Seismic strain in the Altai-Sayan active seismic area and elements of collisional geodynamics

Russian Geology and Geophysics 48 (2007) 536–557 www.elsevier.com/locate/rgg

Seismic strain in the Altai-Sayan active seismic area and elements of collisional geodynamics S.V. Gol’din †, O.A. Kuchai * Institute of Petroleum Geology and Geophysics, Siberian Branch of the RAS, 3 prosp. Akad. Koptyuga, Novosibirsk, 630090, Russia Received 19 September 2006

Abstract Seismic strain estimated from about 900 earthquake mechanisms in the Altai-Sayan area indicates that the area evolves mainly under N-S compression caused by the India-Eurasia collision. Plastic flow in the mountains of the western and central Altai-Sayan area is controlled by convergence of aseismic rigid blocks, including the Dzungarian microplate, the Minusa basin, the Tuva basin, Uvs Nuur and other basins in the region of Great Lakes in Mongolia. Earthquake rupture follows the existing fault pattern. The pattern of rigid blocks and mountain ranges correlates well with upper mantle thermal heterogeneity as imaged by seismic tomography. Earthquake mechanisms in the presence of plate convergence depend on different factors. Slip geometry depends on focal depth at a given geodynamic regime, and the latter, in terms of the seismic process, is controlled by lateral (W-E) constraint. Reverse-slip earthquakes most often originate at shallow depths in regions of constrained compression, such as the Tien Shan, and strike slip is the dominant mechanism under non-constrained and moderately constrained compression. The direction of slip is governed by the parallel component of convergence and by the fault pattern. In regions of strain shadow, slip occurs mostly on normal planes, and shallow earthquakes have strike-slip mechanisms. The crust in the collisional region is divided into systems of rigid and plastic blocks (rheological structure) and of fault blocks (fault-block structure). The two types of systems coexist and determine the generally similar but specifically different features of local mass transfer. © 2007, IGM, Siberian Branch of the RAS. Published by Elsevier B.V. All rights reserved. Keywords: Seismic strain; earthquake mechanisms; collision; geodynamics; stress

Introduction The southeastern Gorny Altai in the northwest of the Altai-Sayan area was shocked by a large earthquake quite recently. That was the M = 7.3 Altai (Chuya) earthquake of 27 September 2003. It appears interesting to view the event in terms of the geodynamic framework of the active area lying between ϕ = 46.0−54.5° N and λ = 80−100° E (Fig. 1). We estimate crustal stress and strain using earthquake focal mechanisms, along with GPS data and available faulting-based deformation models. Two main questions arise concerning earthquake mechanisms and seismic strain: (i) which geodynamic features are imprinted in earthquake strain and (ii) which is the major control of actual focal mechanisms. Most authors engaged in geodynamic studies of Central Asia agree that the Altai-Sayan area develops in response to the India-Eurasia collision. There

† Deceased. * Corresponding author. E-mail address: [email protected]

is some controversy about the division of the territory into regions that belong to the collision zone proper and those of collision influence. More controversy concerns the role of specific geodynamic processes associated with lithospheric horizontal compression (Calais et al., 2003): it is either crustal thickening caused by viscous flow and the related isostasy changes that drive active deformation or lateral extrusion in systems of relatively rigid blocks (Calais et al., 2003 and references therein). It is unwise, however, to neglect any physically possible factor. Any movement in an isostatically balanced medium would disturb the equilibrium, and isostatic rebound would occur in any case. Lateral extrusion (kinematic model in Calais et al., 2003) likewise takes place, but hardly it is the main geodynamic agent as too many rocks in the area bear pronounced signature of viscoplastic flow. On the other hand, the crustal thickening (dynamic) model appears to underestimate the part of block kinematics. Our main idea is that the current viscoplastic flow in the lithosphere is driven by the interaction of rigid and plastic blocks. In this respect it is essential to look into seismicity and other geodynamic processes in different parts of a large collision-related region

1068-7971/$ - see front matter D 2007, IGM, Siberian Branch of the RAS. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.rgg.2007.06.005

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Fig. 1. a. Map of M > 3.5 seismicity (black dots) in Altai-Sayan area for 1761 through 2003. b. Map of slip geometry in earthquake mechanisms of Central Asia for 1950 through 1995. 1 — thrust and reverse oblique slip; 2 — normal and oblique slip; 3 — strike slip.

within its general geodynamic framework assumed as the background. The part of Central Asia we study is a place where the deformation pattern changes successively eastward from reverse and strike slip to normal slip (Tapponnier, 1979). Therefore, it is pertinent to compare the Altai-Sayan area, where most earthquakes show strike-slip behavior, with the Tien Shan, where they have mainly reverse mechanisms. Reverse slip in the Tien Shan earthquakes is obviously related to overthrusting along the Tien Shan periphery. Dobretsov and Buslov (1996) attribute the difference in earthquake mechanisms in the two mountain systems to the direction of compression relative to their boundary with the pressing rigid plate of Tarim: orthogonal in the Tien Shan and oblique in the Altai-Sayan area. This explanation is, however, only partly valid as the direction of compression turns out to be less important than the presence or absence of constraint. Furthermore, we compare the western and eastern flanks of the Altai-Sayan area to trace the eastern bound of the collision zone, as earthquakes in the east show both strike-slip

