INTRODUCTION

In (Smirnov et al., 2017; 2018a), based on the earthquake catalog data for the entire period of seismological observations in the Koyna–Warna area of reservoir-triggered seismicity in Western India, we analyzed seasonal seismicity variations due to annual fluctuations of water levels in the reservoirs. It is shown that seasonal seismicity is minimal in May–June when water levels in the reservoirs are lowest. During the rest of the year, the seismicity has three peaks: the fall peak in September, the winter peak in November–December, and the spring peak in February–April. The first peak occurs when water level reaches its seasonal maximum and can be considered as an immediate response of the medium to the applied impact. The two subsequent maxima correspond to the falling phase of the water levels and can be considered as the delayed responses.

The changes in seismicity due to various local natural and anthropogenic geodynamic processes are typically accompanied by the changes in the slope (b-value) of the frequency–magnitude relationship (FMR) (e.g., the review (El-Isa and Eaton, 2014)). The changes in the b-value indicate scale redistribution of a fracture process and may contain information about the nature and scenarios of excitation or relaxation of the seismic process (Smirnov and Ponomarev, 2020). From this standpoint, it is interesting to examine the b-value variations during seasonal fluctuations of seismic activity in the regions of induced and triggered seismicity which include the Koyna–Warna reservoir area.

The first analysis of seismicity associated with artificial reservoirs was conducted by Carder (1945) who investigated Lake Mead—a reservoir formed by the Hoover Dam built in 1931–1936 on the Colorado River, U.S. Interest in studying the effect of reservoir filling on seismicity has increased in the 1960s after several strong earthquakes caused by dam construction: Xinfengjiang, China, 1962, M = 6.2; Kariba, Zambia–Zimbabwe border, 1963, M = 6.2; Cremasta, Greece, 1966, M = 6.3; and Koyna, India, 1967, M = 6.7 (Gupta, 1992; Wilson et al., 2017). The general review of the state of the art of the subject matter is presented, e.g., in (Gupta, 2002; Ellsworth, 2013). Most of the works analyze the magnitude of induced seismic activity; however, there are also publications investigating self-similarity parameters of seismicity. In particular, Smirnov et al. (2018b) and Ruiz-Barajas et al. (2019) revealed the increases in the b-value during filling of the reservoirs formed in seismic regions.

Changes in the FMR b-value have been observed in the seismicity associated with fluid injection in wells (Cuenot et al., 2008; Smirnov et al., 2010; 2013; Bachmann et al., 2011; Vlcek et al., 2014; Martínez-Garzón et al., 2014; Huang and Beroza, 2015; Kwiatek et al., 2015; Mousavi et al., 2017; Alba et al., 2020). In (Smirnov et al., 2010; 2013; Bachmann et al., 2011) it is shown that the development of swarm-like microseismicity caused by water injection in deep wells in geothermal areas is accompanied by a decrease in the b-value with time and with the increase in the fluid injection pressure. Cuenot et al. (2008) and Martínez-Garzón et al. (2014) note a change in the b-value with increasing rate and volume of fluid injection. Vlcek et al. (2014) observed a decrease in the b-value with distance from the injection well. Huang and Beroza (2015) note a drop in the b-value during the main sequence of the Guy–Greenbrier seismic swarm, Arkansas, caused by fluid injection into wells. Mousavi et al. (2017) associate the detected spatial and temporal changes in the b-value in the area of waste water injection into wells with the spatial differences in the arising pore pressure and its changes over time. Besides, a convex-shaped magnitude-frequency distribution (MFD) (Huang and Beroza, 2015; Mousavi et al., 2017) and a change in the slope of the earthquake-size distribution during activation of induced seismicity (Vorobieva et al., 2020) are noted, which the authors of the cited papers attribute to the nonuniform development of the fracturing and to the stress redistribution due to fluid injection. This hypothesis agrees with the conclusions of (Smirnov et al., 2010; 2013) about a gradual formation of the defect structure in the near-well environment under water injection.

There are also known cases of the changes in the b‑value of induced seismicity caused by rock compaction due to fluid extraction from underground reservoirs (Bourne et al., 2014).

