Minimum preshock magnitude in critical regions of accelerating seismic crustal deformation

Bollettino di Geofisica Teorica ed Applicata Vol. 44, n. 2, pp. 103-113; June 2003 Minimum preshock magnitude in critical regions of accelerating seismic crustal deformation C.B. Papazachos University of Thessaloniki, Greece (Received, February 20, 2002; accepted December 10, 2002) Abstract - An important factor for all models that consider the generation of a mainshock as a critical point at the end of an accelerating seismic energy release period is the minimum magnitude considered in the calculations. Using data for preshock sequences that preceded nineteen recent strong mainshocks (M..6.3) in the Aegean area, we have defined the minimum magnitude, M min, of preshocks for which an optimum fit to the accelerated crustal deformation model has been obtained. It is shown that the average difference between the predicted mainshock magnitude, M, and this minimum preshock magnitude, M min, is 1.8.±.0.1 for 6.0..M..7.6, with slightly smaller values (~.1.6-1.8) for M..7.0 and larger values (~.1.8-2.0) for larger events (M..7.0). This assessment of the mainshockpreshock difference is of great practical importance for the identification of critical (preshock) regions. It is shown that similar differences are found for six regions, which, have been suggested, to be presently in a state of accelerated seismic deformation. This result can be considered as further evidence that these regions are in a critical (metastable) state, which can lead to the generation of strong mainshocks (M..6.4) in the next few years. 1. Introduction Systematic research during the last decade has shown that it is possible to identify geographical regions where accelerated seismic energy release takes place through intermediate magnitude shocks (preshocks). This accelerated seismic deformation pattern in these critical regions often leads to the generation of a strong shock (mainshock), which is considered a critical point (Sornette and Sornette, 1990; Sornette and Sammis, 1995; Huang et al., 1998; Jaume and Sykes, 1999). A consequence of this criticality concept is that the time variation of Corresponding author: C.B. Papazachos, Geoph. Laboratory, School of Geology, University of Thessaloniki, PO Box 352-1, Thessaloniki GR-54006, Greece; e-mail: costas@lemnos.geo.auth.gr 2003 OGS 103

Boll. Geof. Teor. Appl., 44, 103-113 Papazachos measures of preshock-mainshock seismic crustal deformation follows a power law. Such seismic deformation measures are typically expressed as: n(t) S(t) = Σ [E i (t)] k, (1) i.=.1 where k takes several values, ranging from k.=.1, in which case S(t) is proportional to cumulative seismic energy or moment, up to k.=.0 where S(t) corresponds to the cumulative number of preshocks. Bufe and Varnes (1993) used the cumulative Benioff strain, S(t), as a measure of the preshock seismic deformation (or seismicity) at time, t, defined from Eq. (1) when k.=.0.5, as: n(t) S.(t) = Σ E i (t) 1 2, (2) i.=.1 where E i is the seismic energy of the i th preshock and n(t) is the number of events (preshocks) which have occurred up to time t. The energy E i of each shock can be easily calculated from the moment magnitude of the shock using appropriate relations. For the time variation of the cumulative Benioff strain they proposed a power law expressed by a relation in the form of: 104 S(t).=.A.+.B (t c..t) m, (3) where t c is the origin time of the mainshock and A, B, m are parameters that can be calculated by the available observations. Although relations of different form have been proposed for the time-to-failure analysis (e.g. Main, 1999), Eq. (3) is the most widely used, as it is compatible with the general failure equation of Voight (1988, 1989), and for B.<.0 and 0.<.m.<.1 it has a finite failure time, t c, (where ds/dt and d 2 S/dt 2 ), while S(t c ).