ISSN 00014338, Izvestiya, Atmospheric and Oceanic Physics, 2011, Vol. 46, No. 8, pp. 962–970. © Pleiades Publishing, Ltd., 2011. Original Russian Text © E.A. Rogozhin, S.L. Yunga, S.N. Rodina, 2011, published in Geofizicheskie protsessy i biosfera, 2011, Vol. 10, No. 2, pp. 22–36.

Specific Features of the Appearance of Seismotectonic Deformations during the Genesis of March 11, 2011, Tohoku Earthquake Source E. A. Rogozhin, S. L. Yunga, and S. N. Rodina Schmidt Institute of Physics of the Earth, Russian Academy of Sciences, ul. Bol’shaya Gruzinskaya 10, Moscow, 123995 Russia email: [email protected]; [email protected]; [email protected] Abstract—The results of investigating the preparation zone of the catastrophic earthquake of March 11, 2011, near the eastern coast of Honshu Island are presented. A retrospective analysis of the focal mechanisms of deep earthquakes in the western part of the Pacific Ocean made it possible to reveal their influence on the zone of the Tohoku earthquake source. The preparation of this earthquake is also investigated within an anal ysis of the seismotectonic deformation processes at the regional level, which includes an estimation of the temporal trends of some key parameters, as well as the detection of their variations and the spatial confine ment of anomalies to the source zone. Keywords: earthquake, focal mechanisms, CMT solutions, seismotectonic deformations, deepfocus fore shocks, Honshu Island, Tohoku earthquake. DOI: 10.1134/S0001433811080081

INTRODUCTION Owing to the development and improvement of the global network of seismic stations, the deepening of methods for interpreting seismograms, and the acqui sition of permanently increasing data volumes, the study of regularities in the character of earthquake focal mechanisms acquires a particular importance. Although for a long time these data were mainly used for analyzing the structural positions of source zones of large earthquakes, a sharply increased information flux has opened up new possibilities for monitoring the seismotectonic deformation process [Rogozhin et al., 1999]. There has been a period of seismic activation at the eastern active margin of the Pacific Ocean since the mid1990s [Rogozhin and Zakharova, 1998]. A whole range of some of the strongest earthquakes occurred on the eastern coasts of Hokkaido and Honshu islands. Strong earthquakes (the 1994 Shikotan, 1995 Neftegorsk, and 1997 Kronotskii earthquakes, as well as the Simushir earthquakes of 2006 and 2007) occurred on Sakhalin Island and in the Kurile–Kam chatka island arc as well. According to the refined Japan Meteorological Agency (JMA) estimate, the magnitude of the 2011 seismic catastrophe was M = 9. For the Tohoku province (Honshu Island, the Japan Archipelago), this magnitude significantly exceeds magnitudes of all seismic events experimentally deter mined in the region [Tohoku…, 2011]. In order to understand the genesis of the source of the Tohoku earthquake, it is necessary, owing to its scale, to invoke

extensive, maximally complete, and statistically repre sentative data from the entire seismic history of the region and in the entire range of hypocentral depths, from the earth’s crust and lithosphere to the upper mantle. The developmental process of the seismic sit uation in the vicinity of the source of the Tohoku earthquake is analyzed below on different scale levels in the context of revealing regular and specific features of the occurrence of seismotectonic deformations (STDs) and the spatial–temporal confinement of key parameter anomalies to the source zone. DATA USED Seismological catalogs of the parameters of the earthquake source provide basic information for STD analysis and for revealing the tendencies and features of the STD development. The determination of the characteristics of earthquake focal mechanisms is widely used in modern seismological practice. These approaches were developed after the introduction of stationary observations of digital broadband seismic stations to the system and the organization of global seismic networks. Their application is based on an analysis of longterm seismic oscillations. The moment tensor components determined by the cen triod method (CMT solutions) are calculated with the use of waveform inversion [Dziewonski et al., 1981]. Such an analysis can be performed in an almost real time regime, as is done, for example, at the National Earthquake Information Center (NEIC), the seismic

