The role of frame definitions in the geodetic determination of crustal deformation parameters

A study of the role of coordinate frame definitions in the determination of crustal deformation parameters is first carried out for the theoretical case where displacement information between two discrete time epochs is continuously available for all area points. The obtained results are next applied to the realistic case where the required continuous information is derived by means of an interpolation of the known coordinate variations at the points of a horizontal geodetic network. The problem is different from the usual one of frame-invariant interpolation, since not only the domain of definition, but also the interpolated quantities, depend on independent choices of coordinate frames. Specific necessary and sufficient conditions for the invariance of derived crustal deformation parameters are given for linear type of interpolations of either the coordinates at the second epoch or of the displacements. With the help of the above conditions the invariance characteristics of two commonly used types of linear interpolations are finally derived, in order to illustrate the practical significance of the results.