3D Gravity Inversion of a Faulted Basement Relief Using the Total Variation Regularization

We present a gravity inversion approach that estimates the basement relief of a fault-bounded sedimentary basin. The sedimentary pack is approximated by a grid of 3D vertical prisms juxtaposed in both horizontal directions. The prisms’ thicknesses represent the depths to the basement and are the parameters to be estimated from the gravity data. To obtain 3D depth-to-basement estimates we use a nonsmooth function, named total variation regularization, which allows the reconstruction of a nonsmooth basement relief. We deduce a compact matrix form of the gradient vector and of the Hessian matrix of the approximation to the total variation function that allows using the regularized Gauss-Newton algorithm. We apply our method to synthetic data from a simulated fault-bounded sedimentary basin. By comparing our result with that obtained with the smoothing regularization, we note the improved resolution of the proposed method in defining the normal faults in the basement relief. Inversion of the gravity data from the onshore and part of the offshore Almada Basin, on Brazil’s northeastern coast, show good correlation with known structural features and confirm the potential of our method in imaging in-depth normal faults in the basement of a sedimentary basin.