Analysis of deformation surveys: A generalized method
A generalized approach to deformation analysis has been developed and successfully applied to five examples of monitoring networks within the activity of the “ad hoc” committee on the analysis of deformation surveys of the International Federation of Surveyors (FIG). The approach is applicable to any type of geometrical analysis, both in space and in time domain, including detection of unstable points in reference networks, and determination of strain components and relative rigid body motion within relative networks. It allows utilization of not only geodetic observations, but also physical mechanical measurements. Functional relations between deformation parameters and various types of observables have been developed. The approach is capable of handling any datum defects and configuration defects in monitoring networks. The problem of datum defects has been approached through the projection theory in the parameter space. The generalized approach consists of three basic processes: preliminary identification of deformation models, estimation of the deformation parameters and diagnostic checking of the models. The MINQUE principle has been adopted for the assessment of multi-epoch observations prior to the final adjustment of monitoring networks. A method of iterative weighted projection in the parameter space has been created or the identification of the deformation models in space domain. Formulation and computation strategies for the estimation of the deformation parameters are provided in detail. The statistic for testing linear hypotheses in the General Gauss-Markoff Model has been formulated using the theory of vector spaces and, from this statistic, all the hypothesis tests used in the different phases of deformation analysis were derived. Compared with other methods, the generalized approach permits a systematic step-by-step analysis of deformations. During the development of the generalized approach some problems encountered by other authors have been rectified. Examples of the problems and their solution are also given in the thesis.