## On the parametrization of seismic anisotropy
for ray-Born inversion

**Morten Jakobsen**,
**Ivan Psencik**,
**Einar Iversen** **&** **Bjorn Ursin**
### Summary

We present a method for frequency domain seismic waveform inversion
in anisotropic media, in which dimensionless weak-anisotropy (WA)
parameters are used and compared with standard elastic moduli
(stiffness parameters) in the Voigt notation. The WA parameters
represent a generalization of conventional Thomsen parameters
and are more convenient for applications than standard elastic moduli.
Despite their name, the WA parameters can be used for anisotropy of
any strength, symmetry and orientation. Their great advantage is that
no a priori knowledge of the orientation of the symmetry axes or planes
is required. The presented method is based on the ray-Born
approximation for the forward modeling and least-squares solution of
the corresponding linear inverse problem. Although we have ignored
non-linear effects of multiple scattering, our results have important
implications for the full waveform inversion (FWI) in anisotropic media.
The Born approximation is commonly used for the calculation of Frechet
derivatives in the FWI.
Since we assume that anisotropy is due to fractures, we consider
the density distribution to be known. Although the presented algorithm
is designed for arbitrary anisotropy, for simplicity, we apply it to
a 2D heterogeneous HTI model with a syncline of a large curvature.
The numerical results show clearly that the inversion results obtained
with the use of WA parameters are much closer to the true model than
the corresponding results obtained with the Voigt stiffness parameters.

### Whole paper

The paper is available in
PDF (101 kB).

*Seismic Waves in Complex 3-D Structures*, **27** (2017), 37-49
(ISSN 2336-3827, online at http://sw3d.cz).