Gravity and magnetic inversion with minimization of a specific functional

Abstract

The nonuniqueness of gravity or magnetic data inversion is well known. In order to remove ambiguity, some authors have sought solutions minimizing a functional describing geometrical or physical properties. Last and Kubik (1983), in particular, developed a method explaining the observed anomaly by structures of minimum volume. In this method the domain where anomalous sources are searched is divided into elementary prisms of a constant density or susceptibility contrast. Each elementary contrast is allowed to vary individually. Thus a contrast distribution is computed. The search for this kind of solution leads in general to geologically more appropriate bodies, but exceptions do occur. In this paper, the technique is broadened to include the search for solutions minimizing the moment of inertia with respect to the center of gravity or with respect to a given dip line passing through it. The resulting structures are both deeper and more compact, precisely as is required in specific cases. Theoretical and actual examples illustrate this flexible inversion technique.

Constrained Two-Dimensional Inversion of Gravity Data

“…We search for anomalous sources collapsed into bodies with their axis defined as "a priori" information. This approach is a simplified implementation of the more generalized method proposed by Guillen and Menichetti [11] and also by Silva and Barbosa [12] that incorporates only the center of gravity and orientation (dip) of the axes as constraints. Instead of automatically finding the extent of the anomaly along the predefined axis orientation (i.e.…”

“…The approach used was proposed by Guillen and Menichetti [11] and by Barbosa and Silva [12,13] with a more generalized formulation. Their inverse model is determined by the estimate of the central depth and dip of the anomalous sources.…”

Minimum‐structure borehole gravity inversion

“…For example, Green (1975) employs a weighted minimum distance method combined with a procedure which forces single density models. Guillen and Menichetti (1984) apply a minimization procedure using the inertia of the anomaly with respects to t he center of t he body or an axis which passes through it.…”

Solving ill-posed magnetic inverse problem using a Parameterized Trust-Region Sub-problem

“…For example, Last and Kubik (1983) imposed a condition that the volume of the causative body to be minimum and have a definite upper boundary for the unknown physical property. Guillen and Menichetti (1984) constrained the source to have minimal moment of inertia with respect to the center of gravity or to an axis of given dip passing through it. Abdelazeem et al (1998) used a quadratic programming with both equality and inequality constraints to invert the gravity anomalies.…”