Prognostic Anomalies of Induced Seismicity in the Region of the Koyna Warna Water Reservoirs, West India

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1 ISSN 69-5, Izvestiya, Physics of the Solid Earth,, Vol. 49, No., pp Pleiades Publishing, Ltd.,. Original Russian Text V.B. Smirnov, R.K. Chadha, A.V. Ponomarev, D. Srinagesh,, published in Fizika Zemli,, No., pp Prognostic Anomalies of Induced Seismicity in the Region of the Koyna Warna Water Reservoirs, West India V. B. Smirnov a,b, R. K. Chadha c, A. V. Ponomarev a, and D. Srinagesh c a Schmidt Institute of Physics of the Earth, Russian Academy of Sciences, ul. Bol shaya Gruzinskaya, Moscow, 995 Russia b Faculty of Physics, Moscow State University, Moscow, 999 Russia c CSIR National Geophysical Research Institute, Hyderabad, India Received June 5, Abstract In, the region of the Koyna Warna water reservoirs in West India was hit by two strong earthquakes, which occurred six months apart and had magnitudes M > 5. The Koyna Warna seismic zone is a typical region of induced seismicity with a pronounced correlation between seismicity and water level variations in the reservoirs. This indicates that the stress level in the region is close to critical; thus, insignificant variations in stress caused by the variations in the water level may trigger a strong earthquake. In order to study the preparatory processes in the sources of the induced earthquakes, in this paper we analyze the seismic catalogue for the Koyna Warna region before a pair of strong earthquakes of. The induced seismicity is found to exhibit prognostic variations, which are typical of preparation of tectonic earthquakes and indicative of the formation of metastable source zones of future earthquakes. Based on the obtained results, we suggest that initiation of failure in these metastable zones within the region of induced seismicity could have been caused by the external impacts associated with water level variations in the reservoirs and by the internal processes of avalanche unstable crack propagation. DOI:.4/S6958 INTRODUCTION The Koyna area in West India presents a classical region of induced seismicity, in which the earthquakes with a magnitude of above 5 occur as long as fifteen years after the initiation of seismicity due to the water reservoir being filled (started in 96) (Gupta and Rastogi, 979; Gupta, Rastogi, and Narain, 97; Gupta, 99; ; Gupta and Iyer, 984; Talwani, 997; Pandey and Chadha, ). The subsequent filling of the Warna water reservoir (started in 965) also resulted in the development of induced seismicity after the water level had reached its maximum (Rastogi et al., 997). The induced seismicity in the Koyna Warna region is of interest due to the fact that before the filling of the Koyna reservoir, this region was believed to be aseismic. Since detailed seismological observations were not conducted in this region at that time, it is quite possible that this area experienced some microseismic activity; however, strong earthquakes with M > 4.5 were absent. After the Koyna water reservoir was filled, high seismic activity arose in this area south of the reservoir, and in 967, the region was hit by the strongest earthquake with magnitude M = 6.. This event partially destroyed the dam. After the filling of the Warna reservoir, which is located 5 km southeast of Koyna, the seismicity spread further south to the region of the new water reservoir. At present, seismicity is concentrated within a relatively small volume of km between the Koyna water reservoir in the north and Warna in the south (Fig. ). The graphs in Fig. show the water level variations (the altitude of the water table above sea level) in the Koyna and Warna reservoirs. The earthquakes with M 4 are also indicated. It is remarkable that the relatively rapid filling of the Koyna reservoir (during two years) was followed by the strongest earthquake with magnitude M = 6.. The impounding of the Warna reservoir was slower by a factor of four; the corresponding strongest earthquake has the magnitude M = 5.5 and was preceded by the foreshocks, in contrast to the event of 967, whose foreshocks were not revealed. It is clearly seen that these strongest earthquakes are delayed with respect to the completion of filling the reservoirs (Simpson, Leith, and Scholz, 988). In (Srinagesh et al., ) it is noted that seismicity is correlated to the segmentation of the fault network. The study of the focal parameters, variations in the pore pressure, and nucleation of seismic sources provided an insight into the mechanics of the induced earthquakes (Chadha et al., 997). Gavrilenko, Singh, and Chadha () presented the hydromechanical model of seismic response. Attempts to predict moderate earthquakes in the Koyna Warna region were made in (Gupta, ). The prediction based on the data on water level variations presented in (Gupta et al., 7) allowed the authors to conclude that short-term prediction of the earthquakes in the region is possible. 4

2 44 SMIRNOV et al Koyna reservoir KRFZ NEZ Patan Faul WEZ 7. Warna reservoir 7. SEZ Fig.. The main faults and lineaments in the Koyna Warna region according to (Talwani, 997) and the three identified seismic zones: North Escarpment Zone (NEZ), South Escarpment Zone (SEZ), and Warna Seismic Zone (WSZ) according to (Singh, Bhattacharya, and Chadha, 8). The epicenters of the earthquakes are shown. The strongest earthquakes are marked by the uppointing (in the northern part of the region) and down-pointing (in the southern part of the region) triangles. The year of the event is indicated near the triangle. The present paper addresses the study of preparatory processes in the earthquake sources on the basis of the data in the catalogue on induced seismicity in the Koyna Warna region. The strong earthquakes in this region are thought to be initiated by the water level variations in the reservoirs. Here, it is assumed, either explicitly or implicitly, that the source zones of the impending earthquakes reside in an unstable state; thus, even insignificant (compared to the strength of the lithosphere) additional stress is sufficient for triggering an earthquake. According to the modern understanding, in the case of tectonic earthquakes, the unstable state of the source zones develops gradually (Sobolev, 99; ; Sobolev and Ponomarev, ), and the processes of preparation of the earthquake source are reflected in the variations of seismic parameters, which are referred to as prognostic anomalies. In, the Koyna Warna seismic zone was hit by two strong earthquakes, which occurred half a year apart and had magnitude M > 5. In order to study the characteristic features of the preparatory processes of the induced earthquakes, in the present work, we a posteriori apply the methods and algorithms that were initially developed for identifying the prognostic anomalies before the tectonic earthquakes for analyzing the induced seismicity before the two mentioned earthquakes. We selected this pair of spatially and temporally close earthquakes for a detailed study in the hope that this seismic doublet was preceded by sufficiently strong anomalies. INITIAL DATA We analyzed the data from the local earthquake catalogue for (Maharashtra, ). We selected this time interval because detailed seismic IZVESTIYA, PHYSICS OF THE SOLID EARTH Vol. 49 No.

