1 Introduction

The need for CO2 free sources of energy has seen an increase in solar, wind, hydrothermal, and nuclear power plants, many of which require local monitoring of micro-earthquakes. Nuclear power plants are monitored to ensure seismic stability of the bedrock (Dojcinovski et al. 2001), and geothermal energy exploitations are checked for potentially induced seismicity (in 2006 water injection to a depth of 5 km induced a ML 3.4 in Basel, Switzerland; Häring et al. 2008). Both types of power plants and others are likely to be built in a region with no known seismic activity. This paper presents a case study proof-tested work-flow to calculate the sensitivity of a local seismic network in a seismically inactive region. Knowing the sensitivity of a local seismic network in 3D is also beneficial for monitoring other underground operations, such as hydraulic fracturing (which caused ML 2.3 and 1.5 in Blackpool, UK; Clarke et al. 2014), waste-water injection (in 2011 this was related to MW 5.7 in Oklahoma, USA; Janská and Eisner 2012) or gas extraction (Baranova et al. 1999). High sensitivity of a seismic network, that is detecting no seismic event, is a reason for claiming that the area is secured/seismically silent-inactive, which might be another argument for building industry projects such as power plants, nuclear waste disposal, or, in our case, a geothermal project.

The ability of a seismic network to detect local micro-earthquakes is a function of the number of stations, their location, seismic noise, local geology, and the detection method. The sensitivity of a seismic network is a spatial monitoring performance in terms of the smallest reliably detectable magnitude, ideally presented in the form of a 3D map, but, in the case of insufficient information, also by a single value representing the magnitude of completeness MC of the whole detection catalog. The magnitude of completeness MC is the magnitude at which it deviates from the Gutenberg-Richter law (Wiemer and Wyss 2000; Leptokaropoulos and Gkarlaouni 2016). Various methods have been proposed to determine network sensitivity. A theoretical sensitivity using the moment magnitude that also depends on the velocity and density model is presented in Hallo (2012). When a seismic network is already operating, the sensitivity can be tested using synthetic seismic events overlying the real seismograms (López-Comino et al. 2017), or by comparing the Pn amplitude-distance curve to the signal-to-noise ratio (SNR) (Sereno and Bratt 1989). In the case of a highly active and long-term monitored region, the sensitivity is calculated from seismic catalogs (Mignan et al. 2011; Fischer and Bachura 2014) or can be derived continuously (Kværna et al. 2002).

In this case study, we propose a method to evaluate the 3D sensitivity of a local network that has no recorded local seismic activity, but uses a detection algorithm well established elsewhere. The sensitivity is based on a theoretical S-wave signal (stronger to P-wave at local scenarios) that exceeds the noise level at numerous stations. The minimal detectable local magnitude ML calculation, as a function of the maximum S-wave amplitude and the hypocentral distance, is adopted from the West Bohemia/Vogtland region (Horálek et al. 2000; Čermáková and Horálek 2015) after testing its transferability by regional earthquakes. This formula is then converted into a function of the station’s noise level and real-scenario peak-to-noise ratio (PNR). Such 3D sensitivity is derived for two local seismic networks in the Czech Republic: WEBNET in West Bohemia for proof-testing the concept using existing local seismic activity and the GRSN in Litoměřice for its application.

1.1 Local seismic networks

The aim is to derive the sensitivity of a local GRSN network that monitors the RINGEN geothermal project (Šafanda et al. 2020) that is being built near Litoměřice, a town in central Bohemia, Czech Republic (Fig. 1). An enhanced geothermal system (EGS) was originally planned at 5 km depth and a pilot 2.1 km deep geothermal borehole was drilled in 2007. At present, the RINGEN seismic network (GRSN) consists of nine surface stations (spaced 1.5–4.5 km apart, one of which is unreliable and was omitted in this study) and two downhole receivers (these were not present at the beginning of this study, so they were omitted). The first two surface stations were installed in 2013, the surface network was completed in 2019, and the downhole receivers started recording in July 2020. Although an efficient automatic detection algorithm Pepin, based on the method of Fischer (2003), was implemented in 2019, no local seismicity has been detected in the Litoměřice region so far, nor by the Czech Regional Seismological Network (Charles University in Prague (Czech) et al. 1973). The most recent algorithm setting requires the detection of at least one P-wave and four S-wave arrivals; the fact that local seismicity data is missing prevents us from determining the network sensitivity using standard methods mentioned above, which motivated us to derive an approach based on known information.

