A level-set method for imaging salt structures using gravity data

We present a level-set method for the inverse gravimetry problem of imaging salt structures with density contrast reversal. Under such a circumstance, a part of the salt structure contributes two completely opposite anomalies that counteract with each other, making itself unobservable to the gravity data. As a consequence, this amplifies inherent non-uniqueness of the inverse gravimetry problem so that it is much more challenging to recover the whole salt structure from the gravity data. To alleviate the severe non-uniqueness, it is reasonable to assume that density contrast between the salt structure and the surrounding sedimentary host depends upon the depth only and is known a priori. Consequently, the original inverse gravity problem reduces to a domain inverse problem, where the supporting domain of the salt body becomes the only unknown. We use a level-set function to parametrize the boundary of the salt body so that we reformulate the domain inverse problem into a nonlinear optimization problem for the level-set function, which is further solved for by a gradient descent method. Both 2-D and 3-D experiments on the SEG/EAGE salt model are carried out to demonstrate the effectiveness and efficiency of the new method. The