Extended S-transformation as a tool for deformation analysis

Abstract

In geodetic monitoring networks, the deformation parameters can be estimated only if the datum of the network has not been changed between measurement epochs. The measurements of a monitoring network must be adjusted so that the datum remains undisturbed. In deformation analysis, similarity transformation is used intensively in order to bring all monitoring campaigns to the same common datum. However, there are geodetic measurements which contain datum definition components. When part of the datum definition contained in the measurements is not constant in time, the estimated deformation parameters could be erroneous. An appropriate approach should be taken to prevent the inclusion of these components in the adjustment of a 4D network. If not, the result is an inevitable mixture between the deformation parameters and the datum components of the measurements. The extended S-transformation allows us to strip the datum content from a set of coordinates that contain the complete contribution of the geodetic measurements to a datumless set of coordinates. Based on the datumless sets of coordinates, the variations in the network geometry can be modelled by means of a physical model without the influence of a datum definition inherent in geodetic measurements. Following a short introduction of the concept of extended free net adjustment constraints, the development of an extended S-transformation is presented. Two examples of a trilateration network and a GPS network are presented for implementing the method.