Induced Earthquake Hazard by Geothermal Power Plants: Statistical Evaluation and Probabilistic Modeling

Geothermal energy is one of the newly developed sources of clean energy production in many countries around the world. Geothermal power plants (GPPs) produce electrical energy using the hot water steam of extracted high-temperature water from the Earth’s crust (at depths of 2−10 km) that activates the electrical turbines (Fridleifsson et al. 2008). Since the volume of extracted water is significantly large, it is not possible to store it in surface reservoirs. In addition, this high temperature water works as a fuel for the GPPs, and the continuous extraction of water without any replacement would destroy the underground water resources. To overcome these problems, the cooled water is injected back into the Earth under high-pressure. This repeated extraction/injection process may cause some changes in the stress magnitude of the underlying Earth layers, thus creating or extending cracks in the crustal rocks. The fractured rocks may trigger a series of small to moderate magnitude earthquakes over a long period (Kraft et al. 2011). Since many GPPs are constructed close to populated areas, the induced vibrations from the operation of GPPs may cause inconvenience for building residents, and also cause damage to the buildings’ structural and nonstructural components (Zastrow 2019). Such undesired vibrations with a high recurrence rate can bring about claims by building owners that, in some cases, lead to GPP shutdown. For instance, the South Korean geothermal power plant in Pohang City was shut down after a severe earthquake with a magnitude of 5.4 occurred in 2017 (Ellsworh et al. 2019; Zastrow 2019). A Similar problem occurred in Basel, Switzerland, after the 3.2 magnitude earthquake of 8 December 2006 (Mignan et al. 2015) due to the local GPP’s activity. Additionally, Khansefid et al. (2022a) showed that GPP-induced earthquakes can cause some levels of disruption to the occupants’ life in vulnerable masonry buildings. Accordingly, it is highly important to study the seismic risk of this type of electric power plants.

A review of literature indicates that there are some research works on the induced seismicity of specific GPP sites. As an early work, Eberhart-Phillips and Oppenheimer (1984) studied the microseismicity of the region around Geysers GPP in California and showed that events occur wherever the steam production exists. However, they could not identify any specific correlation between the injection rate and the magnitude of seismic events. This issue was raised again in other GPPs such as Wairakei (Allis et al. 1985); however, it was shown by Bromley et al. (1987) that increasing the power plant production causes a swarm of events triggered by both extraction and reinjection of fluids. In another work, Charléty et al. (2007) dealt with the effects of flow rate and wellhead pressure on induced earthquake magnitude and its distribution over three main boreholes of Soultz-sous-Forêts GPP in France. In addition, a more comprehensive study of Majer et al. (2007) investigated the relationship between the number, distance, and depth of GPPs’ induced earthquakes and the injection rate for the Geysers, Cooper Basin, Berlin, Soultz-sous-Forêts, and Basel GPPs. Cuenot et al. (2008) simulated the hydraulic water injection in a well of Soultz-sous-Forêts GPP experimentally and traced the wave propagation and microseismic activity of the region using the installed seismological network. It was shown by Nicol et al. (2011) that most of GPP microseismic events occur during the injection and extraction process of the water stream, and are clustered at shallow crustal depths. Moreover, Evans et al. (2012), based on their observations, believed the sites with sedimentary rocks are less seismogenic than the ones with crystalline rocks, and in both cases, faults located near injection wells can increase the seismic activity significantly. In a series of works, Shapiro et al. (2007, 2010, 2013) attempted to obtain the probability of observing an induced earthquake with a given magnitude. Megies and Wassermann (2014) installed several seismometers in the Molasse Basin to trace the induced seismicity by the GPPs located around Munich City, which lead to the recording of several events with a local magnitude of up to 2.4. In some other works, several researchers (Bachmann et al. 2012; Langenbruch and Zoback 2016; Leptokaropoulos and Staszek 2019) tried to evaluate the relationship between the injection rates and the earthquakes’ magnitude in different GPPs. Kwiatek et al. (2015) also worked on the induced seismicity in the northern part of Geysers GPP, due to long-term fluid injection. Cheng and Chen (2018) performed a statistical analysis on the distance of observed seismic events induced by the Salton Sea GPP operation, and found that the magnitude of events located outside the defined ring of a GPP (radius of 2−5 km) is five times less than the ones located near the power plant. Broccardo et al. (2020) estimated the seismic risk of the Geldinganes GPP in Iceland. Their study emphasized the need for reevaluation of the risk by using updated data throughout a power plant’s activity. Convertito et al. (2021) also performed a time-dependent seismic hazard analysis of the St Gallen geothermal field. More recently, Khansefid et al. (2022b) worked on recorded ground motions due to GPP activities to develop a set of ground motion models.

