Investigation of the recent Earth's crust deformations in the territory of Lithuania.

Zakarevicius, Algimantas ; Stanionis, Arminas ; Levinskaite, Daiva 等

1. Introduction

Investigation of the Earth's crust movement is a topical problem that is not only related with formation and use of geodetic networks but also with identification of seismically active territories, forecasting of seismic activity of tectonic faults, construction of environmentally hazardous objects and prospecting of minerals (Stanionis 2005).

Up to the beginning of the last decade of the 20th century, the attention of the world was focused on movement of the Earth's crust in seismically active territories (Anikiene 2008). Seismic events in territories are pre-determined by the seismotectonic potential, i.e. the strongest expectable quake as well as the interdependence between the strength and the frequency of the quake. Seismotectonic potential and deformation of the Earth's crust are interdependent phenomena. They often are caused by the same processes in the entrails of the Earth.

The territory of the Baltic States and adjacent regions distinguishes itself for low seismic activity predetermined by the Earth's crust formed in the Early Precambrian Period and a long distance from seismically active zones. The Earth's crust in the Baltic region is affected by horizontal tectonic tensions and the deformations are concentrated along tectonic faults. When their concentration exceeds the fault resistance threshold, it moves thus causing a quake.

The territory of Lithuania is considered aseismic territory, or territory of low seismic activity. Although its seismic activity is low, as compared to neighbouring countries, nevertheless the historical and current data show that perceptible earthquakes took place in the territory of Lithuania as well (The new nuclear power plant... 2008). In Lithuania, the earliest earthquake was documented back in 1328, in Skirsnemune. The second earthquake, which caused a 1 km long rupture, took place close to Vilnius in January 1909.

In the eastern part of the Baltic region, as in Lithuania, no detailed geodynamic investigation was carried out. Up to the last decade of the 20th century, a negative standpoint on platform areas in respect of their seismic activity existed in the world. It was supposed that no notice-able quakes can occur in platform regions of low seismic activity (up to the magnitude 3 according to the 12-point scale). However, in course of accumulation of the data from instrumental observation of seismic phenomena, the opinion on seismic activity of platform areas and the applicative character of such investigation changed.

In Lithuania, more serious interest in seismic risk zoning was taken after the earthquake in Osmussaare (Estonia) with the magnitude 6-7 (according to the 12-point scale) in the year 1976 (Ilginyte 1998) and the Carpathian earthquake in Romania in the year 1977. In the latter region, quakes were perceptible in the years 1986 and 1990 as well. In Lithuania, registered quakes remained within the magnitude 3-4. On 21 September 2004, the quake of the magnitude 4.4 was registered in Ladushkin (Kaliningrad Region); its focus was situated in the depth of 10 m. The second quake in the same Region (in Primorsk town) reached the magnitude 5. Vibrations caused by the above-mentioned quakes were perceptible in a considerable part of the territory of Lithuania. The intensity of vibrations of the ground in Klaipeda reached the magnitude 5, in Kaunas and Vilnius--approx. 3 (Pacesa et al. 2005).

For investigation of horizontal movement of the Earth's crust, geodetic networks (triangular, trilateral, poligonometry, GPS) are widely used in the entire world ((Hollenstein et al. 2008; Hsu, Li 2004; Kaiser et al. 2005; Mahmoud 2003; Tesauro et al. 2006; Tyshkov et al. 2008; Vigny et al. 2009; Weber et al. 2011; Stanionis 2005; Zakarevicius 2003). If the data on changes of the coordinates of points of geodetic networks are available, the properties of horizontal deformations of the Earth's crust can be assessed and the changes of the geodynamic tensions can be identified.

[FIGURE 1 OMITTED]

The investigation aimed to analyse the regularities of the indications of the horizontal movements of the Earth's crust established according to the data of three different geodetic measurements.

