Stability investigations of various representations of the gravity field

Publisher Website
Google Scholar
Abstract
A number of problems in physical geodesy are improperly posed in the sense that the approximate solution is not continuously dependent on the given observations. A transformation of the minimum norm least squares estimates for different types of gravity representations to the spectral domain, via a singular value decomposition, allows an easy insight into the stability situation of these representations. For the density layer or point mass model, Bjerhammar’s method, and the least squares collocation model the filter expressions are derived which control their stability. It is shown in which way the shape of the filters is influenced by the a priori variance of the measurement noise, the choice of the radius of the Bjerhammar sphere, and the degree variance model.