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center of Harvard University in the United States, and at other centers. Since the beginning of the 1970s, CMT solutions have been being regularly determined within the frameworks of research projects from data of more than 100 digital stations of the global seismic network and a catalog of the parameters of the centroid moment tensor for earthquakes around the world with M ≥ 4.5 is published. This catalog is available for as far back as 1976 at www.seismology.harvard.edu and at some other sites. Since the longterm component of seismic waves is used for constructing CMT solutions, it can be assumed that data on focal mechanisms relate to the main rupture phases in strong earthquake sources and carry information about their general integral characteristics. The goal of this work was to identify the solutions, which in some indicators differ substantially from typical solutions, and to reveal the spatial–temporal relation between deepfocus fore shocks preceding large crustal earthquakes. ANALYSIS OF DEEPFOCUS SOURCES OF THE SUBDUCTION ZONE IN THE VICINITY OF HONSHU ISLAND According to the current notions of plate tectonics, strong seismic events in the zone of trenches located in the northwestern part of the Pacific Ocean owe their origin to the process of subduction of the Pacific Plate under Eurasia. This circumstance largely controls the mechanism of deepfocus foreshocks preceding large crustal earthquakes. Spatial–temporal relations between such events were noted by K. Mogi [1973, 1988]. Terminologically, deepfocus sources in the subduction zone of the lithospheric plate, in most cases, can be rather conditionally classified as fore shocks, mainly on the basis of their position in space and time. In the strict sense, the term “foreshock” suggests the substantiation of the interrelation between deepfocus and crustal sources, which is necessary for its application. The study of the distribution of com pression axes (P axes) of deepfocus sources showed that their projections onto the surface intersect in the zone of a potentially strong earthquake. Based on this fact, intersections of these axes can serve for the “visual” identification of potentially hazardous zones [Rogozhin et al., 2000; Zakharova and Rogozhin, 2000, 2006]. It seems that deepfocus foreshocks (with hypocenters at the depth H > 70 km), according to their compression axes, point to the preparation zones of future large earthquakes. In the context of the mediumterm prediction of strong earthquakes in the seismic focal Benioff zone, the authors of this work turn to the results of investiga tions into the spatial–temporal interrelation between deepfocus earthquakes of the backarc basin, which precede the strongest shallowfocus seismic shocks in the area of the oceanic deep trench. As a result of such investigations, the occurrence time and place of the IZVESTIYA, ATMOSPHERIC AND OCEANIC PHYSICS

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Kronotskii earthquake were predicted in more than a halfyear prior to the event, which occurred in Febru ary 1997. In the course of investigations developing the Mogi [1973, 1988] method, the deepfocus foreshocks of the 1994 Shikotan (Mw = 8.3) and 1997 Kronotskii (Mw = 7.8) earthquakes were considered and specific features of the deep remote foreshocks were related to those of subsequent strong crustal events. Similarly, the deepfocus foreshocks of the large Simushir earth quakes of 2006 and 2007 were revealed and analyzed. These earthquakes were predicted in a timely manner and the prediction was published [Zakharova and Rogozhin, 2006]. It was attempted in these investiga tions of deepfocus seismicity to retrospectively esti mate the duration of the foreshock stage of the prepa ration period of strong earthquakes from the data over 1982–2004 [Rogozhin et al., 2000; Zakharova and Rogozhin, 2000, 2006]. Source zones of strong earthquakes of this region (1999, Mw = 6.9; 2001, Mw = 6.4; 2002, Mw = 6.4; 2003, Mw = 7.0) are studied in work [Zakharova and Rogozhin, 2006]. It is important to emphasize that the zone of the 2003 earthquake located east of Honshu Island was also identified as the possible zone of a much larger earthquake, and it was inferred that earth quakes with Mw ≥ 8.1 may occur soon in this zone [Zakharova and Rogozhin, 2004]. Subsequently, the source of the Tohoku earthquake of March 11, 2011, was precisely in this zone. Since the continuations of axes are not intersected exactly at the same place, we developed a modified approach which makes it possible to introduce the quantitative characteristic for this method through calculating the parameter of the density of intersec tions in the cells of the specified grid covering the region of expected strong earthquakes. Such an updat ing of this method allowed us to construct a map of the introduced parameter of the density of intersections and rank and outline the revealed prognostic zones by drawing their contours. The constructions based on our analysis of deep focus foreshocks of the catastrophic earthquake of March 11, 2011, with successive approaches to the event over the periods of 10, 5, and 3 years prior to its occurrence, are presented in Figs. 2, 3a, and 3b, respectively. The preparation zone of the catastrophic earth quake of March 11, 2011, is clearly outlined from the results of a modified method for an analysis of deep focus sources. Therefore, the manifestations of deepfocus seis micity in a prolonged time interval can be used to solve the problem of identifying precursors of strong crustal events. Vol. 46

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Fig. 1. Source zone of the 2003 earthquake with Mw = 7.0 (small ellipse); the large ellipse is the zone of the potential source with Mw ≥ 8 and circles are the diagrams of focal mechanisms of foreshocks. The lines coming out of them continue the compression axes P [Zakharova and Rogozhin, 2004, 2006].

