Downward continuation of gravitational field quantities to an irregular surface by spectral weighting

In geophysical and geodetic studies, gravity inversion is typically performed such that observed gravity values are first continued downward onto a regular (planar, spherical or spheroidal) surface by solving an inverse integral transform, which originates from a classical solution to the first boundary-value problem in potential theory. A typical example is continuing gravity observed at the topographic surface down to the mean sea level (geoid). Nowadays, gravity-dedicated satellite missions and aerial gravimetry provide gravity data above the topographic surface in addition to classical terrestrial gravity observations. For specific purposes (such as gravity data combination and validation, or quasigeoid determination), satellite and aerial gravity observations have to be continued to the irregular topographic surface. In this study, we address this issue by formulating a functional model for a spectral downward continuation of selected gravitational field quantities to an irregular topographic surface. Moreover, we generalize this functional model to allow for transformation between different types of gravitational field quantities. In particular, we derive spectral weights for estimation of the disturbing potential or disturbing/anomalous gravity at the Earth’s surface by combining the first-, second- and third-order radial gradients of the disturbing potential (disturbing gradients). The correctness of the developed combined spectral estimator is verified in a closed-loop test based on synthetic satellite disturbing gradients. The combined spectral estimator is applied to simulated satellite disturbing gradients polluted by a realistic Gaussian noise. Results of the numerical experiments show that the combined spectral estimator puts the highest importance on the least polluted disturbing gradient, while the contribution of the least accurate disturbing gradient is negligible. An important advantage of this spectral combination method is that no matrix inversion with numerical instabilities requiring regularization is needed.