and extensional (rifting) mechanisms. The question is whether this difference is due uniquely to collisional geodynamics or the seismicity west of Baikal is driven mostly by plume activity beneath the thin rifted crust, as it is hypothesized, for instance, by Zorin et al. (1997, etc.). We rather support a compromising idea that hot mantle does influence the regional geodynamics but is rarely the immediate cause of events. As we noted, much knowledge of active deformation in the Altai-Sayan area comes from seismology. Systematic seismic studies in the region began in the 1960s. Notable contributions, with both instrumental seismicity and historic account data, were made by N. Zhalkovsky, V. Gaisky, I. Tsibulchik, and G. Tsibulchik (Blagovidova et al., 1986; Rastvorov and Tsibulchik, 1983; Tsibulchik, 1967; Zhalkovsky et al., 1995). Zhalkovskii (Blagovidova et al., 1986; Zhalkovskii et al., 1995) noted low seismicity in the Kyzyl and Uvs Nuur basins, Dzungaria, and the southeastern region of Great Lakes, and also in the Hangayn mountains. Today, the available instrumental seismicity data complemented with advanced IT

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facilities provide a high-density coverage of the Altai-Sayan area (Emanov et al., 2003). As a result, small-magnitude events were found out to occur in relatively short cycles of one or several years and cluster mainly along the boundaries between basins and mountains, where large events originate as well. This seismicity pattern distinguishes the Altai-Sayan area from the Baikal rift where most earthquakes fall within rift basins. A better insight into the seismic activity of the area has been gained through paleoseismological studies (Chernov, 1978; Delvaux et al., 1995; Khilko et al., 1985; Rogozhin and Platonova, 2002; Zelenkov, 1978).

Seismic strain in the Altai-Sayan area We estimated seismic strain from earthquake mechanism data available since the pioneering study by Rastvorova and Tsibulchik (1983). The fault plane solutions we used were obtained with the standard technique (Kostrov, 1975; Riznichenko, 1977; Vvedenskaya, 1969; Yunga, 1979) using the regional travel time curve for earthquakes within the AltaiSayan area (Tsibulchik, 1967) and the Jeffries-Bullen traveltime tables for distant earthquakes (over 800 km). For the lack of reliable hypocenter locations, the origin depth of earthquakes in the area is assumed to be 15 km. The quality of focal mechanism parameters depends on the number of seismic stations that record the event and their position relative to the source, and on the quality of first arrival picking, i.e, actually on the choice of the crust model. The solutions are better reliable for large earthquakes (M > 4.5) recorded at 35 to 80 stations and less reliable for M < 4.5 events, obtained with 20 to 30 first arrivals. We used solutions for M = 3.5–7.3 (K = 10 to 16, energy scale) shocks that occurred within the Altai-Sayan area, including the aftershocks of the Busiyngol (M = 6.5, 1991) and Altai earthquakes. Seismic strain characterizes crustal deformation associated with slip on rupture planes of different orientations in earthquake sources. It is found as the average strain tensor equal to the summed seismic moment tensors of all earthquakes that occurred in a unit volume for a period of time (T): N

Elm =

1 µVT

∑ M0(n)Q(n) lm ,

n=1

where µ is the shear modulus, V is the averaging volume, ) M0(n) is the seismic moment of the n-th event, and Q(n lm are the components of a unit (normalized) seismic moment tensor of the n-th event in geographic coordinates, expressed via focal mechanism parameters; M0(n) is used as a weight factor. Earthquake strain in localities of small and large events is mainly controlled by the latter. Some workers find it to be a drawback of the method, but it is not necessarily so. Seismic moment, being proportional to amount of slip, is actually a natural strain criterion. Furthermore, they are large events that govern the direction of regional seismic flow whereas small

