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ISSN 0145 8752, Moscow University Geology Bulletin, 2013, Vol. 68, No. 5, pp. 282­288. © Allerton Press, Inc., 2013. Original Russian Text © V.S. Zakharov, 2013, published in Vestnik Moskovskogo Universiteta. Geologiya, 2013, No. 5, pp. 18­24.

On the Mechanism of the Generation of Seismic "Nails"
V. S. Zakharov
Faculty of Geology, Moscow State University, Moscow, 119991 Russia e mail: vszakharov@yandex.ru
Received March 11, 2013

Abstract--The spatial and temporal peculiarities of seismic "nails" are analyzed. Some nails are related to strong earthquakes, or volcanic eruptions, while some do not show any coincidence with any fault zone or other tectonic structures. In some cases, poorly expressed trends in the depths of earthquake occurrence sequences occur. Based on the calculation of the Hurst exponent, a stable tendency in the order sequence for the depths of hypocenters that form a nail has been revealed. This tendency is consistent with self organiza tion models, which demonstrate positive feedback during interactions between fluid flows and tectonic defor mations and have been used to explain the earthquake generation mechanism. The peculiarities of changes in earthquake numbers on the day when a nail is formed agree well with the acoustical emission dynamics during earthquake triggering through water injections, based on the long term experimental data. The most probable mechanism that generates the seismic nails that are not related to strong earthquakes is seismic acti vation under the effects of fluids. Keywords: subvertical clusters of earthquake hypocenters, seismic nails, volcanic eruptions, faults, fluids, acoustical emission, Hurst exponent DOI: 10.3103/S0145875213050086

INTRODUCTION Seismic "nails," which are short lived subvertical seismofocal structures that are isometric in plan view, were discovered by V.N. Vadkovsky (1996, 2012) dur ing study of the spatial distribution of earthquake hypocenters in the region of the Japan Islands. It has been found that these structures consist mostly of weak earthquake sources (M = 2­3); the vertical size of a nail is 10 to 50 km, its depth is no more than 90 km, and the epicentral projection of a nail to the Earth's surface is 2­10 km in diameter. The upper part of a nail may outcrop to the surface. In our previous studies (Zakharov, Karpenko, and Zavyalov, 2013), seismic nails have been discovered in different regions of the world (the Pacific coast of North America, Kamchatka, Japan Islands, and Sulawesi Is.) when analyzing their respective earth quake catalogs. The common feature of these nails is their subvertical configuration and small formation time (from 10 days to 2 months). A significant part of these seismofocal structures is located within subduc tion zones (in the area of a volcanic arc, in the forearc or backarc part, and in the trench zone as well). For illustration purposes, two seismic nails, which both formed south of Honshu Is. in September­November 1990, are shown in Fig. 1. The first was located in the forefront of the Nankai trench (33.2° N, 138.6° E); the range of source depths was 30­80 km. In the begin ning of its formation, M 6.6 (60 km depth) and M 6.0 (42 km depth) earthquakes occurred, while the other

events were less than 5 in magnitude. The second nail was located in the backarc part of the Izu­Bonin sub duction zone (33.7° N, 139.4° E) and consisted of weak earthquake sources. It has been found that some seismic nails are related to volcanic eruptions (i.e., they precede and follow them) and hydrothermal activity. Some nails can be triggered by a strong (M > 5) earthquake, while some nails incorporate these earthquakes among oth ers. For some seismic nails, a clear coincidence to fault zones and other tectonic structures is not seen. In some works (Vadkovsky, 1996, 2012; Shevchenko et al., 2011; Zakharov, Karpenko, and Zavyalov, 2013), the suggestion was made that non coincidence of seismic nails to faults might be caused by motion of fluids. The present paper continues the investigation of the properties and characteristics of these peculiar seismofocal structures, which started in (Zakharov, Karpenko, and Zavyalov, 2013). The aim of the present paper is to analyze the spatial and temporal peculiarities of seismic nails and their relationship to tectonics and geodynamics in order to reveal possible generation mechanisms. MATERIALS AND METHODS The data involved in the present study were: the NEIC PDE catalog (http://earthquake.usgs.gov/ regional/neic) for 1973­2011; the catalog of Japan Meteorological Agency (JMA); the catalog of South

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ON THE MECHANISM OF THE GENERATION OF SEISMIC "NAILS" (b) Depth 0 (a) 10 20 40 50 60 Honshu Is. 70 80 90
34 137.8 34.0 .2 3 138.2 3 3.8 138.6 33.4 3.6 de 139.0 3 u Lon 3 3.2 Latit gitu 139.4139.8 32.8 2.6 de 140.2 32.6

283

10.11.1990 M<6 M>6

Fig. 1. Seismic nails south of Honshu Is. in September­November 1990: (a) the position of the nails, as indicated by a rectangle; (b) the 3D shape of the nails. The epicentral projections of sources, volcanoes (triangles), and plate boundaries (lines) are also indicated. The filled circles are M 6 earthquakes; the empty ones are M < 6 earthquakes.

