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Recent local geodynamics in the central part of the Stolowe Mts.


The Stolowe Mts., the southeastern part of the Sudety Mts. Belongs to the northeastern part of the Bohemian Massif. The mountains cover an area from Polanica Zdroj through Batorow and Karlow in Poland and Police nad Metuji and Adrspach in the Czech Republic to Mieroszow again in Poland (Fig. 1). The typical plate form of these mountains with gentle slopes often turns into high rock cliffs made of ashlar sandstone blocks. The present day layout of the region was shaped mainly in the Upper Cretaceous period, when the strongest tectonic movements had occurred, followed by later wind and water erosion processes, as well as other phenomena. Tectonic movements of smaller intensity still exist as demonstrated by seismic activity of this area. Work by Karnik et al. (1984) showed that in the area of the Stolowe Mts. in the 1883-1979 period 10 earthquakes of the 4 to 7[degrees] MSK-64 magnitude had taken place. According to Schenk et al. (1989) these phenomena are connected, mainly with the present day activity of the Porici-Hronov faults zone as is confirmed by the 1979 earthquake of the 5[degrees] MSK magnitude. The earthquake prediction prepared by Schenk et al. (1991) indicates that in the area of the Stolowe Mts. and their surroundings earthquake of magnitude up to 6.5[degrees] MSK is probable.

The paper presents the results of satellite GPS and gravimetric geodynamic measurements in the area of the central part of the Stolowe Mts performed in the period of 1993-2009.


The gravimetric and satellite network consists of 8 points (Fig. 2) located, in relation to geological and tectonic structure, between Szczeliniec Wielki (919 m a.s.l.) and Ostas (700 m a.s.l.). It has been set up in the spring of 1993 using concrete pillars with heads for forced centering of satellite antenna and for placing gravimeters during epoch measurements.

Measurements of the research network were carried out, in similar atmospheric conditions, in September of 1993, 1994, 1996, 2002 and 2009. Characteristics of epoch satellite GPS observations have been given in Table 1.

During the 1993-1996 period measurements were carried out in several sessions using connecting points between sub-networks. Afterwards measurements were carried out simultaneously on all of the points. Session lengths differ significantly between measurements but because of short vector lengths in the network, satisfactory results even for 1.5h sessions are expected.

Leica GeoOffice v. 6.0 software was used to process all of the observations from 1993 to 2009. Available IGS products: precise orbits, ionosphere models for 1993-2009 measurements were used in calculations. Up to 1993 these products had been unavailable therefore broadcast orbits and standard ionosphere model implemented in the software were used.




Network adjustment was carried out in connection to, assumed stable, point 0204 located in the eastern part of the network. It has also been reference for calculating displacements between 1996 and 2002 performed by Cacon et al. (2003). In the result coordinates in local system and mean coordinate errors presented in Figure 3 have been obtained.

The calculated error values decrease noticeably in the last two years of measurements. This indicates that the decision to extend observation sessions has been correct. The greatest errors were noted for the 1993 adjustment what may be caused by the lack of IGS products. It is also clear that simultaneous measurement of the entire network is better than session solutions.

Gravimetric measurements (contract agreement) have been done with the La Coste & Romberg apparatus by M. Barlik's team from the Warsaw University of Technology. Observations on all of the network's points were carried out in 1994, 2008 and 2009. Unfavorable weather conditions, primarily strong wind, did not allow measurements on points 0204 and 0205 in 1996, 1998 and 2002. Measurements of the acceleration of gravity on the Szczeliniec (0113) were carried out eight times between 1997 and 2009. Observations of all of the research network points have been done using the profile method to eliminate drift from the results of measurements. Processing of results included correction due to height of the instrument over measured point and corrections of the Sun and the Moon influence on the gravimeter readings. Measurements in particular years have been tied to fundamental points in Karlow and Police nad Metuji. The acceleration of gravity values of these points were corrected in 2009 basing on the nearest National Gravimetric Network (POGK'99) point in Klodzko. Accurate corrections to the local values of gravity have been introduced to the network points determined from 1993 to 2009. The gravity on the fundamental point in Karlow in 2009 is 981020,655 mGal. This value has been calculated with [+ or -]17 [micro]Gal mean error.


Coordinates obtained by adjustment and the corresponding variance covariance matrix were used to determine velocities of coordinate changes. To calculate velocities, procedures based on a linear model with least square (LS) solution, developed by the authors in the Matlab[TM] environment, have been used. This approach was used by Brockmann (1997), Kontny (2003), Bosy (2005) as well as Kaplon and Cacon (2009) to estimate velocities in the regional network GEOSUD. It allows using data available from all the measurement periods.