earthquakes readily respond to local crustal features at a smaller scale. The strain estimates are obtained from 439 mechanisms of M = 3.5 to 7.3 earthquakes recorded in the Altai-Sayan area from 1970 through 2003 and, additionally, 453 mechanisms of M > 2.0 events in the western Baikal rift (ϕ = 48−54.5° N; λ = 100−107° E) for 1991–96 reported by Melnikova and Radziminovich (1998). We chose quite a large averaging window (1×1°, at 0.5° step), as the events are not very numerous and strongly scattered, and obtained a smoothed pattern free from details which are often difficult to interpret. It was impossible to achieve equal accuracy and density of calculations over the area because some averaging cells included only one or two events. Within each cell we estimated the directions of principal strain tensor components, the Lode-Nadai parameter (Filin, 1975) and the vertical, longitudinal, and latitudinal strains in geographic coordinates, as a total over the period of observation (1970–2003). The regional pattern we obtained is shown as principal strain directions in Fig. 2, a. Earlier Zhalkovskii et al. (1995) reported these directions for a smaller area and from earthquake mechanisms before 1991. Our data do not bring much change, though we used a larger collection of records. N-S horizontal shortening is especially prominent against the mosaic pattern, which is additional evidence of general N-S compression in the Altai-Sayan area. This inference is supported further by negative N-S strains (εyy) over the greatest part of the territory (Fig. 3), which is in a range of –10–10...–10–7. The N-S direction of regional compression is interpreted hereafter as collisional because its link with the India-Eurasia collision calls no question. Below we show that the collisional direction can slightly depart from longitude being NWN in the west and NEN in the east, or occasionally directed to the northeast. N-S strain is positive in some localities of the study region: Large positive values (up to 10–7) are restricted to the southern Baikal rift but low positive strain of 10–14 to 10–9 appears locally in the Altai-Sayan area as well. Not surprisingly, vertical strain (εzz) is positive over a large part of the area (10–14–10–7) indicating relative uplift. Low negative vertical strain of 10–14 to 10–8, the evidence of subsidence, is found locally throughout the region and reaches 10–8 to 10–7 (i.e., two or three orders of magnitude greater) in the east near Lake Baikal. The W-E component εxx (Fig. 3) is highly variable and alternates between negative and positive. W-E strain is mostly positive in the southwest of the area, east of the Altai, and near the southern tip of Lake Baikal, reaching 10–7 the highest. It is negative and very low (–10–14 to –10–9) between 81 and 99° E and as high as –10–7 east of 99° E. The Lode-Nadai parameter ranges from –0.3 to +0.3 over the area indicating simple shear in the greatest portion of crust, i.e., proximal amounts of shortening and extension within an averaging volume. According to the maps of seismic strain, almost all large earthquakes fall into transitions between positive and negative strains in one or all components. The local strain patterns change in different parts of the

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Fig. 2. Generalized map of principal strain, from earthquake mechanisms in Altai-Sayan area (a) and directions of maximum extension (b) and compression (c), from active faulting data (Trifonov et al., 2002). 1–3 — shortening (horizontal, vertical, at 30–60°); 4–6 — extension (horizontal, vertical, at 30–60°); 7 — faults.

Altai-Sayan area. The northeastern Great Lakes Basin between 50 and 51°30′, and the central East Sayan mountains locally show rifting strains with nearly horizontal (W-E) maximum extension and nearly vertical compression, whereas distinct vertical extension and N-S compression is found north of the Great Lakes “rift zone”, in the neighbor West Sayan. The strain direction changes suddenly from NW in the west to NE in the east near Lake Zaisan. The direction of horizontal compression shows less prominent but quite a clear change along 88° E north of 50° N. The strain change line follows the western edge of the Mongolian Altai and separates the Gorny Altai from the West Sayan (especially, from the Shapshal mountain system), and from West Tuva. Note that the line between the N-NW and N-NE strain directions crosses the epicenter of the Altai (Chuya) earthquake of 2003, which is hardly fortuitous. The position of this line is most likely controlled by the barrier that slows down ductile deformation and induces earthquake nucleation. The rupture in the Altai earthquake is generally parallel to the regional trend of structures and to the seismic moment tensor directions, and is compatible with the regional stress direction. N-NE shortening is traceable along the Sayans and Northern Mongolia. This direction generally holds as far as the southern end of Lake Baikal, while compression is known to change to nearly vertical at nearly horizontal extension within the lake. East of the central Great Lakes region (east of 100°), horizontal compression turns to the northeast across the strike

of main structures. Horizontal compression within the strip between this zone and the Great Lakes Basin generally approaches the N-S direction but locally shifts either to N-NW or to N-NE. Correlation to other data. Trifonov et al. (2002) estimated strain tensors from the geometry and spatial position of faults in a large part of Central Asia. Our data agree with their results (Fig. 2, b, c), which means that strain inferred from earthquake mechanisms provides a faithful record of the current regional geodynamics and that the deformation style has not changed much through tens of thousands of years. Figure 4 shows the planes of maximum shear strain which are the projections to the bisector between principal extension and shortening directions in an averaging volume. The maximum shear strain is parallel to regional faults within the Mongolian Altay, in the southeastern and northeastern West Sayan, and in the zone of Hangayn (Bulnayn) and Agardak faults, i.e., in places of large earthquakes known from instrumental and fault scarp data. The agreement fails locally in the Altai-Sayan area and in the Belin-Busiyngol zone. Note in this respect the mechanism of the M = 6.5 Busiyngol earthquake of 1991 at 51.1° N, 98.13° E which occurred at the site of a past event (Fig. 5). The past earthquake had a normal-slip mechanism whereas the recent event shows leftlateral strike slip on a W-E plane corresponding to nearly horizontal NE compression and SW extension. The position of pressure (P) and tension (T) axes is consistent with the general strain framework of the eastern Altai-Sayan collisional

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Fig. 3. Generalized map of W-E, N-S, and vertical strain tensor components in Altai-Sayan area. 1 — positive strain (extension); 2 — negative strain (shortening); 3 — strain contour lines; 4 — faults.

region. Note that the Busiyngol basin itself, stretching in a narrow N-S strip, is of a rift type. Below we suggest a geodynamic interpretation of this mismatch and try to find out whether the change of slip behavior reflects the east- and

northeastward propagation of collision or the decay of rifting. In terms of this interpretation it is noteworthy that the recent rupture within the source area of a past event shows a small normal slip. Therefore, normal and strike-slip faults may act

