This paper was prepared as a part of the Czech Radioactive Waste Repository Authority project “Research support for the safety assessment of a deep geological repository” which forms an important part of the preparation phase for the construction of deep geological repositories for radioactive waste (hereinafter DGR). The aim of this partial project called “Seismic stability of territory” is to obtain initial parameters for the evaluation of seismicity and evaluation of seismic effects at depth of hypothetical deep geological repository (DGR) for the next time period (Kaláb Z., Šílený J., Lednická M., Jechumtálová Z., Seismic stability of DGR potential sites. - Reviewed technical report 26/2015/ENG, Institute of Geonics of the CAS and Institute of Geophysics of the CAS, Internal SURAO number: 188.8.131.52.3 /ESS: SURAO-2014-2379, Prague, 2015, 108).Seven areas were previously selected as these hypothetical DGR according to the geological criteria (Čertovka, Březový potok, Magdaléna, Čihadlo, Hrádek, Horka, Kraví hora – see Figure 1).
The aim of this paper is to present summary and analysis of seismicity, historical and current seismic events for the Czech Republic area and in the border regions of Germany, Austria and Slovakia, and seismic events prediction in the potential DGR sites for the next time period.The basic source of data on historical earthquakes up to 1990 was the seismic web , which was realized under the project NERA: “Network of European Research Infrastructures for Earthquake Risk Assessment and Mitigation”. The data source of the contemporary earthquakes since 1991 up to the end of 2014 was the CzechGeo website , that was realized as a part of the project “CzechGeo/EPOS – Distributed System of Observatory and Field Measurements of Geophysical Fields in the Czech Republic” (2010-2015, 2016-2019).
Seismicity analysis for seven potential areas of the DGR is elaborated on the basis of data from the catalogues of regional seismic events of the Czech Regional Seismological Network. Seismicity evaluation for these DGR research territories is carried out in order to narrow DGR sites, which is a circle at the distance of 5 km from the boundary of the DGR research territory polygon, and in the DGR research locality, which forms a circle at the distance of 25 km from the border of the DGR research territory polygon (according to State Office for Nuclear Safety: Criteria interpretation of nuclear instrumentation location and proposal their documents, BN-JB-1.14, SÚJB, 2012, in Czech). Seismic events of the last 24 years (1991-2014) were analysed in detail.
Earthquake hazard is defined as the probability of the occurrence of the earthquake effects (expressed in the units of dynamic vibrations), which can be expected in the region under study or in a particular site within a specified time window. The state of the art in the methodology of the earthquake hazard assessment may be characterized as a dispute of the experts. Traditionally two methods have been in use – the deterministic approach, allegedly already obsolete, thanks to the advance in the field, and the probabilistic approach, which is favoured at presence and demanded in the earthquake hazard assessment studies. Opinions of the representatives of both directions are often controversial. Apart from these two approaches mentioned above, a new one is emerging, namely so called neo-deterministic method of the assessment. At present it is not yet a universally accepted alternative to the probabilistic approach dominating now; however, it possesses the potential of delivering a new quality into the task of the earthquake hazard assessment. Evaluation for Čihadlo research locality is presented. The reason consists in the fact that in the category of local earthquakes the event discussed is relatively strong and mainly it is very close to the locality – its distance only slightly exceeds 4 km.
This paper represents a comprehensive study of the area for the purpose of construction of a deep geological repository. Neo-deterministic method (NDSHA) was selected as an extension of the probabilistic method for the modeling of the potential effects of vibration. Such extension is the innovated deterministic approach; its advocates collect arguments topped by the fact that every earthquake is associated with a fault, tectonic structure, the geometry of which together with the acting stress field determine the plane of the slip and the slip direction, in other words the mechanism of the earthquake. Input data for the analysis are taken from study of available seismological databases and determination of seismo-geological local conditions.
2 Research of historical earthquakes
The research of historical earthquakes in the area of the Czech Republic and its surroundings (i.e. 10°–20° eastern longitude and 48°–52° northern latitude), which was processed based on the data of the AHEAD database (the European Archive of Historical Earthquake Data 1000-1899) showed that no very powerful earthquake occurred in the defined area in the defined time period. Strong and moderate earthquakes are located in the vicinity of the Czech Republic, but their macroseismic manifestations on the territory of the Czech Republic are not documented. An exception is formed by the earthquake of Lower Austria in 1590. After the origin of this earthquake, scarce reports of its manifestations are documented virtually “throughout the territory of the Czech Republic”. The description of each earthquake also includes the magnitude Mw, whose size is determined from the intensity of the Io . Map showing the above mentioned earthquakes according to the magnitude Mw is presented in Figure 1.
