Discrete-valued gravity inversion using the guided fuzzy c-means clustering technique

Abstract

The definition of boundaries, in a recovered model from an inversion, can be improved through the incorporation of known physical property values of a small number of geologic units. Directly imposing strict physical property values into a Tikhonov regularized inversion transforms it into an integer programming problem. Solving an integer programming problem can be prohibitively expensive for large problems in practical applications. We have developed a method to approximate a discrete-valued inverse problem by applying the guided fuzzy c-means clustering technique. This method enforces the discrete values to a high degree of approximation within the inversion by guiding the recovered model to cluster tightly around the known physical property values. Using this method, we are able to incorporate the uncertainty in our physical property information and solve the corresponding minimization problem with derivative-based minimization techniques, making this approach more efficient and broadly applicable. We applied the method to gravity inversions with two clusters, where the density contrast is restricted to be equal to either zero, for the background, or an anomalous value. We examine the method using synthetic and field data sets and determine that it recovers models with better distinguished density anomalies when compared with smooth inversion methods.