Analysis of gradiometer tensor fields of anomalous mass distributions

We study the inverse problem for the gradiometer tensor field and the associated notions of well-posedness and conditional correctness. The uniqueness condition for this inverse problem is shown to be equivalent to the uniqueness condition for the external potential's inverse problem. A one parameter family of mean depths to the anomaly is introduced. An inequality is proven that relates these mean depths to the total absolute mass of the anomaly and the Lp norm of the differential curvature. We investigate the stability of the inverse problem with respect to various natural topologies on the space of mass anomalies and the space of gradiometer tensor fields. Lastly, we investigate the global index of the positive eigen-line field of the gradiometer tensor.