We use gravity to estimate rifted margin deep structure with an inversion method that links parameters in the shallow parts of the model to those in the deep parts through an isostatic, uniform extension model. The method provides for variable weighting of prior information, estimates densities and shapes simultaneously, and can be used in the presence and absence of deep seismic data. Synthetic tests of sensitivity to noise indicate that the isostatic extension constraint promotes the recovery of the short wavelength Moho topography, eliminates spatial undulations in deep structure due to noise in the data, and increases the range of acceptable recovered models over no isostatic extension constraint. In application to real data from the Carolina trough, the method recovers models that exhibit anomalously high density in the hinge zone area, apparently anomalously thick crust, and anticorrelation of subcrustal lithospheric densities with crustal densities. The first two features are observed in deep seismic studies. The latter is consistent with melting model predictions.
We then present a unified view of the traditional gradiometric observables---differential curvature, horizontal gradient of vertical gravity, and vertical gradient of vertical gravity, in terms of invariants of the full gradient tensor, and examine their ability to recover subsurface structure through an efficient inversion method. Results of synthetic tests performed on selected complex bodies and noise free data indicate differential curvature and the horizontal gradient of vertical gravity do as well as the full tensor in recovering subsurface structure. In the presence of noise, we find that a mass constraint promotes recovery of smooth models and may be more appropriate than finite difference smoothing. Differential curvature appears to be a useful observable when inverted alone and as an early search technique in full tensor inversion.