The comparison and evaluation of different mathematical models for deformation analysis

Master Thesis


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University of Cape Town

In the analysis of deformations using geodetic techniques, the errors in point positions due to observation errors must be distinguished from movements due to actual deformation. A number of models are available, which offer solutions to this problem. In this study, four of such methods are described and compared: 1. Method using Invariant Functions. 2. Method using Direct Comparison of Co-ordinates. 3. Method using Direct Differences. 4. Method using Niemeier's Comparison of Co-ordinates. The introduction of "false" deformations, caused by errors in translation, rotation and scale, is a very real problem which may be eliminated by processes such as the use of invariant functions (distances and angles) and the sound construction of constraint points. Niemeier's solution to this problem is the use of a free network adjustment which forces the new network into a best fit of the provisional co-ordinates, which generally would be the final co-ordinates of a previous epoch. Although the model advocated for the first three methods above is the minimum constraint adjustment, the free network adjustment may also be used. Similarly, the minimum constraints technique may be employed for Niemeier's method, subject to some necessary modifications. The four methods have thus been compared using both adjustment techniques also. The four methods using both adjustment techniques as well as some variations of methods 1. and 2. above are evaluated using a series of nine simulated test epochs, one reference and eight other, to which known deformations were applied. From the results obtained from the various epochs, the methods are examined for reliability, accuracy and suitability.

Bibliography: pages 124-125.