The diminution in the b-value reflects the enhancement of fracture process on higher scale levels. According to the avalanche-unstable fracture formation concept, this transition is realized through the enlargement of seismogenic faults due to the coalescence of smaller fractures (Sobolev, 2019). In the conditions of industrial geotechnical facilities, the enlargement of sources and, hence, the increase of energies of induced earthquakes is dangerous. In the case of fluid injection into deep wells in geothermal areas, the fact that the gradually increasing earthquake magnitudes reach a certain threshold value is an argument to modify the injection conditions so that to ensure safe operations (Kim et al., 2018; Kwiatek et al., 2019; Langenbruch et al., 2020). The decrease in the b-value is also considered as a parameter for controlling the conditions of water injection in wells (Broccardo et al., 2019; Langenbruch et al., 2020).

Seasonal (annual) variations in seismicity are driven not only by annual changes in water levels in man-made reservoirs (Simpson et al., 2018; Gupta, 2002; Ellsworth, 2013; Gahalaut, 2021) but also modulated by seasonal changes in natural surface hydrological load including precipitation, ice and snow loads (Panza et al., 2011, 2018; Ueda and Kato, 2019). The latter are estimated at a few kPa (Christiansen et al., 2005; 2007; Bettinelli et al., 2008; D’Agostino et al., 2018; Xue et al., 2020), which is an order of magnitude lower than surface load variations driven by seasonal water level fluctuations in reservoirs and comparable to the stresses induced by the Earth’s tides (Manga and Wang, 2015). These impacts are considered as triggering. The intensity of seismicity modulation by seasonal loads on the crustal surface is associated with the peculiarities of tectonic processes (Peresan et al., 2017; Panda et al., 2018; Smirnov et al., 2018a; Gao et al., 2000) and with the changes in the pore pressure and water content of rocks due to surface water infiltration into the upper crustal layers (Panda et al., 2018; D’Agostino et al., 2018; Farquharson and Amelung, 2020). We have not found any special studies of the b-value in the seasonal seismicity variations caused by reservoir operations or surface meteorological loads. Bollinger et al. (2007) only note the difference in the magnitude–frequency graphs for the summertime and wintertime events, which the authors attribute to the difference in the seasonal modulation of earthquakes of different magnitudes. Mallika et al. (2013) studied the changes in the b-value before the M4+ earthquakes in the Koyna–Warna reservoir area. The authors have found that the decreases in the b‑value before the M4+ earthquakes (corresponding to the known precursory scenario) are observed during the phase of increasing loading in the region during the seasonal filling of the reservoir and not observed during the unloading phase. The question about the nature of the revealed effect is not discussed.

The changes in earthquake swarm activity with a presumably fluid initiation of seismicity are discussed in a number of papers (Gibowicz, 1973a; 1973b; Kundu et al., 2012; Laderach et al., 2012; Fischer et al., 2014; Jenatton et al., 2007; Horalek et al., 2015; Potanina et al., 2011; Passarelli et al., 2015). Some detailed studies revealed temporal variations in the b-value (Chiba and Shimizu, 2018; Jenatton et al., 2007; Potanina et al., 2011; Passarelli et al., 2015). In particular, Potanina et al. (2011) and Passarelli et al. (2015) note a decrease in the b-value during the activation (growth) stage of swarm activity and an increase at the relaxation stage.

DATA

Induced seismicity in the Koyna–Warna region is a classic object of study. The state of the art of the research and the results achieved to date are described in the reviews (Yadav et al., 2016; Mikhailov et al., 2017). Two networks of seismological observations covering different time intervals have been deployed in the region. Correspondingly, there are two seismic catalogs based on these observations: the catalog for 1964–2015 compiled by Maharashtra Engineering Research Institute (MERI), India (Maharashtra, 2015) and the catalog for the period starting from 2005 compiled by National Geophysical Research Institute (NGRI) (Shashidhar et al., 2019). The local magnitude scales of these catalogs differ, which affects, in particular, the numbers of the relatively strong earthquakes reported in different publications (more details are presented in (Smirnov et al., 2017; 2018a)).

The absence of a dense seismic network during the impoundment of the Koyna reservoir precludes statistical analysis of the changes in the parameters of seismicity caused by reservoir filling, as it was done, e.g., for the Nurek reservoir (Smirnov et al., 2018b). However, the existing seismic data allow for b-value estimation for the seasonal components of induced seismicity identified in (Smirnov et al., 2017; 2018a).

