Eigenvector analysis of gravity gradient tensor to locate geologic bodies

We have developed a new method to locate geologic bodies using the gravity gradient tensor. The eigenvectors of the symmetric gravity gradient tensor can be used to estimate the position of the source body as well as its strike direction. For a given measurement point, the eigenvector corresponding to the maximum eigenvalue points approximately toward the center of mass of the causative body. For a collection of measurement points, a robust least-squares procedure is used to estimate the source point as the point that has the smallest sum of square distances to the lines defined by the eigenvectors and the measurement positions. It's assumed that the maximum of the first vertical derivative of the vertical component of gravity vector g(zz) is approximately located above the center of mass. Observation points enclosed in a square window centered at the maximum of g(zz) are used to estimate the source location. By increasing the size of the window, the number of eigenvectors used in the robust least squares and subsequently the number of solutions increase. As a criterion for selecting the best solution from a set of previously computed solutions, we chose that solution having the minimum relative error (less than a given threshold) of its depth estimate. The strike direction of the source can be estimated from the direction of the eigenvectors corresponding to the smallest eigenvalue for quasi 2D structures. To study the effect of additive random noise and interfering sources, the method was tested on synthetic data sets, and it appears that our method is robust to random noise in the different measurement channels. The method was also tested on gravity gradient tensor data from the Vredefort impact structure, South Africa. The results show a very good agreement with the available geologic information.