Fig. 1
figure 1

Left: region overview with highlight of West Bohemia region in magenta and Litoměřice in red. Center: WEBNET: subset of the seismic network in Vogtland/West Bohemia — 8 stations used for event detection by Pepin detector. Location of a weak ML − 0.6 event as blue circle. Right: GRSN: map of permanent stations of the seismic network in Litoměřice (station RICC unreliable and so omitted in this study). Location of future hydrothermal well by black circle (map background by Mapy.cz: ⒸSeznam.cz, a.s. ⒸOpenStreetMap )

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The proof-test region for our method of seismic network sensitivity is a seismologically active area of West Bohemia (Fig. 1 center) in Czech Republic, which borders Vogtland in Saxony, Germany (Neunhöfer and Hemmann 2005). Most of the seismic swarms occur in the Nový Kostel (station NKC) region at 6–10 km depth with local magnitudes up to ML 3.8 in 2008 (Čermáková and Horálek 2015). All the 23 permanent stations of the WEBNET seismic network (Institute of Geophysics, Academy of Sciences of the Czech Repub1ic 1991) stream data in real time. Two methodologies are used nowadays for data processing: automatic detection and location by the detector (Fischer 2003) and neural-network (Doubravová from Institute of Geophysics, Academy of Sciences of the Czech Republic, personal communication). Neural-network detections are manually picked and located; events ML > 0 are presented online. The automatic detection algorithm Pepin analyzes the waveforms of 8 stations (spaced 4–8 km apart) surrounding the most active area of Nový Kostel, and the results are published online in near real time. It is this eight-station subset and Pepin detector results that we use in our study.

2 Methodology

By the sensitivity of a seismic network, we understand a 3D map of the minimum detectable magnitude, when considering reasonable limits of an applied earthquake detection method. The calculated seismic network sensitivity is focused on networks such as the Litoměřice area where stations are separated by only a few kilometers, without any known seismic activity and with potential seismic activity in the first few kilometers underground. This setting allows us to draw the following assumptions:

First, for a seismically inactive region, the detection algorithm utilizing a signal amplitude that exceeds the background noise level is to be used. The reason is that the more sensitive methods, such as cross-correlation (Janská and Eisner 2012) or neural network (Perol et al. 2018; Doubravová and Horálek 2019), require knowledge of the waveform(s) of local seismic events, which is missing in the area of interest.

Second, in the far field, S-wave amplitudes are greater than P-wave amplitudes depending on the reciprocal of the third power of wave velocity (e.g., Shearer (2009) and an example in Fig. 2), especially on horizontal components, and there are very weak, if any, surface waves. This means that it is the S-wave signal (above noise level) that triggers the detection algorithm, especially for the weak events. Therefore, if the magnitude is determined using the S-wave peak amplitude, the minimal detectable magnitude is a function of the noise level of the horizontal components of the triggering station. Note that instead of using the SNR, where the signal value is an average over a short time window, as used for the STA/LTA (Trnkoczy 2012), we use (S-wave) peak-to-noise ratio (PNR) because it is directly connected to the magnitude calculation (Section 2.3).

