We present a stable and efficient 3D gravity inversion method to delineate the smooth basement relief of a sedimentary basin. The interpretation model consists of a set of 3D vertical prisms whose thicknesses represent the local depths to the basement and are the parameters to be estimated. The processing time is substantially reduced by using approximations of the gradient vector and of the Hessian matrix. The estimates of the basement depths are stabilized through the Tikhonov regularizing operator using local information on basement depths. Because the computations involve sparse matrices, we employ algorithms that solve sparse linear systems and which reduce drastically the processing time. Besides, we present a procedure to estimate the free variables which are scalars that stabilize the depth estimates and accelerate the convergence of the iterative nonlinear procedure. Tests with synthetic and real data attest the method efficiency and efficacy. • Proposing a method to delineate the relief of a homogeneous basement. • Stabilizing the solution through of the Tikhonov regularizing operator. • Using too local information on basement depths to produce stable solutions. • Appling the proposed method to synthetic data produces consistent results. • Appling the proposed method to real data from the Recôncavo Basin, Brazil.
Monteiro et al. (Wed,) studied this question.