2. Methodology of indications of horizontal movements of the Earth's crust

In the territory of Lithuania, points of the triangular geodetic network were formed in the year 1942; while points of the GPS network of the class 0 and the class 1 were formed in the year 1993 and repeatedly measured in the year 2007. The total of 45 joint points is used for investigation of movement of the Earth's crust.

The accuracy of the triangular network in the territory of Lithuania is defined by the mean square errors equal to 0.3"-1.2" for measurement of angles and the relative errors equal to 1:295000-1:206000 for measurement of sides (Zakarevicius 2003; Stanionis 2005). The relative errors of the vectors of the chords for connection of points equal to 1 * [10.sup.-7] and the ones of ellipsoid heights--to 2 * [10.sup.-7]. The errors of the geodetic latitude and the geodetic longitude of points of GPS of the class do not exceed 9 mm, and the error of ellipsoid height does not exceed 30 mm (Zakarevicius 2003; Stanionis 2005). The maximum relative error of chords of the GPS network of the class 1 equals to 1.7 * [10.sup.-7] (Petraskevicius, Ramanauskas 1995; Skeivalas 2008). Errors of coordinates of points in the directions of the meridian and the parallel do not exceed 6 mm in respect of points of the class 0.

In the territory of Lithuania, horizontal movement of the Earth's crust was explored in works by A. Zakarevicius in 2003 and A. Stanionis in 2005. So, for verification of the reliability of the available data and assessment of the regularities of the indicators of horizontal deformations of the Earth's crust obtained from the data on measurements in three epochs according to joint points of the triangular and GPS networks, a scheme of a network for repeated measurements consisting of 69 finite elements (triangles) other than provided in works by Zakarevicius 2003 and Stanionis 2005 is required (Fig. 1).

If changes in coordinates of points of the triangular and GPS networks are known, deformations of the Earth's crust are computed for the area of the finite element (Atkociunas, Nagevicius 2004). The model on shifts of points (Gamal, Kato 1998; Zakarevicius, Stanionis 2007):

[DELTA]X = A * E, (1)

where: [DELTA]X--the vector of shifts of planar coordinates of the points; A--the matrix of deviations of planar coordinates of the points from their average values; E--the vector of the parameters of horizontal deformations of the Earth's crust, where

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (2)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (3)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (4)

The values included in the formula (2-4):

[DELTA][x.sub.i] = [x'.sub.i] - [x.sub.i], [DELTA][y.sub.i] = [y'.sub.i] - [y.sub.i], [x.sub.i], [y.sub.i],--the planar coordinates of the points in the first measurement; [x'.sub.i], [y'.sub.i]--the planar coordinates of the points in the second measurement; i = 1, 2, ... n--numbers of points; [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] deviations of the planar coordinates of points of the geodetic network from their average values; [[alpha].sub.x], [[alpha].sub.y]--shifts of the final element in the directions of abscissas and ordinates; [[epsilon].sub.xx], [[epsilon].sub.yy]--relative linear deformations; [[epsilon].sub.yy]--relative shear deformations; [omega]--turn of the finite element.

The vector of the parameters of horizontal deformations of the Earth's crust is assessed by the least-squares method (Zakarevicius, Stanionis 2007):

E = [([A.sup.T] * A).sup.-1] * [A.sup.T] * [DELTA]X. (5)

The relative dilatation of the finite element (Zakarevicius, Stanionis 2007):

[DELTA] = [[epsilon].sub.xx] * [[epsilon].sub.yy]. (6)

The maximum and the minimum relative elongations of the most important horizontal deformation (Zakarevicius, Stanionis 2007):

[[epsilon].sub.1] = 1/2 * ([DELTA] + [gamma]), (7)

[[epsilon].sub.2] = 1/2 * ([DELTA] - [gamma]), (8)

were

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (9)

The direction of the maximum relative elongation (Zakarevicius, Stanionis 2007):

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (10)