As in our previous works (Smirnov et al., 2017; 2018a), in this study we consider the data of the MERI catalog (Maharashtra, 2015) covering a longer time interval than the NGRI catalog. The MERI catalog contains a total of 6996 earthquakes. The preliminary analysis of the data has revealed three stages in the catalog corresponding to the upgrading of the seismic network and characterized by a stepwise decrease in the magnitude of completeness (Smirnov et al., 2017) from 4.2 in 1962–1983 to 3.0 in 1983–1995 and to 2.0 in 1995–2015. In order to ensure data homogeneity in terms of magnitude of completeness, we selected the catalog events with magnitudes starting from 3.0 and chose the time interval from 1983 to 2015. This interval overlaps the time span of the impoundment of the Warna reservoir in 1985–1993 and its operation. The working catalog of the M3+ earthquakes for these 33 years contains 596 events, i.e., on average, 18 events per year or 1.5 events per month. Figure 1 shows the graph of the magnitude–frequency distribution based on these data.

Fig. 1.
figure 1

Magnitude–frequency graphs of M3+ earthquakes in Koyna–Warna area based on MERI catalog (Maharashtra, 2015): (1) histogram of catalog data, statistical errors of histogram are shown in gray; (2) Gutenberg-Richter approximation.

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SEASONAL VARIATIONS IN b-VALUE

With an average seismicity rate of 18 events per year, the volume of the M3+ working catalog does not allow for obtaining the b-value estimates within each annual cycle; therefore, we used the superposed epoch analysis procedure which proved to be effective in studying various patterns of transient seismicity (Hainzl, 2004; Rodkin, 2008; Smirnov and Zavyalov, 2012). Thus, we compiled a composite annual catalog which comprises the earthquakes occurred during the entire 33-year period ordered with respect to their intra-annual time of occurrence, with the year of occurrence disregarded (the time of the event in the composite catalog is its time of occurrence in a year regardless of the specific year itself). The composite catalog provides the statistics of 50 events per month which allows for computing moving-window estimates of the seismicity parameters and identifying their intraannual variations.

In 1999, 2000 and 2005, the region was hit by the relatively strong earthquakes accompanied by the aftershocks, which, given the rather small overall statistics, distorts the estimates substantially. Therefore, we totally excluded these years from the analysis, and the total number of the events dropped accordingly to 512 (43 events per month).

Figure 2 shows the seismicity rate (number of earthquakes per unit time) and the b-value calculated from the composite catalog data. The seismicity rate values estimated from the composite catalog were reduced to the initial level (without epoch superposition). The upper- and lower-bound estimates of the b‑value were calculated using the modified maximum likelihood method (Potanina et al., 2011) which takes into account the systematic bias arising in the case of right censoring of data. The seasonal time is measured from the beginning of water level increase in the reservoirs. The annual cycle is closed in a circle so that January follows December. For clarity, the annual cycle in Fig. 2 is repeated twice in order that the “slitting up” of the year does not interfere with seeing the entire picture of the variations. The identical repeating annual cycles are separated in Fig. 2 by a vertical dashed line.

Fig. 2.
figure 2

Seasonal variations of seismicity rate and b-value in Koyna–Warna area of reservoir-triggered seismicity: (1, 2) annual component of water levels in Koyna and Warna reservoirs, respectively (reservoir depths in vicinity of dams); (3) seismicity rate, confidence interval of estimates is shown by color filling; (4, 5) b-value lower- and upper-bound estimates (using the method of (Potanina et al, 2011)) and their confidence intervals (shown in gray). Annual cycle in diagram is repeated twice, vertical dashed line shows boundary between repeated images.

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The color filling in Fig. 2 shows the one-sigma confidence intervals for the seismicity rate and b-value estimates. However, given the small size (40–50 events) of the monthly samples of the composite catalog (40–50 events), the standard confidence intervals based on the asymptotic estimates may not be quite correct. Therefore, statistical modeling was performed on random synthetic catalogs.

The stochastic modeling was carried out, firstly, in order to obtain a direct estimate of the variability of b‑value and seismicity rate with a sample’s volume corresponding to the real earthquake catalog. Secondly, the presence or absence of a purely methodological correlation between the estimates of the b‑value and earthquake rate was checked: the known bias of the maximum likelihood estimate (MLE) can appear as a change in the b-value estimate with changing sample’s volume, and in the case of simultaneous estimation of the seismicity rate and b-value, the MLEs can be correlated (Sadovsky and Pisarenko, 1991).

Stochastic modeling was conducted through generating a synthetic catalog with given event distributions in time and magnitude. The multiply generated synthetic catalogs were then subjected to the same analysis as the real seismic catalog, with calculating the mean estimates and standard deviations of seismicity rate and b-value (Smirnov and Ponomarev, 2020).

