Using Bayesian methods for the parameter estimation of deformation monitoring networks

Abstract. In order to investigate the deformations of an area or an object, geodetic observations are repeated at different time epochs and then these observations of each period are adjusted independently. From the coordinate differences between the epochs the input parameters of a deformation model are estimated. The decision about the deformation is given by appropriate models using the parameter estimation results from each observation period. So, we have to be sure that we use accurately taken observations (assessing the quality of observations) and that we also use an appropriate mathematical model for both adjustment of period measurements and for the deformation modelling (Caspary, 2000). All inaccuracies of the model, especially systematic and gross errors in the observations, as well as incorrectly evaluated a priori variances will contaminate the results and lead to apparent deformations. Therefore, it is of prime importance to employ all known methods which can contribute to the development of a realistic model. In Albertella et al. (2005), a new testing procedure from Bayesian point of view in deformation analysis was developed by taking into consideration prior information about the displacements in case estimated displacements are small w.r.t. (with respect to) measurement precision.

Within our study, we want to introduce additional parameter estimation from the Bayesian point of view for a deformation monitoring network which is constructed for landslide monitoring in Macka in the province of Trabzon in north eastern Turkey. We used LSQ parameter estimation results to set up prior information for this additional parameter estimation procedure. The Bayesian inference allows evaluating the probability of an event by available prior evidences and collected observations. Bayes theorem underlines that the observations modify through the likelihood function the prior knowledge of the parameters, thus leading to the posterior density function of the parameters themselves.