3. Results on indications of horizontal deformations of Earth's crust

Using the formulas (1)-(10), the indicators of horizontal deformations in the territory of Lithuania were assessed according to the data on measurements in three epochs (version I--the changes of coordinates between the points of the triangular network of the year 1942 and the points of the GPS network of the year 1993; version II--the changes of coordinates between the points of the triangular network of the year 1942 and the points of the GPS network of the year 2007; version III--the changes of coordinates between the points of the GPS network of the year 1993 and the points of the GPS network of the year 2007). The identified properties of the horizontal deformations include relative linear deformations, relative shear deformations, relative dilatation, the maximum and the minimum elongation of the most important horizontal deformations and the directions of the maximum elongation. In Table 1, the maximum and the minimum elongation of the most important horizontal deformations, and dilatation are provided. In Table 2, the limits of changes of relative linear deformations and relative shear deformations between the data on measurements in three epochs are provided.

First of all, let's compare the indicators of horizontal deformations of the Earth's crust provided in the version I and the version II.

In the direction of the maximum elongation of the most important of horizontal deformations, positive values prevail. In the version I, deformations of 59 triangles of 69 are positive; and in the version II, deformations of 52 triangles are positive. The principal area of negative deformations is concentrated in the triangles 39-41, i.e. in the northern part of the territory of Lithuania (the territory of Linkuva Ridge).

In the direction of the minimum elongation of the most important of horizontal deformations, negative values prevail: in the version I, deformations of 61 triangles are negative; and in the version II, deformations of 62 triangles are negative. The maximum negative value of the minimum relative elongation is found in the triangle 52 and the maximum positive elongation--in the triangle 22.

In both versions, the maximum negative value of the maximum relative elongation is found in the triangle 4 and the maximum positive value of it--in the triangle 23 (Table 2).

Dilatation of 38 out of 69 triangles (the version I) and 42 triangles out of 69 (the version II) is negative. In both versions, the maximum negative value of the maximum dilatation is found in the triangle 51 and the maximum positive value of it--in the triangle 20.

If data on geodetic measurements (triangular and GPS) of different accuracy are used in investigation of movement of the Earth's crust, only general regularities of its indicators can be identified. For assessment of reliability of the values of individual numerical indicators of horizontal deformations of the Earth's crust, the data of the repeated measurement of Lithuanian GPS networks of the class 0 and the class 1 were used (the version III).

In the version III, in the direction of maximum relative elongation, positive horizontal deformations prevail (the total of 50 triangles) and in the direction of the minimum relative elongation, negative deformations prevail (the total of 66 triangles). The principal area of negative deformations is concentrated in the middle part of Lithuania (the triangles 33-36 and 43-46). Positive deformations are found in the triangles 1, 4 and 23. Values of dilatation are negative in 45 triangles. More considerable changes of dilatation are found in the north--in the zones of faults near Telsiai and Mazeikiai.

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

At Figs 2 and 3 isograms of the maximum and the minimum elongation of the most important horizontal deformations are provided.

As it can be seen from the isograms, the dislocation of isolines of the indicators of the maximum and the minimum elongations related to the most important horizontal deformations coincides in the version I and the version II. In the version III, the dislocation of isolines of the indicators differs from two first versions; however, the general trends remain unchanged.

Changes of the gradients of horizontal movements are more significant at potentially seismogenic zones. They are particularly significant in the zone of faults near Raseiniai. Less significant changes are found in the zones of faults near Taurage as well as in the eastern and southeastern parts of Lithuania.

More significant changes of the minimum relative elongation take place in zones of faults of Klaipeda and Telsiai regions (between the faults of Silale and Taurage regions) and in zones of faults in the south-eastern Lithuania. In addition, territories of the Middle Lithuania, Jurbarkas and Raseiniai regions should be singled out as well.

The obtained results show that the undertaken investigation, presented in this paper, ant the obtained indicators of horizontal deformations of the Earth's crust correlate with the results of the works carried out by A. Zakarevicius (2003) and A. Stanionis (2005). Although the territory of Lithuania is considered an aseismic region, summarization of the results of the investigation on horizontal movement of the Earth's crust suggests that the territory of Lithuania is geodynamically active. In all versions, the values of the gradients of the maximum and the minimum elongation of the most important horizontal movement are fixed at borders of deep blocks of the lithosphere.