SPECIFIC FEATURES OF THE OCCURRENCE OF STDS AND THEIR SPATIAL–TEMPORAL CONFINEMENT TO THE TOHOKU SOURCE ZONE The considered centroidmoment tensors pre sented in the CMT catalog are determined for each tensor m under the condition of the zero trace spur(m) = λ1 + λ2 + λ3 = 0, where λ1, λ2, and λ3 (λ1 ≥ λ2, λ2 ≥ λ3) are the eigenvalues of the tensor m. At the same time, the condition of the equality to zero (det(m = 0) is not imposed for the determinant det(m) = λ1λ2λ3, so the CMT differs from the model of double dipoles without the moment that is traditionally used in the solutions of focal mechanisms. If twodipole sources corre spond to the movement on one rupture place, then a more general threedipole model, which is called the nondipole couple (NDC) source in the foreign litera ture, is used [Frohlich, 1995]. In order to elucidate the physical nature of three dipole sources, notions about the complex character of rupturing in sources, when movements on several planes occur simultaneously, are usually used [Lukk et al., 1976; Yunga and Vesson, 1979; Frohlich, 1995; Lutikov et al., 2010; Shevchenko et al., 2010]. Note that some large earthquakes in Eurasia have a complex structure not only according to seismological data, but also according to the results of field examinations [Rogozhin, 2000]. The Lode–Nadai coefficient μCMT = 3λ2/(λ1 – λ3), whose absolute value varies from 0 to 1, can be used as an example reflecting the measure of complexity of earthquake sources of the NDC type. At μCMT = 0, the source is modeled as a pair of double dipoles without the double couple (DC) moment. If |μCMT| = 1, NDC sources relate to the most complexly

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Fig. 2. The Tohoku earthquake source zone based on an analysis of deepfocus hypocenters (circles) in the back arc basin in the 10year period preceding the event. In Figs. 2, 3, and 9, the Tohoku earthquake epicenter is shown by a star; the dashed line indicates the characteristic strike of the aftershock region.

constructed, socalled compensated linear vector dipole (CLVD), sources. However, the values close to the limiting value are not noted in the region under consideration. The constructions were performed for revealing specific features in the temporal trend of the parame ter |μCMT| in the entire time interval available for anal ysis, where it will be expedient to identify the 5year period (from 2006 through 2011) (Fig. 4). The analysis shows that a significant variation related to the prepa ration period of the Tohoku earthquake takes place in the last interval (2010–2011). In order to reveal possible time variations in the reconstructed pattern of development of the STD pro cess, we used the method for calculating the average CMT solutions, determining their characteristics, and estimating the indicator of the deviation of typical and individual focal mechanisms [Yunga, 1990]. The STD characteristics were calculated both for the entire available time interval from 1976 through 2011 and for moving annual intervals with a shift of one month. Within each time interval in the circular region of averaging with the radius R = 2.5° and in the depth interval 0–70 km, we summarized the matrices of the CMT tensors m reduced to the unit intensity (the intensity is determined by the quadratic invariant the 1/2 power). The diagram of the calculated average mechanism over the period 2006–2011 in the circular

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Fig. 3. The Tohoku earthquake source zone based on an analysis of deepfocus foreshocks in the (a) 5year and (b) 3year periods preceding the event.

cylindrical vicinity of the Tohoku earthquake is pre sented in Fig. 5. The average tensors 〈m〉, as well as their compo nents corresponding to generalizedplane and cutting deformations, were analyzed for eigenvalues. We also determined the Lode–Nadai relation μSTD between the eigenvalues (deformation type) and the orientation of principal axes. At μSTD = –1, bilateral compression (uniaxial elongation) takes place in a macrovolume; at μSTD = +1, uniaxial compression takes place. It is difficult to fix distinct threshold values on this stage of investigation. These values can be taken as the characteristic ones, which are the difference between average values and the characteristic variation swings over the entire period of records. The results of calculations of the background STD characteristics in the source zone of the Tohoku earth quake over the period 2006–2011 are presented in Figs. 6 and 7. The time scan of the direction of shortening defor mation reflects the stable background orientation of the principal compression axis P in the range Az = IZVESTIYA, ATMOSPHERIC AND OCEANIC PHYSICS

