A parametric level-set approach to the global gravity inversion of small bodies

Most spacecraft missions to small bodies provide the gravity field of their targets. As the extended gravity field is an expression of the mass distribution within the body, it can provide information about its interior structure, and that in turn can constrain its origin and history. We present a method to detect density anomalies within a small body from the global gravitational potential. As is well known, such an inverse problem is ill-posed [1], and requires regularization. Our main assumption, which mitigates the non-uniqueness of the problem, is that the interior of the body is composed of a finite number of domains, in which the density is uniform. The boundary of each domain is therefore a surface, that we describe as the level-set of a function. This approach, known as the level-set method, has been extensively used in local inversions of Earth’s gravity measurements [2]. It simplifies the manipulation of complex shapes, which in our case delimit the density anomalies. In order to reduce the dimensionality of the problem, we employ parametric expressions for the level-set functions. The aim is then to determine the parameters of each level-set function, which describe the location and size of the anomalies, along with the density within each anomaly and the bulk density of the body.