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Fig. 4. Map of maximum shear strain in Altai-Sayan area. 1 — maximum shear strain; 2 — faults.

within one and the same tectonic regime. An example of sudden strain change is found, for instance, in the Baikal rift where strain and tectonomagnetic observations in southern Central Baikal showed a switch from general extension to compression in 1992–93 (Dyad’kov et al., 2000). The strain change in the transition zone of the eastern Altai-Sayan area is even less surprising than within the rift. More evidence of past deformation comes from fault scarps produced by prehistoric earthquakes. Data on past earthquake rupture (Delvaux et al. 1995; Khilko et al., 1985; Rogozhin and Platonova, 2002; Zelenkov, 1978) in the Altai-Sayan area were used to infer the horizontal P and T directions from slip geometry and orientation of fault planes. Strain was reconstructed assuming that horizontal compression and extension are directed at 45° to strike-slip planes, horizontal extension is at 90° and compression is nearly vertical to normal planes, and horizontal compression is at 90° and extension is nearly vertical to thrust planes. At intermediate slip geometries (reverse and oblique slip), principal compression (extension) are directed at angles between 45 and 90°. Rupture planes in the sources of large earthquakes strike along large regional faults (Fig. 5). The predicted mechanisms of large past earthquakes (no dates in Fig. 5) show N-NE compression, which is in line with our results. However, compression in the western Mongolian Altay appears directed to the northeast in solutions for paleoearthquakes and to the northwest in the historic events. Therefore the boundary between areas of NW and NE compression is unstable and changes with time. The discrepancy between past and modern earthquake mechanisms

holds east of the Mongolian Altay: Compression keeps to the general NE direction but tends more to the north in historic seismicity and more to the east in paleoearthquakes. Active deformation is recorded in velocities of horizontal motion derived from GPS data. We used GPS measurements along the S-N profile Lhasa-Novosibirsk running from the Lhasa station in Tibet, through Urumqi (West China), and on through the source area of the Altai (Chuya) earthquake in southern Gorny Altai, as far as the plainland in the north of the Altai-Sayan area (Gol’din et al., 2005). The velocity pattern relative to the Novosibirsk reference frame is shown in Fig. 6. The GPS-derived velocities indicate shortening between Tibet and the West Siberian plate at 22 mm/yr. Mean annual rate of N-S compression is 1 mm per latitude degree (assuming that the southern boundary of the West Siberian plate follows 53° N) or 1⋅10−8 per year. Compression accelerates rapidly between the Ukok station 60 km south of the Altai earthquake and the stations Kurai, Chagan-Uzun and Ust’-Ulagan 40–80 km north of it. The convergence rate reaches 8–9 mm/yr within a relatively short distance of 100 km (an order of magnitude faster than the regional convergence) and the N-S compression strain is as fast as 10–7/yr. According to the mechanism of the Altai earthquake, this strain rate corresponds to NW shear strain of 2⋅10−7 per year. Note that the velocities of the Lhasa, Urumqi, and Ukok stations lie on the same straight line (Fig. 6). This might indicate the absence of ongoing earthquake nucleation between the three stations, but GPS data are too scarce for being certain. A more reasonable implication would be that the

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Fig. 5. Generalized map of past earthquake rupture in Altai-Sayan area after (Delvaux et al., 1995; Khilko et al., 1985; Rogozhin and Platonova, 2002; Zelenkov, 1978) and possible compression and extension directions in sources of large earthquakes. 1 — compression; 2 — extension; 3 — rupture plane orientations; 4 — faults. Numbers are dates of large earthquakes (only historic).

regional convergence between Lhasa and Ukok corresponds to creep and seismic flow* produced by numerous small events. Therefore, the too rapid convergence in the source area of the Altai event is consistent with both elastic strain (released in the earthquake) and quasi-plastic flow which is an order of magnitude faster than creep. Unfortunately, the amount of quasi-plastic flow (if any) cannot be estimated from the available scarce data.

Block structure of the Altai-Sayan area and earthquake mechanisms Block structure of the Altai-Sayan area. The reported facts provide solid evidence that recent deformation within the Altai-Sayan area has been driven mainly by regional (collisional) compression. Of course, local factors are important as well. Evaluating their contribution requires better understanding of deformation under regional compression in large areas between distant converging rigid parts of superplates off the immediate plate contact (collision zone proper). The today’s southern edge of the Eurasian superplate east of 54° E delineates the southern borders of the Turan, Kazakhstan, and West Siberian plates and the Siberian craton. The area between * The term seismic flow is meant in the sense as it was defined in (Riznichenko, 1977).