Most of the existing work has dealt with the induced seismicity by geothermal power plants from the physics-based point of view and there are only a few studies (Mignan et al. 2015; Langenbruch et al. 2020) on the seismic risk assessment of such earthquakes, which points to need for probabilistic models, developed based on the statistical characteristics of earthquakes. Accordingly, this research is an attempt, from the engineering perspective, to initially examine the effects of geothermal power plant activity on the induced seismicity identified in four GPP zones around the world, and then propose a probabilistic model for simulating the seismic events due to the operation of GPPs. First, the general information of GPPs and their injection rates were collected from different sources. All of these GPPs continue in operating status. The induced earthquake data obtained during their operation period were also supplemented from several online earthquake catalogs. These data were filtered by considering the minimum completeness magnitude of the catalog. Also examined were the effects of geothermal activity, especially the injection rate, on the properties of recorded events such as moment magnitude, focal depth, and the distance of events from GPP stations. Using the proposed database, a probabilistic model was developed to simulate, randomly, earthquakes induced by the GPP activity. The model procreates the number of probable events per month, their magnitudes, focal depths, as well as their distance from a GPP station based on the power plant’s average operational injection rate per month. In the last step, the model was validated through application of different methods. Generally speaking, this model is a powerful tool for scientists and engineers who are interested in and in charge of estimation of seismic risk due to the operation of geothermal power plants.

A total of eight active GPPs located in the United States, Germany, France, and New Zealand are selected for further analysis. Each of these power plants contains several active water injection wells. The Geysers geothermal plant is located in northern California, the United States. This GPP started operating in 1960 and is known as one of the biggest natural geothermal sites in the world. The Salton Sea and the Brawley GPPs are constructed in the Imperial Valley region of southern California, the United States, with the starting operation date of 1982. These two power plants are located in the close proximity to each other. Therefore, they are considered as a single GPP zone called “Imperial.”. In central Europe, four GPPs are operating near the border of Germany and France in the Rhineland area using the enhanced water circulating systems. The Landau and the Insheim GPPs are located in western Germany and have started their operation from the years 2007 and 2012. The Soultz-sous-Forêts and the Rittershoffen GPPs are located in eastern France and have been operating since 2008 and 2016. The four GPPs are grouped as a “Rhineland” GPP zone. The last GPP is Kawerau, which is located near the town of Kawerau inland from the Bay of Plenty, the northern coast of North Island, New Zealand, and its injection wells started operating in 1993. The information summary of these GPP zones is presented in Table 1, while their location map is shown in Fig. 1.

The exact location of the Geysers, Salton Sea, and the Brawley power plants are collected from the Geothermal Prospector (Getman et al. 2015), a web GIS framework developed by the National Renewable Energy Laboratory. The detailed data of monthly water injection throughout geothermal activity are archived in the California Department of Conservation website (California Department of Conservation 2020). The information of GPPs in Germany and France is available on the website of Geothermal Information System, called GeotIS, (Pester et al. 2010), which is supported by the Federal Ministry for Economic Affairs and Energy of Germany. The location of Kawerau GPP in New Zealand is adopted from the Global Energy Observatory (Gupta and Shankar 2018) website, and the injection rates are available in the Bay of Plenty Regional Council catalog (Bay of Plenty Regional Council 2018). The injection flow rates of all wells per month for each of the GPP zones are shown in Fig. 2. These flow rates are illustrated for the whole period of GPPs operation. Different GPPs report their injection rate with different time windows of daily, monthly, or even yearly. As it can be seen, the GPPs operate in the Imperial, Geysers, and Kawerau zones work with a higher injection rate (2000−3000 l/s) in comparison with the ones in the Rhineland zone (200−400 l/s).

As is typical of all research work that focuses on the development of probabilistic models to study seismicity, earthquake catalogs play a key role in the final quality and accuracy of the model. Since there is no separate earthquake catalog for the events induced by human activities, especially the ones caused by GPPs, a major challenge is to create such a catalog.¹ For the selected GPP zones, different online credible sources of earthquake event catalogs are used. For the Geysers and Imperial zones, the United States Geological Survey (2020) is used. In the case of the Rhineland zone, the data published by the International Seismological Center catalog (2020) is adopted. For the Kawerau GPP zone, the catalog presented by the Geological Hazard Information for New Zealand (2020) is employed to collect the microseismic data. Only some criteria are taken into account to select the seismic data: (1) Events related to the time period of GPP operation are considered for this study; (2) The events that occurred within the shallow focal depth (around 1−10 km) are collected based on the depth of GPP wells varying from 500 m to 5 km (see Table 1); and (3) A spatial window with a radius of approximately 25 km around the power plants is considered as a surrounding possible area of earthquake occurrence.