4. Conclusions

The properties of the Earth's crust movement and their regularities assessed according to the data of geodetic measurements of different accuracy reflect general trends of the movement only. More detailed values of numerical indicators of horizontal deformations of the Earth's crust were obtained while carrying out investigation according to the repeated GPS measurement.

The limits of changes of relative linear and relative shear deformations are: [[epsilon].sub.xx] varies between -16.300 * [10.sup.-6] and 11.960 * [10.sup.-6], [[epsilon].sub.yy] varies between -26.200 * [10.sup.-6] and 14.040 * [10.sup.-6], [[epsilon].sub.xy] varies between -28.163 * [10.sup.-6] and 27.674 * [10.sup.-6] (versions I and II); [[epsilon].sub.xx] varies between -0.645 * [10.sup.-6] and 0.787 * [10.sup.-6], [[epsilon].sub.yy] varies between -0.467 * [10.sup.-6] and 1.147 * [10.sup.-6], [[epsilon].sub.xy] varies between -1.066 * [10.sup.-6] and 0.788 * [10.sup.-6] (version III).

The limits of the dilatation varies between -27.580 * [10.sup.-6] and 8.612 * [10.sup.-6] (versions I and II); between -0.799 * [10.sup.-6] and 1.488 * [10.sup.-6] (version III).

The limits of changes of the maximum relative elongation are: [[epsilon].sub.1] varies between -1.608 * [10.sup.-6] and 20.832 * [10.sup.-6], [[epsilon].sub.2] varies between -29.424 * [10.sup.-6] and 1.397 * [10.sup.-6] (versions I and II), [[epsilon].sub.1] varies between -0.296 * [10.sup.-6] and 1.160 * [10.sup.-6], [[epsilon].sub.2] varies between -0.874 * [10.sup.-6] and 0.328 * [10.sup.-6] (version III).

After summarizing the results of the investigation on horizontal Earth's crust movement, it may be supposed that the territory of Lithuania is geodynamically active.

A distribution of the values of gradients of the maximum and the minimum relative elongations of the most important horizontal movements in all versions is found at borders of deep blocks of the lithosphere.

doi: 10.3846/20296991.2012.679769

Received 19 January 2012; accepted 21 March 2012

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Algimantas Zakarevicius (1), Arminas Stanionis (2), Daiva Levinskaite (3)

Department of Geodesy and Cadastre, Vilnius Gediminas Technical University, Sauletekio al. 11, LT-10223 Vilnius, Lithuania

E-mails: (1) algimantas.zakarevicius@vgtu.lt; (2) arminas.stanionis@vgtu.lt (corresponding author); (3) gkk@vgtu.lt

Algimantas ZAKAREVICIUS. Prof., Dr Habil at the Department of Geodesy and Cadastre, Vilnius Gediminas Technical University, Sauletekio al. 11, LT-10223 Vilnius, Lithuania. Ph +370 5 237 0630, Fax +370 5 274 4705, e-mail: algimantas.zakarevicius@vgtu.lt.

A graduate from Kaunas Polytechnic Institute (now Kaunas University of Technology, geodetic engineer, 1965. Doctor's degree at Vilnius University, 1973. Dr Habil degree at VGTU, 2000. A member of the Geodetic Commission of Estonia, Latvia and Lithuania. Research training at Geodetic Institute of Norwegian Mapping Authority, 1994. The author of more than 150 publications and 3 monographs.

Research interests: investigations into the recent geodynamics processes, formulation of geodetic networks.

Arminas STANIONIS. Assoc. Prof., Dr at the Department of Geodesy and Cadastre, Vilnius Gediminas Technical University, Sauletekio al. 11, LT-10223 Vilnius, Lithuania. Ph +370 5 237 0629, Fax +370 5 274 4705, e-mail: arminas.stanionis@vgtu.lt.