3 PROGNOSTIC ANOMALIES OF INDUCED SEISMICITY IN THE REGION 45 information is available on it due to the deployment of a sufficiently dense seismic network in the Koyna Warna zone in 995 (Mandal, Mabawonku, and Dimri, 5). The catalogue contains information about 48 earthquakes with magnitude M. The catalogue was subjected to preprocessing that included identification of the aftershocks and estimation of the magnitude of completeness and its variations in time and space (Smirnov, 9). THE MAGNITUDE SCALE The catalogue provides local magnitudes M of seismic events. By analyzing the data from the local seismic network in the Koyna Warna region for , Mandal, Rastogi, and Sarma (998) derived the relationship that links local magnitude (coda length magnitude) M with seismic moment M and moment magnitude M w : log ( H m) = ( 8 ±.)M + ( 9.54 ±.4), () () The last formula indicates that the local magnitude is close to the moment magnitude. Dependence () provides the basis for deriving the relationship between the local magnitude and the physical parameters of the source (energy and size), which are used in the procedures for identifying the aftershocks and estimating the q value one of the parameters characterizing the seismicity (see below). In (Smirnov, ) it was noted that the proportion between the size l of the seismic source and the corresponding values of seismic moment and energy of the earthquake is described by the following formula: () loge( J) = logl( km) +. (4) Relationship () almost coincides with the Purkaru Berckhemer formula (Purkaru and Berckhemer, 98). We do not know the regional relationships between the local magnitude and physical parameters of the source, and therefore we have to use global average relations () (4). Substituting () into () and then into (4), we obtain or and M M w = (.948 ±.)M + (.5 ±.9). l( km) = - logm ( N m) 5.7, M =.7logl( km) + 4. logl( km) =.46M.89 loge( J) =.8M (5) (5a) (6) 66 М Time, year Fig.. The variations in the water level (water table altitude above sea level) and the earthquakes with M 4 in the Koyna Warna seismic zone: () Koyna; () Warna. Water table altitude above sea level IDENTIFICATION OF THE AFTERSHOCKS In order to eliminate the effects of anomalous clusters of the earthquakes on the estimated parameters of background seismicity, the catalogue should be cleaned from the aftershocks. The presence of spatiotemporal clusters of aftershocks underestimates the fractal dimension of seismicity and distorts the estimates of seismic activity. The anomalously low b-values (the slope of the frequency magnitude diagram for the main event) complicate statistical analysis of the time variations in this parameter (Kagan, 4; Helmstetter, Kagan, and Jackson, 6). The aftershocks are spatially and temporally localized groups of the earthquakes that are caused by the corresponding main events. In their statistical properties, the aftershocks differ from the ensemble of the background seismic events; therefore, in the study focused on background seismicity, the aftershocks are typically excluded from consideration. The analysis of the dynamics of aftershock sequences is a separate problem (Smirnov and Ponomarev, 4). The procedure of aftershock identification used in our study was developed and tested for sufficiently strong tectonic earthquakes, in which the source of the main event was significantly larger than the error of aftershock location (which allowed the authors of the algorithm to disregard the location error) (Molchan and Dmitrieva, 99; 99; 99; Molchan et al., 996). In our case, the location error indicated in the catalogue is km, which is commensurate with the size of the source of the earthquake (according to (5), the source with a size of about km corresponds to an earthquake with M = 4). It is also known that the parameters of the aftershock sequences differ between the induced and tectonic seismicity (Gupta, Rastogi, and Narain, 97; Gupta and Rastogi, 979). Due to these facts, it is insufficient to formally apply the procedure of aftershock identification: the results of identification require special analysis. IZVESTIYA, PHYSICS OF THE SOLID EARTH Vol. 49 No.

