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Recent relative vertical movements in the tectonic zone of the Sudety Mts.

INTRODUCTION

The geological structure of the Sudety Mts. having the nature of a block is defined as a mosaic because of the large variety of rocks and numerous dislocations separating tectonic units of different ages and structure (Stupnicka, 2007). Recent seismic activity in this area is confirmed by the size of the earthquakes as 5.5[degrees] MSK, observed in the area of Jilovice Fault (Prochazkova, 1989), in the tectonic zone Ponci-Hronov (Zednik et al., 2001) and the active tectonic region Hruby--Jesenik (Jechumtalova and Sileny, 2014).

The geodetic and geological research in the Sudety Mts. based on the periodical GPS measurement in the last quarter of the 20th century showed horizontal movement slip of the main tectonic zone of the Sudety Mts. and Fore-Sudetic block (Cacon et al., 2004, 2010; Kaplon and Cacon, 2009; Kaplon et al., 2014; Kontny, 2003; Schenk et al., 2003). These same GPS measurements showed no significant changes of vertical movements of these tectonic zones because results of GPS measurement (vertical component - absolute height) are not determined with high precision. The vertical movements of the Earth's crust surface in the Sudety Mts. area are confirmed by repeated measurements of basic levelling lines, 1st and 2nd order, which include the period of the last 50 years of the 20th century (Wyrzykowski, 1985; Kowalczyk, 2006; Vanko and Vyskocil, 1987; Vyskocil, 2002). Figures 1, 2 and 3 show the isolines of velocities of vertical movements of the Earth's crust surface in the Sudety Mts. as maps encompassing the area of Poland and the Czech Republic. Wyrzykowski (1985) showed on the map (Fig. 1) the results based on measurement on Polish levelling networks in the years 1952-1956 and 1975-1977. Kowalczyk's (2006) results are showed in Figure 2, including measurements of the same networks in 1975-1977 and 1997-2003. In Figure 3 Vyskocil (2002) showed isolines of velocities of vertical movements of the Earth's crust surface in the area of Karkonosze-Jeseniky based on measurements on Czech levelling networks in the years 1960-1973 and after 1990 for selected levelling lines. Measurements of these levelling networks performed after 1990 for selected levelling lines have not yet been included in this study. It should be noted that graphic image changes of the Earth's crust surface presented in three figures, although they are not complementary on both sides of the Polish-Czech border in the Sudety Mts., confirm the theory of recent mobile geological structure of this area. The results of this research intend to describe relative changes in movements of blocks of rocks on their borders in coincidence with the main tectonic faults. Due to the limited number of levelling lines (possible to use) and intersecting these tectonic faults, it is impossible to investigate all blocks of rock extracted in the geological research.

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

METHODOLOGY

The calculations contained only these levelling lines, which were measured in at least two measurement epochs (Fig. 4). The archival data contained sets of height differences between benchmarks in research period. They were the basis for determining the relative stable reference benchmark in each line. The calculations were carried out according to the formulae in (Wyrzykowski, 1993).

The first step involved calculating the root mean square error (RMSE) of height differences of the analysed levelling section ([MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]):

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

where:

[m.sub.0]--RMSE of 1km [mm], (1st order lines 1 mm, 2nd order lines 2 mm)

[R.sub.i]--length of section between two benchmarks [km].

Then the height difference change between measurement epochs ([r.sub.i]) was calculated for each section:

[r.sub.i] = [DELTA][h.sup.II.sub.i] -[DELTA][h.sup.I.sub.i] (2)

where:

[h.sup.II.sub.i]/ [h.sup.I.sub.i]--height differences respectively for the two measurement epochs.