A graduate from Vilnius Gediminas Technical University (VGTU) (Master of Science, 2002). Doctor's degree at VGTU, 2005. The author and co-author of more than 30 research papers. Participated in a number of international conferences.

Research interests: investigations geodynamics processes, GIS, investigations of deformations.

Daiva LEVINSKAITE. Doctoral student at the Department of Geodesy and Cadastre, Vilnius Gediminas Technical University, Sauletekio al. 11, LT-10223 Vilnius, Lithuania. Ph +370 5 274 4703, Fax +370 5 274 4705, e-mail: gkk@vgtu.lt.

A graduate from Vilnius Gediminas Technical University (VGTU) (Master of Science, 2008 A co-author of more than 3 publications.

Research interests: investigations geodynamics processes, investigations of deformations. Table 1. Characteristics of the Earth's crust horizontal deformations Triangle Triangulation--[GPS.sub.1993] No. (version I) [[epsilon].sub.1] [[epsilon].sub.2] [DELTA] * [10.sup.-6] [10.sup.-6] [10.sup.-6] 1 1.342 -2.704 -1.362 2 -0.473 -6.701 -7.174 3 1.921 -6.125 -4.204 4 -1.608 -9.375 -10.983 5 0.874 -6.442 -5.569 6 0.274 -4.525 -4.251 7 -0.458 -6.982 -7.440 8 3.927 -6.039 -2.113 9 2.010 -0.709 1.302 10 2.697 -0.618 2.079 11 2.820 0.868 3.688 12 2.655 -0.144 2.511 13 0.400 -0.896 -0.496 14 0.671 -3.375 -2.704 15 1.245 -3.643 -2.398 16 -0.571 -9.642 -10.213 17 3.727 0.745 4.473 18 3.639 -2.188 1.451 19 7.412 -6.393 1.019 20 7.789 0.823 8.612 21 2.312 0.474 2.786 22 2.440 1.397 3.837 23 19.922 -15.308 4.614 24 -0.849 -3.604 -4.453 25 0.981 -3.536 -2.555 26 0.701 -0.959 -0.258 27 4.010 -4.860 -0.850 28 4.526 -5.112 -0.586 29 1.956 -4.848 -2.892 30 0.439 -2.855 -2.415 31 2.877 -0.619 2.258 32 1.498 -0.813 0.685 33 5.992 0.023 6.015 34 3.773 -1.166 2.607 35 7.164 -7.573 -0.409 36 3.279 -8.822 -5.543 37 2.579 -2.123 0.457 38 2.085 -2.174 -0.089 39 -0.537 -11.220 -11.757 40 -0.521 -7.044 -7.565 41 -1.231 -4.892 -6.123 42 2.599 -5.023 -2.424 43 1.401 -2.929 -1.528 44 1.942 -1.676 0.266 45 1.890 -3.794 -1.904 46 -0.360 -3.834 -4.194 47 1.216 -2.904 -1.688 48 2.900 0.664 3.564 49 3.189 0.809 3.998 50 2.457 -5.138 -2.681 51 0.053 -27.633 -27.580 52 15.184 -29.424 -14.240 53 3.947 -5.248 -1.301 54 14.407 -20.618 -6.211 55 0.297 -1.184 -0.887 56 3.064 -1.174 1.890 57 2.745 -1.131 1.613 58 4.059 -2.737 1.322 59 1.600 -2.849 -1.249 60 2.140 -1.595 0.545 61 1.606 -0.523 1.083 62 0.697 -1.294 -0.598 63 0.515 -1.710 -1.195 64 0.007 -4.448 -4.442 65 6.657 -4.113 2.544 66 3.460 -1.204 2.256 67 1.513 -1.193 0.320 68 5.088 -3.506 1.582 69 -0.589 -3.501 -4.090 Triangle Triangulation--[GPS.sub.2007] No. (version II) [[epsilon].sub.1] [[epsilon].sub.2] [DELTA] * [10.sup.