3D Focusing Inversion of Gravity Data Based on an Arctangent Stabilizing Functional

In 3D gravity inversion, a regularization technique must be introduced in order to deal with the non-uniqueness and stability of the inversion process. For this purpose, stabilizing functionals based on minimum norm and maximum smoothness have been utilized as the regularization item in the objective function of gravity inversion, but yield a smoothed distribution of subsurface density which does not give a clear delineation of the boundaries of blocky geological units. Although some functionals such as minimum support and minimum gradient support functionals have been applied to focusing inversion of potential field data, these functionals need to be provided with a suitable focusing parameter for successful inversion. In this paper, we have developed a focusing 3D inversion of gravity data based on an arctangent stabilizing functional. To deal with the numerical solution to the gravity inversion problem, the arctangent-function-based stabilizing functional is first reformulated in pseudo-quadratic form as a weighting matrix. The Gauss Newton (GN) minimization scheme is then employed to perform an optimization process. For the stabilizing functional introduced in this study, there is no need to determine in advance two optimum parameters involved in the stabilizing functional. A test on synthetic examples demonstrates that the boundaries of the anomalous bodies recovered are sharper and the density values are also closer to the true model. We also apply this approach to field gravity data collected from the San Nicolas deposit in Mexico, illustrating that the inversion result shows good consistency with the a priori information available.