Observation equations of a linear model of horizontal velocities (a) (1):


are solved on the account of minimizing condition of the least squares method (LS) for the weighted sum of squared velocities estimation residuals (v). Knowing the weight matrix (P) as the inverse of the covariance matrix consisting of coordinates covariance matrices from the epoch solutions ([C.sub.y]) (2):

[v.sup.T] Pv = min,

P = [C.sup.-1.sub.y],

([A.sup.T] PA)x - ([A.sup.T] Py) = 0, (2)

as the result coordinates for a reference epoch and velocity components of point location are obtained (x). In addition to them we obtain the estimates of the mean errors of coordinates and velocities, located in the diagonal of the resultant covariance matrix ([C.sub.x]) (3):

x = [([A.sup.T] PA).sup.-1][A.sup.T] Py,

[C.sub.x] = [??].sup.2.sub.0][([A.sup.T] PA).sup.-1],

[[??].sup.2.sub.0] = [v.sup.T] Pv / n - k. (3)

To assess quality of the developed model residua values of velocity components are used. The residua of the velocities are shown below (Fig. 4) as well as velocities and their mean errors. The maximum residual values amount to [+ or -]15 mm and are sporadic (0201). It is noticeable that measurements carried out in 1993 show the greatest divergence from the rest. This may be caused by very short measurement sessions and lack of IGS products unlike the other measurements.

Figure 7 contains map of determined velocities together with the confidence error ellipses [alpha] = 95 %. It is noticeable that significant linear velocities have been recorded for point 0203 only. Assuming outlying direction and value of velocity of the point 0203 it is possible that this may be the result of the self-movement of the measuring pillar.


Results of gravimetric measurements in the research network carried out between 1993 and 2009, after correction and reference to POGK'99, became the basis for analysis of relative changes of acceleration of gravity. Accuracy of gravity changes on particular points in the analyzed periods was assessed with a mean error of [m.sub.[DELTA]g] = [+ or -]24 [micro]Gal.

Figures 5 and 8 shows linear velocities of gravity changes on particular research points. These velocities were obtained using the LS method (1, 2, 3) similar as for the GPS data. All epoch gravity acceleration values were treated as equally erroneous with the [m.sub.[DELTA]g] error. Insignificant velocities within the accuracy limits for the 1993-2009 period, refer to observations on points 0201, 0202, 0203, 0204 and 0110. Significant velocities with the probability 95% ([v.sub.[DELTA]g] [greater than or equal to] [+ or -]2[m.sub.v[DELTA]g]) have been recorded on points: 0200 (-4.23 [micro]Gal/year), 0205 (-4.57 [micro]Gal/year), 0206 (-3.88 [micro]Gal/year), 0113 (+5.85 [micro]Gal/year). It is characteristic, that velocities are changing from the negative values in the NNW part of the network (0200, 0205) to the positive values at sites on top of the Szczeliniec Wielki in the SE part of the network (0110, 0113). Character of these changes is shown in Figure 8.


Results of five epoch satellite GPS measurements and eight gravimetric observations in the 1993-2009 period on research network points in the area of central part of the Stolowe Mts. constitute a basis for assessment of present day geodynamic conditions of this region.





Horizontal velocity vectors of points (Fig. 5), except on point 0203, are within the confidence ellipses ([alpha] = 95%). For points: 0200, 0201, 0202, 0205 these vectors maintain NW direction. Direction of velocity vectors of two points (0203 and 0206) located in the central part of the Policky and Belsky Fault zone is SW with point 0203 moving with significant velocity 2mm/year. Two points on the Szczeliniec (0110 and 0113) move with insignificant velocity in SE direction.

Velocities of acceleration of gravitational force on these same points of the research network (Fig. 5) proves the existence of the acceleration of gravitational force velocities pattern for the area of interest. A negative trend of velocities in the NNW part of the network is decreasing towards SE direction and finally is positive in Szczeliniec Wielki Massif: 0113 (+5.85 [micro]Gal/year) and 0110 (+9.36 [micro]Gal/year). These positive changes may be interpreted as tendency to lower the Szczeliniec Wielki Massif.


To achieve a connection between estimated velocities and tectonic structure of the research area, the agglomeration (Fig. 6) was made with the use of three dimensional vector of standardized GPS and gravimetric velocities. Standardized Euclidean distances have been used as measure of similarity in agglomeration, and Ward method as linkage method using square sum of distances within all groups. The results (Fig. 6) indicate the occurrence of similarity zones correlated with the known tectonic structures in the research area. These are comparable to earlier results presented by Cacon et al. (2003). The division includes: group 1--NE of the Belsky Fault (0204, 0205 and 0206), group 2--NW side of the Policky Fault (0200, 0201 and 0202), group 3--SE of the Czerwona Woda Fault Zone (Szczeliniec Wielki, 0110, 0113). Site 0203 located between the Policky and Belsky Faults was classified as outlying. These facts should be taken into consideration in further interpretations concerning recent geodynamic conditions of this area.


