Index theory-based algorithm for the gradiometer inverse problem

Abstract

We present an Index Theory based gravity gradiometer inverse problem algorithm. This algorithm relates changes in the index value computed on a closed curve containing a line field generated by the positive eigenvector of the gradiometer tensor to the closeness of fit of the proposed inverse solution to the mass and center of mass of the unknown. We then derive a method of determining bounds on the unknown’s center of mass and/or total mass and apply it as a function of gradiometer observables. Both observational errors and the varieties of possible mass distributions generating the gradients are taken into account for the bounds.