## First-order ray tracing for qP waves in inhomogeneous,
weakly anisotropic media

**Ivan Psencik** ** & **
**Veronique Farra**
### Summary

We propose approximate ray-tracing equations for
qP-waves propagating in smooth, inhomogeneous,
weakly anisotropic media. For their derivation, we use
perturbation theory, in which deviations of anisotropy
from isotropy are considered to be the first-order quantities.
The proposed ray-tracing equations and corresponding
traveltimes are of the first order. Accuracy of
the traveltimes can be increased by calculating a second-order
correction along first-order rays.

The first-order ray-tracing equations for qP-waves
propagating in a general weakly anisotropic medium
depend on only 15 weak-anisotropy parameters (generalization
of Thomsen's parameters). The equations
are thus considerably simpler than the exact ray-tracing
equations. For higher-symmetry anisotropic media
the equations differ only slightly from equations for
isotropic media. They can thus substitute for the traditional
isotropic ray tracers used in seismic processing.
For vanishing anisotropy, the first-order ray-tracing
equations reduce to standard, exact ray-tracing equations
for isotropic media. Numerical tests for configuration
and models used in seismic prospecting indicate
negligible dependence of accuracy of calculated traveltimes
on inhomogeneity of the medium. For anisotropy
of about 8%, considered in the examples presented, the
relative errors of the traveltimes, including the second-order
correction, are well under 0.05%; for anisotropy
of about 20%, they do not exceed 0.3%.

### Whole paper

The reprint is available in
PDF (312 kB).

*Geophysics*, **70** (2005), D65-D75.

SW3D
- main page of consortium ** Seismic Waves in Complex 3-D Structures **.