90°–120° with the average value Az = 111°. A sharp deviation from this range is traceable in 2010–2011 (Fig. 6). In the time series of the parameter μSTD char acterizing the type of STDs, the background regime of compression or transpression changes to a regime of extension in the last critical interval (Fig. 7). The coefficient k of the similarity between the indi vidual normalized CMT matrix m reduced to the unit intensity and the average CMT solution 〈m〉* is deter mined by the scalar product k = m : 〈m〉*, where the colon means the convolution of tensors with respect to two indices. The temporal trend of the coefficient of similarity of individual mechanisms and the average CMT solution constructed for the period 2006–2011 is presented in Fig. 8. A sharp anomaly clearly manifests itself in the mis match interval 2009–2011. The spatial pattern of anomalies of the coefficient of similarity between indi vidual mechanisms and the average solution is pre sented in Fig. 9. Therefore, the process of STD occurrence in the region of Honshu Island and the deepsea trench is characterized by the presence of stable longterm ten Vol. 46

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dencies and sharp anomalies confined to the spatial– temporal vicinity of the catastrophic earthquake source manifest themselves against this background. Evidently, these features of the STD occurrence can be associated with the preparation process of the main rupture opening. RESULTS AND DISCUSSION The analysis of CMT solutions from the standpoint of estimating specific features of the seismogenesis made it possible to reveal the stage of a more notice able occurrence and prevalence of oneact movements against the background of a longterm predominance of relatively complicated sources of the NDC type. At this stage, the fraction of sources of the NDC type decreases and, accordingly, the deviation of CMT ten sors from the model of double dipoles without a moment is at a minimum. In this case, movements in sources mainly occur on unit rupture planes and sources having a complex structure become much rare. It must be noted that, analogously with our anal ysis of data aimed at verifying the NDC method, the same analysis of CMT solutions was performed for the vicinities of source zones of the destructive earthquake of September 12, 2007 (Mw = 8.5), in the southern Sumatra region and the strongest catastrophic earth quake of February 27, 2010 (Mw = 8.8), in Chile, which yielded similar results in respect to the specific features of NDC sources. It was proposed in work [Yunga et al., 2005] that NDC sources of such a complicated character of

Fig. 5. Diagram of the average mechanism constructed on the basis of CMT solutions over the period 2006–2011 in the Tohoku earthquake source zone with the use of the lower hemisphere projection; the points where the princi pal axes of extension and compression reach the focal sphere are shown by filled and open circles, respectively; the region of extension is shown in black; the converging arrows show the direction of maximal compression.

deformations in the source with simultaneous multiple movements on interacting ruptures be considered from the standpoint of the manifestation of selforga nized criticality (SOC) [Turcotte, 1999]. In respect to time, the physical interpretation of NDC effects can be associated with the influence of the forming source of a large earthquake on the surrounding volume of the geophysical medium, which reveals the properties of Azimuth P 160°

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Fig. 6. Temporal trend of the azimuth of the maximal com pression axis P over the period 1976–2011 in the vicinity of the Tohoku earthquake source zone.

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Fig. 7. Temporal trend of the Lode–Nadai coefficient in the vicinity of the Tohoku earthquake source zone over the period 1976–2011.

dynamic systems at the qualitative level [Lukk et al., 1996]. The behavior of such dynamic systems is char acterized by both stages of stability and bifurcation periods with transitions to a critical unstable stage of development [Gokhberg et al., 2004]. Stages of the chaotic component domination in the STD process change to periods of manifestations of the determinate component. The kinematics of movements can also reflect the fractal structure of the geophysical medium and SOC effects [Lukk and Yunga, 1989; Yunga, 1993b]. Source mechanisms of crustal earthquakes and anomalous zones reflecting disturbances in the developing defor mation process, which are identified on the basis of such mechanisms, are of prognostic interest [Yamash ina, 1979; Yunga, 1996]. Source mechanisms identi fied by this indicator are actually anomalous with the noncharacteristic orientation of rupture planes and movements on them. For example, the source zones of the Hokkaido earthquake of September 25, 2003, and the Simushir earthquakes of November 15, 2006, and January 13, 2007, were previously identified on the basis of an analysis of variations in the CMT solution, both in the retrospective aspect and during the real time monitoring of the seismic situation [Yunga, 1996; Rogozhin et al., 1999; Rogozhin and Yunga, 2000; Zakharov et al., 2009]. The results of a reconstruction of the regional field of STDs make it possible to shed new light on the spa tial–temporal interrelations between interplate and intraplatetype sources. In the seismic focal zone under consideration, the principal axis of compression is oriented across the strike of the island arcs and gen tly plunges toward the deepsea trench [Yunga and Rogozhin, 1998, 2000]. The extension axis is steeply IZVESTIYA, ATMOSPHERIC AND OCEANIC PHYSICS

