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 homo-geneous media. It consists essentially of a downward con-tinuation of the observed anomaly and the division of the continued anomaly by a scale factor involving the den-sity contrast between the media. The knowledge of the interface depth at isolated points is used to estimate the depth d1 of the shallowest point of the interface, the den-sity contrast Ap between the two media, and the coeffi-cients cI and c2 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 us-ing gravity data, the proposed method: (1) takes into ac-count the presence of an undesirable linear trend in data; (2) requires just intervals for both Op (rather than th