Time-dependent seismic hazard in Bobrek coal mine, Poland, assuming different magnitude distribution estimations
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The purpose of this study is to evaluate seismic hazard parameters in connection with the evolution of mining operations and seismic activity. The time-dependent hazard parameters to be estimated are activity rate, Gutenberg–Richter b-value, mean return period and exceedance probability of a prescribed magnitude for selected time windows related with the advance of the mining front. Four magnitude distribution estimation methods are applied and the results obtained from each one are compared with each other. Those approaches are maximum likelihood using the unbounded and upper bounded Gutenberg–Richter law and the non-parametric unbounded and non-parametric upper-bounded kernel estimation of magnitude distribution. The method is applied for seismicity occurred in the longwall mining of panel 3 in coal seam 503 in Bobrek colliery in Upper Silesia Coal Basin, Poland, during 2009–2010. Applications are performed in the recently established Web-Platform for Anthropogenic Seismicity Research, available at https://tcs.ah-epos.eu/.
KeywordsInduced seismicity Magnitude distribution Bobrek mine Time-dependent hazard assessment
Earthquake catalogs constitute a robust and beneficial tool for a variety of seismic analyses. Since seismicity is directly associated with physical quantities and mechanical properties of the crust such as strain accumulation, pore–fluid interactions and frictional response of the rupture zones, earthquakes provide a major source of information that cannot be usually obtained by direct measurements. Spatial and temporal seismicity rate anomalies are essentially reported as the most frequent intermediate-term precursory phenomenon in timescales varying from a few days to several years. The use of the well-established Gutenberg–Richter (G–R) law has been routinely incorporated into many seismic hazard assessment studies (e.g., Cornell 1968; Convertito et al. 2012). Alternatively, non-parametric approaches can be performed for hazard assessment evaluation under certain conditions (e.g., Kijko et al. 2001; Lasocki and Orlecka-Sikora 2008).
Seismic events may be controlled by either natural or anthropogenic factors. During the last decades, the rising demands for energy and minerals have sharpened the problem of hazards induced by exploration and exploitation of georesources (Davis et al. 2013). Among the diverse technologies capable of inducing earthquakes, one of the most well studied origins of anthropogenic hazard is underground mining. The undesirable rockmass response to mining operations was firstly observed back in the eighteenth century and during the last years it is being constantly reviewed and documented (e.g., Gibowicz and Lasocki 2001; Li et al. 2007; Gibowicz 2009, and references therein). A variety of factors control the rockmass fracturing and nucleation process in mines such as tectonic stresses accumulation, removal of material from the mine, explosions and the interaction among seismic events and rockbursts. The instability of mining activities, especially when they are extended, may result in the residual subsidence and localized or generalized collapsing, potentially with significant societal and economic impacts. There are numerous documented cases where mining-induced seismicity has caused personnel injuries, production losses, extensive damage to infrastructure, collapse of drifts and stopes, and occasionally, fatalities. For all these reasons, seismic hazard assessment in mines is a task of paramount importance.
Bobrek Mine is a hard coal mine located in Bytom city in the area of USCB, Poland (Fig. 1). USCB constitutes one of the most seismically active mining areas worldwide, with almost 56,000 mining tremors of energy E > 105 J recorded between 1974 and 2005 (Stec 2007). The analysis of our study was based on selected set of data connected with exploitation in panel No. 3 in coal seam 503. This dataset is retrieved due to the specially organized virtual Laboratory for Monitoring Mining Induced Seismicity (LMMIS) where seismic data and technological data, such as mining front advance, were gathered. The seismic data had been prepared based on integration of two seismological networks operating at different scales (registration of events in the near and far seismic field). Additionally, information about the geology and the tectonics of the area was available. This set of data is integrated as an episode, which comprehensively describes a geophysical process induced or triggered by human technological activity, posing hazard for populations, infrastructure and the environment. All the data from this episode are available on TCS-AH platform as BOBREK MINE: local seismicity linked to longwall mining (https://tcs.ah-epos.eu/#episodes:BOBREK).
Events with M L ≥ 2.8 which occurred in analyzed period of time
Four different magnitude distribution estimation methods are applied presented in the following sub-sections. Hazard parameters are calculated and plotted for each one of the time windows for which sufficient data are available in order to perform the necessary calculation. A different minimum number of events in each window is considered for the calculations to be performed, according to the method selected: for unbounded Gutenberg–Richter method it is 7; for upper-bounded Gutenberg–Richter method it is 15; and for non-parametric kernel-based methods it is 50 events.
Note that for the Unbounded models (GRU and NPU) an infinite upper magnitude limit, M max, is considered whereas in the Truncated (upper-bounded) approaches (GRT and NPT) M max is evaluated using the Kijko–Sellevoll generic formula (Kijko and Sellevoll 1989; Kijko 2004; Lasocki and Urban 2011). If convergence is not reached the Robson and Whitlock (1964) simplified formula is used: M max = 2M maxobs–M max2obs, where M maxobs and M max2obs stand for the largest and second largest magnitudes in a given catalog, respectively.