3 Research of current earthquakes
Research of earthquakes for the defined area in period 1900 - 1990 was once again processed using the European database  (see Figure 2). It is evident from it that on the territory of the Czech Republic, only a very small number of earthquakes was recorded, and very weak ones at that. The most intensive earthquake was recorded in the area of the town Náchod on January 10, 1901 (02:30 a.m.) with the magnitude of Mw = 5.1. For this earthquake, Kárník  indicates the magnitude of 4.9 and the intensity of Io = 6 (maximum observed intensity). The magnitude of all other earthquakes on the territory of the Czech Republic was below 5. In the Czech Republic and its surroundings, only 14 earthquakes of magnitude over 5.0 were recorded in the period in question.
The catalogues of regional seismic events (e.g. http://czechgeo.cz) were used for the processing of the contemporary seismic events from 1991 to the end of 2014 (Figure 3). From the perspective of obtaining information about all known earthquakes and other vibrations, even of very small magnitude, this catalogue is the most comprehensive, as it is based on the registration of all stations of the Czech Regional Seismological Network (now 24 stations) and also of local networks on the territory of the Czech Republic. On the territory of the Czech Republic, no tectonic shock of a magnitude greater than 5.0 was registered in the evaluated time period. The most intense tectonic shock was recorded in the district of Nový Kostel in Western Bohemia May 31, 2014 (10:37 a.m.) with the value of local magnitude ML = 4.4  (local magnitude as determined from the records of the stations of the Czech Regional Seismological Network).
In the surroundings of the Czech Republic, only 3 seismic events with magnitude Mag (estimated by international data centres - ISC, NEIC, SED…) over 5.0 were registered in the evaluated time period, one of which is not a tectonic shock, as it represents a mining shock from the Lubin district (Poland). According to the processed catalogues, ML did not exceed the value of 5.0.
Charts in Figure 4 plot the dependency of magnitude of seismic events on time in each of the DGR research localities (not considering technical seismicity - mining and chemical explosion in quarries). Each tectonic shock is displayed in the graphs with two values of magnitude, i.e. ML and Mag values; if one or both magnitudes have not been determined, the value is plotted as a small grey symbol at “0”.
It may be stated in summary that magnitudes ML or Mag in the surroundings of any of the DGR research localities do not exceed the value of 2.3. The strongest tectonic shock with local magnitude ML = 2.3 was registered at the DGR research locality Magdaléna on January 13, 2007 (8:30 a.m.), about 22 km from the border of the research territory polygon. Another tectonic shock with local magnitude ML = 2.1 was registered on January 2, 1996 (5:05 a.m.), about 4 km from the border of the research territory polygon in Čihadlo and about 25 km from the border of the research territory polygon in Hrádek. Other tectonic shocks in DGR locations only reached magnitude (ML or Mag) less than 2.0, magnitude was not determined for a number of the events.
4 Neo-deterministic approach
Extension of the probabilistic approach is the innovated deterministic approach, so called neo-deterministic approach (NDSHA – neo-deterministic seismic hazard assessment). Its advocates [4–7] collect arguments topped by the fact that every earthquake is associated with a fault, tectonic structure, the geometry of which together with the acting stress field determine the plane of the slip and the slip direction, in other words the mechanism of the earthquake. The mechanism is the crucial factor ruling the seismic energy radiation as for its spatial distribution. For the specific configuration source (the hypocentre location, fault geometry, stress field) – site of the observation (the locality under study) it largely decides whether the seismic load will be strong or weak (even with a strong earthquake). This knowledge, together with details of the transfer of the seismic energy from the focus to the site of observation, is not present in the probabilistic method of the earthquake hazard assessment at all. This fact constitutes the main argument of the supporters of the neo-deterministic approach who emphasize the fact that the probabilistic approach ignores the detailed scenarios of earthquakes potentially threatening the locality under study and, thus, distorts notably the resulting values of the earthquake hazard estimate.
Contrary to the probabilistic method, the neo-deterministic approach is based on the concept of scenarios of particular earthquakes. This concept and a precise synthesis of the wave-field available, thanks to gathering the detailed information on the properties of the medium, allow determining useful engineering parameters quantifying the seismic loading. In this way, the scenario maximizes the benefit from the available information on the medium between the earthquake focus and the site of observation and from the pattern of the seismic energy radiation as well. Various alternatives of the approach are at hand in dependence of the knowledge available from a detailed field survey: (i) on the magnitude of the particular event only, (ii) with additional information on the strike and possibly also the dip of the fault nesting the particular earthquake, (iii) finally with full information on the direction and amount of the slip along the fault.
Summarizing the arguments, neo-deterministic approach may be marked as an extension of the traditional deterministic method on a higher level of the quality and as the desirable enhancement of the probabilistic estimation. As such, it possesses the power to synthesize a new quality in the task of the earthquake hazard assessment.