Fig. 2
figure 2

A weak local seismic event near Nový Kostel, West Bohemia, automatically detected and located by Pepin with two P-waves and six S-waves on 2nd January 2020 02:44:50 UTC. Automatically assigned ML − 0.6, depth 8 km, latitude 50.2522, and longitude 12.4444. Blue waveforms are filtered 7–30 Hz and have similar scales in μ m/s. Red dashed line shows noise level from 100 days, which in this case is high above real noise on stations KVC and KRC. Red star highlights the highest peak in display (in SKC it does not represent event waveform) labeled with corresponding PNR. A subplot with mean PNR of horizontal (EN) components shows that the value of PNR is not a smooth function of distance from the source (stations are sorted by distance), but the second closest station has the fourth greatest PNR. Six PNR values are above the triggering threshold (PNR = 3), although the triggering stations differ from Pepin triggering one

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Third, usually a seismic event must trigger at minimum three stations, but due to the S-wave radiation pattern, these triggering stations are not necessarily only the closest ones. An example of a local event ML − 0.6 is shown in Fig. 2, where the waveforms are arranged according to the distance to the event, but the second closest station LBC shows a significantly smaller PNR. To account for the focal mechanism effect on amplitudes, we decided to set the algorithm to use one additional station to the number of stations required to trigger S-wave.

2.1 Noise level

Each station is characterized by its noise level, which is a function of human activity, weather, geology, and time. Assigning a single value characterizing such complex behavior is tricky and different statistical approaches can be taken. In our case, the noise value is defined as the root-mean-square (RMS) of filtered waveforms; due to the application of the L2 norm, the noise level value is sensitive to noise bursts or artificial noise peaks, which are likely to cause false triggers, making noisy stations less useful for detection. The RMS method therefore fails in stations with extreme values of spikes and these need to be handled individually, for example by advanced filtering.

We searched for an optimal band-pass filter similar for both GRSN and WEBNET that would suppress major noise and enhance the high-frequency signal of weak local events. Spectrograms of GRSN stations showed coherent 35 Hz noise at PLO station and therefore the upper cutoff frequency was set to 30 Hz. Several lower cutoff frequencies were tested on weak events from WEBNET, and the filter 7–30 Hz proved to give the highest PNR when tested on weak events (see an example of the effect of three different band-pass filters on East component of event ML − 1.1 from 2018 in Fig. 1 in the supplement). Therefore, this study uses waveforms filtered by 7–30 Hz, unless mentioned otherwise.

Since the S-wave is essential for our approach, it is practical to take into account only the horizontal components, which carry most of the S-wave signal. The noise level in Table 1 was calculated from the horizontal components of the first 100 days of the year 2020 because there was only minor seismic activity in West Bohemia. The average noise level of seismic networks varies by 10 times: 0.021 μ m/s in West Bohemia and 0.26 μ m/s in Litoměřice. Such a difference is also inside a network, as presented in Fig. 3 on SKAC and GTCLT station from GRSN. Day/night variation of noise is more pronounced in GRSN. These differences are likely due to differences in geology and because the noisier GRSN stations are situated at busy/industrial spots. To show the relevance of the noise level, the noise level is displayed as a red dashed line over real event waveforms of WEBNET stations in Fig. 2.

Table 1 Station’s noise level is the RMS of horizontal components filtered 7–30 Hz from the first 100 days of year 2020
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Fig. 3
figure 3

GRSN: low noise station SKAC on left, noisy station GTCLT on right. RMS noise level during day (red) and night (blue) overlying smooth record (moving RMS in 100s window, black) from a working day (Thursday 9th April 2020). Standard deviation of 100 day/night values highlighted by shadowed areas. Note that the noise y-scale varies by 10 times

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2.2 Detection algorithm

The automatic detection algorithm Pepin operating both in West Bohemia, Iceland (Fischer et al. 2022) and Litoměřice requires the recognition (trigger) of at least one P-wave and four S-wave arrivals. It is the smallest recognized S-wave amplitude that defines the triggering PNR of an event. To find a representative minimal triggering PNR, we analyzed the PNR of detected WEBNET events from the first 100 days of the year 2020, when only weak background seismic activity occurred. This allowed us a visual examination of the waveforms and to understand the outcome of detection.

