Statistical tests for detecting movements in repeatedly measured geodetic networks

Abstract

Geodetic networks with two or more measuring epochs can be found rather frequently, for example in connection with the investigation of recent crustal movements, in the field of monitoring problems in engineering surveying or in ordinary control networks. For these repeatedly measured networks the so-called congruency problem has to be solved, i.e. possible changes in the geometry of the net have to be found. In practice distortions of bench marks and an extension or densification of the net (differences in the 1st-order design) and/or changes in the measuring elements or techniques (differences in the 2nd-order design) can frequently be found between different epochs. In this paper a rigorous mathematical procedure is presented for this congruency analysis of multiple measured networks, taking into account these above-mentioned differences in the network design. As a first step, statistical tests are carried out to detect the epochs with departures from congruency. As a second step the individual points with significant movements within these critical epochs can be identified. A numerical example for the analysis of a monitoring network with 9 epochs is given.