Since the seismic data are collected from different sources, their magnitudes are reported in different scales, including moment magnitude (M_W), local magnitude (M_L), and duration magnitude (M_D). To homogenize all data, scales of M_D and M_L are converted to M_W, which is more familiar to the earthquake and structural engineers and scientists who are the target community of the proposed model. Different equations (Table 2) are applied to convert the magnitudes for each of the GPP regions.

After homogenizing the earthquake catalogs, it is necessary to refine them and remove the events recorded below the magnitude level that the seismometer networks could reliably and consistently record. Accordingly, the minimum completeness magnitude (M_C) of each catalog is calculated for the 10 year time-windows using the entire range magnitude method (Ogata and Katsura 1993), which is more comprehensive and stable than many other existing methods in the literature (Woessner and Wiemer 2005). The uncertainties of the completeness magnitude are also considered by obtaining their standard deviation using the Monte Carlo bootstrapping method (Efron and Tibshirani 1993). The results for each of the GPP zones during different time windows are shown in Table 3 along with the maximum moment magnitudes obtained by Kijko’s (2004) methodology. With the passing of time, the M_C decreases in all catalogs, which implies the improvement of seismic networks responsible for recording the events during the decades since a GPP began operation. Fortunately, after eliminating the events with magnitudes lower than M_C, an acceptable number of events remain for each of the GPP zones for further analysis (Table 3). The spatial distribution of the remaining data, showing their magnitudes, is depicted in Fig. 3. Clearly, earthquakes with higher magnitudes occur closer to the GPP stations’ wells.

The last, but not least important issue about the earthquake catalogs is the existence of background seismicity by other possible sources in the GPP zones. In the Geysers and Rhineland GPP zones, there are no considerable seismic events before the commencement of water injection. Therefore, the catalogs contain no tangible background seismicity. In the Kawerau GPP area, there were few microseismic activities before 2006 that are likely induced events connected to that GPP because of their shallow depth and proximity to the power plant. Owing to the lack of available data for injection rates during its early years of operation, the Kawerau GPP is evaluated only from 2006. In the case of the Imperial zone, there were some seismic events before injection began. However, the focal depths of these events, as well as their magnitudes, are considerably higher than the range of events that occurred after the GPP operation starting date. Thus, it can be inferred that the available catalog of the Imperial zone also contains no tangible and affecting background seismicity. In the end, after all of these controls for selecting the data, it is still possible that a limited number of unrecognized tectonic earthquakes exists in the catalog.

The statistical relationships between the frequency and other features of earthquakes and the injection rate of geothermal power plants was studied in previous research works (Majer et al. 2007; Shapiro et al. 2010; Halldorsson et al. 2012; Kwiatek et al. 2015). However, most of these earlier works focused on the statistical analysis of induced seismicity caused by the water injection in a single well. In this study, with a regional perspective, the effect of water injection in multiple active wells in the different GPP zones is considered. It is helpful to develop a probabilistic model capable of simulating seismicity considering GPP zones with multiple injection wells. From the risk assessment point of view, it is not enough to know the effects of only a single injection well. In an area with several wells, their cumulative effects are important on the people, buildings, and other infrastructure of the region. In this regard, the statistical properties of the main characteristics of earthquakes induced by geothermal power plant activity are evaluated for all the GPP zones, including moment magnitude (M_W), focal depth (D), and the distance of the epicenter of seismic events to the GPP site (R). All of these parameters are important and effective in the imposed seismic risk to the built environments in the vicinity of GPPs. M_W is implicitly a measure of released energy in these earthquakes, while focal depth can show the relationship between the depth of injection wells and the hypocenter of earthquakes. In addition, the distance of the event epicenter to the GPP site shows the radius around the GPP zone, in which the earthquake occurrence is probable.

