Statistical analysis of CGPS time series

Abstract

All points on the surface of the Earth are moving. To define the velocity of a given point, we can place a GPS receiver there and measure the coordinates every day. After collecting enough data, we can generate a time series of three coordinates, North, East and Height directions. The most used technique to determine such displacements, is the linear model.

The main objective of this thesis is to show how to estimate the velocity of a given point, using statistical methods to improve the results.

The improvement of the site velocity achieved by exluding all signals that are not tec- tonic origine (seasonal variations, spacially correlated noise reduction ).

Time series for all directions contain gaps(missing data), outliers, offsets and various data length.

The data discontinuities are detected and corrected by a simple algorithm, based on binary search to detect the time of abruption. The outliers are eliminated by using robust estimation techniques. Simulation is used to fill the gaps.

The data obtained from permanent GPS-stations in Norway and some other European countries are unevenly sampled. We therefore use the Lomb-Scargle method to perform spectral analysis. This allows us to detect annual and interannual variations.

The methods of Principal Components (also known as Empirical Orthogonal Functions, or EOF) and Factor Analysis are used to correct for common fluctuations. We use data from 8 permanent GPS-stations (SATREF) in these investigations.