A novel traveltime tomographic approach is applied to anisotropic media, limited to 2D geometry at present. A general anisotropic Eikonal solver based on a discontinuous Galerkin method is combined with an efficient adjoint formulation for multiparameter least-squares inversion. This new approach is tested considering synthetic crosshole ground-penetrating radar data. The configuration of the groundpenetrating radar survey is inspired by a real experiment done on layered carbonate media disturbed by the presence of a deep gallery, which induces a localized high-electromagnetic contrast. This made it possible to define a well-adapted general workflow in this context. We notably show that, under the elliptical anisotropic assumption, the parametrization based on vertical and horizontal velocities provides less biased results than those obtained by considering the vertical velocity and the relevant Thomsen parameter. The initial vertical and horizontal velocity models are identical and built from an isotropic inversion. The presence of the high-contrast gallery generates a weak diffraction pattern, which is taken into account in our tomography approach. It also creates potential artefacts due to the model discretization, which are mitigated by a model regularization term within the definition of the misfit function. This general workflow is then applied to the real experiment dataset. The vertical and horizontal velocity images provide similar structures as those previously obtained by isotropic full waveform inversion, complemented by an image of a rather weak elliptical anisotropy.

Complex Padé Fourier finite-difference migration is a stable one-way wave-equation technique that allows for better treatment of evanescent modes than its real counterpart, in this way producing fewer artifacts. As for real Fourier finite-difference (FFD) migration, its parameters can be optimized to improve the imaging of steeply dipping reflectors. The dip limitation of the FFD operator depends on the variation of the velocity field. We have developed a wide-angle approximation for the one-way continuation operator by means of optimization of the Padé coefficients and the most important velocity-dependent parameter. We have evaluated the achieved quality of the approximate dispersion relation in dependence on the chosen function of the ratio between the model and reference velocities under consideration of the number of terms in the Padé approximation and the branch-cut rotation angle. The optimized parameters are chosen based on the migration results and the computational cost. We found that by using the optimized parameters, a one-term expansion achieves the highest dip angles. The implementations were validated on the Marmousi data set and SEG/EAGE salt model data.