4 46 SMIRNOV et al. M ms M Aft.7.6 Bath s law validity area.5 M.4 ms M Aft =.6 ± M ms Fig.. The difference in magnitudes between the main event and the strongest aftershock. The interval corresponding to the Bath s law M ms M Aft =.6 ±.46 (according to (Shcherbakov qand Turcotte, 4)) is shaded in gray. M c Time, years Fig. 4. The variations in the magnitude of completeness of the catalogue: () the initial estimates; () the smoothed curve; () the average level over In order to assess whether the formal identification of the aftershocks is valid, we can use Bath s law (Båth, 965), according to which the difference in magnitudes between the main shocks and the strongest aftershock is a constant that does not depend on the magnitude of the main event. Shcherbakov and Turcotte (4) estimated this difference at.6 ±.46. Figure displays the difference between the magnitudes of the main event (M ms ) and strongest aftershock as a function of M ms for the aftershock sequences revealed by the formal procedure of aftershock identification. It can be seen that Bath s law only fits the aftershock sequences of the main events with M ms 4. The clusters that are formally identified as aftershocks of weaker events, contradict Bath s law, and, formally, identification of the corresponding clusters should be treated as incorrect (for these weak main events, our identification procedure works incorrectly). Thus, only the aftershocks identified for the main events with M ms 4 (which make up 44% of all earthquakes) were eliminated from the catalog. THE MAGNITUDE OF COMPLETENESS The approaches to estimating the magnitude of completeness are based on the concept of the powerlaw energy distribution of the earthquakes. In this case, the frequency magnitude relation is linear (e.g., see (Wiemer and Wyss, ) and references therein). If part of the earthquakes is missing, the points for the corresponding magnitudes will lie above the frequency magnitude graph, which defines the phenomenon of the bending of the frequency magnitude graph at low magnitudes. Therefore, the problem of finding of the magnitude of completeness, in terms of statistics, is reduced to answering the question of whether the observed energy distribution of the earthquakes is fitted by the power law. The statistical problem was formulated in this way and solved in (Pisarenko, 989; Sadovskii and Pisarenko, 99. In these works, the authors provide a strict statistical solution of the problem, which makes it possible to automate the entire procedure of the analysis by only specifying the level of significance for testing the corresponding hypotheses (Smirnov, 9). The time variations in the magnitude of completeness are shown in Fig. 4. The graph indicates that, starting from 996, the catalogue can be treated as uniform in terms of the magnitude of completeness. The sharp drop, compared to 995, is likely to reflect the upgrade of the seismic network carried out at that time (Mandal, Mabawonku, and Dimri, 5). The average magnitude of completeness over is.. In order to exclude the effects of random variations in the magnitude of completeness on the estimates of the b value, we applied selection M.. The estimation of the magnitude of completeness over the entire data set for (without binning in time intervals) also gives its average value of.. After the elimination of the aftershocks and selection by magnitude, the volume of the resulting dataset for was 57 events. The statistical estimate of the earthquake location error, which is independent of the residuals of the solution of the hypocenter location problem presented IZVESTIYA, PHYSICS OF THE SOLID EARTH Vol. 49 No.

5 PROGNOSTIC ANOMALIES OF INDUCED SEISMICITY IN THE REGION 47 in the catalogue, is discussed below in the section devoted to the fractal properties of seismicity. THE STATISTICAL PROPERTIES OF SEISMICITY The b-value. The b-value (the slope of the frequency magnitude graph) is evaluated by the standard maximum likelihood estimator for the ungrouped and uncensored sample (Aki, 965): b loge = , M M where M is the average magnitude and M is the minimum magnitude in the sample, which is equal to the magnitude of completeness in our case. The statistical error of b is calculated as a square root of the asymptotic variance (Kendall and Stuart, 96): S b = b/ N, where N is the number of seismic events used for estimation of b. The fractal dimension d of the set of hypocenters. The fractal properties of seismicity can be described by various fractal dimensions (Feder, 988). In this work, we used two dimensions, namely, the correlative and cluster dimensions. Estimation of correlation dimension relies on the statistics of distances between the pairs of points (the hypocenters or epicenters of the earthquakes); i.e., it is based on the correlation integral n( Δ r) C(r) = , N where n(δ r) is the number of all possible pairs of events, the distance Δ between which does not exceed r and N = N(N )/ is the total number of all possible pairs of events. For fractal objects, C(r) r d, where d is the fractal correlation dimension. The correlation dimension can be estimated from relatively small samples of the data (the advantages and shortcomings of this approach are reviewed in (Kagan, 7; Pisarenko and Pisarenko, 995)). In this work, we evaluated the statistical error of the correlation dimension by the direct estimation method referred to as the jackknife technique, which relies on the analysis of the statistical function of influence (Huber, 98; Mosteller and Tukey, 977). This method allows one to assess the part of the error that is due to the finite volume of the sample (Sidorin and Smirnov, 995). The cluster dimension shows how the mass of the cluster of the events grows with the increase of the linear dimension of the cluster (Feder, 988). In our case, the mass of the cluster with size r means the number of the earthquakes N r that fall in the sphere with a radius r centered at the barycenter of the cloud of the events. For fractal objects, N r r d, where d is the cluster dimension. The statistical estimation of cluster dimension can be reduced to the estimation of the index in the power-law distribution (Smirnov, ). We note that the correlation dimension can be understood as a certain average of cluster dimension: if, instead of centering the sphere at the barycenter of the cloud, we successively place the center of the sphere at each point of the cluster, then the average value N r over all these points will be proportional to the correlation integral (Sidorin and Smirnov, 995). In the case of uniform fractals, the cluster and correlation dimensions coincide (Feder, 988). In this work, we used the correlation dimension when analyzing the time variations in the fractal properties of seismicity over small samples in the given time windows, and the cluster dimension when analyzing the spatial variations in the fractal properties. q-value. The generalized frequency magnitude relation for the earthquakes (Kossobokov and Mazhkenov, 988; 994; Keilis-Borok, Kossobokov, and Mazhkenov, 989; Chelidze, 99; Bak et al., ) which takes into account the self-similarity of the seismicity distribution in energy and space provides the basis for evaluating the physical parameters of failure in the lithosphere from the seismic statistics data (Smirnov, ; Smirnov and Zavyalov, 996; Smirnov and Ponomarev, 4). In particular, using this relation, it is possible to estimate the duration of the failure cycle in the lithospheric material as a function of the size of the failure zone (the size of seismic source) (Smirnov, ; Kossobokov and Nekrasova, 4). In the generalized frequency magnitude law, the duration of the failure cycle τ (which is inverse to the average recurrence time of the earthquakes in the domain of the size of seismic source) is a power-law function of the size of the failure zone (the size of the earthquake source l): τ(l) = τ (l/l ) q, where τ is the duration of the failure cycle related to the events of the selected size l : q = αb d. (7) The coefficient α determines the scaling in the relationship between the magnitude and the size of the source: M = αlogl + β. The parameters τ and q can be evaluated from the catalogue data (Smirnov, ). In the present work, we only used the estimates of the q-value calculated by formula (7). The results presented in (Keilis-Borok, Kossobokov, and Mazhkenov, 989; Smirnov, ; Kossobokov and Nekrasova, 4) indicate that the duration of the failure cycle in the background seismicity insignificantly depends on magnitude: the q-value is close to zero. This means that in the case of background seismicity, the probability of failure is uniformly distributed over the sizes of the defects or other features of the rocks under failure that determine the sizes of seismic sources. However, the frequency magnitude relationship only depends on the geometrical structure of the heterogeneities in the medium IZVESTIYA, PHYSICS OF THE SOLID EARTH Vol. 49 No.