A total of 242 events were automatically detected and located. The waveforms were visually checked to remove false detections (or considered real if also detected by the neural-network). As presented in Fig. 2 in the supplement, we identified 11% of false detections (27 events, 12 of which are distant events with incorrect locations). These false detections had no effect on the overall magnitude of catalog completeness (MC − 0.4), when derived as the maximum of magnitude distribution (deviation from Gutenberg-Richter law in Wiemer and Wyss 2000). Note that the neural-network detected an additional 45 events above MC in this region, but this might be because the Pepin locations of corresponding events were outside the selected region.

The triggering PNR of each event was derived, using the noise level of the corresponding station. As illustrated in the supporting plots in the supplement Fig. 3 (top 2 charts), the triggering peak-to-noise ratio of the 242 detections mentioned begins at PNR 2, but only 17 of 215 real events occurred with PNR< 3, which makes the threshold PNR 3 a reasonable input for the sensitivity calculation. A further positive indication is that the PNR 3 removes 10 of 17 false detections.

It was also tested whether the number of triggering stations increases with the increasing event magnitude and decreasing depth. Only a weak correlation was found and the magnitudes of events with 4, 5, and 6 S-triggers generally overlap (see Fig. 3 bottom chart in supplement). The reason behind is likely the random distribution of noise that makes detectability of (weaker) signals random as the noise bursts may interfere with signal arrival. The effect of noise on the number of triggering stations is reduced for stronger seismic events, whose signal is generally above most noise. The mean ML in triggering groups is pointed by squares and increases for 6, 7, and 8 S-triggers.

2.3 Local magnitude

The amplitude of a seismic signal recorded at a station is a function of the event magnitude, the distance between the earthquake and the station, the earthquake mechanism, and a local amplification. We adopt the following formula for magnitude calculation that is used at the WEBNET in West Bohemia/Voglant (Horálek et al. 2000, revisited by Čermáková and Horálek 2015):

$$ \begin{array}{@{}rcl@{}} M_{Li} &=& \log\left( A_{S_{\max}}\right) - \log (2\pi) \\ &&+ 2.1 * \log (R_{i}) + C_{i} - 1.2 \end{array} $$
(1)

where MLi is a local magnitude derived at the ith station, \(A_{S_{\max \limits }}\) is an absolute value of the maximum total amplitude of the S-wave ground velocity measured in μ m/s, Ri is the hypocentral distance of the ith station in kilometers, and Ci is the station correction. Each event is represented by an average magnitude ML. The maximum errors are ± 0.2ML, when only a subset of 4 to 5 stations is used (Čermáková and Horálek 2015). It is not linked to any regional magnitude.

Transferability of this local magnitude calculation (Eq. 1) to the Litoměřice region was tested on the closest regional events from Lubin (Poland, Fig. 1 left). Only 48 Lubin events with ML > 2.5 had a signal above the noise level, both in West Bohemia and Litoměřice in the first half of the year 2020. To enhance the peak-to-noise ratio of such regional events, the waveforms were filtered 1–10 Hz. Magnitude was calculated from the peak amplitudes of the horizontal components, without any station correction. Each station shows a bulk shift between reported M and calculated ML. Network corrections were derived as the mean difference of the station ML bulk shifts. This is similar for both networks: ML 0.65 for GRSN and ML 0.54 for WEBNET. Station corrections Ci were derived correspondingly and WEBNET station corrections are in accordance with the station corrections given in Čermáková and Horálek (2015) (Fig. 4 in the supplement). The similarity of network correction and correspondence of station corrections for WEBNET shows that the formula for local magnitude from West Bohemia is transferable to the Litoměřice region as is. Resulting station corrections of GRSN stations are presented in Table 2.

