Gravity source moment inversion: A versatile approach to characterize position and 3-D orientation of anomalous bodies

Abstract

We present a 3-D gravity interpretation method based on the inversion of source moments employing the series derived from the gravity anomaly expansion in multipoles and retaining moments up to second order only. It presents the advantages of being essentially linear and allowing a straightforward computer implementation. The method requires neither an explicit assumption about the source geometry nor a priori knowledge about the density contrast distribution, which may even be nonuniform. The method assumes implicitly: (1) that the source fits in the interior of an imaginary sphere whose center coincides with the source center of mass and whose radius is smaller than the depth to the source center of mass relative to the measuring plane, and (2) that the spatial density distribution presents three ortogonal planes of symmetry intersecting at the source center of mass. The first assumption can be met by upward continuing the observed anomaly. When both assumptions are met, the method produces reliable and stable estimates of the total anomalous mass, the coordinates of the center of mass, the three principal axes directions of the anomalous body, and the relative importance among the axes. The method is particularly suited for interpreting compact, isolated or disjoint, but spatially correlated sources. The method is sensitive to an incomplete removal of the regional field (presumably superimposed on the residual anomaly of interest) because the unremoved part of the regional field may strongly affect the estimates of the residual source moments.