6 48 SMIRNOV et al. 4 М Time, years Fig. 5. The variations in the induced seismicity and water level: the variations in the water table altitude above sea level in the () Koyna reservoir and () Warna reservoir; the strongest earthquakes (with their magnitudes) in the () northern and (4) southern parts of the region. The locations of the epicenters of these events are shown in Fig.. (Aki, 98; King, 98; Turcott, 99; Grigoryan, 988; Smirnov, 997; Corral, 5). The studies of the aftershock sequences and transient seismic regimes revealed substantial deviations of the q-value from zero and regular time variations of this parameter, which indicate that in these cases, redistribution of failure over the scales took place (Smirnov and Ponomarev, 4; Smirnov et al., ; Smirnov and Zavyhalov, ). The RTL parameter. The intervals of seismic quiescence and subsequent foreshock activation are identified by the RTL algorithm (Sobolev and Tyupkin, 996; 997; 999; Huang, Sobolev, and Nagao, ; Sobolev, Huang, and Nagao, ), which outputs the RTL parameter. The latter is a product of three functions: epicentral function R, time function T, and energy function L: n ri Rxyzt (,,,) = exp Rs, r i= n t ti Txyzt (,,,) = exp Ts, (8) t i= L( x, y, z, t) = n l -- i p r i = L s. Water table altitude above sea level Here, x, y, and z are the spatial coordinates of the analyzed point in the seismically active zone and t is time. r i and t i are the epicentral distance of the current earthquake with magnitude M i to the analyzed point and its time. l i is the linear size of the source of the current seismic event, which is calculated in our case from its magnitude by formula (5a). The coefficient r characterizers the decay in the influence of the earthquake that occurred on the current point in a seismically active region with increasing distance to this point. The coefficient t specifies the decrease in the influence of the previous earthquakes at the time moment under study (the seismic memory), and coefficient p describes the contribution of a given earthquake. When p =,, or, the contribution of the earthquake is proportional to the length of the rupture in the source, the area of the rupture, or the energy of the earthquake, respectively. The values of r, t, and p are found empirically at the stage of training the algorithm as the values that provide the most intense anomaly before the test events (Huang, Sobolev, and Nagao, ). The corrections R s, T s, and L s remove the longterm trend from the corresponding functions. In the present study, these corrections were determined by linear approximation on the time interval preceding moment t. Finally, RTL is normalized to its root mean square deviation calculated over the entire interval of observations before the analyzed time t. This allows us to quantify the anomaly relative to the background variations. The pattern of prognostic RTL variations has the following form: the decrease in RTL from zero (the long-term background level) corresponds to seismic quiescence, and its subsequent recovery to the background level or above reflects the stage of foreshock activation (Sobolev, Huang, and Nagao, ; Sobolev, a; b). THE PATTERN OF SEISMICITY The time variations in the induced seismicity and water table altitude (above sea level) in the Koyna and Warna water reservoirs are displayed in Fig. 5. The graphs exhibit a feature that was noted in (Pandey and Chadha, ): the strongest earthquakes (with the magnitude above 4) occurred during the phase of decreasing water level. Pandey and Chadha () identified two cycles in the occurrence of the strongest events before 996: the earthquakes pertaining to one cycle occurred during the phase of the impounding of the reservoir, while the earthquakes of another type mainly took place during the water discharge. After 996, the cycle of the events confined to the filling of the reservoir disappeared. The nature of these cycles is associated with the variations in the strains (.75.5 bar) caused by the propagation of the front of the water diffusion to the hypocentral depths due to the changes in the surface load in response to the changes in the water level in the reservoirs. The change in the character of seismicity after 996 is probably related to the filling of the Warna reservoir, which was completed in 99. It can also be seen in Fig. 5 that the mentioned cyclicity in the occurrence of the earthquakes is broken after the doublet of the strongest earthquakes of March, (M = 5.) and September 5, (M = 5.) (except for the aftershocks of these earthquakes, the seismic events with M > 4 disappear after IZVESTIYA, PHYSICS OF THE SOLID EARTH Vol. 49 No.