Table 2 GRSN station corrections Ci with corresponding standard deviation σi derived from 48 seismic events ML > 2.5 from Lubin region, Poland
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2.4 Simplified work-flow

Knowing parameters such as a station’s noise level and location, minimal PNR for detection, and the required number of triggering stations (T), the area of potential earthquakes is represented by a 3D grid. For each grid point (x, y, z), the minimum detectable magnitude for station i is computed as

$$ \begin{array}{@{}rcl@{}} M_{Li} (x, y, z)& =& \log (N_{i}*PNR) - \log (2\pi) \\ &&+ 2.1 * \log (R_{i}) + C_{i} - 1.2 \end{array} $$
(2)

where Ni is the noise level in micrometers per second and PNR represents the minimum triggering PNR of the S-wave (3 in our case). To account for the varying amplitudes due to the focal mechanisms, we set the minimal detectable magnitude at a point (x, y, z) as the (T + 1)th smallest value of MLi (5th in our case).

3 Network sensitivity results

A highly sensitive seismic network can detect earthquakes of smaller magnitudes than a less sensitive one. Quantification of network sensitivity is done using the minimal magnitude that a network can detect. The network sensitivity calculation presented here is a function of the location of the seismic station, the station’s representative noise level, detection algorithm parameters such as PNR and the number of triggering stations, and the area of interest defined by its coordinates. Since all the factors are known or calculated for both the West Bohemia and Litoměřice region, the corresponding sensitivities are presented below.

3.1 West Bohemia region — lessons learnt

The noise levels for the simulation of WEBNET sensitivity were derived using seismograms from the first 100 days of the year 2020, the station corrections were adopted from Čermáková and Horálek (2015), and the condition of PNR> 3 was outlined in Section 2.2 Detection algorithm; the simulations with 5 triggering stations resembles the 4 triggering stations of automatic detection algorithm.

The results of the application of Eq. 2 to WEBNET are displayed as a 3D view in Fig. 4. To relate the sensitivity to the known seismicity, the sensitivity cross sections are overlaid by seismic activity in years 2016–2021 in Fig. 5. It shows that the known seismicity lies in the region of the network with sensitivity starting at ML − 1.3 near Nový kostel (NKC) at depth 6 km and going down to ML − 0.8 for the south flank activity (between SKC and KVC) at depth of 10 km.

Fig. 4
figure 4

WEBNET: network sensitivity resembling detector setting (later recognized as the minimal detectable magnitude Mm). Isolines are spaced by ML 0.1, and bolder ones are multiples of ML 0.5. Seismic stations are shown by red triangles with the station names

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Fig. 5
figure 5

WEBNET: depth slices of network sensitivity resembling detector setting (latter the minimal detectable magnitude Mm). Gray isolines are spaced by ML 0.1, bolder ones are multiples of ML 0.5. Subplot titles note the slice’s depth below mean sea level. The sensitivity map is overlain by seismic activity in 2016–2021 in blue points and by seismic stations in black triangles with stations’ names

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The simulation of network sensitivity in Figs. 4 and 5 follows the setting of the automatic detection algorithm (triggering PNR 3 at a minimum 5 stations). To compare the simulations with real network sensitivity, the calculated sensitivity is compared to the network sensitivity derived from the events automatically detected by Pepin in 2014–2018. To achieve a meaningful comparison, both simulations and catalog data were confined to the area of greatest activity, i.e., a 2×4 km rectangle NE of Nový Kostel (NKC) at a depth of between 6 and 11 km, see Fig. 6. The simulation is represented by an average sensitivity at corresponding depth slices (yellow triangles with the corresponding values in yellow). The result of automatic detection is represented both by individual event hypocenters (blue circles) and by the magnitude of catalog completeness MC at each depth slice ± 0.5 km (red stars). Interestingly, the simulated sensitivity magnitudes envelop the very weakest catalog events, being slightly more optimistic. Another alignment between the simulated and real sensitivity is demonstrated for an active area at the southern flank of the network, and the setting and the results are shown in the supplement in Fig. 5.

