The diagonal elements of the gravity gradient tensor, as recorded by the Bell airborne Gravity Gradient Survey System (GGSS), are used to determine the basement topography in southwestern Oklahoma. This determination is accomplished through a nonlinear inverse procedure based on the conjugate gradient algorithm. The resulting model contains a ridge of shallow basement material (< or =3.0 km deep) trending east-southeast. This ridge is bounded on the north and the south by basement troughs; the northern trough extends as deep as 10.0 km. The gradient field which results from this model fits most of the GGSS observations within their estimated errors of 12.0 E (1 Eotvos = 10 (super -6) mGal/cm). The model is in general agreement with a set of available oil well depths to the basement and with inferred faults in these igneous rocks. To assess the derived solution, the problem was linearized about the final model and the linear parameter resolution and parameter covariances were computed. Generally, the basement depths are well resolved and the resolution matrix is diagonally dominant. Furthermore, the parameter standard errors are small: 72 parameters out of 98 have errors less than 1.0 km.