=.A has a finite value, as in the case of earthquakes (Bufe and Varnes, 1993). Bowman et al. (1998) considered critical circular regions to identify accelerating seismicity patterns along the San Andreas fault system. They proposed an algorithm to quantify the accelerated Benioff strain by minimizing a curvature parameter, C, which is defined as the ratio of the root-mean-square error of the power-law [Eq. (3)] fit to the corresponding fit error of the standard linear variation of S(t) with time. C is less than 1 for accelerating (m.<.1) or decelerating (m.>.1) Benioff strain release and almost equal to 1 for a steady (linear) variation of Benioff strain with time. Papazachos and Papazachos (2000, 2001) used elliptical critical regions for the Aegean area and proposed the following five relations as additional constraints to the model of the accelerating seismic deformation (Benioff strain): log R.=.0.41 M..0.64, (4)

Minimum preshock magnitude in critical regions Boll. Geof. Teor. Appl., 44, 103-113 log B.=.0.64 M.+.3.32, (5) M.=.0.85 M 13.+.1.52, (6) log t p.=.5.81..0.75 log s r, (7) A.= S r t p. (8) where R (in km) is the radius of the circle with area equal to the area of the elliptical critical region, M is the magnitude of the mainshock, M 13 is the average magnitude of the three largest preshocks, t p (in years) is the duration of the preshock sequence, S r (in Joule 1/2 /yr) is the long-term Benioff strain rate in the examined area, s r is the same quantity reduced to the area of 10 4 km 2 and A, B are the parameters of Eq. (3). To quantify the compatibility of the values of parameters R, B, M, t p, and A calculated for a seismic sequence, with those determined by Eqs. (4), (5), (6), (7) and (8), they defined a parameter P, corresponding to the sum of the probabilities calculated for each of the left-side parameters in these equations, assuming that the observed deviations of each parameter follow a normal (Gaussian) distribution. Furthermore, Papazachos et al. (2002a) showed that the quantity q.=.p/(m*c) can be used as a measure of the quality of each solution. Finally, on the basis of the a posteriori prediction of past mainshocks (M.>.6.0) the following relations have been defined for the cutoff values of the previously mentioned quantities. C..0.60, m..0.35, P..0.45, q..3.0. (9) The main goal of the present work is to define the magnitude, M min, of the smallest preshock which should be considered in the cumulative Benioff strain [Eq. (2)] and its relation to the main shock magnitude, M, for each one of the critical regions of recent strong mainshocks in the Aegean area. The assessment of M min is of theoretical importance since it enables the quantitative definition of the term intermediate magnitude seismicity, that is, of the often described as small and intermediate size events which precede a main shock of a given magnitude. Moreover, it is also of practical importance because it can be used as an additional constraint in the systematic search of accelerating preshock seismic deformation patterns, hence increasing the predictive capabilities of the model. 2. Method and data The method applied in the present paper is based on the research work described briefly in the introduction and more particularly on an algorithm (Papazachos, 2001) based on the previously presented Eqs. (4) to (9). According to this algorithm, all shocks (preshocks) larger than a given threshold magnitude M min with epicenters in an elliptical region, centered at a certain point (epicenter of a mainshock or assumed epicenter of an oncoming mainshock) 105

Boll. Geof. Teor. Appl., 44, 103-113 Papazachos are considered, and the parameters of Eq. (3), as well as the curvature parameter, C, are estimated. These calculations are repeated by applying a systematic search of a large set of values for the azimuth, z, of the large ellipse axis, its length, a, ellipticity, e, and the time, t p, from the start of accelerating seismic deformation. Moreover, several magnitudes (typically ranging from 5.8 up to the magnitude of the largest known earthquake in the area, M max ) are considered, and several origin times for the assumed future mainshock, as well as for several values of the magnitude, M min, of the smallest considered preshock (ranging typically between M min.