Gravitational and magnetic anomaly inversion using a tree-based geometry representation

Abstract

Gravitational and magnetic anomaly inversion of homogeneous 2D and 3D structures is treated using a geometric parameterization that can represent multiple, arbitrary polygons or polyhedra and a local-optimization scheme based on a hill-climbing method. This geometry representation uses a tree data structure, which defines a set of Boolean operations performed on convex polygons. A variable-length list of points, whose convex hull defines a convex polygon operand, resides in each leaf node of the tree. The overall optimization algorithm proceeds in two steps. Step one optimizes geometric transformations performed on different convex polygons. This step provides approximate size and location data. The second step optimizes the points located on all convex hulls simultaneously, giving a more accurate representation of the geometry. Though not an inherent restriction, only the geometry is optimized, not including material values such as density or susceptibility. Results based on synthetic and measured data show that the method accurately reconstructs various structures from gravity and magnetic anomaly data. In addition to purely homogeneous structures, a parabolic density distribution is inverted for 2D inversion.