Fig. 6
figure 6

WEBNET simulated vs. real sensitivity in high activity zone. Left: seismic activity as detected by automatic detection algorithm in highly active area NE of Nový Kostel (station NKC). Seismic events displayed as ML vs. depth below mean sea level in blue circles. A magnitude of completeness (red star with red label) is calculated separately for each depth range (gray rectangles in background). Average simulated sensitivity in this region (yellow triangles with yellow labels here, depth layers in supplement in Fig. 5 left) is enveloping the observed seismic activity. Right: map view of the simulated sensitivity at depth 9 km (in color)

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To conclude, when the simulation of seismic network sensitivity resembles the detector setting, the simulation correlates in depth with the minimal magnitude detected in years 2014–2018. Therefore, the simulation of network sensitivity is called the minimal detectable magnitude Mm when the setting is in line with the detection algorithm parameters.

3.1.1 Simulated M C

It would be more convenient to simulate the network sensitivity in terms of the magnitude of catalog completeness MC instead of minimal detectable magnitude Mm. However, the magnitudes of detected events correlates with the number of triggering stations only for the higher number of triggering stations (Fig. 3 bottom chart in supplement) and this correlation is not unique (events with 6 triggers cover the whole magnitude range). Therefore, to simulate the magnitude of completeness (hereinafter denoted MCS), we use the fact that when two additional triggering stations are simulated, the depth variation of the simulated sensitivity (green triangles with labels in Fig. 7 left) is fairly consistent with the catalog-derived MC (red stars in Fig. 7 left). Such MCS by two additional triggering stations can be understood as cases when random above-average noise bursts cover up the signal at two normally triggering stations, and therefore, in order for the event to be detected, the signal needs to exceed the standard noise level on other two normally not triggering stations.

Fig. 7
figure 7

Simulated sensitivity per depth in confined regions: minimal detectable magnitude Mm in yellow triangles (and yellow values) and magnitude of completeness MCS in green triangles (and green MCS values) represents random distribution of noise. Magnitude of completeness MC99 in smaller white triangles represents more stationary variation of noise. WEBNET on the left: average network sensitivity simulated in highly active area NE of Nový Kostel (Fig. 6 right), overlaid by seismic activity as detected by automatic detection algorithm Pepin in this region (blue circles) and its magnitude of completeness per depth (red star with red label). GRSN on the right: average network sensitivity simulated 1×1 km around well

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The WEBNET sensitivity simulation with 7 of 8 triggering stations shows simulated MCS variation from − 0.7 to − 0.4 between 6 and 11 km in the high activity zone, which complies with the observed MC. Depth cross sections of simulated MCS are displayed in Fig. 6 in supplement, which shows two highly sensitive regions: first triangle in the SouthEast of the network, and second an oval in the North-West area of the network. The reason for existence of two maxima is that when using 7 of 8 stations, only the weakest station can be omitted during detection. Therefore, the second weakest one must be used. This makes the two weakest stations play an important role (KRC for NE region and SKC for SW region) and because they are so far away, the network sensitivity is divided in two regions. Individual sensitivities of WEBNET stations are shown in Fig. 10 in supplement.

3.2 Litoměřice region — knowledge applied

The noise level and station corrections for the simulation of GRSN network sensitivity were derived using seismograms of the first 100 days of the year 2020. The PNR> 3 assumption is taken from the WEBNET, and the requirement of 5 triggering stations resembles the 4 triggering stations of the applied automatic detection algorithm.

The simulations show a sensitivity maximum of Mm surrounding the well as expected, with a prolongation in the NE-SW direction, see the 3D view in Fig. 8 and the depth cross sections between 2 and 5 km in Fig. 9. This means that GRSN starts detecting events from ML − 0.8 and ML − 0.4 at depths of 2 and 5 km near the well.