=.4.0 and M min.=.5.7 in steps of 0.1) are used. All these calculations are repeated for a grid of points, which spans the investigated area with the desired density (typically using a 20-50 km spacing). From all solutions that fulfill relations (9), the one for which C and q have the relatively lower and higher values, respectively, is considered the best solution, allowing us to define the optimum value for M min. The calculated time t c, which corresponds to the best solution, is considered as the estimating time of the oncoming mainshock, while the average of the three values of M calculated by Eqs. (4), (5), (6) for the best solution is considered as the magnitude of the mainshock. The geographical mean of the grid points for which relations (8) are fulfilled is considered as the epicenter of the mainshock. This method has been applied to two sets of data. The first set concerns two complete samples of past, strong, shallow mainshocks in the Aegean area (34.N 42.N, 19.E 30.E). The first sample includes all mainshocks, that have occurred in the study area since 1950 with M..7.0. The second sample includes all mainshocks since 1980 in the same area with M..6.3. The second data set, to which this method has been applied, concerns six strong (M..6.4) mainshocks that are expected to occur in the study area within the next few years, for which a probabilistic prediction of the epicenter, magnitude and origin time has been recently presented (Papazachos et al., 2002a, 2002b, 2002c). The data (epicenter coordinates, magnitude, occurrence time) of the mainshocks, as well as of their preshocks have been taken from the catalogue of Papazachos et al. (2000), updated up to the end of 2001 from regional bulletins. The completeness of these data has been determined by checking the time variation of seismicity for the whole catalogue for different threshold magnitude levels, as well as the corresponding Gutenberg-Richter curve plots. Finally, the completeness levels adopted are: M..5.2, M..5.0, M..4.5, M..4.0, starting from 1911, 1950, 1965, 1980, respectively. Magnitudes are either originally reported moment magnitudes or equivalent moment magnitudes (for smaller events) calculated by proper formulas (e.g. Papazachos et al., 1997). The typical error in magnitudes is ±.0.3 and the typical error in the epicenters is 20 km. The minimum number of preshocks considered for each sequence was taken to be equal to 20, similar to previous studies in the area (Papazachos and Papazachos, 2000, 2001). 3. Results In the first nineteen lines of Table 1, information is given for the past nineteen corresponding mainshocks, while in the last six lines information is presented for the corresponding predicted future mainshocks. The second and third columns of the table list the 106

Minimum preshock magnitude in critical regions Boll. Geof. Teor. Appl., 44, 103-113 Table 1 - Information on the past nineteen mainshocks (1-19) and on the six expected mainshocks (20-25) of the Aegean area. No Date ϕ.n λ.e M W M M min n q R e z t S 01 1952, 12, 17 34.4 24.5 7.0 6.9 5.2 22 05.6 181 0.90 030 1922 02 1953, 03, 18 40.0 27.5 7.4 7.6 5.6 29 04.6 262 0.95 000 1920 03 1953, 08, 12 38.1 20.6 7.2 7.3 5.3 30 04.6 215 0.95 090 1930 04 1954, 04, 30 39.3 22.3 7.0 7.3 5.3 31 06.9 175 0.95 090 1932 05 1955, 07, 16 37.6 27.1 6.9 7.0 5.2 22 06.9 175 0.95 150 1920 06 1956, 07, 09 36.6 26.0 7.5 7.6 5.6 30 07.8 294 0.70 150 1929 07 1957, 04, 25 36.5 28.6 7.2 7.4 5.4 28 03.2 217 0.95 150 1930 08 1968, 02, 19 39.5 25.0 7.1 7.0 5.3 21 07.3 175 0.95 030 1933 09 1970, 03, 28 39.2 29.4 7.1 7.2 5.3 23 09.7 186 0.80 030 1945 10 1980, 07, 09 39.3 22.8 6.5 6.1 4.5 24 08.3 077 0.70 000 1965 11 1981, 02, 24 38.1 23.0 6.7 7.0 5.2 25 04.7 186 0.95 000 1966 12 1981, 12, 19 39.0 25.3 7.2 7.3 5.3 43 03.0 217 0.80 030 1951 13 1983, 01, 17 38.1 20.2 7.0 7.2 5.3 26 04.2 215 0.95 060 1967 14 1983, 07, 05 40.3 27.2 6.4 6.3 4.6 21 06.4 086 0.90 060 1970 15 1995, 05, 13 40.2 21.7 6.6 6.7 5.0 22 09.0 128 0.95 060 1970 16 1995, 06, 15 38.4 22.2 6.4 6.7 4.9 32 03.9 