Ph.D Thesis
Ph.D Student Shahar Lior Geodetic Estimation of Tectonic Movements in Complicated Fault Surroundings: Northern Israel as a Case Study Department of Civil and Environmental Engineering Professor Gilad Even-Tzur

Abstract

The study presents an extended mathematical solution of geodetic control networks. This solution extracts the deterministic ingredient that defines the entire control network. This extraction differentiates between the network coordinates and the deterministic parameters that are liable to bias the solution. The extraction is made possible by mapping the standard solution from a vector space that includes the network coordinates affected by the deterministic ingredient to a different vector space in which the coordinates are not affected by this ingredient. We distinguish between two types of global deterministic parameters, which are revalued as an inherent part of the standard solution of a control network: geometric parameters and physical parameters. The geometric parameters express the internal deformation of the standard network, while the physical parameters express the physical interpretation of some of the kinematic parameters that define the network model, usually including the velocity field.

The adjustment system for the estimation of parameters values is defined according to a basic assumption regarding datum stabilization over time. This assumption, however, is not necessarily correct. The algorithm used in this study minimizes the problematic nature of this basic assumption by differentiating and distinguishing between the measurements and the datum components, thus eliminating the possibly erroneous effects of the assumption. This algorithm is capable of improving the quality of measurements and thus improving the ability of the control network to monitor deformations.

The mathematical estimation of parameter values that describe geophysical reality requires the use of a dynamic model. The definition of a stable datum requires the extraction of the global physical parameters, which enables the definition of a datum that more closely reflects the geophysical reality of the control network and prevents systematic error from spreading from the raw measurements to the system for the estimation of parameters. The extraction thus prevents systematic error from being erroneously interpreted as a deformation.

This study includes the development of a statistical application based on the Bayesian approach. This approach interprets probabilities differently than a stochastic approach and has proven to be an efficient way of integrating available data into the system for estimating parameter values. In the case of geodetic control networks, important information is available, obtained from geodetic measurements or other research sources; however, using current methods, this information is usually not taken into consideration by the system for estimating parameter values.