The next step was determination of RMSE of height difference change [r.sub.i]:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

In the next step the stability of benchmarks was determined separately for each part of the levelling line. The relative stable benchmark must satisfy the condition that the height difference change ([r.sub.i]) between measurement epochs could not exceed (at the significance level [alpha]=0.05) the "double error" = two times ([MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII])

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] 4)

The specified relative stable reference point is the basis for calculating the height benchmarks ([H.sub.I]; [H.sub.II])for which the RMSE ([MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]) are calculated

on the basis of:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] 5)

where:

2[L.sub.i]--duble length between the benchmark set and relative stable benchmark [km].

To standardize the results of this analysis velocities of height change ([MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]) of analysed

benchmarks were calculated according to the formula:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] 6)

[FIGURE 4 OMITTED]

where:

[t.sub.II];[t.sub.I]--year of measurement respectively for the two epoch of measurements

The root-mean-square error of height change velocities for individual benchmarks are calculated using the formula:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)

Significant displacement was detected using criterion given by the formulae (4) and (5).

Course of action with the use of the above formulae the relative changes of height benchmarks were calculated. Selected parts of levelling lines used in this paper are shown in Figure 4.

EXAMPLE OF THE ANALYSES

Figure 4 presents the state levelling networks that are located in the area of Poland and the Czech Republic. These fragments are marked on the analysed levelling lines.

The repeated precision levelling data of the Polish territory were measured in campaigns: II (1952-1956), III (1975-1977) and IV (1997-2003). The levelling data for the Czech Republic were measured in years 1940-48 and 1975. The archival data in this analysis include results of field measurements based on repeated 1st order precise levelling, which accuracy was determined on level mo=1mm/km in order to unify heterogeneous data in the area of the Sudety Mts. (Polish and the Czech Republic). The data structure for the vertical movement calculation includes height differences between the benchmarks taking into account comparation and temperature corrections for rods. These analyses were performed for fragments of levelling line (Fig. 4) based on principles, which were presented in section "Methodology". Results of these analyses are shown on example of the Czech levelling line part (Fig. 5). This line has been measured in 1948 and 1975. Quantitative data are shown in Tables 1 and 2.

[FIGURE 5 OMITTED]

The analysed part of the levelling line consists of 21 benchmarks that intersect the tectonic fault.

Table 1 shows the height differences between benchmarks in two measurement epochs, which formed the basis for the calculation of height difference change between epochs (2). Additionally the associated statistics are calculated: RMSE of height differences (1), double error of height difference - the maximum acceptable error of height differences change (3), and indication of benchmark stability (4). It also indicated stable and unstable height differences in both measurement epochs. Among the analysed values the unchanged height differences were recorded between benchmarks 90-91 and 91-94. For further analysis the stable point number 91 was adopted. Table 1 presents stability of height differences between benchmarks in research period (data obtained from the Land Survey Office of the Czech Republic).

In the next step the height of the benchmarks in two measurement epochs was determined in terms of the reference point number 91. These data are presented in Table 2, which presents the height differences (2), RMSE for determined height (5), double error of determined height, velocities of height change (6) and RMSE of velocities of height change (7). New benchmark heights were calculated as referenced to relative stable point in research epochs.

Significant displacement of benchmarks is marked in bold.

The graphic illustration of the changes of height benchmarks along the levelling lines is shown in Figure 6. Generally it can be stated that the south-west tectonic fault part is subsidence while the north-east tectonic fault part is uplift.

Significant velocities of change of height benchmarks are marked with a dot (Fig. 6). The mean value of these changes is shown in Figure 6 (-0.3 mm/year and -0.1 mm/year) which concerns the tectonic zone to 3 km from the tectonic fault.

ACTIVITY OF TECTONIC ZONES IN THE SUDETY MTS.

Results of these analyses covering the area of the Sudety Mts. are presented in Figure 7. Different directions and values of velocities of benchmarks vertical changes in each tectonic zone in the area under study confirmed the geological block structure of the Sudety Mts. The maximal changes concern the Intrasudetic zone, as well as the area of the Porici-Hronov tectonic zone. The most active tectonic zones should include also the area between the towns Kraliky and Svitavy along the levelling line EF. Main tectonic faults (Sudetic Marginal fault, Jilovice fault and Lusatian thrust) which form borders of the Sudety Mts. have low tectonic activity.