The frequency and cumulative density function (CDF) of these parameters in each of the GPPs, as well as the empirical cumulative probability density functions of observing an earthquake, with a given value or less for each of the parameters, is illustrated in Fig. 4. The figure indicates that the moment magnitude of events varies almost from 0.5 to 3, and in very rare cases, it goes above 3, while still remaining below 4. The medians of observed moment magnitudes are 1.10, 1.75, 1.70, and 1.40 for the Imperial, Geysers, Kawerau, and Rhineland GPP zones. Most of these events occur in shallow depths. The focal depth of recorded events ranges from 1 to 10 km (considering the imposed limit on the focal depth) with the medians of 4.3 km, 4.5 km, 5.0 km, and 4.0 km for the Imperial, Geysers, Kawerau, and Rhineland GPP zones. The comparison of these values with the well depths of Table 1 shows meaningful consistency. In some cases, however, the focal depths are higher than the maximum well depth, which can either be due to the changes in the pore pressure level in the deeper crust layers (Brown and Ge 2018) or the uncertainties in their estimation process. In addition, the epicenter-to-GPP distance of catalog seismic events depicts most of the earthquakes occurring close to GPP stations. They started from 100 m, while the medians for the Imperial, Geysers, Kawerau, and Rhineland GPP zones are 2.8 km, 1.3 km, 2.9 km, and 1.8 km, respectively. Approximately, 93% of the induced earthquakes occur within a 10 km radius of GPP zones. It is also important to note that there are some levels of uncertainty in the reported epicentral location of the events, which can affect the calculated distance, especially in a short distance range (Woessner et al. 2010). Many of the databases used in our model have increased their accuracy over time. In addition, in the case of a distance calculation, at each GPP site, the GPP central location is first calculated by averaging the latitude and longitude of all injection wells. Then a radius of 25 km is considered for selecting the events. After that, the distance of each event is obtained as the distance between the event epicenter and the nearest GPP well in each zone. Therefore, injection in multiple wells simultaneously can leads to a higher range of distances, in comparison with the case of considering earthquakes due to injecting water in only a single well.

The relationship between the injection rate and the moment magnitude is another important variable in understanding the induced seismic events by the GPPs. Fig. 5 represents the variation of monthly injection rate, as well as the average and maximum magnitude of seismic events per month for all periods of GPPs operation. Despite the increase in the injection rate during the operational years, there are no general significant changing trends in the average and maximum magnitude of monthly earthquakes. In the Kawerau zone, a slight increase is observable in both parameters, but in the Imperial and Rhineland zones, a gradual reduction is seen. Finally, in the Geysers zone, no significant change is visible.

To assess the features of moment magnitudes of induced seismic events more precisely, the Gutenberg–Richter (Gutenberg and Richter 1954) equation in the logarithmic form is considered and its coefficients are calculated for each of the four GPPs’ catalog considering M_C.

where a and b are the Gutenberg–Richter (G–R) coefficients. M is the moment magnitude and N is the number of events with a magnitude greater than M.

To investigate the effect of GPPs’ injection rate on the G–R coefficients, first, the available catalogs for all GPP zones are divided into different groups per their injection rates. Therefore, bins of 500 l/s are considered based on the availability of data at different injection rates. Next, for each group of each GPP zone, a separated G–R equation is fitted, and the coefficients are obtained. Fig. 6 shows the fitted G–R equations and observed data for all GPPs, which implies good fitness. Table 4 reports the a and b coefficients of all GPPs for different injection rates (IR). The rise in the injection rates increases the a-value, while the b-values at different zones do not follow a tangible monotonic trend. The b-values vary around 1.05−1.33, 1.06−1.28, 0.73−1.07, and 0.8 for the Geysers, Imperial, Kawerau, and Rhineland, while the a-values of these GPP zones are around 3.5−5.94, 3.11−4.37, 3.18−4.43, and 3.07, respectively. In the previous works, for the Geysers (Leptokaropoulos and Staszek 2019), Imperial (Cheng and Chen 2018), and Rhineland (Cuenot et al. 2008), the average of b-values equals to 1.05−1.25, 0.78−1.07, and 1.29, respectively. Some of these values slightly differ from the average of b-values in this research, which can be due to the usage of different event catalogs. However, by considering the results of Table 4 for different injection rates, the proposed results of previous research works are in the same ranges as those of this study.

We compared the main characteristics of the proposed database in this study with the ones presented and used in the previous research works by other scientists. As is shown in Table 5, the proposed catalog of this research covers a wider range of data from different GPP zones in different countries than does previous research. Also, the covered ranges of injection rates, moment magnitudes, focal depths, and time periods of collected data are significantly broader than the available databases. Therefore, this developed database will provide more opportunities for researchers to study the features and characteristics of GPP-induced earthquakes in the future.

In this part of the article, a model is developed through a probabilistic framework to consider the uncertainties related to the induced seismicity by GPPs operation.

This research dealt with the important challenge posed by induced seismicity initiated at geothermal power plants around the world. Accordingly, power plant information and the corresponding seismic data related to four important GPP zones worldwide were collected. These data are statistically analyzed, and their main characteristics, consisting of event magnitude, focal depth, and epicenter-to-GPP distance, are rigorously examined. From an engineering perspective, a probabilistic model was developed and validated that is capable of simulating random seismic events induced by GPPs. This model is a tool in the hand of the earthquake and structural engineers and scientists who are interested in evaluating the seismic risk of induced earthquakes by GPPs on the built environment via sampling methods such as Monte Carlo since it provides the opportunity to simulate future probable earthquake event scenarios.