the northern edge of India and the southern edge of Eurasia belongs to Eurasia geologically but mechanically it is rather a zone of lithospheric shear instability against the relatively constant stress from the India-Eurasia convergence. That is what we call the collisional region. The convergence direction depends on the chosen frame of reference whereas geodynamics deals with the very change of distance between convergent plates, independent of coordinates. Note that the region influenced by the India-Eurasia collision (collisional region meant in a broad sense) has evolved as progressive northward propagation of the shear instability front, or the front of ductile deformation. One may think it is the collisional stress that propagates to the north. Yet, stress sets in very rapidly (in geological time) because of relatively low solid-state viscosity of lithosphere, but the flaws that eventually cause shear instability accumulate at much longer characteristic times. Low seismicity of all large basins within the Altai-Sayan area and its surroundings is a key point in geodynamic interpretation of the strain pattern. They are especially the Great Lakes and Dzungarian basins, and also the Tarim plate which controls elastoplastic flow south of the Altai-Sayan area and interacts with the Dzungarian microplate. Quiescence of large areas within active seismic belts can be due either to high plasticity that prevents accumulation of elastic stress or, on the contrary, to high rigidity that makes the respective lithospheric blocks move as a whole and be low

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Fig. 6. GPS-derived velocities along profile Lhasa-Novosibirsk (Gol’din et al., 2005).

deformable (in the presence of softer ambient material). Furthermore, high plasticity produces high residual strain which shows up as folding and mountain growth. The rigidity alternative appears more plausible because the low seismic basins are the lowest elevated parts of the Altai-Sayan area and its southwestern surroundings. The low ridges in the region of Great Lakes rather indicate the block structure of lithosphere than plasticity of the blocks themselves. The position of the rigid blocks is the principal local control of the direction and behavior of plastic flow. Note again that by plasticity we mean shear instability with respect to the long-lived ultimate stress at a given (low) total . strain rate ε. However, the same material may behave in an almost ideal elastic way with respect to fast processes such as seismic waves, tides, or Earth’s natural vibration. Speaking of a collisional region as a system of rigid and plastic blocks (low seismic basins and more active mountains), it appears pertinent to refer to mesostructure of plastic materials revealed by SEM and other advanced scanning techniques in loading experiments (Panin, 1998). Materials in the plastic state were found out to acquire a mesostructure consisting of rigid domains subject to translation and rotation, and flow bands. Two essential points in the theory are that (i) plastic state is self-similar at different scales and (ii) plastic materials develop mesostructure by self-organization during plastic deformation rather than have it a priori. The original uneven rigidity of lithosphere also matters (as well as the temperature patterns in the crust and upper mantle), but the original rigidity-plasticity contrasts increase further by deformation. On the other hand, the zones that are mostly plastic at some scale have a similar mesostructure at a lesser scale. In our case, the smaller-scale structures are the low-seismic basins of Uvs Nuur, Zaisan, Minusa, and Tuva (Kyzyl) and smaller basins in southern Siberia, Tuva, and northern Mongolia. The crust has a still finer rigid-plastic division, which not necessarily shows up on the surface but builds a mesostructure in nucleation areas of large earthquakes and holds for periods comparable with nucleation time of one or several large events about the same place. The recent crustal movements in the region obviously bear signature of preseismic processes. Of course, we do not mean any basin being a rigid domain. Rift basins are highly seismic. As for pull-apart basins, they

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likely hold their shear stability and, hence, are highly rigid themselves, but we cannot be absolutely positive. There is no universal concept of block in the geological literature. A block is often meant as a body bounded by faults of the same scale, which appears to disagree with the above ideas. However, there is no controversy. The above considerations stem from the rheological heterogeneity of crust and its natural rigid-plastic division. This heterogeneity obviously controls the general pattern of elastic and plastic strain in the crust and lithosphere. On the other hand, one cannot neglect the structure of faulted crust with a network of narrow “soft” faults, which are the causative for seismic slip. Our main thesis is that (i) the relative position and distance changes in the system of rigid domains (blocks) controls the flow, and seismic activity, in plastic zones (mountains) whereas (ii) the fault pattern controls the specific flow kinematics. The two systems (of rigid-plastic blocks and fault blocks) are equally important agents in the seismic process. Note that the master role belongs to rigid blocks in the former system and to soft faults in the latter one. How is the block structure of the collisional region linked to the upper mantle structure? In recent 3D velocity images (Bushenkova et al., 2003), the Great Lakes Basin roughly fits a zone of high P velocity (cold zone) at depths between 30 and 130 km (Fig. 7). A narrow neck of this high-velocity zone joins an anomaly with its southern edge within the northern Gorny Altai. This pattern agrees with heat flow data for southern West Siberia. Another high-velocity zone underlies Dzungaria (at the same depths). The Mongolian Altay mountains, on the contrary, overlie low-velocity hot mantle (at depths from 30 to 430 km). Mantle is hot also west of Lake Baikal beneath the southern Siberian craton, south of Lake Baikal, and east of the Great Lakes region beneath the Hangayn. The link of the crustal structure with the upper mantle thermal pattern is obvious. Thus, self-organization of plastic material as a mesostructure consisting of rigid domains and flow bands appears to be largely controlled by the upper mantle temperatures, at least at the large scale. The fact that most of large rigid blocks both in the Tien Shan and Altai-Sayan areas are Precambrian microcontinents (Buslov, 2004) hardly is fortuitous but may indicate the effect of the geodynamic prehistory on the rheological division of the crust. Parallel convergence. Choice of model. Convergence of rigid blocks (plates or microplates) is of special interest in terms of rock mechanics in collisional regions. The knowledge of stress at convergent boundaries provides clues to the earthquake mechanism controls. The first thing is to choose a deformation model. The choice depends on space and time scales of the process in point. Earthquake processes, including nucleation, relaxation, and earthquake cycle, with their characteristic times from one to thousand years (we conventionally call it a seismic interval) are of intermediate duration. They belong neither to geologically long processes in which the solid Earth’s rinds behave as highly viscous Newtonian or nonlinearly viscous fluid nor to short-term elastic processes (see above). Kasahara (1985) also distinguished a seismic time