The cumulative magnitude distribution function, F(M), is calculated with respect to the selected method:
Unbounded GR law (GRU)
Truncated GR law (GRT)
Non-parametric approaches (NPU and NPT)
Parameter values defined
Mining tremors occurrence is strongly associated with the excavation operations and therefore, seismicity properties and hazard parameters are estimated as a function of time and front advance. For this purpose, only the fraction of events which satisfies predefined properties is considered for such calculations. These events are selected after applying the following constrains: The completeness magnitude of the catalog was identified by considering the stations distances from the focal areas and the signal to noise ratio (Mutke et al. 2016). In such way M min was set equal to 0.6. The margin along front strike (equal for both directions of the front strike) and distance along the front advance (equal for both in front of and behind the front) was set equal to 50 and 100 m, respectively, following Kozłowska (2013). Calculations were performed for overlapping time windows generated in three different modes: According the “time mode”, events included in subsequent 30-day time windows were considered, overlapping per 1 day. In this approach time windows of the same span are used for hazard parameter evolution estimation. In the “events mode”, the time windows are selected in such a way that they include equal number of events (also overlapping per one day) and therefore the parameter estimation errors are comparable in all the datasets. Finally, in the “front mode”, a subsequent time window starts at the time point when the front advance is moved from the position it was in the beginning of the previous time window, to a distance indicated by a predefined value. In this case, the time windows correspond to approximately equal material mass removal from the mine (those windows are also overlapping per 1 day). The parameters set for our analysis in those three modes were 30 days in the “time mode”, 80 events in the “event mode” and 50 meters in the “front mode”. Finally, the event magnitude for the mean return period and the exceedance probability evaluation was set to 3.0, equal to the second largest magnitude in the dataset.
It can be observed that in the case of events (2) and (3) activity rate increases, although in different manner, before the occurrence of considered events (Fig. 5a). The opposite statement can be done for event (4), where for both time and front windows activity rate decreases before the event. However, slight increase shortly before the event is observable in the case of event window mode which due to the constant amount of events in each window is more sensitive in detecting sudden changes in occurrence rates. Additionally, it is worth mentioning that only the curve resulting from event windows shows a evident peak in activity rate before event (3). In the case of other windows the increase is slight.
Changes in b-values before the occurrence of strong events are also not completely consistent with each other. Before events (2) and (4) decrease of b-value can be observed. However, before the occurrence of event (3), b-value increases in the case of all window types. Again, changes in the case of curve obtained using event window mode are the largest (Fig. 5b).
Previous analysis (Fig. 8, 9, 10) of parameters’ changes before events (2), (3) and (4) leads us to the following conclusions concerning expectance of events on the basis of time-dependent hazard calculations. First, on the basis of temporal changes of activity rate, b-value, exceedance probability and return period, event (4) can be considered as the most expected one (activity rate increase, b-value decrease, high exceedance probability according to all methods, relatively short return period). Second, estimations of exceedance probability and return period with kernel-based methods do not give any possibility to predict the event (2) despite the fact that activity rate and b-value changes can suggest the occurrence of an impending strong event.
Discussion and conclusions
The use of fundamental observational and empirical parameters such as activity rate and G–R b-value may prove to be helpful in evaluation of seismic hazard for specific study areas such as longwall mining. The G–R b-value has a clear physical interpretation, defining the relative proportion of the number of large events to small events. Anomalies in seismicity rates and b-value can be considered as an indicator of the stress state in rock mass (e.g., low b-values may indicate growing of stress, Scholz 1968). These anomalies are capable to lead to strong tremors and thus provide high seismic risk. Information of such kind can, therefore, be a premise for the decision to use specific measures to prevent bumps and adjust mining operations. Probability of the strong events occurring is higher when b-value is decreasing and simultaneously activity rate is increasing. In the present study, this case is clearly observed for events 2 and 4 for all window types (with the exception of b-value for event 2, which slightly increases when time window is considered). However, the activity rate is increased in all cases studied (Fig. 8a).
The need of introducing a non-parametric estimation for magnitude distribution arose from observed deviations of specific catalogs from G–R law in both natural and induced seismicity. Especially, induced seismicity exhibits diverse seismogenic processes in comparison with natural seismicity and it strongly depends on the human technological and production activities (Kijko et al. 1987; Trifu et al. 1993; Fritschen 2010; Maghsoudi et al. 2014). Two causes had been considered responsible for inconsistency of G–R law with the observed events distribution. The coupling between tectonic stresses and mining activities in Bobrek mine has been studied by Marcak and Mutke (2013). Specifically for event 2, Kozłowska et al. (2016) showed that it was a tectonic event triggered by the ongoing exploitation and that the subsequent seismicity was a result of combined tectonic, coseismic and mining-induced stresses.
First, this inconsistency was attributed to the presence of broadly defined types of mining events (e.g., Gibowicz and Kijko 1994): events directly related to the mining operations and events resulting from the release of residual tectonic stresses accumulated in the rock mass. These two types of events are characterized by extensively different properties and features. Second, the non-linearity was attributed to the local geology and tectonics, i.e., heterogeneity and discontinuity of the rock structures with different thickness, strength, different in various parameters. For example, Naoi et al. (2014) showed that the distribution of magnitudes is consistent with the G–R relationship only when events closely linked to blasting are not taken into account.