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Fig. 8. Temporal trend of the coefficient of similarity between individual mechanisms and the average solution over the period 2006–2011 in the Tohoku earthquake source zone.

inclined toward the ocean. At such an orientation of the compression axes, the mutually intersecting sur faces parallel to the island arc are shearing planes. One of these surfaces is an almost pure thrust of the island arc over the deepsea trench; the other is a reverse fault of lower parts of the nearisland slope onto its upper parts steeply dipping under the trench. The real geological structures (the large lowangle thrust of crystalline rocks underlying the nearisland slope over loose sedimentary formations of the trench plunging under the island arc, on the one hand, and the series of steeply dipping (in eastern bearings) reverse faults expressed in the slope relief as several subparallel ridges with rocks of the acoustic basement cropping out loose sediments on the slope, on the other hand, which were revealed with the use of geo morphological and seismic methods) correspond to these surfaces on the nearisland slope. The acting planes in the sources of interplate and intraplate earth quakes of the island arc are confined precisely to these structures. Moreover, it is as if the sources of both types, crossing in the earth’s interior under the near island slope, mutually determine one another. The subvertical reverse fault “blocks” the free movement on the deep thrust surface. This barrier is broken by an earthquake of the interplate type, and, at the same moment, a new seismic barrier appears on the subvertical fault. This new barrier hampers the free movement of the reversefault sides and, some time later, it becomes broken in the process of an intraplate type earthquake. A rapid alternation of movements of both types is often observed at the same places nearby. The existence of extended seismic barriers under the continental slope of the island arc is possibly responsible for nontypical movements and elements of incompatibility of the regional field of STDs and the sharp heterogeneity of stresses in the lithosphere and the entire Benioff zone. As a consequence, seismolog ical and other anomalous phenomena manifest them Vol. 46

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selves in large territories and can be precursors to forthcoming strong earthquakes [Yunga, 1993a; Rogozhin et al., 1999]. It would be of interest to consider specific features of the aftershock process against the background of typical seismic events on the nearisland slope and in the trench. If the conditions of subhorizontal com pression across the strike of structures are, on the whole, typical of seismic events, the relationship of the cutting and horizontal STD components changes immediately after the main event. The principal axis of maximal compression acquires a much steeper incli nation under the oceanic plate. Subvertical normal faults with downward motions of the nearisland block with respect to the structures of the deepsea trench are predominant. In this case, the orientation of compression in the horizontal plane is determined not quite stably, and it varies in the entire possible range of directions, from sublatitudinal to meridional. Many focal mechanisms of the after shock series differ considerably from the typical solu tions characteristic of the entire preceding time. Thus, over the entire period of detailed investigations from 1976 to March 2011, a priori anomalous solutions amounted only to 4%, whereas their relative number sharply increased to 16% after the main shock.