[FIGURE 6 OMITTED]

[FIGURE 7 OMITTED]

CONCLUSION

The result of research shows the relative vertical movements of the tectonic zones in the Sudety Mts. in the last half-century of the 20th century. This is another verification of the geodynamic mobility of this area. The movements are characterized by values between +0.8 and -0.8 mm/year. The largest of them are located in the Intrasudetic zone (Western Sudetes), where the changes indicate subsidence (from -0.2 to -0.8 mm/year). In the Eastern Sudetes the largest, positive values of these movements (+0.8 mm/year) are located in area of the Ponci-Hronov tectonic zone. In external geological structures of the Sudety Mts. to the north-east from the Sudetic Marginal fault there are subsidences in its west part up to -0.2 mm/year, while the east part tends to uplift +0.3 mm/year. On the south-west zone from the border of the Jilovice fault and Lusatian thrust there are movements of subsidence to -0.2 mm/year. The presented quantitative values of this research have a cognitive character consistent with the qualitative results of geological research concerned with the geological block structure of the Sudety Mts. The utilitarian research aspect is related to adequate protection of the proposed road infrastructure and modernized transit routes intersections of the mobile Sudetic fault. This involves the possibility of activating tectonic movements and vibration induced by heavy car transport. This also applies to large new engineering investments on the active tectonic faults.

The discussion of the tectonic activity of the Sudety Mts. focused on the analysis of changes of height of each benchmark in the tectonic zones is a further step in the research of recent geological activity of this area. It is reasonable also to extend the analysis for repeated measurements of the levelling lines of 2nd order. Results of previous research and their extent may be the basis for detailed interpretation of the geological block structure of the Sudety Mts.

DOI: 10.13168/AGG.2015.0055

ARTICLE INFO

Article history:

Received 9 February 2015

Accepted 25 November 2015

Available online 15 December 2015

ACKNOWLEDGMENTS

The archival data of repeated measurement levelling lines were obtained from the Central Office Documentation Geodesy and Cartography in Warsaw (Poland) and the Land Survey Office of the Czech Republic. The research was supported by project CZ 1.05/2.1.00/03.0097--regional centre "AdMAS".

REFERENCES

Cacon, S., Kaplon, J., Kontny, B., Weigel, J., Svabensky, O. and Kopecky, J.: 2010, Recent local geodynamics in the central part of the Stolowe Mts. Acta Geodyn. Geomater., 7, No. 3 (159), 335-342.

Cacon, S., Svabensky, O., Kontny, B., Weigel, J., Jamroz, O., Cmielewski, K., Bosy, J., Kaplon, J. and Machotka, R.: 2004, Deformation analysis of the upper part of the Earth crust in the Snieznik Massif (Polish and Czech sides between 1993 and 2003). Acta Geodyn. Geomater., 1, No. 3 (135), 59-67.

Jechumtalova, Z. and Sileny, J.: 2014, Seismic loading of the Industrial Zone Triangle. Department of Seismology, Institute of Geophysics, Academy of Sciences, Prague.

Kaplon, J. and Cacon, S.: 2009, Research on the marginal Sudetic fault activity with use of GPS and precise levelling techniques. Acta Geodyn. Geomater., 6, No. 3, 323-329.

Kaplon, J., Kontny, B., Grzempowski, P., Schenk, V., Schenkova, Z., Balek, J. and Holesovsky, J.: 2014, GEOSUD/SUDETEN network GPS data reprocessing and horizontal site velocity estimation. Acta Geodyn. Geomater., 11, No. 1 (173), 65-75. DOI: 10.13168/AGG.2013.0058

Kontny, B.: 2003, Geodetic research of contemporary kinematics of the main tectonic structures of the Polish Sudetes and the Fore-Sudetic Block with the use of GPS measurement. Scientific papers of the Agricultural University of Wroclaw, 468 pp, dissertation, CCII.

