Gravity inversion of basement relief stabilized by equality constraints on depth

We present a gravity interpretation method for estimating the relief of an arbitrary interface separating two homogeneous media. The upper medium is discretized into rectangular, juxtaposed prisms whose thicknesses represent the depths to the interface and are the parameters to be estimated from the gravity anomaly. To stabilize the inversion, we introduce two kinds of constraints on the depths. The first one requires proximity between the observed and computed depths at isolated points such as those obtained from boreholes (absolute equality constraint). The second one requires that groups of depths approximately follow an established linear relationship among them (relative equality constraint). Both kinds of constraints are imposed in the least-squares sense. This stabilization procedure does not bias the solution either toward an initial approximation, or toward the null solution. The method is applied to synthetic data, producing a good reconstruction of a complex basement consisting of several structural high and lows. It is also applied to real data of Reconcavo Basin, Brazil, leading to a sharper definition of the basement structures as compared with previous gravity interpretations of the area.