The procedure of generating a synthetic catalog included creating two independent datasets of the same volume: a dataset of the event times and a dataset of the event magnitudes.

The dataset of the event times of the synthetic catalog was formed based on random generation of exponentially distributed time intervals \({{{{\tau }}}_{i}}\) between successive events (corresponding to the Poisson point process):

$$P\left( \tau \right) = \alpha {{e}^{{ - \alpha \tau }}}.$$
(1)

In contrast to (Smirnov and Ponomarev, 2020), the distribution parameter \({{\alpha }}\) was not constant but slowly varied with time simulating seasonal seismicity variations. For parameter \({{\alpha }}\), we adopted the following formula:

$$\alpha \left( t \right) = {{\alpha }_{0}}\left( {1 + \beta \cos \left( {\frac{{2\pi }}{T}t + \varphi } \right)} \right).$$
(2)

Period \(T\) was specified at 1 year; parameters \({{{{\alpha }}}_{0}}\) and \({{\beta }}\) were determined from the real catalog data: \({{{{\alpha }}}_{0}}\) is the average seismicity rate (the ratio of the total event number to the length of the total time interval); \({{\beta }} = \frac{{{{A}_{{{\text{max}}}}} - {{A}_{{{\text{min}}}}}}}{2}\) is half of the peak-to-peak seismicity rate. We did not seek to fit the curve of the seismicity rate of the synthetic catalog to that of the real catalog. The variable seismicity rate was introduced to check whether there is an artifactual correlation between the estimates of b-value and seismicity rate with the available volume of catalog data. The phase \({{\varphi }}\) was not considered and for simplicity set to zero in (2).

The dataset of magnitudes was created by generating random numbers with exponential distribution

$$P\left( M \right) = \lambda {{e}^{{ - \lambda M}}}$$
(3)

with \(\lambda = b\ln 10\), which corresponds to the Gutenberg–Richter law with parameter \(b\). The b-value was assumed to be 1.4—the b-value calculated over the entire seismic catalog. The random magnitudes generated according to the distribution (3) were added to the magnitude of completeness of the real catalog \({{M}_{0}} = 3\).

The generated synthetic catalog has the same size as the real catalog—it includes 512 events. Each event in the synthetic catalog was assigned a time value from the generated time dataset and a magnitude value from the magnitude dataset. Then, based on the synthetic catalog, a composite annual catalog was created in the way as it was done for the real catalog and the moving-window estimates of the seismicity rate and b-value were calculated using the same programs as for the real catalog. This procedure was repeated numerous times, and the mean values and standard deviations of the estimated parameters were calculated. Based on the special tests, we selected the version with 10 000 repetitions.

The results of the stochastic modeling on random catalogs are shown in Fig. 3 which also depicts the b‑value estimates from the real catalog (see Fig. 2).

Fig. 3.
figure 3

Seismicity rate and b-value based on stochastic modeling data: (1) seismicity rate based on random catalog according to formula (2), one-sigma interval is shown by color filling; (2) b-value based on random catalog, with parameter \({{\lambda }}\) in formula (3) constant in time; one- and two-sigma intervals are shown by color filling 3 and dashed lines 4, respectively; (5, 6) b-value estimates for real catalog (coincide with curves 4 and 5 in Fig. 2).

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It can be seen in Fig. 3 that the estimates of the constant b-value specified in the model do not change with the changes in the seismicity rate in the random catalog. This means that with actual sample volumes, artifactual correlation between the estimates of the b‑value and seismicity rate is absent.

The estimates of the relative error (the standard deviation to mean ratio) from the data of the stochastic modeling yield, on average over the entire time interval, 0.086 for the b-value and 0.080 for the rate of seismic activity. The relative errors for the real data (shown in Fig. 2) estimated as the ratio of the MLE error to the estimated quantity itself are 0.083 for the b-value and 0.082 for the seismicity rate. The latter practically coincide with the “direct” estimates of the corresponding quantities based on stochastic modeling, which indicates the correctness of the asymptotic estimates of the MLE errors on the statistics of the actual sample sizes of 40–50 events. Therefore, in the analysis and interpretation, one can use the confidence intervals shown in Fig. 2.

Figure 3 shows that the seasonal variations in the b‑value estimated from the real catalog go beyond the one-sigma interval (66% level of significance) but are within the two-sigma interval (96% level of significance) of the random catalog with a constant distribution parameter (3).

