Fast gravity inversion of basement relief

Abstract

Gravity interpretation of large sedimentary basins requires a large number of observations and of parameters estimations, so the development of very efficient gravity inversion methods applicable to such environments is of utmost importance. We found that the highly efficient Bott's method can be cast in the framework of Gauss-Newton's method for minimizing nonlinear functions. Also, we extended Bott's method to (1) be applicable to sedimentary basins with density contrast between the sediments and the basement decreasing with depth according to different laws, (2) optimize the modulus of the parameter correction vector, (3) stabilize the solution by imposing that it be smooth, and (4) quit the iteration according to an objective and effective criterion. To keep up the efficiency of Bott's method, stable solutions were obtained by applying a moving average to the usually unstable solution obtained at the last iteration. Solutions as efficacious as those obtained by the usual nonlinear method were produced by the present extension at a much smaller computation time. Nonlinear methods, with different implementations for solving a linear system of equations, required between one and two orders of magnitude more time to produce similar solutions using between 2000 and 3000 parameters and observations, for example.

Three-Dimensional Gravity Inverse Modeling for Basement Depth Estimation Integrating Maximum Difference Reduction (MDR), Trend Surface Analysis (TSA) and Total Variation Regularization

“…Bott's method has been successfully transformed in the Gauss-Newton form [6]. Analogously, the incorporation of the MDR3D method in the inversion scheme can also be done by replacing the diagonal elements of the Jacobian matrix with the MDR3D formula.…”

“…Other approaches of gravity forward modeling and inverse modeling in the spatial frequency domain have been proposed by Parker [3] and Oldenburg [4]. However, the resulting solutions were not stable, so that the concept of Tikhonov regularization was introduced to stabilize the computation process [5,6]. In its applications, the Tikhonov regularization has several variants, such as smoothness, total variation, minimum support, gradient minimum support, minimum entropy, etc.…”

“…In its applications, the Tikhonov regularization has several variants, such as smoothness, total variation, minimum support, gradient minimum support, minimum entropy, etc. [6,7].…”

“…Thus the concept of regularization and also constraints can be added into the Bott method [6]. The regularization method most commonly used is smoothing.…”

Efficient gravity inversion of discontinuous basement relief

“…Further, this approach demands a large number of evaluations of the gravity fitting functional, usually involving logarithms and inverse tangent functions. Silva et al (2014) argue that in the near future, the amount of potential field data collected over promising basins may far surpass the computer memory and speed required to process them in an acceptable time. In the past 10 years, the increase in memory and processing speed of single CPU units has been modest and the immediate alternatives to increase them were concentrated on the use of computer clusters and parallel computing.…”