137 0.80 120 1982 17 1997, 10, 13 36.5 22.2 6.4 6.6 4.8 41 03.1 114 0.90 090 1965 18 1997, 11, 18 37.6 20.6 6.6 7.0 5.3 22 04.3 186 0.95 030 1984 19 2001, 07, 26 39.1 23.4 6.3 6.4 4.7 22 03.5 102 0.95 000 1990 20 2002.5 40.0 27.2 N/A 6.4 4.6 30 07.9 089 0.95 070 1959 21 2002.8 36.4 22.8 N/A 6.8 5.1 27 11.2 150 0.95 030 1962 22 2003.2 35.5 27.7 N/A 6.6 4.9 21 10.7 123 0.90 060 1976 23 2003.2 41.3 21.2 N/A 6.7 5.0 22 05.0 132 0.90 030 1969 24 2003.5 36.5 27.0 N/A 6.8 5.2 27 05.9 150 0.95 150 1975 25 2003.5 39.7 28.8 N/A 7.0 5.3 21 08.8 175 0.70 030 1972 date and epicentral coordinates of the already occurred or predicted mainshocks. In the fourth column the observed magnitudes, M w, of the nineteen past mainshocks are listed and in the fifth column the retrospectively predicted magnitudes, M, of the already occurred mainshocks and the predicted magnitude of the six expected mainshocks are given. The epicenters of the mainshocks presented in Table 1 are also plotted in Fig. 1, where gray circles show the epicenters of the past mainshocks, while open circles denote the predicted epicenters of expected mainshocks. The remaining columns of Table 1 list the minimum preshock magnitude, M min, which corresponds to the best solution obtained in the present work, the number, n, of observations, the parameters q, R, e, z, for the best solution (maximum q value), as well as the starting year, t s, of the preshock sequence. Fig. 2 shows an example of the application of the method previously described. In the figure, the spatial variation of the curvature parameter, C, is shown for the broader area of the Kozani-N.W. Greece 1995 event (M W.=.6.6) six months before the mainshock, using two values of ΔM.=.M-M min. For the optimum ΔM value (=.1.7, Fig. 2a) a large, very low C (~.0.2-0.3) area is clearly identified not far from the mainshock epicenter (~.70 km), which almost disappears when using smaller magnitude events (ΔM.=.2.0, Fig. 2b). A similar behaviour is found for the q parameter, as well as when larger magnitude events (smaller ΔM) are used. Fig. 3 shows a plot of the difference of M min from the predicted, M, mainshock magnitude as 107

Boll. Geof. Teor. Appl., 44, 103-113 Papazachos 42 20 22 24 26 28 42 40 40 38 Aegean Sea 38 36 34 Eastern Mediterranean M 7.5 7.0 6.5 6.0 20 22 24 26 28 36 34 Fig. 1 - Epicenters of the nineteen mainshocks, that have already occurred (gray circles) and epicenters of the six expected mainshocks (open circles), for which properties of the preshock (critical) regions are studied in the present paper. a function of the corresponding magnitude (M). It can be easily seen that a more or less linear relation applies and the corresponding least squares best-fit linear equations is: M..M min.=.0.27.m..0.08 σ.=.0.1. (10) A similar equation is derived when M min is related to the observed magnitude but with a higher scatter. Eq. (10) shows that the ΔM.=.M-M min difference is only weakly influenced by the mainshock magnitude, e.g. for a mainshock with a typical magnitude of M.=.6.2 the difference is equal to ΔM.=.M-M min. ~.1.6, while for M.=.7.2 the difference is equal to ΔM.=.M-M min. ~.1.9. This result can be used to narrow the limits to the minimum preshock magnitude considered in the search for the optimum solution for prediction purposes, hence saving significant processing time. Tests using Eq. (10) show that considering three ΔM values (e.g. 1.7, 1.8 and 1.9 for M.=.7.0) is adequate so that the best solutions that fulfill the criteria presented in Eq. (9) are retrieved. 108

Minimum preshock magnitude in critical regions Boll. Geof. Teor. Appl., 44, 103-113 Fig. 2 - Spatial variation of the curvature parameter C (ratio of accelerated deformation model RMS versus linear variation RMS), as computed 6 months before the Kozani-N.W. Greece 1995 event (M.=.6.6), using a M M min of a) ΔM.=.1.7 and, b) ΔM.=.2.0. It is clearly seen that a very low C area (C.~.0.2-0.3) is identified not far (~.70 km) from the epicenter of the main event when the optimum ΔM.=.1.7 value is used. Higher ΔM values (use of smaller magnitude events) leads to much higher C values, which do not allow the clear identification of the accelerated deformation behaviour. 109