DISCUSSION

In Fig. 2 it can be seen that the rate of seismic activity reaches its absolute maximum in December–March, during the period of water level fall in the Koyna and Warna reservoirs. A small relative increase in seismicity rate is also observed in September–October when the water level in the reservoirs is close to its annual maximum. These seasonal maxima in seismic activity in the Koyna–Warna region have been previously detected using other methods both based on the MERI (Smirnov et al., 2017; 2018a) and NGRI catalogs (Arora et al., 2017). The activation of seismicity in September–October is interpreted as an immediate response to the water level rise in the reservoirs due to the immediate buildup in the pore pressure resulting from the additional compression of the rock matrix under the weight of the reservoir water. The maximum in February–March is considered as a delayed response. In Fig. 2 (on the composite annual interval), this maximum merges with the additional winter activation in December–January which appeared after 2005 (Smirnov et al., 2018a). The delay of the response relative to the maximum water levels in reservoirs is believed to be due to the pore pressure buildup caused by gradual diffusion of water into the Earth’s crust through the bottom of the reservoir (Durá-Gómez and Talwani, 2010; Simpson et al., 2018). An alternative interpretation of the peak activity in December–March coinciding with the fall of reservoir water levels is the idea of H. Gupta who hypothesized that the reservoir-triggered seismicity is affected by the unloading of a region during the decreases in the water levels in the reservoirs (Gupta, 2001).

In our previous publications we noted that the ratio between the maxima of seasonal seismicity in the immediate and delayed responses varies with time (Smirnov et al., 2018a; Smirnov and Ponomarev, 2020). The immediate response after filling the Warna reservoir was substantially weaker than after filling the Koyna reservoir, whereas the delayed response, on the contrary, has increased. The dominance of the delayed response over the immediate response is clearly seen in Fig. 2. We recall that the results shown in Fig. 2 are derived from the data for 1983–2015, i.e., mainly during and after the filling of the Warna reservoir in 1985–1993. In (Smirnov et al., 2018a), we hypothesized that that the seasonal response of seismicity during the filling of the Warna reservoir differs from the response during the filling of the Koyna reservoir because of the different conditions of fluid initiation: in contrast to the Koyna reservoir, the Warna reservoir was filled in the vicinity of the region of reactivated seismicity, whereas the Koyna reservoir filling took place in the aseismic region.

The graph of the seasonal variations in the b-value in Fig. 2 shows that there are two maxima and two minima during the year. The minima in October and March are approximately concurrent with the months of the maxima in the seasonal seismic activity: immediate (September–October) and delayed (February–March).

The maxima in the b-value (the peaks in January and September-August) cannot be unambiguously attributed to a certain phase of seasonal seismicity: the autumn maximum falls on the minimum in the seismicity rate, whereas the January maximum covers the maximum in December–January. At the same time, neither fall on the minimum or maximum of reservoir water levels, but both occur during the intervals of water level rises or falls. Thus, it is not clear whether the times of the maxima in the b-value should be correlated to the pattern of changes in seismic activity or to the cycle of water level fluctuations. In the attempt to elucidate this, we analyzed the data of the laboratory experiment on cyclic fluid initiation of the fracture process in a sample of granite.

LABORATORY EXPERIMENT

The experiment was carried out in the Geophysical observatory “Borok” of Schmidt Institute of Physics of the Earth of the Russian Academy of Science (IPE RAS). A general description of the laboratory instruments is presented in (Patonin et al., 2013; 2018). The tested granite sample KBH-5-548-1 was taken from a depth of 548 m from the Phansavale well (KBH05) (Khanna et al., 2020) as part of the scientific deep drilling program in the Koyna–Warna region of reservoir-triggered seismicity, western India (Gupta, 2017). The seasonal pore pressure variations caused by the reservoir water level fluctuations were modeled in the laboratory experiments by given cyclic increases and decreases in the pore pressure of water in the tested sample.

The experiment was conducted at constant confining pressure of 10 MPa. Axial loading tests were performed with strain control. Before water injection, the sample was loaded to 100 MPa (~90% of ultimate strength), then the load was reduced to 90 MPa and water injection began. Water was pressurized into the pore space of the sample through one end face, and the other face was impermeable to water (Fig. 4).

Fig. 4.
figure 4

Loading history of granite sample KBH-5-548-1: (1) axial strain created by press punch displacement; (2) axial load; (3) confining pressure; (4) pore pressure; (5) AE activity.

