Resolution and variance operators of gravity and gravity gradiometry

Abstract

Gravity gradiometry represents a new potential field data set which may better constrain the density structure of the earth. Using singular value (spectral) decomposition of the gravity and gravity gradient kernels, the model parameter resolution and model parameter variance of the two data types are compared using data from the Defense Mapping Agency and a recently acquired collection of airborne gradient measurements from Bell Aerospace Textron’s Gravity Gradient Survey System (GGSS). The GGSS was flown over a portion of southwestern Oklahoma, where the gravitational anomaly from the buried Wichita basement rocks is over 60 mGal. The corresponding maximum vertical gravity gradient was found to be 46.2 Eötvös. The determination of the subsurface density structure is cast as a linear inverse problem and, for comparison, a nonlinear inverse problem. For both the linear and nonlinear inversions, the gravity gradients improve the resolution and result in smaller variances than the vertical component of gravity. The density resolution and variance were computed for a subset of tracks from an airborne gravity gradient survey made in the summer of 1987. For the linear inversion, the resolution of the density is not adequate below the second layer (20 km). Furthermore, the estimated error of the actual gradient observations for a resolution of 0.9 km is 10E, for which the maximum error of the density values is [Formula: see text]. The linearized resolution of the boundary perturbations is better, with most parameters being well resolved. The standard errors for the layer perturbations are less than 1 km for the shallower layer (5.0 km) when using the gradiometer data. For the deeper layer (25.0 km), the maximum error is larger, 4.3 km.