A modified least-squares collocation method for the determination of crustal deformation: first results in the Swiss Alps

Abstract

SUMMARY The calculation of recent crustal movements and the associated crustal deformation rely on a suitable interpolation of geodetic measurements with repetition cycles of years or decades and modern GPS permanent networks. A common interpolation methods is the least-square collocation (LSC). LSC requires some a priori assumptions about the characteristics of the velocity field, that is, stocasticity in Moritz's definition of LSC. We present a novel approach, called adaptative LSC (ALSC) to the interpolation of non-stochastic fields, which encompass the traditional LSC and the block model as special cases. This modified collocation method is based on the empirical estimation of a anisotropic and inhomogeneous covariance function of the interpolated field. The method has been tested on synthetic data that simulate geodetic measurements over a triple plate junction and with real data from precise levelling measurements over the Swiss Alps. In both cases, ALSC gave better and more stable results, compared to LSC and other interpolation methods, such as smoothed splines.