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Fig. 7. Integrate cross sections of P-wave velocities at different depths, from tomographic inversion (Bushenkova et al., 2003). Residuals are in percentage relative to velocities in reference model.

interval as intermediate between fast (elastic and brittle-elastic) and slow mainly viscous processes. Dynamic phenomena taken at the seismic time scale

(postearthquake relaxation, earthquake cycle, slip, etc.) have been often simulated using viscoelastic models (Smith and Sandwell, 2004). Creep has a characteristic time of a year or

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less but creep-related strain increment is too small against the permanent elastic strain in seismogenic crust which actually controls seismic failure. No doubt, plastic deformation works at the characteristic times of earthquake nucleation in the conditions of excess mechanic energy in source areas. It plays an essential part in stress distribution in lower crust, and also within thermal anomalies in middle and upper crust (Nikolaevskiy, 2006). Furthermore, plate convergence below the seismogenic depth goes entirely by plastic flow. An elastic-viscoplastic model thus appears to be the best choice to simulate the evolution of a crust fragment at the seismic time scale. However, we chose a linearly elastic ideal-strength reference model corrected for plastic flow. There is no need to include solid viscosity, as stress in the steady regime (which controls earthquake mechanisms) coincides with purely elastic static stress within the limits of linear viscoelastic models. Moreover, when looking into the causes of specific earthquake mechanisms, we are interested in the ordering of the σx, σy, and σz components and in its dependence on depth and general deformation conditions rather than in the stresses themselves. Of course, the order of stresses can change in some cases, e.g., under very intense ductile deformation, but the latter can be only local within seismogenic crust, otherwise large brittle failure would be impossible. Thus, the elastic model is good for typical mechanisms in typical cases. Another simplification is neglect of effects from nonlinear elasticity which inevitably arise under the high crustal stress. We neglect this nonlinearity for the same reason: it cannot change the stress order. Neglecting nonlinearity liberates us from the problem of estimating all parameters of nonlinear elasticity and allows us to use analytically simple equations with all necessary relationships in the explicit form. More so, there is no reason to care about nonlinearity having neglected plasticity. Pore pressure neither affects the stress order and is thus taken into account only where we specify the orientation of rupture planes in terms of the Coulomb-Mohr criterion. Our guiding principle is to use the most sophisticated and exhaustive models in specific cases (e.g., deformation in the vicinity of a source area) but to simplify the model as far as to get a qualitative idea of general trends in typical cases that represent quite a large class of phenomena. The degree of simplification is in a way the matter of understanding, intuition, and luck. More specifically, we assume that the nonlinearity of elastic strain and the presence of plastic strain (within seismogenic crust) causes smooth changes to the functions σx(z), σy(z), σz(z) at which the order of stress components and its change at critical depths (as well as the order of the critical depths) are topologically invariant in typical cases. Then, the theory becomes phenomenological. The characteristic depths have to be tied to the real depths via some parameter. For this we use the collisional component of elastic strain, the most “hypothetical” parameter of the model. Besides the physical constraints, the model has geometrical constraints: both the convergent rigid blocks and the soft blocks subject to deformation are assumed to be depth-infinite uniform rectangular prisms that contact along parallel vertical

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Fig. 8. Lateral compression in a sequence of rigid (1) and soft (2) blocks.

planes. The absence of depth stratification is quite a serious constraint. Lateral compression of a vertically stratified medium involves only the most rigid layers (hatched in Fig. 8). It is easy to show that the compression stress σy is higher in rigid layers (roughly proportional to rigidity). Therefore, the plane z = 0 in our model corresponds rather to the surface of consolidated crust than to the day surface. Inasmuch as the elastic moduli generally increase with depth, σy increases faster than our model predicts. Furthermore, the depth-dependent increase in lateral stress can be faster than that of σz driven by the overburden load only, because stress dissipates more rapidly in the upper crust due to mountain growth, and the elevated part of mountain terrains is largely unloaded. Thus, strictly speaking, the model cannot be extrapolated to depths below brittle (seismogenic) crust. It appears natural to consider two extreme cases (Fig. 9, a, b) because the tectonics of a collisional region is generally controlled by both the relative position and motion of rigid blocks. One case is laterally constrained uniaxial compression (or simply constrained compression) when rigid blocks on the sides (horizontal hatching in Fig. 9, a) lock lateral extrusion from the space between two blocks (oblique hatching in Fig. 9, a). The other case is that of non-constrained compression implying free lateral extrusion (Fig. 9, b). Both cases are modeled using an x-infinite model (Fig. 9, c) with all stress and strain parameters independent of x. It should be noted that speaking of constrained or non-constrained compression we are well aware that any crustal deformation is constrained (which is responsible for complex termination of any normal or strike slip). However, we now deal with stress rather than strain, and the two are not necessarily interchangeable. The rigid blocks are assumed to have the same elastic properties, and the medium between the blocks spaced at the distance l is characterized by the moduli λ and µ and the density ρ. The two blocks have the same set of parameters λ0, µ0, and ρ0. Their convergence ε0 = ∆l /l (collisional strain) is assumed to be prespecified. The model is symmetrical about

