Anisotropie matrix-free tomography using discontinuous Galerkin of GPR data acquired between boreholes in Rustrel carbonates

Summary An increasing number of Ground-Penetrating Radar (GPR) studies takes benefit from illumination capabilities provided by dense acquisitions between boreholes. Traveltime tomography, migration and full waveform inversion provide high-resolution images to be interpreted. Tomography is often performed under an isotropic assumption, although anisotropy may exist at different scales. A new tomography approach is investigated based on an anisotropic Eikonal solver for the forward problem and an adjoint formulation for inverse problem. The misfit gradient is computed directly without expressing the sensitivity matrix, leading to explicit contribution of anisotropic parameters. The parametrization of elliptical anisotropy based on vertical and horizontal velocities is preferred to a parametrization based on Thomsen parameters for a realistic synthetic example, inspired from a real example of GPR transmission tomography between two boreholes in a carbonate environment where an old gallery exists. The vertical velocity is nicely recovered while the anisotropy contribution stays small. However, the real application provides similar results either through a layered isotropic model or through a smoother anisotropic model. Geological information is, therefore, needed for further specific interpretation.