Gravity and magnetic data are inverted jointly in terms of a model consisting of an interface separating two layers having a constant density and magnetization contrast. A damped least-squares inversion is used to determine the topography of the interface. The inversion requires knowledge of the physical property contrasts across the interface and its average depth. Since the relationship between model parameters and data is weakly nonlinear, a constant damped least-squares inverse is used during the iterative solution search. The effect of this inverse is closely related to a downward continuation of the field to the average interface depth. The method is used to map the base of the Sept-Iles mafic intrusion, Quebec, Canada, and the shape of the central uplift at the Chicxulub impact crater, Yucatan, Mexico. At Sept-Iles, the intrusion reaches a thickness of [Formula: see text], coincident with the maximum gravity anomaly, south of the intrusion center. At Chicxulub, the top of the central uplift is modeled to be [Formula: see text] deep and has a single peak form.