Three-dimensional gravity inversion using graph theory to delineate the skeleton of homogeneous sources

Abstract

We developed a new strategy, based on graph theory concepts, to invert gravity data using an ensemble of simple point masses. Our method consisted of a genetic algorithm with elitism to generate a set of possible solutions. Each estimate was associated to a graph to solve the minimum spanning tree (MST) problem. To produce unique and stable estimates, we restricted the position of the point masses by minimizing the statistical variance of the distances of an MST jointly with the data-misfit function during the iterations of the genetic algorithm. Hence, the 3D spatial distribution of the point masses identified the skeleton of homogeneous gravity sources. In addition, our method also gave an estimation of the anomalous mass of the source. So, together with the anomalous mass, the skeleton could aid other 3D methods with promising geometric a priori parameters. Several tests with different values of regularizing parameter were made to bespeak this new regularizing strategy. The inversion results applied to noise-corrupted synthetic gravity data revealed that, regardless of promising starting models, the estimated distribution of point masses and the anomalous mass offered valuable information about the homogeneous sources in the subsurface. Tests on real data from a portion of Quadrilátero Ferrífero, Minas Gerais state, Brazil, were performed for complementary analysis of the proposed inversion method.

IGUG: A MATLAB package for 3D inversion of gravity data using graph theory

“…In this section we briefly review the gravity inversion based on graph theory. For more details the readers should refer to Bijani et al (2015).…”

“…A new diagnostic approach is presented for determining a suitable choice for λ, requiring a limited number of solutions for a small set of λ. This contrasts the use of the L-curve which was suggested for estimating the λ in Bijani et al (2015). Simulations for synthetic examples demonstrate the efficiency and effectiveness of the implementation of the algorithm.…”

“…The model parameters are the Cartesian coordinates and total mass of the point masses, and the algorithm yields the reconstruction of the skeleton of the body with the obtained coordinates and total mass. Here, as described in the following sections, we present a MATLAB package to implement gravity inversion based on some extensions of the graph theory approach of Bijani et al (2015).…”

“…Non-linear inversions have been stabilized by constraining the density variation with depth (Chakravarthi & Sundararajan, 2007) and applying a total variation regularization (Martins et al, 2011). In the graph theory approach of Bijani et al (2015) the equidistance function stabilization was introduced.…”

“…Overview of main scientific contributions. Bijani et al (2015) introduced the use of graph theory for the three dimensional inversion of gravity data.…”