In detail, the neo-deterministic analysis means to derive the engineering parameters important for assessing the amount of endangering the particular civil structure or locality (commonly the horizontal peak ground acceleration) by theoretical modelling of the wave-field in the locality under study, excited by an earthquake representing a probable threat. The crucial parameters for the wave-field modelling are (i) the configuration – the mutual position of the locality and endangering earthquake, which contains information on the distance and the directivity of the radiation, and (ii) the model of the medium, which is necessary to compute the transfer of the radiated energy from the focus into the site of observation.
The configuration can be taken into account in several ways. One of them is seismic zoning – mapping the seismoactive faults or areas containing potentially dangerous earthquakes, and evaluating their effect on endangering the locality under study. Common approach consists in estimating the danger of the fault/zone by situating the earthquake of the proper size into the point of the zone, which is closest to the locality under study. This procedure may however overestimate the effect, because the extrapolation described needs not be valid. Then, for the purpose of the neo-deterministic analysis it may be more appropriate to perform the evaluation of the seismic load of the locality under study for a set of earthquakes selected on the basis of the past seismicity.
5 Evaluation of the peak ground acceleration (PGA) by theoretical modelling of the wave-field
To evaluate the peak ground acceleration as a measure of the earthquake hazard assessment at selected localities of intended nuclear waste disposals invoked by expected seismic events, we used a modification of the computer package AXITRA by Dr. Olivier Coutant from the Joseph Fourier University in Grenoble, France. It is the software widely used within international seismological community to model the wave-field in 1-D layered media. The package is written in the FORTRAN language and is in the open status, accessible, e.g., at the ORFEUS (Observatories and Research Facilities for European Seismology) webpage .
Computer package AXITRA is a code performing the mathematical method “reflectivity” designed to evaluate Green’s functions – response of horizontally layered medium composing of arbitrary number of plan-parallel homogeneous layers to unit excitation . Then, according to the representation theorem, Green’s functions determine for a seismic source with an arbitrary mechanism and for sever basic types of source time functions the theoretical seismogram optionally in the ground displacement, velocity, or acceleration. Contrary to ray methods, which generate separately individual wave phases (direct waves P and S, reflected waves, converted waves etc.), the method of reflectivity synthesizes in the point of observation the complete wave-field; it means both body waves and surface waves. While it is a disadvantage for tracking individual seismic phases, it is just strength when estimating characteristics of seismic radiation as a whole, because it avoids an underestimation of seismic effects due to undesirable missing a phase, which appears to be dominant contrary to the prior expectation. Evaluation of the seismic response requires coordinates of the source – earthquake focus, coordinates of the station in the site of observation, and characteristics of the medium, through which seismic waves propagate for the source to the site of the observation. The computer package AXITRA – and the reflectivity method itself – assumes a 1-D layered model, each homogeneous elastic layer with an attenuation described by its thickness, velocities of the P and S wave vP a vS, density γ and quality factor Q: QP corresponding to the attenuation of the P wave and QS related to the S wave. Characteristics of the wave-field in the locality studied – and, thus, the maxima of the acceleration explored in the localities of the interest – generally depend largely of the characteristics of the medium, and to obtain a reliable assessment it is needed to perform the evaluation with several alternative models, which can be for the particular locality considered as realistic.
For estimation of the peak ground motion due to an expected earthquake those methods are especially advantageous, which synthesize complete wave-field. They however perform with 1-D inhomogeneities only, in the practice along the vertical axis. To construct an average 1-D model, we nevertheless take advantage of availability of 2-D models resulting from recent active seismic experiments performed in the first decade of the century, namely CELEBRATION 2000 and SUDETES 2003 . We evaluated the Green’s function corresponding to the localities of the designed repositories by using the computer package AXITRA.
6 Neo-deterministic analysis of Čihadlo research locality
Each one out of the seven localities – potential waste repositories were assessed by the neo-deterministic evaluation of the seismic wave-field excited by selected individual events and determining the maximum loading. Basic results of neo-deterministic analysis of a near earthquake of Čihadlo research locality are presented here.
From the list of the events related to each of the localities we selected two strongest earthquakes and evaluated the horizontal peak ground acceleration of the synthetic wave-field. Because these events are exclusively weak earthquakes, we did not consider a finite duration of the source time function, but assumed the Brune source model. In this way, the source description is simplified to include the only parameter, namely the corner frequency. Taking into account the magnitudes of the events, we have fixed the corner frequency at the value 50 Hz. Resulting PGA values for both the surface and the depth of 500 m at the considered localities were calculated. An example of the Green’s function for the locality Čihadlo and local earthquake from January 2, 1996 (ML = 2.1) is in Figure 5.