7 PROGNOSTIC ANOMALIES OF INDUCED SEISMICITY IN THE REGION 49 these two quakes). The cyclicity partially recovers three years after the second large event. The first of the two mentioned earthquakes fits well into the cyclicity of the events corresponding to the drop in the water level in the reservoir. The second earthquake falls out of this cycle: it occurred during the increasing phase in the water level. The locations of the earthquakes revealed in Fig. 5 are shown in Fig.. It is seen that the cyclicity of the strong events mentioned above is accompanied by the regular alternation of the events in the northern and southern parts of the Koyna Warna seismic zone. The annual rhythm is not only present in the occurrence of the strongest events; it is revealed in the entire seismicity. Figure 6 shows the estimate of the harmonic component in the earthquake flow for the catalogue without aftershocks, which is calculated by the method developed by A.A. Lyubushin (Lyubushin et al., 998; Lyubushin, 7). The calculations were carried out by the original author s software placed by the author for open access on the Internet. The sequence of the earthquakes is considered as a point process with the intensity varying with time as λ(t) = μ( + αcos(ωt + ϕ). If α =, the process is Poissonian; if α >, it is superimposed by the harmonic component with frequency ω. The algorithm used in our study allows the geophysicist to estimate the amplitudes of the harmonic components α at different frequencies throughout the interval specified by the user. Thus, the procedure is an analogue of the spectral analysis applied to the point processes. It is seen in Fig. 6 that the spectrum of oscillations in the intensity of the flow of seismic events contains the peaks at a period of one year and the groups of peaks with multiple frequencies (with periods of.5,.5, and.5 years). Another clearly pronounced periodicity is observed at a period of two years, which is probably due to the above-mentioned alternation of strong events in the southern and northern segments of the seismogenic zone. The interpretation of the peak at a period of.5 years is unclear because of the insufficient length of the catalogue analyzed ( years). The algorithm and the program developed by Lyubushin implement spectral analysis of the point process in a moving time window and provide the corresponding spectrogram, which reflects the time variations in the spectrum of the flow of seismic events. The spectrogram calculated for the Koyna Warna catalogue is shown in Fig. 7. The calculations were carried out in a time window of years, which moved along the time axes with a step of. year. The abscissa axis measures the time corresponding to the end of the time window. The intensity of shading in Fig. 7 is proportional to the current amplitude of the spectral component (calculated in the given time window) with period T, the logarithm of which is plotted along the α λ(t) = μ( + αcos(ωt + ϕ)) T, year Fig. 6. The spectrum of the earthquake flow: () the spectrum; () the periods corresponding to the multiple frequencies. ordinate axis. The horizontal bands in Fig. 7 correspond to the spectral peaks (harmonics) identified in Fig. 6. It is seen in Fig. 7 that the amplitudes of these harmonics vary with time; in particular, they decrease after the doublet of the strongest events in. Thus, these earthquakes do not only break the cyclic rhythm of the strongest events but also weaken the intensity of the overall cyclicity associated with the annual variations in the height of the water level in the reservoirs. THE FREQUENCY MAGNITUDE GRAPH The frequency magnitude graph (in the range of the magnitudes of completeness) for the interval is presented in Fig. 8 for the full catalogue and for the catalogue after elimination of the aftershocks. The b-value for the aftershock-free catalogue is b =.4 ±.4, which coincides with the estimate b =. from (Singh, Bhattacharya, and Chadha, 8). THE FRACTAL DIMENSION The graphs of the correlation integrals calculated for the sets of hypo- and epicenters of the earthquakes are shown in Fig. 9. The fractal dimensions estimated from the slopes of the corresponding linear approximations are d =.8 ±. for the epicenters and d =.59 ±.5 for the hypocenters. The estimate d =.8 appreciably exceeds the value d =.7 reported in (Singh, Bhattacharya, and Chadha, 8). Most likely, the discrepancy between these estimates is due to the fact that the aftershocks were not eliminated from the catalogue used in (Singh, Bhattacharya, and Chadha, 8) for calculating the estimate. Our estimates of the fractal dimension of seismicity agree well with the estimated dimension of the network of the faults obtained in (Sunmonu and Dimri, ). For the Koyna Warna region (block IV in the nomenclature of Sunmonu and Dimri ()), the authors of the quoted work derived an estimate of.65 IZVESTIYA, PHYSICS OF THE SOLID EARTH Vol. 49 No.