As a result, magnitude distribution complexity may arise, characterized by number of modes or bumps in magnitude density. Evidences for the existence of multimodal earthquake size distribution were presented in many papers (e.g., Gibowicz and Kijko 1994; Gibowicz and Lasocki 2001; Lasocki and Orlecka-Sikora 2008). Magnitude distribution may statistically significantly differ from the exponential distribution but the differences may be small (Urban et al. 2016). G–R model seems often inadequate to describe the earthquake size distribution.
To evaluate which estimation method would be more appropriate in our dataset, we performed statistical tests to examine the compatibility of earthquake size distribution with exponential distribution. First, we used Kolmogorov–Smirnov (K–S) goodness-of-fit one-sample test to check whether earthquake size distribution statistically differs from the exponential distribution. Details of this procedure and the corresponding findings in several cases of induced seismicity are described in the paper of Urban et al. (2016). Second, we examined the earthquake size distribution for its complexity using smoothed bootstrap test for multimodality. Multimodality test allows us to examine the presence of irregularities in the distribution of given magnitude values by demonstrating the presence of more than one mode or more than one bump in the probability density function (Lasocki and Papadimitriou 2006; Lasocki and Orlecka-Sikora 2008). These features indicate the presence and mixing of different processes generating the events.
In the K–S test case, we test the null hypothesis H 0: the distribution of magnitude is exponential. To verify H 0, we estimate p values and compare them with the adopted significance level α = 0.05. A small p value suggests that the null hypothesis may be false. In the test for multimodality case, we test two null hypotheses: H 0 1 : density function of earthquake size distribution has no more when 1 mode; H 0 2 : density function of earthquake size distribution has no more than 1 bump. Due to the fact that the magnitude randomization gives slightly different p-values and significances of the considered null hypotheses, we assumed as a final value its mean value (from 1000 magnitude randomized catalogs) considering their standard deviation as well.
The results from K to S test strongly suggest that earthquake size distribution is not exponential with mean p equal to 4.6 × 10−7 and standard deviation equal 3.9 × 10−7. Because we estimate G–R b-value from the sample it requires calculation of additional statistics (D m) (Urban et al. 2016). The value of the (D m) is 2.82 which confirms previous results with the significance at least equal to 0.01.
The mean significance of considered null hypotheses from test for multimodality is 0.11 for H 0 1 with standard deviation equal 0.02 and 0.04 for H 0 2 with standard deviation equal 0.02. The results indicated that with 89–96% probability magnitude distribution is more complex than linear model.
Based on the results of K–S test and smoothed bootstrap test for multimodality, the non-parametric method for estimate of hazard parameters would be more appropriate. On the other hand, non-parametric technique starts to be effective for sample sizes starting from 200 events (Kijko et al. 2001). However, the hazard analysis performed in the present study considers time windows which contain diverse and mainly smaller number of events. Taking into account the size of the dataset we may conclude that segmentally, the G–R model is a good approximation for this type of analysis, providing also more comprehensive and stable results.
The obtained results strongly depend on the data number contained in the analyzed windows. According to that, event window approach may be preferable because it leads to identical or at least comparable uncertainties of the estimated parameters (equal size data samples are tested—see “Appendix A”).
Unbounded and upper-bounded GR approaches lead to similar results (see also “Appendix A”). In the same way, unbounded and upper-bounded non-parametric methods also lead to similar results. On the other hand, there are distinct differences between parametric and non-parametric estimation techniques.
Kernel-based methods exhibit sharp fluctuations of estimated parameter values, which are essentially, not practical in terms of prediction implications for datasets of such size. However, they seem to provide consistent results when event windows are considered.
On the basis of all methods’ results, the last event (4) can be considered as the most expected one. It should be noted that there are several other windows for which exceedance probability is practically 1, when the G–R approaches are considered.
The analysis of the catalog as a whole strongly indicates that earthquake size distribution does not obey G–R relation. However, smaller datasets in the analyzed windows show that G–R relation is an adequate approximation providing more stable results.
The authors would like to thank Stanisław Lasocki for his valuable comments regarding methodological issues. The comments and suggestions of two anonymous reviewers were much appreciated. This work was supported within statutory activities No3841/E-41/S/2016 of Ministry of Science and Higher Education of Poland. This work was accomplished in the framework of IS-EPOS: Digital Research Space of Induced Seismicity for EPOS Purposes project, funded by the National Centre for Research and Development in the Operational Program Innovative Economy in the years 2013–2015 and EPOS Implementation Phase project funded from the Horizon 2020—Research and Innovation Framework Programme, call H2020—INFRADEV-1-2015-1 in the years 2015–2019. All calculations and some of the figures were made into the IS-EPOS web-platform for anthropogenic seismicity research available at https://tcs.ah-epos.eu/.
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