GEODETIC NETWORK DEFORMATION BASED ON GPS DATA IN THE BALTIC REGION

. For investigating horizontal deformations of geodetic networks, the data of GPS measurements of the epochs about 1992 and 2003 were used. To avoid the impact of the discrepancy of the systems of coordinates upon the parameters of the deformations, the method of tensor analysis was applied using the method of finite elements. A geodetic network consists of 19 triangles; 15 geodetic ground benchmarks observed by GPS method were used. The horizontal deformations of geodetic network in the territory of the Baltic Sea region were calculated. The maximum relative strain in the territory of the Baltic Sea region varies between +0,03×10 –6 and +0,58×10 –6 and is positive within the whole territory; the minimum relative strain varies between –0,93×10 –6 and +0,03×10 –6 ; and the dilatation varies between –0,35×10 –6 and +0,16×10 –6 .


Introduction
Horizontal deformations of the Earth's crust can be identified from the changes of the geodetic coordinates and other elements of the benchmarks of geodetic networks by performing the repeated geodetic measurements (El-Fiky, Kato 2006;Lagios et al. 2007;Lidberg et al. 2006Lidberg et al. , 2007Masson et al. 2007;Riguzzi et al. 2006;Šliaupa et al. 2006;). The measurements can be performed in the continuous or differential regimes.
Among the latest geodetic network measurement technologies the GPS is the most widely used investigation system (Skeivalas 2008). The repeated measurements of those networks enables an investigation of horizontal deformations.
The objective of the presented study is to evaluate the applicability of tensor analysis and finite element modelling for evaluation of the horizontal strains by geodetic measurements. The geodetic network of the Baltic regions was investigated. Relative maximum and minimum horizontal strains, direction of maximum strain and dilatation were calculated.

Data
Data of GPS campaigns of 1992 and 2003 GPS were used. The network consists of 19 triangles (Fig. 1) comprising 15 geodetic ground benchmarks.   (Jaworski et al. 2002). Five 24 hourduration sessions were performed for a quality assurance of the Polish part of the EUREF-POL´1992 campaign (Zielinski et al. 1994 (Jivall et al. 2005a(Jivall et al. , 2005b. The campaign included mainly permanent GPS stations in the Nordic and Baltic areas as well as Island, Greenland and Svalbard. In Latvia, Lithuania and Denmark also geodetic points of ETRS 89 were included. The processing of the NKG GPS 2003 campaign was carried out by 4 analysis centres using 3 different software packages (Bernese version 4. Finally all coordinates were converted to plane coordinates of the Transverse Mercator projection (Table 1).

Method of calculating the horizontal deformations
Horizontal deformations of the geodetic network are determined by repeated measurements of the geodetic network. The method of determining the horizontal deformations is based on the comparison of site coordinates calculated according to measurements done at different time (Stanionis 2005;Zakarevičius 2003;. When having plain coordinates of geodetic network points (x, y) and changes of geodetic network coordinates calculated according to the data of repeated measurements ∆x, ∆y it is possible to describe horizontal deformations of the geodetic network by the second-rank tensor (Zakarevičius 2003;Zakarevičius, Stanionis 2004): where The tensor elements (1) are calculated by finite element approach (Zakarevičius 2003).
here: ε 1 -maximum principal strain, ε 2 -minimum principal strain. Relative dilatation: Maximum and minimum strains are perpendicular to each other. The direction of maximum strain with respect to abscissas axes is defined: The relative errors of the network chords (zero class) do not exceed ≈ 0,1×10 -6 .

Horizontal deformations of GPS network
The repeated GPS measurements revealed the horizontal changes in the coordinates of benchmarks; in other words, the network was deformed during the period of 1992-2003.
Using the afore-described approach the two-dimensional (2-D) model was constructed.
The horizontal deformation parameters of 19 geodetic network triangles were calculated using equations (1-6) (Fig. 1). The maximum and minimum principal strains, the direction of the maximum relative strain, the dilatation were calculated. The parameters of horizontal deformations are calculated for the gravity centre of a finite element (triangle).
The horizontal geodetic network parameters have been calculated applying Mathcad program ( Table 2).

Geodynamic interpretation
Three different regions, i.e. West Lithuanian-West Latvian, East Lithuanian-East Latvian, and NW Estonian, are identified as showing different deformation regimes. These provinces closely correlate with the major lithotectonic domains of the crystalline basement. In the western province the calculated horizontal strain is dominated by NNW-SSE extension at a rate -0,5×10 -8 to -1,5×10 -8 yr -1 , while the second principal strain rate axis is compressional. The eastern strain province is dominated by contractional deformation regime; the strain rate reaches -3×10 -8 yr -1 with a N(N)W-S(S)E orientation of maximum compression. The north-eastern part of Estonia is subject to a bi-axial extension, which is also revealed in the Middle Lithuanian transitional zone.
The identified strain rates are compatible to those obtained from other cratonic areas (e.g. Fennoscandian Shield, North America, and India). Furthermore, the domination of extensional deformations in the western and northern parts of the Baltic region correlate with the GPS data from Fennoscandia.