Gravity inversion of basement relief constrained by the knowledge of depth at isolated points

We present an interpretation method for the gravity anomaly of an arbitrary interface separating two homogeneous media. It consists essentially of a downward continuation of the observed anomaly and the division of the continued anomaly by a scale factor involving the density contrast between the media. The knowledge of the interface depth at isolated points is used to estimate the depth d(1) of the shallowest point of the interface, the density contrast Delta rho between the two media, and the coefficients c(1) and c(2) of a first-order polynomial representing a linear trend to be removed from data. The solutions are stabilized by introducing a damping parameter in the computation of the downward-continued anomaly by the equivalent layer method. Different from other interface mapping methods using gravity data, the proposed method: (1) takes into account the presence of an undesirable linear trend in data; (2) requires just intervals for both Delta rho (rather than the knowledge of its true value) and coefficients c(1) and c(2); and (3) does not require the knowledge of the average interface depth z(o). As a result of (3), the proposed method does not call for extensive knowledge of the interface depth to obtain a statistically significant estimate of z(o); rather, it is able to use the knowledge of the interface depth nt just a few isolated points to estimate d(1), Delta rho, c(1), and c(2). Tests using synthetic data confirm that the method produces good and stable estimates as far as the established premises (smooth interface separating two homogeneous media and, at most, the presence of an unremoved linear trend in data) are not violated. If the density contrast is not uniform, the method may still be applied using Litinsky's concept of effective density. The method was applied to gravity data from Reconcavo Basin, Brazil, producing good correlations of estimated lows and terraces in the basement with corresponding known geological features.