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Injection of water into the dry sample caused the formation of a macrofracture through the entire sample, accompanied by intense acoustic emission (AE) and drop of axial stresses due to the reduction of the bearing capacity of the sample (a more detail description and discussion of this stage of the experiment is presented in (Smirnov et al., 2020)). The formation of a macrofracture in the sample can be considered as a model analog of the in situ formation of the Donichawadi fault zone along the strike of the source of the M6.3 earthquake of December 10, 1967 which occurred in the vicinity of the Koyna dam after watering of part of the Earth’s crust due to the impoundment of the reservoir (Smirnov et al., 2018a; Goswami et al., 2020).

At the stage of cyclic increases and decreases of the pore pressure, the axial strain rate was kept constant, and the stress variations seen in the graph in Fig. 4 reflected the changes in the effective mechanical properties of the sample.

Recording the acoustic signals by the system of acoustic sensors located on the cylindrical surface of the sample allowed the formation of a catalog of acoustic events similar to the earthquake catalog. However, the size of the acoustic catalog proved to be insufficient for statistical analysis.

A special sensor built into the punch of the press and pushed by it against the end face of the sample provides a much higher sensitivity which allows obtaining an order of magnitude larger samples of pulses corresponding to the acoustic events. The set of the times and amplitudes of these pulses is similar to a seismic catalog recorded by a separate seismic station. These data do not allow locating the AE sources but they are suitable for analyzing the integral (over the entire sample) changes in seismic activity and b-value with time. As the energy class of the acoustic events we used the quantity \(K = 2\log A\) where \(A\) is the amplitude of the AE pulse in arbitrary units. Absolute calibration of the sensor was not performed and therefore it was not possible to correlate the \(A\) value to the absolute displacement in the acoustic wave. More details on the AE recording system and the principles of the analysis of AE signals are presented in (Smirnov and Ponomarev, 2020).

We analyzed the data of two series of the tests with controlled changes in the pore pressure (Fig. 4). Each series consisted of three cycles of smooth increases and decreases of pressure. We selected this experimental procedure according to the shape of the water level variations in the reservoirs (see Fig. 2).

As in the analysis of seasonal seismicity variations in the Koyna–Warna region, in the laboratory experiment we also used the superposed epoch method. For each series of the three cycles of increasing and decreasing pore pressure, we compiled a composite catalog of AE events. Based on this catalog, we calculated the estimates of the changes in the acoustic emission rate and in the b-value using the same techniques as when analyzing variations in seismicity. As an example, Fig. 5 shows the magnitude–frequency (MF) graphs for each of the three cycles of pore pressure increases-decreases in the first series of tests and the magnitude–frequency graph for the composite catalog. It can be seen that the MF graphs for the individual cycles have a similar shape and a close slope, which supports the correctness of using the superposed epoch analysis method and the validity of the composite catalog as a catalog characterizing the entire series.

Fig. 5.
figure 5

Magnitude-frequency graphs for individual cycles (1, 2, 3) and composite catalog (4) of AE events of first series.

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Figure 6 depicts variations in acoustic activity and b-value for two series of cyclic pore pressure fluctuations shown in Fig. 4. As zero time, we took the moment when the pore pressure reaches the maximum in each cycle of the increase and decrease of pressure. As in the analysis of the field data, the estimate was conducted in a moving window with a given number of events which was shifted with a given step.

Fig. 6.
figure 6

Acoustic emission rate and b-value variations estimated from composite catalogs of acoustic emission in event windows containing 120 events shifted by 20 events: (a) first series (pore pressure change by 1 MPa); (b) second series (pore pressure change by 2 MPa); (1) pore pressure; (2) AE rate, (3) b-value; (4) energy class K of AE events.

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In Fig. 6 it can be seen that acoustic activity reaches its maximum approximately at the maximum pore pressure. The patterns and probable nature of the delays of fluid-initiated activation of the fracture process are discussed in detail in (Smirnov et al., 2020), including for the granite sample tested in this study, and here, we do not touch upon this issue.

Figure 6 also shows that the minimum b-value falls approximately on the maximum activity, as it was noted for seasonal seismicity in the Koyna–Warna region (Fig. 2). In the experiment, just as in the natural (field) conditions, during one cycle of the increasing–decreasing pore pressure, the b-value has two maxima. The first maximum falls on the phase of pressure increase. The second maximum occurs at the pressure decrease phase but is observed on the different segments of the decrease interval in the two studied series. In the second series, there is also an additional maximum at the pressure drop phase, but its amplitude and statistical significance are lower than those of the two main maxima. It is not yet clear whether the difference of the b-value peculiarities in the first and second series is natural or accidental. But we can confidently conclude that in the considered experiment, the b-value during one cycle of increasing-decreasing pore pressure has two maxima and one minimum.