Boll. Geof. Teor. Appl., 44, 103-113 Papazachos 2.4 2.2 2.0 M-M min 1.8 1.6 1.4 1.2 6.0 6.5 7.0 7.5 M Fig. 3 - Plot of the difference M..M min between the magnitude of the smallest preshock, M min, in the best solution (largest q) and the magnitude of the mainshock, M, as a function of M. Circles are used for the mainshocks that have already occurred and triangles for the expected mainshocks. 4. Discussion The results presented in the present work show that we can define a minimum preshock magnitude, M min, which is roughly equal to 0.75 M (M is the expected mainshock moment magnitude) for which an optimum solution of the accelerated deformation model is obtained. However, there are several other values of M min for which the model of accelerated seismic deformation, as expressed by Eqs. (4) to (9), still applies. When testing a large number of M min values, far from the values given by Eq. (10), an upper and a lower limit of ΔM have been defined, beyond which the criteria of Eq. (9) are not fulfilled. The existence of a lower value, ΔM low, is clearly a result of the limited number of data available when using large M min values due to the fixed minimum number of preshocks considered for statistical reliability of the model (e.g. n..21). On the other hand, the existence of an upper limit, ΔM up, for this difference (small M min ) can be understood within the physical concepts behind the model expressed by Eq. (3). This upper limit, ΔM up, for the difference between the mainshock magnitude and the corresponding smallest preshock magnitude has also been estimated for all the previously described past nineteen mainshocks investigated in the present paper (Table 1) for which Eq. (9) are valid. The determined upper limits, ΔM up, vary between 1.7 and 2.4 with a mean value equal to 2.1 and a standard deviation ±.0.2, about 0.4 units higher than the average optimum ΔM value. This means that for mainshocks of M.=.6.1, 6.5, 7.0 and 7.5 the model described by Eq. (3) holds within the context of constrains given by Eq. (9), if the preshocks 110

Minimum preshock magnitude in critical regions Boll. Geof. Teor. Appl., 44, 103-113 considered have magnitudes larger than about 4.0, 4.5, 5.0 and 5.5, respectively. Hence, smaller preshocks do not follow the accelerated seismic deformation behaviour. This result strongly supports the idea that it is the time variations of the intermediate magnitude seismicity, that prepare the generation of the mainshock, while the small magnitude seismicity is randomly distributed (Rundle et al., 2000). If we assume that the empirical relations between the magnitude and the fault length, L, and seismic moment, M 0, (logl = 0.51M 1.85; logm 0 =1.5M.+.16.05; Papazachos and Papazachou, 1997) derived for strong shocks, hold also for smaller shocks, we can conclude [using Eq. (10)] that for the generation of a strong mainshock (M.=.6.0..7.5) activation of neighbouring faults with a length larger than approximately the mainshock-fault-length/8 (typically 2 12 km) and seismic moment larger than ~.0.2% of the mainshock moment must precede and lead to the generation of the mainshock. Thus, the transfer of stress from smaller to larger faults (Turcotte, 1999) starts from faults of such dimensions. When ΔM takes values close to ΔM up (~.0.4 magnitude units smaller than the optimum ΔM), the smaller magnitude events (seismic moment between 0.07 and 0.2% of the mainshock magnitude) not only do not participate in this stress-transfer process but also do not allow the identification (due to their large number) of the accelerated seismic energy release behaviour. The results obtained in the present study can be affected by the data completeness, since M min is limited by the higher complete data magnitude threshold during the whole preshock period (from t s up to t c ). In Fig. 4, the estimated M min values are plotted against the starting year of the accelerating preshock period before each mainshock, t s, (last column in Table 1). For each case, the mainshock magnitude is plotted and the area of incomplete data is also shown (the t s axis corresponds to M.