The overall very low level of the PGA values is exceeded markedly by the evaluation at the locality Čihadlo excited by the local earthquake from January 2, 1996. The reason consists in the fact that in the category of local earthquakes the event discussed is relatively strong (but much weaker than the distant earthquakes) and mainly it is very close to the locality – its distance only slightly exceeds 4 km. As the evaluation depends on the configuration source-station and on the velocity model, we performed the PGA evaluation excited by the event both for two additional alternative velocity models, and for a series of the hypocentre depths.
It can be seen in the Table 1 that the synthetic horizontal peak ground acceleration is maximized for the velocity model 1 (Table 2), i.e. the simple 1-D model derived as a horizontally layered approximation of the 2-D model obtained from the active seismic measurements within the project SUDETES 2003 . Two versions of the velocity model (model 2 and 3), assuming a thin sub-surface low-velocity layer, demonstrate that such layer damps the peak ground motion, in the investigated configuration it reduces it roughly by one half of the original value. This fact is encouraging – in reality sub-surface layers with low velocities are frequent, thus the reducing of the earthquake effects comparing to an un-weathered rock massif with high velocities may be expected realistically.
It can be expected a priori that for a near event the effect of the hypocentre depth on the wave-field will be crucial. The reason is that a decrease in the depth implies a significant reduction of the hypocentre distance and, thus, an increase of the amplitudes of seismic waves. In addition, mutually closer arrival times of individual seismic phases may cause a constructive interference. Synthetic tests confirmed this expectation (see Table 3), while for the focus which is deeper than about 3 km the PGA remains below about 0.5 m⋅s−2, for the foci above about 1km depth the PGA level is around 1 m⋅s−2. However, for weak local events the determination of the focal depth is rather uncertain, it is often assumed a priori to be several km. Then, the PGA remains below about 0.5 m⋅s−2.
At the same time, it should be stressed that the PGA obtained is determined as a maximum across all the orientations of the mechanism; it is thus an upper estimate of the earthquake motion for the considered configuration source-station. It can be read from Figure 6, that the maximum occurs for a horizontal slip along a fault inclined by circa 400 - 500 with the azimuth about 900, it means for an E-W oriented fault. In the case that an indication of the fault direction from geology is available, there is a chance to decrease the estimate of the peak ground motion adequately.
Earthquakes, with magnitude higher than 5.0, have not occurred in the Czech Republic since 1991. The most intense earthquake described in the historical period occurred on September 15, 1590 in the Niederroesterreich region (Austria); its reported intensity is Io = 8–9 (Mw = 6.06 ± 0.47).
A detailed review of earthquakes within the years 1991 - 2014 was performed for each of the individual locations of DGR potential sites. In summary it can be stated that in the vicinity of any DGR potential site the value of ML or Mag has not exceed the value 2.3. With an exception of three earthquakes, the magnitude (ML or Mag) higher than 2.0 has not been reached in DGR potential territories; the magnitude has not been determined at all for a number of events.
The method of a direct evaluation of the PGA value by synthesizing the complete wave-field in the locality under study, which is excited by local or regional earthquakes potentially endangering the site, is advantageous mainly thanks to limiting the number of parameters that are largely uncertain. The configuration of the forward task is usually well defined in horizontal coordinates, but commonly ill-posed concerning the depth.
Based on the processed literature and database review and numerical modelling, it is possible to conclude that the impact of seismic events (vibration) on the stability of rock massif at the depth of 500 m and on the deep geological repositories will be very low in a next time period. The maximum estimated vibration effect did not exceed the ground acceleration of 0.518 m⋅s−2 and the underground acceleration is 0.22 m⋅s−2 at the depth of 500 m in any of the investigated site and in any of the numerical experiments simulating uncertainty in the depth of the foci and partially uncertainty in the velocity model as well. It is not possible to include additional related information in the estimation, such as the degradation of the rock massif, type of the fill around the containers and the containers themselves as a result of on-going geochemical processes and ageing. It cannot be expected from these studies that earthquakes exceeding the magnitude of 5 or more could occur in any one of the sites and therefore the load of the underground structures in question by vibrations obviously will not be substantial or damaging.
This research/publication is the result of Radioactive Waste Repository Authority project „Research support for Safety Evaluation of Deep Geological Repository“, Internal SURAO number: 184.108.40.206.3 / ESS: SURAO-2014-2379.
The data acquisition was supported by the project of large research infrastructure CzechGeo/EPOS, No. LM2010008 and LM2015079, and project NERA: “Network of European Research Infrastructures for Earthquake Risk Assessment and Mitigation”.
This research is partly sponsored by Research Program of Academy of Sciences of the Czech Republic, OZ30860518.
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Published Online: 2017-07-07