New estimation/prediction techniques for the determination of crustal deformations in the presence of prior geophysical information

Abstract

The estimation of crustal deformations of the Earth from repeated baseline measurements is a singular problem in the absence of prior information. It could be solved by well-known techniques of g-inverse algebra within the framework of a Singular Gauss-Markov Model leading e.g., to BLIMBE (Best Linear Minimum Bias Estimator) or MINOLESS (Minimum NOrm LEast Squares Solution). However, these solutions may not be physically meaningful in view of some independently derived geophysical results. But after introducing these geophysical findings as a-priori information into the linear model, the problem will no longer be singular and can be solved by means of “Improved Linear Estimation” as well as of “Best Linear Prediction”, depending on the way the original model has been expanded. Several alternative estimators and/or predictors are compared with respect to their characterizing properties (homogeneous linear, inhomogeneous linear, biased, unbiased, minimum mean square error, minimum variance, etc.), and the respective gains in efficiency are given.