The presence of complex sources, both at the after shock stage and in the preceding period, is character ized by the close values 〈NDC〉 = 0.12 and 〈NDC〉 = 0.15, respectively; i.e., on average, these indicators do not statistically differ. Significant distinctions are noted for the index of ordering of focal mechanisms χ = 〈k〉, which is also expressed in terms of the inten sity of the average mechanism matrix calculated through the averaging of unit matrices [Yunga, 1990]. In regards to information content, the temporal trend of the parameter χ is inferior to the time series of the correspondence coefficients k; therefore it is not pre sented here. Nevertheless, at the stage 1976–2011, χ = 0.85, and for the aftershock series March 11–April 11, 2011, χ = 0.42. Note that, in this case, such a small value of this parameter corresponds to a rather sub stantial disordering of the STD process in its after shock realization. In order to obtain a statistically reliable result at χ = 0.42 with a 95% significance level, the calculated samples must include at least 13 individual focal mechanisms [Yunga, 1990]. In other words, for small sample volumes characteristic of the aftershock sequences of events, the risk of obtaining an accidental result in the analysis of the time series of the parameter χ was very high, which is far from being favorable for understanding the nature of extremely complex pro cesses of STD occurrence. At the same time, the results of STD calculations carry important informa tion about the seismic process from the standpoint of selforganized criticality. The disordering reflects the chaotic character of the STD process, and it manifests itself in the mutual partial suppression of deformation increments. The calculations of the STD type described by the Lode– Nadai coefficient for the period 1976–2011 yield μSTD = 0.3, and μSTD = 0 for the period March 11– April 11, 2011. The observations described above suggest the pres ence of a certain dissipative effect (“dilatancy relax ation”) at the aftershock stage. This effect arises when, under the static action of gravitation during the dynamic action of the main rupture and the subse quent strike slips and normal faults under complex hydrodynamic, geothermal, and rheological condi tions, elements of the entire hierarchical structure of the multimillion volume (in cubic kilometers) of the rock massif, which is disturbed by a natural catastro phe, experience stagebystage nonuniform subsid ence [Agaronian et al., 1992]. CONCLUSIONS This work investigates the preparation zone of the Tohoku earthquake of March 11, 2011, at the eastern margin of Honshu Island in the Japanese Archipelago. We attempted to analyze the interrelation of seismicity in the lithosphere and mantle in two essentially differ ent depth intervals characteristic of the seismic focal

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subduction zone. The successive analysis of deep focus sources clearly reveals the preparation zone. The STDs and spatial–temporal realizations of STD release are reconstructed based on the data of the CMT catalog. Spatial–temporal anomalies in the trend of the STD process associated with the prepara tion of the catastrophic event source are revealed against the background of longterm tendencies of this process. Events for which focal mechanisms differ substantially from typical ones are regarded as an indi cator of anomalous physical conditions in sources. The revealed effects call for a further special consider ation within the framework of investigations of a seis mogenesis nature. Therefore, geodynamic manifestations of both the crustal and deepfocus seismicity can be regarded as precursor indicators of the catastrophic Tohoku earth quake of March 11, 2011, which opens up prospects for their further inclusion into the field of seismoprog nostic investigations [Rodkin and Tikhonov, 2011; Sidorin, 2011; Shebalin, 2011]. ACKNOWLEDGMENTS We are grateful to A.Ya. Sidorin and to an anony mous reviewer whose recommendations and com ments were taken into account in this work. This work was supported in part by the Russian Foundation for Basic Research (project no. 110500205a). REFERENCES Agaronian, V.G., Geodakian, E., Danilova, M., and Yunga, S.L., Aftershock Focal Mechanisms of the Spi tak Earthquake, Tectonophysics, 1992, vol. 202, no. 2/4, pp. 227–231. Dziewonski, A.M., Chou, T.A., and Woodhouse, J.H., Determination of Earthquake Source Parameters from Waveform Data for Studies of Global and Regional Seismisity, J. Geophys. Res., 1981, vol. 86, pp. 2825– 2852. Frohlich, C., Characteristics of WellDetermined Non DoubleCouple Earthquakes in the Harvard CMT Catalog, Phys. Earth Planet. Int., 1995, vol. 91, issue 4, pp. 213–228. Gokhberg, M.B., Garagash, I.A., Nechaev, Yu.V., Rogozhin, E.A., and Yunga, S.L., Geomechanical Model of the China Lake Seismic Cluster in Southern California, in Issledovaniya v oblasti geofiziki (Research in Geophysics), Moscow: OIFZ RAN, 2004, pp. 90–98. Lukk, A.A., Yunga, S.L., and Leonova, V.G., General View of the Nodal Surface during Crustal Earthquakes, in Sbornik Sovetskoamerikanskikh rabot po prognozu zem letryasenii (Collection of Soviet–American Works on Earthquake Forecasting), Sadovskii, M.A., Ed., Dush anbe: Donish, 1976, vol. 1, book 2, pp. 60–72. Lukk, A.A. and Yunga, S.L., Fractality and the Stress Strain State of the Earth’s Crust in the Garm Region, in Geologiya i geofizika Tadzhikistana (Geology and Geo physics of Tajikistan), Dushanbe: Donish, 1989, no. 2, pp. 259–276. IZVESTIYA, ATMOSPHERIC AND OCEANIC PHYSICS

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