Analytical optimization of a DInSAR and GPS dataset for derivation of three-dimensional surface motion

A revised method for derivation of three-dimensional surface motions maps from sparse global positioning system (GPS) measurements and two differential interferometric synthetic aperture radar (DInSAR) interferograms based on a random field theory and Gibbs-Markov random fields equivalency within Bayesian statistical framework is proposed. It is shown that the Gibbs energy function can be optimized analytically in the absence of a neighboring relationship between sites of a regular lattice. Because the problem is well posed, its solution is unique and stable, and additional regularization in the form of smoothness is not required. The proposed algorithm is simple in realization, does not require extensive computer power, and is very quick in execution. The results of inverse computer modeling are presented and show a drastic improvement of accuracy when both GPS and DInSAR data are used.