N

30

09.11.1990

ern California Earthquake Data Center (SCEDC, http://www.data.scec.org) and that of the Northern California one (NCEDC, http:quake.geo.berkeley.edu) for 1967­2010; and the catalog of the Kamchatka Division of the Geophysical Survey, Russian Academy of Sciences (http://data.emsd.iks.ru) for 1962­2011. The accuracy of the definition of coordinates is highly important for the present investigation, since the fine seismicity structure is considered. The error in coordinate definition is 5­10 km for the PDE and Kamchatka catalogs, < 1 km for the JMA catalog, and < 3 km for the SCEDC and NCEDC catalogs (mostly < 1 km). Note that different catalogs utilize different magnitude types and we indicate this. The source size is ignored here; it is believed to be a point with the respective spatial coordinates and mag nitude. This is reasonable because, first, investigation of source processes is beyond the scope of the present study, and, second, seismic nails consist mostly of weak earthquakes whose source sizes are insignificant, e.g., for M 5 earthquakes (which are quite rare in nails), the source extent does not exceed 4 km (Kasa hara, 1981); for the weaker events, it is less but still within the error of coordinate determination. To investigate the characteristics of seismic nail formation, we determined the trends in the time sequence of focal depths, the distribution of events in time, and the Hurst exponent (Lukk et al., 1996; Tur cotte, 1997). The values of the Hurst exponent allow
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us to distinguish the time dependences that have a sta ble tendency (persistence) at H > 0.5 from those char acterized by its absence (antipersistence) at H < 0.5. REVEALING THE TRENDS IN THE SEQUENCE OF FOCAL DEPTHS It has been reported in previous works (Vadkovsky, 1996, 2012; Zakharov, Karpenko, and Zavyalov, 2013) that analysis of the time sequences of focal depths for all studied sesimofocal structures do not allow one to reveal any trend of focal depth changes with time. We made a more detailed study to identify linear trends for all these sequences, The examples of these estimates for seismic nails that were located south of Honshu Is. and in Hokkaido Is. are presented in Fig. 2. The results show that the value of the linear regres sion slope is close to zero for most sequences. The val ues of the correlation coefficient under approximation are significantly less that 0.5 in all cases (usually 0.1­ 0.2), and the standard deviations of the obtained slope values are comparable in their absolute values with the values proper (or the former even exceed the latter). This generally verifies the earlier conclusion about the absence of clear trends. Nevertheless, the slope value for a few seismic nails is significantly more than zero. In particular, the seismic nails that formed after the Kolo and Karymsky volcanoes eruptions have a quite discernible trend of a focal depth increase. This is probably related to the processes that accompany the
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284 Depth, km 30 40 50
2 1

ZAKHAROV (a) Depth, km 0 5 10 15
1

(b)
2

60 70 80 90 21.09.90 05.10.90 19.10.90 02.11.90 16.11.90
2

20 25 30 35 40 30.01.89 02.01.89 27.02.89 27.03.89 13.03.89 16.01.89 13.02.89
2

Fig. 2. The time series of earthquake source depth values during the formation of different nails: (a) south of Honshu Is., Septem ber­November 1990; (b) Hokkaido Is., January­March 1989. The trends (1) and 95% confidence interval (2) are also shown. The filled circles are M 6 earthquakes; the empty ones are M < 6 earthquakes.

eruption. Remarkably, for the seismic nail that formed prior the 1980 Mount St. Helens (Cascade Range) eruption, a weak trend towards depth reduction is identified, probably due to seismicity induced by magma uplift and implementation of the mechanism described in (Kilburn, 2003). Note that for most nails located in the areas of vol canic arcs (four of six) the Student criterion t > 2, which indicates the validity of the revealed trends (p = 0.95) despite the low values of the correlation coefficient. For the two remaining nails, t > 1.6 and the validity of the trends is p = 0.9; in the author's opinion, this is related to the vertical motion of fluids or melt. How ever, the different directions of the revealed trends must be explained precisely. Valid trends have also been revealed for nails in California and for some oth ers that are not related to eruptions, for example, the nails shown in Fig. 2. THE HURST ANALYSIS AND REVEALING PERSISTENT TENDENCIES Hurst analysis allows one to find hidden regulari ties in a time series of focal depths. The values of the Hurst exponent, H, were determined for the ordered sequence of hypocentral depths in a nail. It was found that the H values validly exceed 0.5 (within the range 0.57­0.69). The errors of H determination are no more than 0.05 and the correlation coefficient during linear regression is at least 0.98; The Student criterion indicates the high validity of the approximation. As described above, these values of H mean the presence of a persistent tendency in these sequences.