The results of epoch satellite GPS and gravimetric measurements carried out in the research network in the central part of the Stolowe Mts. in 1993-2009, indicate present-day geodynamic activity of the area including the Policky, Belsky Faults and Czerwona Woda Fault Zone located in close neighborhood to the Porici-Hronov fault zone. In the Polish part of the Stolowe Mountains, in the area of the Gory Stolowe National Park, geodynamic research has been started in 2008 (Cacon et al., 2009). The results of this research will contribute to the assessment of present-day activity in this part of the Sudety Mts.

Significant and insignificant horizontal movements of points and significant changes of gravity in the past 16 years have been registered. Agglomeration of the research points with the use of the estimated velocities indicates correlation of the behavior of the benchmarks and the location of the main tectonic zones within the research area. These data correspond with the results of seismic activity researches presented in the cited publications and confirm that the research area is tectonically active.

These facts substantiate the necessity to continue this research of both learning and practical significance.


The research has been carried out with the support granted by the Ministry of Science and Higher Education (MNiSW) by means of "Geo-ecological conditions of natural environment of the Gory Stolowe National Park" grant no. 09002904, and with support of Czech research project MSM 0021630519.

Data processing server, financed from the research grant MNiSW N52001431/2095 funds and Matlab[TM] Software (lic. no 101979) made available through the WCSS (Wroclaw Centre for Networking and Supercomputing, grant have been used for calculations and analyses carried out in this work.


Brockmann, E.: 1997, Combination of solutions for geodetic and geodynamic applications of the Global Positioning System (GPS), Geodatisch-geophysikalische Arbeiten in der Schweiz, Band 55, Schweizerische Geodatische Kommission, Institut fur Geodasie und Photogrammetrie, Eidg. Technische Hochschule Zurich, 121-123.

Cacon, S., Kopecky, J., Kaczalek, M., Makolski, K., Kaplon, J., Kontny, B. and Bosy, J.: 2003, Results of the geodynamic investigations in the Stolowe Mts. Research area. Acta Montana, Series A, No. 24 (131), 109-116.

Cacon, S., Wojewoda, J. and Kaplon, J.: 2009, Geodynamic studies in the Gory Stolowe National Park area. Acta Geodyn. Geomater., 6, No. 3 (155), 331-338.

Kaplon, J. and Cacon, S.: 2009, Research of the marginal sudetic fault activity with the use of GPS and precise leveling techniques. Acta Geodyn. Geomater., 6, No. 3 (155), 323-329.

Karnik, V., Prochazkova, D. and Broucek, I.: 1984, Catalogue of earthquakes for the territory of Czechoslovakia for the period 1880-1980. Travaux Geophysiques, 555, 155-186.

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 measurements. Zeszyty Naukowe Akademii Rolniczej we Wroclawiu, Nr 468, Seria Rozprawy, 202, 1-146, (in Polish, with English summary).

Schenk, V., Schenkova, Z. and Pospisil, L.: 1989, Fault system dynamics and seismic activity--Example from the Bohemian Massif and the Western Carpathians. Geophys. Transactions, 35, 101-116.

Schenk, V., Gitis, V. G., Schenkova, Z., Mantlik, F., Kottnauer, P., Yurkov, E.F. and Shehukin, Yu.K.: 1991, Maximum earthquake prediction in Central Europe given by the GEO-1.2 Expert System. Proceed. 6 Int. Conference on Seismic Zonation, Stanford, 83-91.

Stefan CACON (1) *, Jan KAPLON (1), Bernard KONTNY (1), Josef WEIGEL (2), Otakar SVABENSKY (2) and Jiri KOPECKY (3)

(1) Institute of Geodesy and Geoinformatics, Wroclaw University of Environmental and Life Sciences, Grunwaldzka 53, 50- 357 Wroclaw, Poland, tel/fax.: +48713205617

(2) Department of Geodesy, Brno University of Technology, Veveri 95, 662 37 Brno, Czech Republic, tel.: +420-541147211

* Corresponding author's e-mail:

(Received June 2010, accepted August 2010)
Table 1 Conditions of satellite
GPS observations.

Year    Antenna type                 Session       Number of
                                      length       sessions
                                                    per day

1993    ASH700228D                  1 h 30 min         3
1994    ASH700228D                  1 h 30 min         3
1996    ASH700228D, ASH700718B    1 h 30 min-4 h       2
2002    ASH700228D, ASH700718B,        9 h             1
2009    LEIAT502, LEIAX1202GG,       2 x 10 h          1
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Author:Cacon, Stefan; Kaplon, Jan; Kontny, Bernard; Weigel, Josef; Svabensky, Otakar; Kopecky, Jiri
Publication:Acta Geodynamica et Geromaterialia
Article Type:Report
Geographic Code:4EXCZ
Date:Jul 1, 2010
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