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Fig. 9. Simplified models of deformation in collisional regions. 1 — strain types, as in Fig. 2; 2 — rigid blocks; 3 — strain shadow.

the planes x = 0 and y = 0. The Earth surface z = 0 is assumed plane and stress-free: = 0, τiyz = 0. σiz = 0, τixz z = 0 z = 0 z = 0

∂τxz

∂σ ∂τ ∂σy ∂τyz + = 0, z + yz = − ρg, ∂y ∂z ∂z ∂y

Z = λε0 /ρg.

(1)

With regard to gravity and x independence, the equation of static equilibrium is ∂τxy

It follows from (5) that the strain εzz is positive as far as the depth

The interval (0, Z) can be interpreted as the part of the soft block that participates in mountain growth. From (4) and (5),

(2)

σx (z) = −

λ (2µε0 + ρgz), λ + 2µ

where σy, etc. are the normal stresses and τxy, etc. are shear stresses. Laterally constrained deformation is formulated as

σy (z) = −

λ  2µ ε + ρgz. λ + 2µ  υ 0

∂y

+

∂z

= 0,

εxx = 0, and laterally non-constrained deformation as σx = σ0 + βσz,

(3)

where σ0 is a small value and the factor β is taken from an additional condition. First we neglect the conditions at the contact between soft and rigid blocks. In fact, we consider an infinite gravitating prism (−∞ ≤ x ≤ ∞, −l / 2 ≤ y ≤ l / 2, z ≥ 0) with the constant strain εyy = −ε0. Note that the model appropriately simulates convergence with its conditions placed along the boundary of a conventional soft block within the plasticity zone. We call it non-contact compression. Then, there are no conditions for shear stress while normal stress depends uniquely on z. Therefore, the two first equilibrium equations are trivially satisfied, and the last one becomes ∂σz ∂z

= − ρg.

Taking into account the free-boundary conditions, σz = −ρgz. Laterally constrained compression. By Hooke’s law (at εxx = 0), σx = λ(−ε0 + εzz), σy = − (λ + 2µ)ε0 + λεzz, −ρgz = (λ + 2µ)εzz − λε0.

(4)

The latter equation gives εzz =

λε0 − ρgz (λ + 2µ)

.

(5)

(6)

  Stresses can be better compared if calculated for some specific Poisson’s ratio. Poisson’s ratio in the crust typically ranges from 0.25 to 0.30 (Puzyrev, 1993). The lower bound, or even a smaller ratio, is more realistic. The reason is that the block structure of the crust matters more in static stress (geodynamic processes) than in wave propagation. Seismic velocities correspond to the scales from grain structure to sizes a few orders of magnitude the grain size. The more evident the discrete structure of material and the larger the scale where it shows up, the lower Poisson’s ratios relative to those in the material of blocks. Note that the effective νe of a dense (face-centered) package of balls with their Poisson’s ratios ν is ν/(8 − 5ν), which gives νe ≅ 1/ 20 at ν = 1/ 3 (irrespective of the ball size). The equation λ = µ corresponds to ν = 0.25. (But Poisson’s ratio may be higher in the more ductile lower crust.) For ν = 0.25 1 3

σx (z) = − (2µε0 + ρgz), σy (z) = − 1 (8µε0 + ρgz). 3

Note also that plasticity is influenced by the fact that shear modulus decreases to zero in extreme corresponding to ν = 1/ 2, where the curves σz(z) and σy(z) become parallel, as follows from (6). The depth dependence of the principal stresses is shown in Fig. 10 (heavy line). The magnitude of σz always increases monotonically with depth, which controls the growth of the two other components (besides local factors). Thus, the characteristic depth where σz(z) crosses σx(z) and σy(z) is the key topological parameter of stress between two convergent blocks in quite a large range of cases. Before the point z* z∗ = λε0 / 2ρg

(7)

S.V. Gol’din and O.A. Kuchai / Russian Geology and Geophysics 48 (2007) 536–557

Fig. 10. Depth dependence of principal stresses for different compression regimes. See text for explanation.