CHANGE OF EARTHQUAKE NUMBERS ON THE DAY OF SEISMIC NAIL FORMATION The study revealed that the character of the earth quake number distribution on the day of seismic nail formation for cases related to eruptions, strong earth quakes, and neither of these two phenomena. Figure 3a presents the earthquake number distribu tion in time on the day when a seismic nail formed after the M 7 Karymskoe earthquake of January 1, 1996. This pattern is typical for the nails triggered by a strong initial event: the nail formed south of Honshu Is. after an M 6.6 earthquake (Fig. 3b); the nail near Kodiak Is. was related to an M 6.8 earthquake in 1999; and that in the area of Inyo, California, was induced by an M 5 earthquake in 1998. These nails are likely to be the aftershock sequences of strong earthquakes and demon strate a power law drop in earthquake numbers accord ing to Omori law (Kanamori and Brodsky, 2004). For the seismic nails with no strong events at their beginning, the shape of the diurnal earthquake num ber distribution in time is different. Figure 4a presents the diurnal change of earthquake numbers in March­ April 1983 for a nail that formed in Hokkaido Is. (Vad kovskii, 2012; Zakharov, Karpenko, and Zavyalov, 2013). Analysis of this distribution does not allow us to distinguish a uniform power law drop in earthquake number with time. The analogous dependences are observed for a seismic nail that emerged in 1998 in the area of the Long Valley caldera in California (Fig. 4b) and for many others as well. The remarkable feature is the presence of intermediate peaks in these distribu tions. The occurrence of seismic nails is a fading pro cess, but the fading pattern likely differs from that of earthquake aftershocks. For seismic nails that are related to volcanic erup tions, the daily based earthquake number distribution is of irregular character; however, an intermediate
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ON THE MECHANISM OF THE GENERATION OF SEISMIC "NAILS" N 350 300 250 200 30 150 100 50 0 30.12.95 06.01.96 19.01.96 20.01.96 27.01.96 20 10 0 21.09.90 05.10.90 19.10.90 02.11.90 16.11.90

285

(a)

60 50 40

(b)

Fig. 3. Variations in diurnal earthquake numbers during the formation of seismic nails following strong earthquakes: (a) after the M 7 Karymskoe earthquake of January 1, 1996; (b) south of Honshu Is., September­November 1990, after the M 6.6 earthquake of September 24, 1990.

N 35 30 25 20 15 10 5 0

(a)

60 60 50 40 60 50 40 30 20 10

(b)

0 18.03.89 06.03.90 26.02.90 02.03.90 10.03.90 17.01.89 16.01.89 03.03.89 08.03.90 28.02.90 04.03.90 02.01.89 01.02.89 02.04.89
Fig. 4. Variations in diurnal earthquake numbers during the formation of seismic nails that were not related to strong earthquakes: (a) 1989, Hokkaido Is.; (b) 1990, Long Valley caldera, California.

peak can also be distinguished. An example of such a dependence is presented in Fig. 5 (the 1980 Mount St. Helens eruption). LONG PERIOD EARTHQUAKES It has been found by seismologists and volcanolo gists that an active role in the generation of so called long period (low frequency) earthquakes is played by fluids (Gorel'chik and Storcheus, 2001). The long period character of earthquakes is usually determined on the basis of spectral analysis of seismic records; however, in the present case these records are unavail able. It can be indirectly derived from the ratio between body wave magnitude mb and moment mag nitude Mw. The mb/Mw ratio characterizes the relative contribution of high and low frequency seismic radi
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ation, because body wave magnitude mb is determined mostly by high frequency seismic vibrations and moment magnitude Mw is produced by the low fre quency component of seismic emission (Kanamori, 1983). Low values of this ratio indicate a long period character of earthquakes. Unfortunately, the data on different magnitude types are available only for a few earthquakes within seismic nails, e.g., one of the events in the structure of a seismic nail that formed in the area of the Aleutian Islands in 2010 is characterized by mb/Mw = 5.2/5.6, which indicates a long period character. RESULTS AND DISCUSSION In (Vadkovsky, 2012), based on the Markov proper ties of focal depth sequences in a seismic nail, it was
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286 N 14 12 10 8 6 4 2 0 25.03.80 08.04.80 22.04.80 06.05.80

