On the gravimetric inverse problem in geodetic gravity field estimation

Gravity field estimation in geodesy, through linear(ized) least squares algorithms, operates under the assumption of Gaussian statistics for the estimable part of preselected models. The causal nature of the gravity field is implicitly involved in its geodetic estimation and introduces the need to include prior model information, as in geophysical inverse problems. Within the geodetic concept of stochastic estimation, the prior information can be in linear form only, meaning that only data linearly depending on the estimates can be used effectively. The consequences of the inverse gravimetric problem in geodetic gravity field estimation are discussed in the context of the various approaches (in model data spaces) which have the common goal to bring into agreement the statistics between these two spaces. With a simple numerical example of FAA prediction, it is shown that prior information affects the accuracy of estimates at least equally as the number of input data. Received: 25 April 1994; Accepted: 15 October 1996