Estimation of Height Anomalies from Gradients of the Gravitational Potential Using a Spectral Combination Method

In this study, we apply a spectral combination method for estimation of height anomalies from gradients of the gravitational potential measured by satellites. The spectral combination method is used for solving over-determined problems within gravity field modelling when multiple types of gravity data are collected and used for recovery of unobservable quantities (typically the gravitational potential). The method applies solutions to geodetic boundary-value problems formulated in spherical approximation for gradients of the gravitational potential of up to the third order. Spectral forms of the solutions are combined using spectral weights defined under the condition of minimizing the global mean-square error of the estimators. Mathematical models are implemented and tested using gradients synthesized from a global geopotential model which allows for closed-loop testing of the estimators. The tests reveal among others that horizontal derivatives of the gravitational potential influence recovered values more than their vertical counterparts.