Sammendrag
The objective of this thesis is to increase the understanding of land motion, using
statistical analysis of the available three-dimensional (3-D) time series from Continuously
operated Global Positioning System stations (CGPS). A primary goal
has been to search for new procedures and determine a spectrum of univariate
CGPS time series. A new program package has been developed for adjustment
and spectral analysis of the CGPS time series for possible future studies. This
will take into account the possibility of weighting and managing, non-stationary
and time series with missing data. The least squares spectrum and its relation to
covariance and correlation functions are explained in detail. Different estimation
methods of such functions that are used to visualise temporal correlations have
been tested. A challenge of the work has been the handling data jumps revealed in
the numerical investigations, that vitally affect the estimation of correlation functions
and spectra.
The work has also included numerical analyses of two independently pre-processed
data sets from a Norwegian and a European network of CGPS. The spectral analysis
has shown large contributions of annual cycles for most series. In addition
semi-annual and three-month cycles have been found. After the removal of these
effects, the resulting spectra estimated from the residual series of CGPS time series
shows similarities with Markov-processes that are closely related to white
noise processes. The detection of a Chandler-like period is more surprising because
this period should have been corrected for in the pre-processing stage of
CGPS time series. A Principal Component Analysis (PCA) has been implemented
to determine the spatial pattern of CGPS data. So far this has not been performed
either for a network of Norwegian CGPS stations or for a network covering the
whole of Europe. The results from both analyses confirm that the first mode obtained
up to 50 percent of the overall variance in all station series. In addition to
a high inter-station correlation, only slightly decreasing as a function of distance,
this implies at least one common effect for the entire network. The spatial and
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partially temporal pattern for the first three modes in CGPS data show similarity
with corresponding modes extracted from predictions of atmospheric loading
of surface displacements. These relations have been further investigated for the
purpose of deriving possible model relations. Numerical investigations using the
derived models to correct the CGPS data for the atmospheric loading effect have
shown a possible sample variance reduction of up to 10 percent for the vertical
component of CGPS data.
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