ZAKHAROV

20.05.80

Fig. 5. Variations in diurnal earthquake numbers during the formation of the seismic nail that was related to the 1980 Mount St. Helens eruption. The triangle indicates the moment of the beginning of the catastrophic eruption on May 18, 1980.

inferred that a seismic nail formed in the entire depth interval and no predominant direction (upwards or downwards) was typical for it. The detailed analysis carried out by the author in the present paper extends these results. Weak but quite valid trends were revealed for most of the considered sequences. The results of Hurst exponent definition indicate the presence of a stable tendency (persistence) in the ordered sequence of depths for the hypocenters that form a nail. This sequence is not random, but possesses a certain deter minative character and a kind of memory. The memory of this process manifests itself in the way that the present state is caused by the values of control variables in both current and past time moments. The presence of memory in natural pro cesses (Hurst effect) is explained by power law relax ation. The memory emerges when the response of a system to an external effect is not instant, but is imple mented as a long term transitional process. In this case, the effect caused the changes integrates (accu mulates) (Lukk et al., 1996). The revealed peculiarities of the manner in which seismic nails form can help in the search for the gener ation mechanisms of these structures. It was shown in (Vadkovsky, 1996, 2012; Shevchenko et al., 2011; Zakharov, Karpenko, and Zavyalov, 2013) that the mentioned peculiarities (geometry and formation rate) of seismic nails suggest a possible role of fluids in their origination. In this case, the memory effect can be caused by the relaxation of viscous fluid in a porous medium, which is a typical phenomenon for most problems of nonstationary and nonlinear filtering. An alternative explanation is the relaxation of stresses that build up on faults in the form of series of weak earth quakes. The surface manifestations of these faults may be absent, especially when the small magnitudes of

most earthquakes that form seismic nails are taken into account. It is thought that these mechanisms do not contra dict each other. The modern ideas about the role of fluids in the generation of earthquakes allow us to con sider both these mechanisms as one. The mechanism of self organization with positive feedback during interactions between fluid flows and tectonic defor mations was used to explain the mechanism of earth quake generation in (Kissin, 2009). The following model was suggested: under the effect of fluids, the strength (first of all, shear strength) of rocks decreases. This occurs due to both mechanical and physical chemical effects. In the latter case, the most important role is played by the Rebinder effect, which is an adsorption decrease in strength (Rebinder and Shchukin, 1972). Due to reduced strength, tectonic slips are activated and, in their order, these provide additional fluid migration. As a resulting of these slips, heat is released and the temperature rises, leading to even higher metamorphic dehydration of rocks. Water release and increase in fluid pressure is accompanied by a decrease in effective stress, creating conditions that are favorable for the further development of shear deforma tions. It has also been noted that these processes are pos sible in initially dry rocks, if P­T conditions are favorable for water release in the shear zone proper. Thus, according to (Kissin, 2009), a close relation ship between tectonic processes and fluid flows is determined by the self organization mechanism that occurs due to "mutual induction": fluid flows activate tectonic processes and tectonic processes lead to the intensified migration of fluids, and, remarkably, each of these phenomena can be a trigger. Note that the "origination of the subvertical element of the fluid sys tem is caused by the presence of a weakened zone that formed under the effect of either tension or shear stresses and deformations. Such a weakened zone ... can be a conduit for upward migration of deep fluids and a zone of slip occurrence" (Kissin, 2009, p. 95). It is also important to note that interaction between fluid flows and tectonic deformation is highly nonlin ear in character and this nonlinarity is determined pri marily by fluid effects. Nonlinear systems are charac terized by a high dependence of system behavior on parameters (for example, on P­T conditions). If the medium parameters in nonlinear systems reach cer tain critical values, very rapid changes and reconstruc tions can take place in the system. Nonlinear positive feedback leads to a self accelerating avalanche like evolution of the process (Prigozhin and Stengers, 1986). Such a super rapid emergence of processes for a short time period in open nonlinear structures was named a "blow up regime" (Knyazeva and Kurdyumov, 2002). This approach is used to explain rapid tectonic phenomena, and, in particular, earth quakes. This is especially applicable to so called trig gered earthquakes. In the author's opinion, a similar mechanism may be implemented during the genera
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ON THE MECHANISM OF THE GENERATION OF SEISMIC "NAILS" dN/dt 10.0 1.0 0.1 0.01 0.001 0.0001 1 dN/dt 10.0 1.0 0.1 0.01 0.001 0.0001 1 10 100 1000 10 000 100 000 1 000 000 Seconds 1 2 4 6 8 10 Time, days 10 10 100 (b) 1000 10 000 100 000 Seconds 1 0.1 N 100 1.0 (d) 10.0 100.0 Time, days 10 N 100

