The Treatment of Time Continuous GPS Observations for the Determination of Regional Deformation Parameters

Abstract

The calculation of invariant deformation parameters, entering in the constitutional equations of crustal dynamics, requires information on the geometry of the crust in the study region, which is continuous in both the time and spatial domain. The use of continuously observing GPS stations provides geodetic data which are practically timecontinuous and must be only spatially interpolated. A strategy is developed for the treatment of dense series of horizontal coordinates from a regional GPS network, which are typically exhibiting a timelinear behavior. The role of the choice of reference system is examined for the removal of trend before the spatial interpolation as well as the determination of the motion of the region as whole with respect to the ITRF or of the relative motion of tectonically homogeneous sub regions. Rigorous formulas are presented for various horizontal deformation parameters and their intrinsic time derivatives, without the usual infinitesimal approximations. Finally the problem of quality assessment for the derived parameters is investigated completely ignoring the questionable formal statistical characteristic of the original geodetic data. A realistic numerical example demonstrates the suggested techniques, involving spatial interpolation by the classical finiteelement method. A software package in standard C language has been developed in order to implement the proposed algorithms.