8 5 SMIRNOV et al. log(t, year) Time, years Fig. 7. The spectrogram of the earthquake flow (see text for explanations)..5 T, year.5.6 for the network of the faults on the surface and the extrapolation of.65 for the volumetric dimension. The agreement between the estimates of fractal dimensions for seismicity and for the network of the faults supports the hypothesis according to which the spatial distribution of seismicity is governed by the geometrical structure of the lithospheric heterogeneities. The up- and down-pointing triangles in Fig. 9 mark the boundaries of the scaling zones (linear segments in the graphs of the correlation integrals), or the N M Fig. 8. The frequency magnitude graph of the earthquakes with M.: () the catalogue without aftershocks; () the entire catalogue; () the approximation with b =.4. outer and inner limits, in the terminology of Mandelbrot (). In application to seismicity, the upper limit is typically controlled by the size of the cluster of the events, while the lower limit is determined by the location error of these events. In our case, the upper limit is observed at about 7 km, which corresponds to the lower (latitudinal) extent of the Koyna Warna seismic zone. The lower limit (about 5 m) is far below the formal average residuals of the event location presented in the catalogue. According to the catalogue, these residuals characteristically decrease with increasing magnitude (Fig. ) and average about km for the epicenters and about km for the hypocenters. The actual location errors of the seismic events of are discussed in (Srinagesh and Sarma, 5). In particular, in Fig. of the quoted paper, these authors show the location errors for a series of quarry explosions that were produced in the southern segment of the seismic network and recorded by the network. These errors average about m for the epicenters and about 5 m for the depths. Our estimates of the inner limit of the scaling interval are closer to these values than to the residuals quoted in the catalogue. Mandel et al. (5) note that the upgrade of the seismic network in the Koyna Warna region has substantially reduced the location errors after 995. Thus, the statistical estimates of the location errors, which are found to be a few hundred meters in the IZVESTIYA, PHYSICS OF THE SOLID EARTH Vol. 49 No.

9 PROGNOSTIC ANOMALIES OF INDUCED SEISMICITY IN THE REGION 5 present study, can be treated as realistic and used for estimating the dimension of the fractal cluster. q-value In order to estimate the average q-value q = αb d, we used the estimates b =.4 ±.4 and d =.59 ±.5 quoted above and the coefficient α =.7 from formula (5). With these values, we find that q =. ±.5, i.e., on average, the q value can be assumed to be zero for the region overall and for the entire time interval This situation is characteristic of the background state of seismicity (Smirnov, ), when the fields of strength and stresses are consistent with each other in some sense (Smirnov, ; Smirnov and Ponomarev, 4) and b = 7d/α (Aki, 98). By the example of seismicity initiated by water injection in the well, it was demonstrated in (Smirnov et al., ) that the stage of formation of induced seismicity is marked by positive q values, which decrease with the evolution of the induced seismicity. The analysis of the difference between d and αb during the filling of the Nurek water reservoir indicates that the q-value drops to zero within a few years after the completion of the impounding (Smirnov, Cherepantsev, and Mirzoev, 994). These results suggest that seismicity in the Koyna Warna zone can be assumed to have matured by the time interval considered in our study. The map showing the spatial distribution of the q-value is presented in Fig.. The average error of the estimates is.6, and only the q-values that differ from zero by at least this value are plotted on the map. It can be seen that the northern and southern segments of the Koyna Warna zone distinctly differ in terms of the q-value. However, it is unclear whether this difference is due to physical factors or is caused by the poor location of the events in the northern part of the region, where the artifacts forming linear vertical and horizontal chains of epicenters are apparent. These linear artifacts reduce the d-value and, correspondingly, overestimate the q-value. THE ANOMALIES IN SEISMICITY The RTL anomaly. For calculating the spatial and temporal variations in RTL, we used the following parameters of the algorithm: r = km, t = 9 days, and p = (see formula (8)). We found that the doublet of the strongest (M > 5) seismic events during the considered interval (the earthquakes on March, with M = 5. and September 5, with M = 5.) was preceded by a characteristic anomaly in RTL, which reflected the seismic quiescence followed by activation of seismicity. Similar anomalies in the Koyna Warna region were noted in (Sashidhar et al., ). The maps showing the distribution of the RTL parameter at different time instants are presented in Fig.. The time variations in RTL in the peak area of the anomaly (the ellipse in Fig. c) are shown in Correlation integral m. d =.8 7 m d =.6 Fig., where also the time instants corresponding to the maps presented in Fig. are indicated. A sharp burst in RTL at the beginning of 998 is associated with the aftershocks of the earthquake of February, 998 with magnitude M =.. We recall that the formalized procedure of aftershock identification only allowed us to eliminate the aftershocks with M 4 from the catalogue. We found it unnecessary to remove the aftershocks of the mentioned earthquake manually, because the peak in RTL caused by these after- 7 km Distance, km Fig. 9. The correlation integrals: () for the epicenters; () for the epicenters; () the limits of the scaling interval. Location error, km Magnitude Fig.. The average location error of the () hypocenters and () epicenters of the earthquakes as a function of magnitude. IZVESTIYA, PHYSICS OF THE SOLID EARTH Vol. 49 No.

10 5 SMIRNOV et al q Fig.. The map of q-value. The grid spacing is... shocks does not hinder the analysis of the anomaly preceding the events of. It is seen in Fig. that the RTL anomaly arose in the source zone of the second earthquake (Fig. b). At the stage of the maximal seismic quiescence (minimum RTL, the maps in Figs. c and d), the anomaly captures the area with a size of about 5 km (which is commensurate with the aftershock areas of the events of with M 5). Figure c shows a clear local activation in seismicity (marked by the positive anomaly in RTL) after the strong event of June 7, 999 (M = 4.7), which probably distorts the shape of the negative anomaly. We note that the enhancement in seismic activity after the event of 999 is revealed despite the fact that the aftershocks of this event have been removed from the working catalogue. At the stage of activation, the negative anomaly in RTL is seen to split into two parts (Fig. e shows two spots close to the future epicenters of the first and second events) and then disappears in the region of the second earthquake (Fig. f). Van Stiphout, Schorlemmer, and Wiemer () showed that the estimates of seismic activity are sensitive to the procedure of catalogue declusterization. IZVESTIYA, PHYSICS OF THE SOLID EARTH Vol. 49 No.