Fig. 8
figure 8

GRSN: network sensitivity as the minimal detectable magnitude Mm. Gray isolines are spaced by ML 0.1

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Fig. 9
figure 9

GRSN: network sensitivity as depth slices of the minimal detectable magnitude Mm, representing the detection of events with PNR> 3 at minimum 5 stations. Gray isolines are spaced by ML 0.1. Subplot titles note the slice’s depth below mean sea level. The sensitivity map is overlaid by seismic stations in labeled black triangles and the well location as a white diamond

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The network sensitivity in terms of the magnitude of completeness MCS was simulated with 7 triggering stations out of the 8 in total. Horizontal slices in Fig. 10 show two conjoined maxima, with the stronger one near the LMP station. The magnitude drop in sensitivity between these maxima is MCS − 0.3. Existence of such double maxima is similar to the case in West Bohemia — they are driven by the two least sensitive stations, which are LMP and PLO (see individual station sensitivity in supplement Fig. 8). In Litoměřice near the well, the completeness magnitude varies in depth from MCS − 0.6 at depth 2 km to MCS − 0.1 at depth 5 km.

Fig. 10
figure 10

GRSN: network sensitivity as depth slices simulating the magnitude of completeness MCS (PNR> 3 at minimum 7 stations). Gray isolines are spaced by ML 0.1. Subplot titles note the slice’s depth below mean sea level. The sensitivity map is overlaid by seismic stations in labeled black triangles and the well location as a white diamond. Summary of the average minimal and complete magnitude per depth is displayed in Fig. 7 for both GRSN and WEBNET

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If a network operator wants to judge the effectiveness of each station independently, it is reasonable to look at the minimal detectable magnitude Mm of individual stations. At GRSN, it shows that the stations’ sensitivity varies greatly (by ML 1.3 at depth 2 km, Fig. 8 in supplement) which means that the more sensitive half of the stations covers all the area in terms of detection, and the other half is used for detection only in their (limited) surroundings and in the case of outage of the more sensitive stations.

A question could be raised if all the stations need to be used for detection in order to maintain the network sensitivity. The test of individual station’s sensitivity mentioned above suggests that some stations could be omitted. The sensitivity simulations with only six stations, omitting LMP and PLO from the standard stations set, confirm only a little effect on the minimal detectable magnitude Mm near the well. If the condition of triggering stations was reduced by one, the station KAM could be skipped as well. Even more of possible setups of detection algorithm are presented in Fig. 9 in supplement.

4 Discussion

Local-scale seismic monitoring uses a grid of stations separated by a few kilometers, but not all of them might actually be enhancing the ability of the seismic network to detect events. The reason for this is that the recorded noise level, together with station’s correction, can undermine the station’s sensitivity.

In this paper, we present/apply a method and work-flow to evaluate the network’s sensitivity in 3D, focused on cases where there is no local activity recorded and a verified event detection method is in operation. We proof-tested our approach to the network sensitivity in the long-term monitored seismoactive region of West Bohemia/Vogtland and applied it to a geothermal project being developed in Litoměřice, both in the Czech Republic. The 3D network sensitivity defined as the minimum detectable magnitude Mm is a function of network geometry, detection algorithm setting, and the noise level of each seismic station. Mm is simulated in a 3D underground grid, where each point is assigned a magnitude of the weakest seismic event which signal exceeds three times the noise at five stations. It corresponds to the detection algorithm setting requiring four S-wave triggers; the one additionally simulated triggering station covers the case of a small S-wave amplitude due to the focal mechanism. We also show that sensitivity simulated for additional two triggering stations matches the magnitude of completeness MC and therefore we call it the simulated magnitude of completeness MCS. The most likely reason is the non-stationary noise behavior which by average eliminates two normally triggering stations for events of MC.

