We have developed a local level-set method for inverting 3D gravity-gradient data. To alleviate the inherent nonuniqueness of the inverse gradiometry problem, we assumed that a homogeneous density contrast distribution with the value of the density contrast specified a priori was supported on an unknown bounded domain D so that we may convert the original inverse problem into a domain inverse problem. Because the unknown domain D may take a variety of shapes, we parametrized the domain D by a level-set function implicitly so that the domain inverse problem was reduced to a nonlinear optimization problem for the level-set function. Because the convergence of the level-set algorithm relied heavily on initializing the level-set function to enclose the gravity center of a source body, we applied a weighted L1-regularization method to locate such a gravity center so that the level-set function can be properly initialized. To rapidly compute the gradient of the nonlinear functional arising in the level-set formulation, we made use of the fact that the Laplacian kernel in the gravity force relation decayed rapidly off the diagonal so that matrix-vector multiplications for evaluating the gradient can be accelerated significantly. We conducted extensive numerical experiments to test the performance and effectiveness of the new method.

You do not currently have access to this article.