Inverse gravimetry by multipole expansions

Abstract We introduced a two-step method of multipole expansions for the inverse gravimetry problem in two- and three- dimensions. The source was regularized to be elliptic or rectangular for efficiency and robustness. In the first step, we estimated the center of the source by back tracing the measured gravity fields. In the second step, we solved a linear system with the measured gravity fields to estimate the mass, dipole, and quadruple of the source expanded about the estimated source center, then solved the nonlinear equations for the source parameters. We derived the error bounds for the parameters of the source in the presence of measurement noises. We demonstrated the accuracy and robustness of the method by numerical examples.