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.
The paper is available in PDF (101 kB).