287

(a)

(c)

Fig. 6. Comparison of the experiments to study the acoustic emission and the investigation of seismic nail evolution in time. On the left, the number of acoustic pulses dN/dt per second in the experiments, after (Sobolev et al., 2010): (a) mechanic load; (b) water injection. On the right, variations in diurnal earthquake numbers during the formation of a seismic nail: (c) after the 1996 Karymskoe earthquake; (d) formed in 1990 in the area of the Long Valley caldera, California. The lines denote dependence according to Omori law.

tion of seismic nails: fluid supply into a weakened zone when fluid concentration or pressure are at critical val ues can trigger an earthquake, or a quick series of earthquakes that form a nail. A suggestion that is similar in sense was made in (Gufeld, 2012), but triggering of theoretical "deep focus ruptures" and rapid nail shaped seismicity structures was related to hydrogen flows: "... the most active interaction with the medium can be related to ascending hydrogen flows and pre existing structural features." It is supposed that above the Moho discon tinuity a nail zone corresponds to the initial stage of a future rupture owing to the interaction between the medium and a localized ascending hydrogen flow. The fluidometamorphic model of seismotectogen esis, which was suggested by M.V. Rodkin (2006), is close to the above ones. According to it, alterations in the lithosphere, which are accompanied by a decrease in strength, take place under the catalytic effect of deep aqueous fluids; the important role is played by the metastable state of the fluid distributed at the boundaries of rock grains. It is believed that these models explain both the spatial and temporal peculiarities of seismic nails.
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These ideas about the role of fluids are supported by the results of laboratory experiments. In (Sobolev et al., 2010; Sobolev and Ponomarev, 2011) the dynamics of acoustical emission during triggering by water were considered in long term experiments. Injection of a small (< 0.1% of the model volume) amount of water led to the activation of acoustical emission, which occurred with a time delay. The authors of the cited works believed that the triggering of the acoustical emission was related to a local decrease in strength (probably due to the Rebinder effect) and an increase in stresses near metastable cracks; this viewpoint does not contradict the trigger ing mechanism. Strong events occurred between weak ones, by analogy with earthquake swarms. It was noted that the character of acoustical emission growth and decrease in time was significantly different under dif ferent experimental conditions: a step wise mechani cal load leads to a power law reduction of earthquake number with time according to Omori law (Fig. 6a), while water injection produces a clearly expressed peak in the intensity of acoustical emission (Fig. 6b).
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CONCLUSIONS To conclude, let us compare the results of the experimental works described above and the results of the investigation of seismic nail formation patterns that were obtained by the author. As described, nails that form after strong earthquakes show a reduction of earth quake numbers according to a power law. Figure 6c pre sents the log­log plot of this dependence for a nail that was followed by the 1996 Karymskoe earthquake. It is seen that this curve is clearly consistent with that for Omori law and the experimental results for the case with no water injection (Fig. 6a). In contrast, seismic nails that are not generated by strong earthquakes demonstrate a clear peak in the diurnal number of earthquakes. Figure 4d gives an example of this dependence for a nail that formed in 1990 in the area of the Long Valley caldera in a log­log plot. Similar distributions of the diurnal number of earthquakes have been revealed for many seismic nails. The similarity between these dependences with the experimental results for the case of water injection indicates a fluid related mechanism of generation for the latter type of seismic nail. Thus, the most probable mechanism of the genera tion of seismic nails that are not related to strong earthquakes is activation of seismicity by fluids. ACKNOWLEDGMENTS The catalogs of California and Japan earthquakes were used courtesy of the World Data Center for Solid Earth Physics. The author is sincerely grateful to N.A. Sergeeva, M.G. Lomize, N.V. Koronovsky, D.A. Simonov, M.V. Rodkin, and V.B. Smirnov for their discussions and help. This work was supported by the Russian Founda tion for Basic Research (project no. 13 05 01033). REFERENCES
Gorel'chik, V.I. and Storcheus, A.V., Deep long period earthquakes beneath Klyuchevskoi volcano, in Geodi namika i vulkanizm Kurilo Kamchatskoi ostrovoduzhnoi sistemy (Geodynamics and volcanism of the Kuril Kamchatka island arc system), Petropavlovsk Kam chatskii: IVGiG DVO RAN, 2001, pp. 373­379. Gufel'd, I.L., Geologic implications of amorphization in the lithosphere and upper mantle structure, caused by hydrogen degassing, Geodin. Tektonofiz., 2012, vol. 3, no. 4, pp. 417­435. Kanamori, H., Magnitude scale and quantification of earthquakes, Tectonophysics, 1983, vol. 93, pp. 185­ 199. Kanamori, H. and Brodsky, E.E., The physics of earth quakes, Rep. Prog. Phys., 2004, vol. 67, pp. 1429­1496.