11 PROGNOSTIC ANOMALIES OF INDUCED SEISMICITY IN THE REGION 5 (a) (b) (c) Oct. 9, Mar., July, 999 RTL (d) (e) (f) Sep. 4, 999 Jan. 7, Mar., Fig.. The RTL maps for different time instants. The epicenters of the following earthquakes are shown: () March, (M = 5.); () September 5, (M = 5.); and () June 7, 999 (M = 4.7). The ellipses in the maps (c) and (e) contour the areas in which the time variations of RTL shown in Figs. and 4, respectively, were calculated. When filtering the catalogue, we eliminated the aftershocks of seven earthquakes, four of which occurred earlier than the pair of the events of considered in the present study (these are the earthquakes of 996, 997, 998, and 999). Their aftershock sequences lasted at most 6 months, and their spatiotemporal aftershock areas do not intersect with the spatiotemporal domain of the considered anomaly in RTL. Therefore, the revealed anomaly cannot be the result of the procedure of aftershock elimination. The anomalies in the b-, d-, and q-values. The estimates of the b-value, the fractal dimension of the set of hypocenters, and the q value require a larger statistical base than the estimates of RTL; therefore, we estimated these parameters in a moving time window over the entire Koyna Warna seismic zone. We used the windows containing a given number of events, which ensured that the estimates were statistically reliable (the window covered events and was shifted by events). For determining the b-value, we calculated the maximum likelihood estimate; the fractal dimension was estimated by the method of the correlation integral; and the q-value was calculated by formula (7) with α =.7 according to (5). The variations in these parameters are depicted in Fig.. A characteristic anomaly is clearly seen to precede the events of : the b-value initially increases and then drops. The graph of fractal dimension d increases sharply after the strong events of 998 (M = 4.) and 999 (M = 4.7). The increases in the d-value after the strong earthquakes were noted in (Smirnov and Ponomarev, 4). The events of were preceded by a slightly decreased d-value. The q-value, to a significant extent, follows the variations in the b-value, since the variations in the d-value are less contrasting than in the b-value. Figure shows that the anomalies in the b-, d-, and q-values are confined in time to the stage of IZVESTIYA, PHYSICS OF THE SOLID EARTH Vol. 49 No.

12 54 SMIRNOV et al. RTL b, d Time, years increasing RTL; i.e., they occur during the enhancement stage of seismic activity. However, care should be executed when comparing the RTL curves with the parameters of seismicity shown in Fig., because the estimates of RTL have far lower time resolution than the estimates of the b-, d-, and q-values. (In order to provide the sufficient spatial resolution of the estimates of RTL, the time scale of this parameter should be coarse). THE DISCUSSION а b c d e f q Fig.. The time variations in () RTL, () d-value, () b-value, and (4) q-value. The initial estimates (the points) and the smoothed curves are shown. The horizontal dashed lines are the zero levels for RTL and q-value; the RTL variations are calculated for the spatial area shown by the ellipse in Fig. c; (5) the time instants corresponding to the maps in Fig. ; (6) the strongest earthquakes (corresponding to those shown in Fig. 5). The fact that annual cyclicity in seismic activity disappears after the doublet of the strong earthquakes of can be attributed to the release and redistribution of stresses by these seismic events. This effect was observed in the laboratory experiment on studying the acoustic response to the periodic variations in the load (Ponomarev et al., ). The experiment with a granite specimen consisted in producing natural sudden slips (stick-slips) along a preliminarily grown fracture zone against the background cyclic modulation of the axial load under confining pressure. The modulation depth was a few percent, and even this small value turned out to be sufficient for the formation of a wellpronounced cyclicity in the acoustic activity. It was found that even not very large stick-slips, at which the stress release did not exceed %, temporarily violated the cyclicity in the acoustic activity for a certain time interval. This supports the hypothesized mechanism of disrupted cyclicity in the Koyna Warna zone, because the release of % of the average tectonic stresses in the sources of the earthquakes appears to be quite feasible. The dynamics of the revealed anomaly in RTL corresponds to the bay-like scenario, which is typical of the evolution of the source of a tectonic earthquake. According to this scenario, the initially formed seismic quiescence is followed by seismic activation (Sobolev and Ponomarev, 4). The variations in the b-value, the fractal dimension d, and the q-value also correspond to the scenario of the preparation of the source of a tectonic earthquake. The significant transition of q into the interval of positive values before the events of indicates that the intensity of the failure processes increases on the smaller scales. The subsequent decrease in q (as well as the decrease in b) marks the redistribution of failure from the smaller scales towards the larger scales, which is typical of the preparation of tectonic earthquakes (Sobolev, ; Zavyalov, 6; Enescu and Ito, ; Bachmann, Wiemer, and Woessner, ; Sobolev, ). The decrease in the d- value before the events of points to the higher degree of clustering of the earthquakes, which is known to be the characteristic preparatory process of a tectonic earthquake (Sobolev and Ponomarev, ; Kagan, Rong, and Jackson, ; Console et al., 7; Scholz, ; Sobolev, ). Thus, the anomalies in seismic parameters that preceded the pair of earthquakes in indicate that a source zone was formed in the region of the induced seismicity by the scenario of formation of a source zone of a tectonic earthquake. Such zones emerge as a result of the evolution of fracturing through gradual coalescence and enlargement of the cracks (on the scale of seismicity, the cracks are understood as the sources of the earthquakes). After their formation, these zones reside in a metastable state, and their failure (the occurrence of a new earthquake) can be caused by internal factors and initiated by insignificant external impacts (Sobolev, ). In the latter case, we mean the triggering effect, and the occurrence time of the earthquake is determined by both the time when the formation of the metastable source zone is completed and the time when the triggering mechanism initiates the source. This is important to take into account when constructing the algorithms for forecasting the induced seismicity, which should include monitoring the formation of metastable source zones and their initiation by external factors. Since the two earthquakes of are very close to each other in time and space, we cannot conclude with confidence whether the identified anomalies in the b-, d-, and q-values are associated with the preparation of the first or second event, or these earthquakes should be considered as a single doublet. The spatial resolution of the RTL maps with r = km used in our analysis is about km, which is approximately half the distance between the epicenters of the earthquakes of. This allows us to consider the variations in RTL close to the source of each of these earthquakes separately. IZVESTIYA, PHYSICS OF THE SOLID EARTH Vol. 49 No.