Kowalczyk, K.: 2006, Modelling of the vertical movements of the Earth's crust with the help of the collocation method. 8th Bilateral Poland-Italy Geodetic Meeting, Wroclaw. 22-24 June, 2006.

Prochazkova, D.: 1989, Weak earthquake of Aug. 10, 1987 connected with the Jilovice fault (Northern Bohemia). Studia Geoph. Geod, 33, No. 1, 97-100. DOI: 10.1007/BF01649634

Schenk, V., Schenkova, Z., Cacon, S., Kontny, B., Bosy, J. and Kottnauer, P.: 2003, To geodynamic interpretations of GPS data monitored on the East Sudeten network. Acta Montana, Ser. A, Geodynamics, No. 24 (131), 87-97.

Stupnicka, E.: 2007, Polish regional geology, revised third edition. University of Warsaw, Warsaw, (in Polish).

Vanko, J. and Vyskocil, P.: 1987, The map of vertical crustal movements in Czechoslovakia. Journal of Geodynamics, 8, 143-150. DOI: 10.1016/0264_3707(87)90032-9

Vyskocil, P.: 2002, Vertical movements at the territory of Karkonose-Jeseniky Mts, first estimation. Acta Montana, 20, 124, 119-123.

Wyrzykowski, T.: 1985, Map of recent absolute vertical velocities of movement the surface of the Earth's crust in the Polish area on scale 1:2500000. Institute Geodesy and Cartography, Warsaw, (in Polish).

Wyrzykowski, T.: 1993, The use of precision levelling to designate recent vertical movements of the Earth's crust and the impact of these movements on leveling. In: Precise levelling: geometric levelling, trigonometric levelling, satellite levelling and hydro levelling, Ed. Laudyn, I.,II, PPWK, Warsaw, 725-764, (in Polish).

Zednik, J., Pospisil, J., Ruzek, B., Horalek, J., Bouskova, A. and Jedlicka, P.: 2001, Earthquakes in the Czech Republic and surrounding regions in 1995-1999. Studia Geoph. Geod., 45, 267-282. DOI: 10.1023/A.102208412758

Adrian KACZMAREK (1), Stefan CACON (1)* and Josef WEIGEL (2)

(1) Wroclaw University of Environmental and Life Sciences, Institute of Geodesy and Geoinformatics, ul. Grunwaldzka 53, 50-357 Wroclaw, Poland

(2) Brno University of Technology, Faculty of Civil Engineering, Institute of Geodesy, Veven 95, 602 00 Brno, Czech Republic

* Corresponding author's e-mail: stefan.cacon@igig.up.wroc.pl
Table 1 Determination of relative constant reference benchmark
for the analysed part of the levelling line.

                          Height difference
                            [DELTA]h [m]

                        Epoch of measurement

Benchmarks

from    to    Length       1948         1975         Height
                of                                 difference
              section                             change r [mm]
               [km]

70      71     0.47      -2.92554     -2.91799         7.55
71      72     0.61     -22.23039    -22.22924         1.15
72      74     1.80      -5.56178     -5.56337        -1.59
74      75     0.56       2.39008      2.38889        -1.19
75      76     0.34      -0.94446     -0.94762        -3.16
76      77     0.48      -1.16046     -1.16158        -1.12
77      78     0.33      -2.61260     -2.60582         6.78
78      80     1.61      20.99866     21.00151         2.85
80      81     1.14      13.15458     13.15994         5.36
81      84     2.70     -19.52932    -19.53064        -1.32
84      86     0.46      -5.24099     -5.23985         1.14
86      87     0.26       5.85923      5.85784        -1.39
87      90     0.56       8.96982      8.97348         3.66
90      91     10.16      1.34450      1.34440        -0.10
91      94     0.66      -2.87139     -2.87010         1.29
94      96     0.73      21.28022     21.27661        -3.61
96      98     1.34     -69.78730    -69.79333        -6.03
98      99     0.56     -23.92936    -23.91814        11.22
99      100    0.65     -18.64652    -18.64736        -0.84
100     101    0.71     -14.73366    -14.73020         3.46

