Gravity inversion of basement relief using approximate equality constraints on depths

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. The density contrast of each prism is assumed to be constant and known. 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 the depths (relative equality constraint). Both kinds of constraints are imposed in the least-squares sense. We illustrate the method performance by applying it to a synthetic anomaly produced by a simulated basement relief consisting of four narrow and adjacent structural lows. Only two structural lows produced isolated gravity lows. Nonetheless, the whole basement topography was successfully reconstructed with an average error of 4% of the maximum relief amplitude. In this example, the relative constraints established that the thicknesses of adjacent prisms should be as close as possible to each other (overall relief smoothness). As absolute constraints we used point information about the basement depth at five points. In addition to the overall relief smoothness, other relevant geologic information, such as localized relief smoothness, occurring at structural terraces, for example, can be incorporated by assigning different weights to the relative equality constraints. The method was applied to the gravity anomaly of Reconcavo Basin, Brazil, leading to a sharper definition of the basement features relative to previous gravity interpretations of this area.