Understanding curvatures of the equipotential surface in gravity gradiometry

The concept of curvatures of equipotential surfaces is of theoretical and practical importance in gravity gradiometry because curvatures describe the shape of equipotential surfaces, which can yield information about the shape of the source. Although the fundamentals of curvatures are well-established, their connection to modern gravity gradiometry and the associated applications in exploration geophysics remain areas of active research. In particular, there is a misunderstanding in the calculation of the said curvatures directly from measured gravity gradient data that are now widely used in exploration geophysics. The error stems from the incorrect use of the formulas in a fixed user coordinate system that are only valid in a rotated coordinate system. We demonstrate that the gravity gradient tensor must be rotated to a local coordinate system whose vertical axis is aligned with the local anomalous gravity field direction so that the curvatures of the anomalous equipotential surface can be calculated correctly using these classic formulas. To facilitate practical application, we present theoretical and practical aspects related to coordinate systems and rotations of the gravity gradient tensor. We have also developed an approach for estimating local gravity for use in the curvature calculation by wavenumber-domain conversion from gradient tensors. The procedure may form a basis for developing new interpretation techniques in gravity gradient gradiometry based on curvatures.