Efficient gravity inversion of discontinuous basement relief

Abstract

We have developed a gravity inversion method to estimate a discontinuous basement relief based on an extended version of Bott's method that allows variable density contrasts between sediments and basement, optimizes the modulus of the solution correction at each iteration, and provides for solution stabilization. Initially, we obtain a linear approximation stabilized by the total variation functional that correctly maps the horizontal positions of the existing high-angle faults but produced poor estimates of the basin depths. Subsequent iterations update the depth estimates toward the correct values, at the same time preserving the correct fault horizontal positions. Additionally, we stabilize each solution correction by the smoothness constraint without inverting any matrix. The method was substantially more efficient than the nonlinear method, which solves a system of linear equations by the conjugate gradient method at each iteration. For 3000 parameters, it is almost four times faster than the conjugate gradient, and this ratio increased with the number of parameters.

Estimating free parameters in 2D inversion: example of gravity inversion in a rifted basement

“…; Santos et al . ). If the discontinuities are correctly positioned at the first stage, then the terraces delimited by these discontinuities will also be correctly delineated.…”

“…In the first stage of the inversion procedure, we employ Santos et al ’s. () method to obtain the initial estimate, , through the solution of a linear system of equations using the Barrodale and Robert's () algorithm. In the second stage, the nonlinear, but highly efficient, extended Bott's method (Silva, Santos and Gomes ) is applied from the second iteration on.…”

“…We elected Santos et al's . approach because: (i) it is a very efficient, stable, and reliable method to invert gravity anomalies over sedimentary basins and (ii) it allows for several free parameters.…”

“…So, the scalar is not considered a free parameter. Scalar λ is the regularization parameter, employed in Santos et al .’s () method, which controls the degree of spatial smoothness of the solution, necessary to hold down the increasing solution instability with the number of iterations, characteristic of the extended Bott's method (Silva et al . ).…”

“…We illustrate the proposed principle for the case of a half‐graben which, in a 2D cross section, displays an approximate shape of a scalene triangle. In the methodology section, we present the 2D version of Santos et al.’ s method directed to estimate a faulted basement relief. We selected this method to illustrate our procedure because it contains several free parameters.…”