SUMMARY

In the case of seasonal variations in seismicity in the Koyna-Warna region, we see two cycles of increase and decrease in the rate of seismicity and two cycles of change in the b-value within a year. We attribute this “duplication” to the presence of two mechanisms of initiation of induced seismicity, known as the immediate and delayed responses. These mechanisms were initially identified during the impoundment of the reservoirs (Simpson, 1988) but they are also observed during reservoir operation under a change in the water level in the reservoir (Durá-Gómez and Talwani, 2010; Simpson et al., 2018; Smirnov et al., 2018a). According to these mechanisms, each of the two maxima of the induced seismicity falls on the maximum of pore pressure (this is a simplified version that does not take into account the probable delay of the response relative to the pore pressure due to the finite speed of the developing fracture process (Smirnov et al., 2010; Smirnov and Ponomarev, 2020) or due to the contribution of the rate of change of the water level and pore pressure into the activation of seismicity (Mirzoev et al., 1987; Kapustyan and Yudakhin, 2007; Durá-Gómez and Talwani, 2010). Pore pressure reaches its first maximum at the moment when the reservoir water level is highest due to the immediate (on the time scale of the annual period of water level fluctuations) compression of the pore space of the rock matrix by water column pressure on the reservoir bed. The second pore-pressure maximum which causes the second maximum of seismicity initiation is associated with the time when the diffusion pressure wave in the fault system reaches the earthquake generation area.

The studied b-value variations within the annual cycle show that the minimum b-values fall in the intervals of the maxima of triggered seismicity described above. The same effect was observed in the non-volcanic seismic swarms of presumably fluid origin (Potanina et al., 2011), and its connection with fluid initiation of fracture was demonstrated in the laboratory experiment (Potanina et al., 2015). The generalization of the data on the dynamics of different transient seismicity patterns suggests that this effect is characteristic of transient regimes ovberall (Smirnov and Ponomarev, 2020).

In the pilot laboratory experiment whose results are presented in this paper, the minimum b-value also falls in the interval of the maximum acoustic activity initiated by the pore fluid pressure.

The maxima in the b-value during the annual cycle of natural seismicity, at a first glance, cannot be unambiguously attributed to the peculiarities of variations in seismic activity. However, both maxima seem to be associated with the changes in water levels in the reservoirs: one maximum corresponds to the water level rise phase, and the other, to the fall phase. The laboratory experiment has demonstrated the correlation of the maxima in the b-value to the rise and fall of the pore pressure.

A more detailed comparison of the laboratory and field results should take into account the fact that the laboratory experiment did not perfectly mimic the presumed regime of natural pore pressure fluctuations. The experiment was conducted without modulation of axial load on the sample which could simulate seasonal fluctuations in the loading conditions on the reservoir’s bed, and the stress variations observed in Fig. 4 during the increase–decrease cycles of the pore-pressure are a consequence rather than a cause of failure. In the experiment, we simply set the change in the pore pressure without relating it to the above two mechanisms of the increase in the pore pressure in natural conditions. Our experiment did not allow for the probable differences in the effects of initiation of the fracture process by the increase in the pore pressure due to rock matrix compression in the entire volume (reduction in the volume of the fluid-filled pore space) or by the increase in the pore pressure due to the propagation of its front from the surface towards the interior regions with finite diffusion velocity. Thus, we implicitly assumed that the increase-decrease pore pressure cycle specified in the experiment and the associated increase–decrease cycle of acoustic activity simulate both the instantaneous and delayed responses in natural seismicity. This assumption has not yet been proven, precluding a sound reasoning about the mechanisms of the connection between the b-value in induced seismicity and the fluid regime.