-6] [10.sup.-6] [10.sup.-6] 1 1.357 -2.644 -1.287 2 -1.128 -6.326 -7.454 3 1.663 -6.089 -4.426 4 -1.173 -8.877 -10.050 5 1.262 -6.570 -5.308 6 0.439 -4.729 -4.290 7 -0.127 -7.386 -7.513 8 3.792 -6.174 -2.382 9 2.002 -0.904 1.098 10 2.908 -0.816 2.092 11 2.994 0.986 3.980 12 2.399 -0.259 2.140 13 0.154 -0.923 -0.769 14 0.437 -3.298 -2.861 15 0.420 -3.557 -3.137 16 -0.881 -9.983 -10.864 17 3.665 0.139 3.804 18 3.698 -2.104 1.594 19 7.623 -6.570 1.053 20 7.985 0.492 8.477 21 1.938 0.210 2.148 22 2.463 1.026 3.489 23 20.832 -14.727 6.105 24 -0.953 -3.727 -4.680 25 0.800 -3.285 -2.485 26 0.611 -1.067 -0.457 27 4.032 -4.859 -0.827 28 4.344 -5.396 -1.052 29 1.484 -4.844 -3.360 30 0.057 -3.042 -2.985 31 3.213 -0.833 2.380 32 1.617 -0.661 0.956 33 5.714 -0.289 5.425 34 3.149 -1.341 1.808 35 6.744 -7.710 -0.966 36 3.101 -9.026 -5.924 37 2.835 -2.363 0.472 38 2.246 -2.305 -0.060 39 -0.549 -11.431 -11.980 40 -0.595 -7.150 -7.745 41 -0.826 -4.934 -5.760 42 2.834 -5.152 -2.318 43 1.303 -3.216 -1.913 44 1.618 -1.987 -0.370 45 1.584 -4.102 -2.518 46 -0.487 -4.130 -4.617 47 0.904 -3.135 -2.231 48 3.133 0.379 3.512 49 3.142 0.694 3.836 50 2.307 -5.185 -2.878 51 -0.320 -27.230 -27.550 52 14.974 -28.744 -13.770 53 3.823 -5.615 -1.792 54 13.893 -20.558 -6.665 55 0.264 -1.121 -0.857 56 3.048 -1.076 1.971 57 2.552 -1.226 1.326 58 3.833 -2.800 1.033 59 1.260 -2.950 -1.690 60 1.975 -1.748 0.227 61 1.721 -0.587 1.134 62 0.504 -1.386 -0.882 63 0.453 -1.301 -0.849 64 0.121 -4.141 -4.020 65 6.869 -3.589 3.280 66 3.438 -1.252 2.187 67 1.400 -1.282 0.118 68 4.854 -3.673 1.181 69 -0.686 -3.668 -4.354 Triangle [GPS.sub.1993]--[GPS.sub.2007] No. (version III) [[epsilon].sub.1] [[epsilon].sub.2] [DELTA] * [10.sup.-6] [10.sup.-6] [10.sup.-6] 1 0.349 -0.274 0.075 2 0.477 -0.757 -0.280 3 0.394 -0.616 -0.223 4 0.791 0.142 0.933 5 0.605 -0.344 0.261 6 0.256 -0.295 -0.039 7 0.336 -0.407 -0.071 8 0.059 -0.328 -0.269 9 0.103 -0.307 -0.204 10 0.287 -0.274 0.013 11 0.303 -0.012 0.291 12 0.030 -0.401 -0.371 13 0.044 -0.317 -0.274 14 0.158 -0.315 -0.157 15 0.099 -0.838 -0.739 16 -0.253 -0.397 -0.651 17 0.204 -0.874 -0.669 18 0.210 -0.066 0.144 19 0.296 -0.261 0.034 20 0.228 -0.362 -0.134 21 -0.248 -0.388 -0.636 22 0.079 -0.428 -0.348 23 1.160 0.328 1.488 24 0.084 -0.311 -0.227 25 0.270 -0.199 0.071 26 0.044 -0.243 -0.199 27 0.059 -0.036 0.023 28 0.061 -0.528 -0.467 29 0.047 -0.514 -0.467 30 -0.111 -0.458 -0.569 31 0.573 -0.451 0.122 32 0.344 -0.073 0.271 33 0.060 -0.650 -0.590 34 -0.154 -0.645 -0.799 35 -0.125 -0.431 -0.556 36 -0.142 -0.238 -0.381 37 0.257 -0.241 0.016 38 0.197 -0.167 0.030 39 0.060 -0.286 -0.226 40 -0.037 -0.142 -0.180 41 0.439 -0.076 0.364 42 0.273 -0.167 0.106 43 -0.017 -0.368 -0.385 44 -0.291 -0.345 -0.636 45 -0.296 -0.318 -0.614 46 -0.119 -0.304 -0.423 47 -0.169 -0.373 -0.542 48 0.257 -0.309 -0.053 49 0.050 -0.212 -0.162 50 0.097 -0.292 -0.195 51 0.461 -0.430 0.031 52 0.698 -0.236 0.461 53 -0.004 -0.487 -0.490 54 0.121 -0.574 -0.453 55 0.164 -0.134 0.030 56 0.189 -0.108 0.081 57 -0.070 -0.218 -0.288 58 -0.053 -0.237 -0.290 59 -0.056 -0.386 -0.441 60 0.041 -0.360 -0.319 61 0.293 -0.243 0.051 62 -0.033 -0.251 -0.285 63 0.447 -0.101 0.346 64 0.665 -0.243 0.421 65 0.695 0.041 0.736 66 0.069 -0.139 -0.070 67 0.125 -0.327 -0.202 68 -0.149 -0.251 -0.400 69 -0.081 -0.183 -0.264 Table 2. Characteristics of the Earth's crust horizontal deformations Triangulation--[GPS.sub.1993] (version I) [[epsilon].sub.xx] x 10-6 -16.160-11.960 [[epsilon].sub.1] x [10.sup.-6] [[epsilon].sub.yy] x 10-6 -26.200-12.890 [[epsilon].sub.2] x [10.sup.-6] [[epsilon].sub.xy] x 10-6 -28.163-27.674 [DELTA] x [10.sup.-6] Triangulation--[GPS.sub.2007] (version II) [[epsilon].sub.xx] x 10-6 -16.300-11.880 [[epsilon].sub.1] x [10.sup.-6] [[epsilon].sub.yy] x 10-6 -25.650-14,040 [[epsilon].sub.2] x [10.sup.-6] [[epsilon].sub.xy] x 10-6 -27.957-26.882 [DELTA] x [10.sup.-6] [GPS.sub.1993]--[GPS.sub.2007] (version III) [[epsilon].sub.xx] x 10-6 -0.645-0.787 [[epsilon].sub.1] x [10.sup.-6] [[epsilon].sub.yy] x 10-6 -0.467-1.147 [[epsilon].sub.2] x [10.sup.-6] [[epsilon].sub.xy] x 10-6 -1.066-0.788 [DELTA] x [10.sup.-6] Triangulation--[GPS.sub.1993] (version I) [[epsilon].sub.xx] x 10-6 -1.608-19.922 [[epsilon].sub.yy] x 10-6 -29.424-1.397 [[epsilon].sub.xy] x 10-6 -27.580-8.612 Triangulation--[GPS.sub.2007] (version II) [[epsilon].sub.xx] x 10-6 -1.173-20.832 [[epsilon].sub.yy] x 10-6 -28.744-1.026 [[epsilon].sub.xy] x 10-6 -25.550-8.477 [GPS.sub.1993]--[GPS.sub.2007] (version III) [[epsilon].sub.xx] x 10-6 -0.296-1.160 [[epsilon].sub.yy] x 10-6 -0.874-0.328 [[epsilon].sub.xy] x 10-6 -0.799-1.488