=.4.0 which is the data completeness threshold after 1980). The examination of Fig. 4 shows that, although the data set is relatively limited, the M min values are similar and stable over time for each magnitude range, during the whole examined period (1920-2001). In only three cases (events 1, 5 and 10 in Table 1, denoted by circles in Fig. 4) the M min values are equal to the corresponding completeness magnitude (top border of the incomplete data area). Therefore, in these cases the actual minimum magnitude may be even smaller, although comparison with similar magnitude events that lie in the complete data area does not support this suggestion. In order to check the effect of these events on our results, we have excluded these three events and repeated the estimation of Eq. (10). The use of the remaining 17 events resulted in ΔM.=.M-M min.=.0.28m.-.0.09 (σ.=.0.08), which is practically identical to the proposed Eq. (10). Hence, the magnitude completeness of the examined data set does not seem to affect the results obtained in the present study. It is of importance to notice that the values defined for the optimum value of the difference between the mainshock and the minimum considered preshocks [Eq. (10)] are not far from the qualitative proposal of Jaume and Sykes (1999), who suggested a typical difference of 2-3 orders of magnitude on the basis of the results available at the time. Moreover, the minimum magnitude values (~.1.6-2.0) obtained in the present study are almost identical to the minimum magnitudes originally used by Bufe and Varnes (1993), who suggested (as a rule-of-thumb ) using a minimum magnitude of about two magnitude units or less below the expected mainshock magnitude. This similarity suggests that the results obtained in the present study [e.g. 111

Boll. Geof. Teor. Appl., 44, 103-113 Papazachos 5.5 7.6 7.6 7.4 7.37.37.0 7.2 7.3 7.2 7.0 7.0 6.9 7.0 M min 5.0 4.5 Incomplete data 6.6 6.1 6.7 6.3 6.7 6.4 4.0 1920 1940 1960 1980 2000 t S (yr) Fig. 4 - Variation of M min with the starting time of the acceleration (preshock) sequence, t S, for each of the examined 19 mainshocks. The moment magnitude is shown for each event and the three events that have M min values at the top border of the incompleteness area (gray-shaded polygon) are denoted by a circle. Eq. (10)], may have a global applicability, at least for active tectonic areas such as California and the Aegean. On the other hand, the minimum magnitude may exhibit much lower values (larger ΔM values) for different seismic regimes, such as areas of thrust subduction events or intraplate earthquakes, depending on the pattern of stress transfer from smaller to larger faults in each seismic region. A possible limitation of the physical concept and practical use of minimum magnitude is the fact that it is probably dependent on the deformation measure used in each study, i.e. the choice of the exponent k in Eq. (1). When using the Benioff strain (k.=.0.5), as we have done here, the contribution of smaller magnitude events becomes more important compared to the larger ones, hence the selection of M min is critical in identifying and quantifying the accelerating deformation behaviour. This problem will be even more pronounced when using the cumulative number of events (k.=.0) but is less important when using the cumulative seismic moment or energy (k.=.1), as large events dominate the summation in Eq. (1). On the other hand, although cumulative moment is a more appropriate measure of observable seismic strain to be used for time-to-failure studies (Main, 1999), it exhibits much more non-linear accelerations and is also more sensitive to errors (e.g. in earthquake magnitude), hence its use in time-to-failure studies is often unstable compared to the Benioff strain (Bufe and Varnes, 1993). It should be pointed out that the obtained results derived for past earthquakes also hold for the six regions in the Aegean area, which have been shown to be at a state of accelerating seismic excitation, since Eq. (10) also applies for these regions (see Table 1). This observation can be considered as further evidence that these six regions are in a critical (metastable) condition, which can lead to the critical point, that is, to the generation of mainshock in the next few years. 112

