Rapid Prediction of Vertical Deflections and Their Statistics for Surveying and Mapping Applications: Three Case Studies

Abstract

The mathematical interaction between the simultaneous rotation of both a coordinate frame and a set of physical vectors in that frame is covered and theoretically and empirically explained. A practical example related to the secular motion of the pole is addressed. A least-squares adjustment is introduced to determine a possible displacement of the geodetic north pole of the frame caused by plausible changes in the coordinates of the observing stations defining the frame due to the rotation of the plates on which these stations are located. Two GPS network examples are investigated using the latest definition of the IGS08 geodetic frame, which was obtained exclusively using GPS data, as published by the International GNSS Service (IGS). The first network is the global GPS/IGS network, and the second one is a GPS/ILS-type single latitude network. The results of this exercise hints at the possibility that the secular global rotation of the frame caused by plate rotations should be accounted for in order to rigorously determine the true velocities of the rotation of the plates.