13 PROGNOSTIC ANOMALIES OF INDUCED SEISMICITY IN THE REGION 55 RTL M = 5. M = 5. Time, years Fig. 4. The time variations in RTL in the areas of the first and the second seismic events shown by the ellipses in Fig.. (See text for explanations). Figure 4 presents the separate time variations in RTL inside the spots of the anomalies in the vicinity of the first and the second event (the corresponding areas are shown by the ellipses in Fig. e). It is seen in Fig. that the first event occurred almost at the minimum of the RTL curve; i.e., the phase of activation was absent for this event. This is probably due to the fact that the first event has a clear triggered origin, and the time of its occurrence is determined by the initiation of failure in the formed metastable zone by the external impact from the fluid diffusion caused by the change in the water level in the reservoir (Rao and Singh, 8; Pandey and Chadha, ). The second event is preceded by the RTL anomaly, whose pattern is typical of a tectonic earthquake: the main event occurs at the stage of activation, which follows the interval of seismic quiescence. (The insignificant repeated increase in RTL in the second spot after the first event is probably due to the elimination of the aftershocks of the first event from the catalogue: the aftershock zone of the first event contacts the spot of the second event.) In the concept of avalanche unstable fracturing, the activation is treated as resulting from the evolution of the avalanche-like coalescence and enlargement of the cracks, which finally leads to the occurrence of the main event (Mjachkin et al., 975). This suggests that the occurrence time of the second event is governed by the evolution of the internal processes of failure in the metastable area and, probably, is not directly related to the action of an external factor. The fact that the second event does not follow a common pattern of a series of the other strong events that occurred during the decreasing phase in the water level supports this hypothesis. CONCLUSIONS. The pair of the earthquakes with M > 5 that occurred on March, (M = 5.) and September 5, (M = 5.) in the Koyna Warna region of induced seismicity was preceded by the variations in seismicity, which are typical of the preparatory processes of tectonic earthquakes. These variations are indicative of the formation of metastable source zones of impending earthquakes.. The results of our study suggest that initiation of failure in these metastable zones in the region of induced seismicity can be caused by either an external impact (due to the water level variations in the reservoir) or the internal processes of avalanche unstable fracture propagation.. The characteristic pattern of induced seismicity in the Koyna Warna region changed after the pair of earthquakes that occurred in. In particular, the clearly pronounced annual periodicity in the release of seismic energy caused by the water level variations in the reservoirs disappeared. ACKNOWLEDGMENTS The work was carried out under the project Seismic regimes in the zones of large natural and anthropogenic impacts in the complex long-term program of cooperation between Russia and India supported by the Ministry of Science and Education of the Russian Federation (State contract no ; Department of Science & Technology, New Delhi (no. B-.59) and CSIR NGRI). The work is also supported by the Russian Foundation for Basic Research (grant no. -5-5). REFERENCES Aki, K., Maximum Likelihood Estimate of b in the Formula logn = a bm and Its Confidence Limits, Bull. Earthquake Res. Inst., 965, vol. 4, pp Aki, K., Probabilistic Synthesis of Precursory Phenomena, in Earthquake Prediction: An International Review, Maurice Ewing Ser., vol. 4, Simpson, W. and Richards, G., Eds., Washington, DC: AGU, 98, pp Bachmann, C., Wiemer, S., and Woessner, J., The Induced Basel 6 Earthquake Sequence: Mapping Seismicity Parameters on Small Scales, in Abstract Book, The nd General Assembly of European Seismological Commission. Montpellier, France,, Montpellier,. Bak, P., et al., Unified Scaling Law for Earthquakes, Phys. Rev. Lett.,, vol. 88, no. 7. doi:./physrev- Lett Båth, M., Lateral Inhomogeneities in the Upper Mantle, Tectonophysics, 965, vol., pp Chadha, R.K., Gupta, H.K., Kumpel, H.J., Mandal, P., Nageswara, Rao, A., Narendra Kumar Radhakrishna, I., Rastogi, B.K., Raju, I.P., Sarma, C.S.P., Satyamurthy, C., and Satyanarayana, H.V.S., Delineation of Active Faults, Nucleation Process and Pore Pressure Measurements at Koyna (India), Pure Appl. Geophys., 997, vol. 5, nos. /4, pp Chelidze, T.L., Unified Fractal Law for Seismicity, Dokl. Akad. Nauk SSSR, 99, vol. 4, no. 5, pp IZVESTIYA, PHYSICS OF THE SOLID EARTH Vol. 49 No.