Minimum preshock magnitude in critical regions Boll. Geof. Teor. Appl., 44, 103-113 Acknowledgments. I would like to thank Charles Bufe and an anonymous reviewer for their constructive comments and suggestions. This work has been partly supported by the Greek Earthquake Planning & Protection Organization (OASP) under project 20,239 and 20,242 Aristotle Univ. Thessaloniki Research Committee and is a Department of Geophysics, Univ. of Thessaloniki contribution number #624/2003. References Bowman D.D., Quillon G., Sammis C.G., Sornette A. and Sornette D.; 1998: An observational test of the critical earthquake concept. J. Geophys., 103, 24,359-24,372. Bufe C.G. and Varnes D.J.; 1993: Predictive modeling of the seismic cycle of the greater San Francisco Bay Region. J. Geophys., 98, 9871-9883. Huang Y., Saleur H., Sammis C. and Sornette D.; 1998: Precursors, aftershocks, criticality and self organized criticality. Europhys. Lett., 41, 43-48. Jaume S.C. and Sykes L.R.; 1999: Evolving release rate prior to large and great earthquakes. Pure appl. Geophys., 155, 279-306. Main I.; 1999: Applicability of time-to-failure analysis to accelerated strain before earthquakes and volcanic eruptions. Geophys. J. Int., 139, F1-F6. Papazachos C.B.; 2001: An algorithm of intermediate - term earthquake prediction using a model of accelerated seismic deformation. In: 2 nd Hellenic Conference on Earthquake and Engineering Seismology, 28-30 November 2001, Thessaloniki, A, 107-115. Papazachos B.C., Comninakis P.E., Karakaisis G.F., Karakostas B.G., Papaioannou Ch.A., Papazachos C.B. and Scordilis E.M.; 2000: A catalogue of earthquakes in Greece and surrounding area for the period 550 BC - 1999. Publ. Geop. Lab., Univ. of Thessaloniki, 333 pp. Papazachos C.B., Karakaisis G.F., Savaidis A.S. and Papazachos B.C.; 2002a: Accelerating seismic crustal deformation in southern Aegean area. Bull. Seismol. Soc. Am., 92, 570-580. Papazachos B.C., Kiratzi A.A. and Karakostas B.G.; 1997: Toward a homogeneous moment-magnitude determination for earthquakes in Greece and the surrounding area. Bull. Seism. Soc. Am., 87, 474-483. Papazachos B.C. and Papazachou C.B.; 1997: The Earthquakes of Greece. Editions Ziti, 304 pp. Papazachos B.C. and Papazachos C.B.; 2000: Accelerated preshock deformation of broad regions in the Aegean area. Pure appl. Geophys., 157, 1663-1681. Papazachos C.B. and Papazachos B.C.; 2001: Precursory accelerated Benioff strain in the Aegean area. Ann. di Geofisica, 44, 461-474. Papazachos B.C., Savaidis A.S., Karakaisis G.F. and Papazachos C.B.; 2002b: Preshock seismic deformation in the northwestern Anatolian fault zone. Tectonophysics, 347, 217-230. Papazachos B.C., Savaidis A.S., Papazachos C.B. and Karakaisis G.F.; 2002c: Precursory seismic crustal deformation in the area of southern Albanides. J. Seismology, 6, 237-245. Rundle J.B., Klein W., Turcotte D.L. and Malamud B.D.; 2000: Precursory seismic activation and critical - point phenomena. Pure Appl. Geophys., 157, 2165-2182. Sornette D. and Sammis C.G.; 1995: Complex critical exponents from renormalization group theory of earthquakes: implications for earthquake predictions. J. Phys. I. France, 5, 607-619. Sornette A. and Sornette D.; 1990: Earthquake rupture as a critical point. Consequences for telluric precursors. Tectonophysics, 179, 327-334. Turcotte D.L.; 1999: Seismicity and Self - organized criticality. Phys. Earth. Planet Inter., 111, 275-293. Voight B.; 1988: A method for predicting volcanic eruptions. Nature, 332, 125-130. Voight B.; 1989: A relation to describe rate-dependent material failure. Science, 243, 200-203. 113

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