Short Note: Strain invariants: Fid-Bau Portal

Short Note: Strain invariants

Vaníček, Petr / Grafarend, Erik W. / Berber, Mustafa

Abstract In the past, the application of strain in geodesy was more or less limited to horizontal geodetic networks, i.e., the applications were distinctly two-dimensional (2D). Strain of three-dimensional (3D) nature has been used in many non-geodetic applications, but it is relatively new in geodesy. Three-dimensional networks are a recent phenomenon in geodesy whose introduction has been predicated on the appearance of 3D satellite positioning techniques. With the introduction of 3D strain descriptors, a question arose of how to relate the 3D descriptors to the 2D ones so they could be easily compared and put in similar schemes, for example, for specification purposes. It has been long established that for the strain descriptors to be useful in studying geodetic networks, for instance in the context of robustness analysis, they must be invariant under any rotation of coordinate systems. They are by nature invariant in any shift of the origin of coordinate systems. The requirements of invariance originate from the overall explicit requirement that the descriptors be sensitive only to the shape of the network and the quality of the observations.