Green tensors for homogeneous
weak transversely isotropic media

**Vaclav Vavrycuk**
### Summary

An explicit analytical formula for the complete elastodynamic
Green tensor for homogeneous unbounded weak transversely isotropic media
is presented. The formula was derived by analytical calculations
of higher-order approximations of the ray series.
The ray series is finite and consists of seven non-zero terms.
The formula for the Green tensor is complete and correct for the whole
frequency range, thus it describes correctly the wavefield at all distances
and at all directions including the shear-wave singularity
direction. The Green tensor consists of P, SV and SH far-field waves
and four coupling waves. Three of them couple P and SV waves, and the fourth
wave couples the SV and SH waves. The P-SV coupling waves behave similarly
to the near-field waves in isotropy. However, the SV-SH coupling wave,
which is called 'shear-wave coupling', behaves exceptionally and it has
no analogy in the Green tensor for isotropy. The formula for the elastostatic
Green tensor is also derived.

### Keywords

Anisotropy, Green tensor, perturbation methods, ray theory,
shear-wave coupling, shear-wave splitting.

### Whole paper

The reprint is available in
PDF (1159 kB !).

*Geophys. J. int.*, **130** (1997), 786-800.

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