Kasahara, K., Earthquake mechanics, Cambridge: Cam bridge Univ., 1981. Kilburn, C.R.J., Multiscale fracturing as a key to forecasting volcanic eruptions, J. Volccanol. Geotherm. Res., 2003, vol. 125, pp. 271­289. Kissin, I.G., Flyuidy v zemnoi kore geofizicheskie i tekton icheskie aspekty (Fluids in the Earth's crust: Geophysi cal and tectonic aspects), Moscow: Nauka, 2009. Knyazeva, E.N. and Kurdyumov, S.P., Osnovaniya sinerget iki. Rezhimy s obostreniem, samoorganizatsiya, tem pomiry (Fundamentals of synergy: Blow up regimes, self organization, temporal worlds), St. Petersburg: Aleteiya, 2002. Lukk, A.A., Deshcherevskii, A.V., Sidorin, A.Ya., and Sidorin, I.A., Variatsii geofizicheskikh polei kak proyav lenie determinirovannogo khaosa vo fraktal'noi srede (Variations in geophysical fields as manifestation of determined chaos in fractal medium), Moscow: OIFZ RAN, 1996. Padhy, S., Mishra, O.P., Zhao, D., and Wei, W., Crustal het erogeneity in the 2007 Noto Hanto earthquake area and its geodynamical implications, Tectonophysics, 2011, vol. 509, pp. 55­68. Prigogine, I. and Stengers, I., Order out of chaos, New York: Bantam Books, 1984. Rebinder, P.A. and Shchukin, E.D., Surface phenomena in solids during the course of their deformation and fail ure, Usp. Phys., 1973, vol. 15, 533­554. Rodkin, M.B., Fluid metamorphogenic model of seismo tectogenesis, in Flyuidy i geodinamika (Fluids and geo dynamics), Moscow: Nauka, 2006, pp. 181­200. Shevchenko, V.I., Aref'ev, S.S., and Lukk, A.A., Subvertical clusters of earthquake hypocenters unrelated to the tec tonic structure of the Earth's crust, Izv., Phys. Solid Earth, 2011, vol. 47, no. 4, 276­298. Sobolev, G.A., Ponomarev, A.V., Maibuk, Yu.Ya., Zakrzhevskaya, N.A., Ponyatovskaya, V.I., Sobolev, D.G., Khromov, A.A., and Tsyvinskaya, Yu.V., The dynamics of the acoustic emission with water initiation, Izv., Phys. Solid Earth, 2010, vol. 46, no. 2, pp. 136­153. Sobolev, G.A. and Ponomarev, A.V., Dynamics of fluid triggered fracturing in the models of a geological medium, Izv., Phys. Solid Earth, 2011, vol. 47, no. 10, pp. 902­918. Turcotte, D.L., Fractals and chaos in geology and geophysics, Cambridge: Cambridge Univ., 1997, 2nd ed. Vadkovskii, V.N., Nature and mechanism of seismic "nails," in Tez. dokl. Lomonosovskie chteniya (Abstr. Conf. "Readings in memory of M.V. Lomonosov"), Moscow, 1996, pp. 63­64. Vadkovskii, V.N., Subvertical clusters of earthquake hypo centers­seismic "nails," Vestn. Otd. Nauk Zemle Ross. Akad. Nauk, 2012, no. 4. doi: 10.2205/2012NZ000110 Zakharov, V.S., Karpenko, A.I., and Zav'yalov, S.P., Seis mic nails in various geodynamic conditions, Moscow Univ. Geol. Bull., 2013, vol. 68, no. 1, pp. 10­16.

Translated by N. Astafiev

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