To examine independently our magnitude of completeness MCS estimate, an alternative approach for MC evaluation can be considered. It follows an idea that the detector detects all the events not disturbed by any noise. In other words, it detects a signal whose amplitude exceeds the amplitude of all the noise. All noise levels can be estimated by the RMS of noise + 3 * standard deviation of noise that corresponds to 99% of the noise. Such MC99 estimate represents the increase of noise on all stations, likely due to harsh weather. It is found that the average network sensitivity for the seismically active zone of West Bohemia/Vogtland calculated for 99% noise level (triangles in Fig. 7 left) follows the trend of MC determined from the catalog (red stars).

For the 99% noise level, the depth cross sections are bulk shifted versions of minimal detectable magnitude Mm (see GRSN sensitivity as MC99 in supplement Fig. 7 and compare with Mm in Fig. 9). A comparison of the average GRSN sensitivity 1 km around well, varying in depth (Fig. 7 right), shows clear correlation between MC determined by two different approaches, with 99% noise simulations showing less sensitivity in depth.

Near the planned geothermal well in Litoměřice, the minimal detectable magnitude Mm varies from ML − 1 at depth of 1 km to ML − 0.3 at 6 km depth (Fig. 7, GRSN on the right). Simulations of the magnitude of completeness MCS show that there should not be any seismic activity near the well with a magnitude above ML − 0.1 that would not be detected at depth 6 km or shallower. No local extremes or steep horizontal decline of sensitivity are found. As such, the area can be considered to be sufficiently monitored and seismically inactive since no local micro-earthquakes were detected so far.

To find stations that have the least effect on detection, it is possible to look at the minimum detectable magnitude Mm in case only a single station was available. The variation in GRSN individual station sensitivities is rather great: ML 1.3 at a depth of 2 km (at well location from ML − 2.2 to ML − 0.9 Fig. 8 in supplement). It is pointing out that three stations (LMP, GTCLT, and PLO) hardly contribute, if the detection requires only four stations. This is due to the variation both in noise level (10 times, Table 1) and in station correction (difference ML 0.9, Table 2). If the least sensitive stations were left out and the detector required to trigger at only three stations, the resulting sensitivity (supplement Fig. 9 bottom left subplot) did not change much from the initial setup (top left subplot).

The overall sensitivity of GRSN is weaker than that of WEBNET due to the greater noise from the industry and the town of Litoměřice. In the area of interest at a depth of 2 km, the difference is ML 0.7 (Fig. 7). Another comparison of seismic networks is in terms of sensitivity decline with depth. The decline of GRSN sensitivity (ML) with depth is steeper than in WEBNET: from 1 to 5 km depth the sensitivity is reduced by ML 0.3 in WEBNET and by ML 0.7 in GRSN. The most likely reason for this is that the network sensitivity at a grid point corresponds to the sensitivity of the weakest station that is accounted for in the detection at this grid point. If this weakest station is close by, the magnitude ML decays rapidly with the distance to this station (depth), as is the case of GRSN where the weak stations are no more than 4 km away from the well. On the other hand, if the weakest stations are further away, the distance to a station does not change with depth so much. This is the case of WEBNET, where the span between stations is greater and the weaker stations are at least 10–12 km away from the active zone. This is why there is less change of sensitivity with depth at WEBNET than at GRSN.

5 Conclusion

A recently developed hydrothermal project in Litoměřice, Czech Republic, is monitored with 8 seismic stations and corresponding sensitivity of the magnitude of completeness MCS − 0.6 at depth 2 km in region where the underground operations are likely to take place. Such or similar sensitivity could be acquired with various settings of the detector: Minimal requirement is three S-wave signal detected at five (particular) stations (supplement Fig. 9 bottom-left subplot).

In conclusion, if a change in network geometry or detection algorithm settings is planned, it is necessary to analyze the expected effect of this change by 3D visualization of the network sensitivity with respect to the actual seismic noise and the working detection algorithm. It comes from the connection of the sensitivity calculation to the real noise data and knowledge of the detection algorithm. Another use is in identifying stations of minor/greatest benefit. When having high sensitivity network and no seismic event detected over an extensive period, as in our Litoměřice case, one can claim the area well monitored and seismically inactive.