Sensitivity Analysis of Full Waveform Inversion in VTI Media

We present a 2D frequency-domain Full-Waveform Inversion method for imaging VTI media. The medium is parameterized by the P and S wavespeeds on the symmetry axis (VP0 and VS0), the density, the attenuation factors and the Thomsen's parameters delta and epsilon. The forward modeling is based on a finite element discontinuous Galerkin method on unstructured triangular meshes which allows for accurate modeling in presence of complex topographies. The optimization relies on a precontioned L-BFGS quasi-Newton algorithm which directly provides the scaled gradients of the misfit function associated with different parameter classes of different unit. The radiation pattern of the anisotropic parameters for the P-P scattering mode are first developed to assess the coupling between the different parameter classes. Second, application of FWI for imaging an anisotropic inclusion from an ideal circular acquisition suggests that VP0, VS0 and the Thomsen's parameters cannot be reconstructed simultaneously because of the coupling between VP0 and epsilon. Hierarchic inversions for VP0 followed by the joint reconstruction of VS0 and the Thomsen's parameters provide more stable results.