Benchmarks

from    to    RMSE height   Double error    Condition r [less
              difference    of difference   than or equal to]
              change [mm]    change [mm]     [absolute value
                                              of [m.sub.r]]
                                              (stable point
                                                  "+")

70      71       0.69           1.94
71      72       0.78           2.21                +
72      74       1.34           3.79                +
74      75       0.75           2.11                +
75      76       0.58           1.65
76      77       0.69           1.96                +
77      78       0.58           1.63
78      80       1.27           3.59                +
80      81       1.07           3.02
81      84       1.64           4.65                +
84      86       0.68           1.92                +
86      87       0.51           1.44                +
87      90       0.75           2.12                +
90      91       0.40           1.12                +
91      94       0.81           2.29                +
94      96       0.85           2.42
96      98       1.16           3.27
98      99       0.75           2.12
99      100      0.80           2.27                +
100     101      0.84           2.39

Table 2 Height changes of benchmarks on part of the levelling line.

              Height referenced to      Height difference
                relative stable           change between
                 benchmark H [m]         epochs [DELTA]H
                                              [mm]

Number of       1948         1975          1948-1975
benchmark

70           553.44430    553.42568          -18.62
71           550.51876    550.50769          -11.07
72           528.28837    528.27845           -9.92
74           522.72659    522.71508          -11.51
75           525.11667    525.10397          -12.70
76           524.17221    524.15635          -15.86
77           523.01175    522.99477          -16.98
78           520.39915    520.38895          -10.20
80           541.39781    541.39046           -7.35
81           554.55239    554.55040           -1.99
84           535.02307    535.01976           -3.31
86           529.78208    529.77991           -2.17
87           535.64131    535.63775           -3.56
90           544.61113    544.61123            0.10
91           545.95563    545.95563            0.00
94           543.08424    543.08553            1.29
96           564.36446    564.36214           -2.32
98           494.57716    494.56881           -8.35
99           470.64780    470.65067            2.87
100          452.00128    452.00331            2.03
101          437.26762    437.27311            5.49

Number of    RMSE of height   Double error
benchmark      difference     of difference
              change [mm]      change [mm]

70                4.79            9.59
71                4.69            9.39
72                4.56            9.12
74                4.15            8.30
75                4.01            8.02
76                3.93            7.85
77                3.80            7.60
78                3.71            7.43
80                3.25            6.50
81                2.88            5.76
84                1.70            3.39
86                1.40            2.80
87                1.20            2.40
90                0.56            1.12
91                0.00            0.00
94                1.15            2.29
96                1.67            3.33
98                2.34            4.67
99                2.57            5.13
100               2.81            5.61
101               3.05            6.10

Number of    Velocity of      RMSE of
benchmark     change of     velocity of
              height V     height change
              [mm/year]      [mm/year]

70              -0.69          0.18
71              -0.41          0.17
72              -0.37          0.17
74              -0.43          0.15
75              -0.47          0.15
76              -0.59          0.15
77              -0.63          0.14
78              -0.38          0.14
80              -0.27          0.12
81              -0.07          0.11
84              -0.12          0.06
86              -0.08          0.05
87              -0.13          0.04
90               0.00          0.02
91               0.00          0.00
94               0.05          0.04
96              -0.09          0.06
98              -0.31          0.09
99               0.11          0.10
100              0.08          0.10
101              0.20          0.11
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Title Annotation:Original paper
Author:Kaczmarek, Adrian; Cacon, Stefan; Weigel, Josef
Publication:Acta Geodynamica et Geromaterialia
Article Type:Report
Geographic Code:4EXPO
Date:Apr 1, 2016
Words:3248
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