In natural conditions, the connection between the dynamics of the delayed response of seismicity and the change in the reservoir water levels seems more complicated than the dynamics of the immediate response. The delayed response is thought of as connected with fluid diffusion front reaching the seismogenic zone, lowering the effective strength in this zone and thus causing intensification of the fracture process which is detected as the delayed response of seismicity. Given that fluid pressure is mainly transferred through a heterogeneous system of faults probably having different permeability and considering the obvious heterogeneity of the seismogenic zone, we cannot expect the dynamics of the delayed response to simply repeat the curve of water level fluctuations on the bottom of the reservoir with a shift in time by some average fluid diffusion time. This is confirmed for the Koyna–Warna region by the theoretical calculations (Durá-Gómez and Talwani, 2010; Gahalaut, 2021). Even if we consider a greatly simplified structure of the region, the pattern of the correlation between pore pressure variations at a depth of a few kilometers and changes in water levels in the reservoirs substantially depends on the supposed geometry of the fault structures in the region and their permeability as well as on a number of other poorly controlled parameters (Talwani, 2007; Gahalaut and Gupta, 2008; Gahalaut, 2021). In fact, we do not know the details of the spatiotemporal distribution of the pore pressure initiating the delayed seismicity response in the region of the reservoirs and, hence, the results of our simplified laboratory experiment cannot be directly compared with the complex dynamics of the delayed response in the natural in situ conditions.

The mechanism of immediate response of seismicity determines a simpler connection between the increase in surface loading on the underlying rock mass (due to the rise in reservoir water level) and the triggered seismic activity (Gahalaut, 2021). The mechanism does not prescribe a delay of the change in the pore pressure relative to the change in the load on the reservoir bed. Assuming that at the stage of immediate response in natural conditions, the temporal behavior of the pore pressure repeats the water level change in the reservoir, we can more confidently correlate the laboratory results to the in-situ observations.

Figure 7 shows the time interval of the curves in Fig. 2 corresponding to the immediate response. The beginning of the interval is specified at the beginning of the seasonal water level rise. Choosing the end of the interval with certainty is difficult because the delayed response may begin until the end of the immediate response. We cannot separate these two responses on the interval where they overlap, there we only consider the interval containing the local maximum of triggered seismicity.

Fig. 7.
figure 7

Seismicity rate and b-value on time interval corresponding to immediate response of seasonal seismicity. Designations are the same as in Fig. 2: (1, 2) annual component of water level in Koyna and Warna reservoirs, respectively; (3) seismicity rate; (4, 5) lower- and upper-bound estimates of b-value; color filling shows confidence intervals.

Full size image

At the water level rise stage (and, thus, at increasing pore pressure, in the context of the immediate response model), the b-value varies (Fig. 7) similarly to the b-value variations observed in the laboratory experiment (Fig. 6) where a slight increase in the b‑value is followed by a more significant decrease coinciding in time with the intensification of seismic activity. These changes corresponding to the crack coalescence and growth scenario (known in seismology as avalanche-unstable fracture formation model) are characteristic of the activation stage of many transient seismicity patterns (Smirnov and Ponomarev, 2020).

A certain delay of the maximum in the seismic response relative to the maximum in the reservoir water level (Fig. 7) can be related to both the delay of the increase in pressure in the rock, not accounted for in the model of immediate response, and to the kinetics of the fracture process itself (Smirnov and Ponomarev, 2020).

CONCLUSIONS

(1) Based on the combination of the technique of superposed epoch analysis with stochastic modeling of random earthquake catalogs, fine features have been identified in the behavior of seasonal components of the reservoir-triggered seismicity in the Koyna–Warna region, India.

(2) Seasonal variations in the Koyna-Warna seismicity caused by the annual variations in water levels in the reservoirs has two local maxima during a year, corresponding to the known mechanisms of immediate and delayed responses of reservoir seismicity.

(3) The b-value of the reservoir-triggered earthquakes varies in a regular way within annual cycle of seasonal seismicity. The minimum b-values fall in the intervals of the maxima in both the immediate and delayed seismic responses. The maxima in the b-value occur during the rise and fall phases of water levels in the reservoirs.

(4) In a pilot laboratory experiment with cyclic increase–decrease of pore pressure in a granite sample from a well in the Koyna–Warna area of reservoir-triggered seismicity, the pore-pressure maximum is observed during the maximum in acoustic activity and minimum in the b-value. The maxima in the b-value occur during both the rise and fall phases of pore pressure.

(5) The character of variations in seismic activity and b-value at the stage of activation of the immediate response of reservoir-triggered seismicity is consistent with the scenario of gradual redistribution of the fracture process from lower to higher scale levels, typical of the activation of transient seismicity patterns. Similar changes in the parameters of acoustic emission have been are observed in the laboratory experiment at the stage of activation of the fracture process by the increase in pore pressure.