σy < σx < σz (with regard to stress sign) which corresponds to reverse slip, and after z* σy < σz < σx corresponding to strike slip. Another change is to normal slip after the cross point of σz(z) and σy(z), where σz < σy < σx. The plane Pyz in a reverse slip is parallel to the x axis and dips at a nonzero angle to the horizon. The strike-slip plane Pyx is vertical (though the respective strain εxy occurs on a horizontal plane). The direction of slip at any side of the plane is always at a high angle to the maximum pressure of particles toward the plane (compression in our case). Let (z1, z2) be the depth interval of seismogenic (brittle) crust. Different possible situations are defined by the order of critical depths z1, z2, z* (at z1 < z2). It would seem reasonable to calculate z* and check it against the hypocenters located in areas of constrained compression. Yet, the ideal-strength linear model we use is too approximate to allow numerical estimates (though the slip geometry obviously depends on earthquake origin depth). Indeed, z∗ = 6.8⋅105⋅ε0 (m) at average crustal velocities assumed to be VP = 6.4 km/s and VS = 3.7 km/s and λ = ρ(V2P − 2V2S). A realistic value of 13.6 km requires that ε0 = 2⋅10−2. Although a strain of 10–2 is very far from the theoretical strength limit of a perfect crystal, it is too high to be actually elastic. The discrepancy is caused by the model simplification. Nevertheless, the model is workable for the blocks that hold shear stability. Namely, it explains why normal slip dominates in sediments under moderate compression. Solving the equation σy(z) = ρgz at VP ≈ 2.5 km/s and VS ≈ 1.5 km/s gives that the depth where σy(z) and σz(z) intersect at ε0 = 10−4 does not exceed 10 km. Any slip below this depth is normal slip. Therefore, the mountain systems and the rigid (low deformable) blocks have basically different strain properties due to a greater role of ductile deformation in areas of shear instability.

547

Thus, to tie the model to a more or less realistic depth scale, we assume that z* in areas of constrained compression coincides with rather deep (if not the deepest) crustal earthquakes. Let it be about 20 km. Therefore, the ratio λε0 /ρg coinciding with the bottom of the vertical extension interval Z corresponds to about 40 km. Of course, the actual z* not necessarily is 20 km but is assumed to be of this order. Hereafter we notify of the conventional depth scale whenever λε0 /ρg = Z is used for approximate depth estimation. At this scale, the seismogenic depth is shown by heavy line on the Z axis in Fig. 10. At z* > z1, shallower earthquakes have reverse and deeper ones have strike-slip mechanisms. At z* greater than both z1 and z2, reverse slip is the dominant mechanism. Of course, it is the most general regularity which may break down in different real situations, but it explains why reverse slip is more frequent in areas of constrained compression. The Tien Shan mountains surrounded by the rigid plates of Tarim, Dzungaria, and Kazakhstan is the classical example. It borders a plastic block of the Pamirs in the southwest but compression in the Pamirs is as intense as in the Tien Shan, where almost all large events have reverse mechanisms (Fig. 1, b). If we assumed in our phenomenological model that z∗ ≈ 20 km and the crust is seismogenic to the depth z2 either above or below z*, the surface of seismogenic crust can be estimated from the condition that the maximum shear stress is close to the shear strength of real solids τ∗. The strength τ∗ of many real solids is known (e.g., Levin et al., 2004) to

be 10−3µ / 2πn, where 1 < n < 10 (µ / 2π is the theoretical strength limit). The maximum shear stress at the depth z (at ν = 1/4 and λε0/ρg ≡ Z = 40 km) is τmax(z) = (1/ 2)|σy − σz| = (1/6)µε0(8 + z / 20) > τmax(0) = (4 / 3)µ⋅10−2 > τ∗.

(8)

This estimate does not mean that brittle failure begins right from the day surface, as our model includes only consolidated crust. The difference τmax(z) − τ∗ represents ductile deformation corresponding to τ ≤ τ∗ in the normal crust state. Therefore, the seismogenic layer is bound from above by the top of consolidated crust. High-density seismological networks do record small earthquakes that originate at depths of 2 km or shallower. In its physical meaning, the critical depth Z (Z = 40 km at the conventional scale) defines the interval that provides mountain building (see above). Unfortunately, the depth of 40 km belongs to the plasticity domain, where our elastic model is hardly applicable. The effect of plasticity might be to increase considerably the depth interval involved in mountain growth. The reason is that Z depends on the convergence of the curves σy(z) and σz(z) in the elastic model. Above we cited arguments why the curves can diverge in the plastic domain, which inevitably leads to a longer interval of vertical extension. Nevertheless, the ordering of Z values estimated for the whole range of geodynamic regimes in a collisional region

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S.V. Gol’din and O.A. Kuchai / Russian Geology and Geophysics 48 (2007) 536–557

using our model is in perfect agreement with relative elevations in the respective areas. Laterally non-constrained compression. First we estimate the bounds of the ratio σ0 /σy(0) that represents the degree of constraint in the absence of gravity. Compression produced in the uniform space by two equal forces F of opposite directions concentrated at the points (0, –l, 0) (0, l, 0) is an example of ideal non-constrained deformation associated with convergence of two zero-length blocks (L = 0), without regard to gravity. The displacement field is the sum of displacement fields from each stress source: ui (x, y, z) = u(+) i (x, y, z) + u(−) i (x, y, z), (i = x, y, z). According to equations from (Landau and Lifshits, 1985), 2 2 ∂ r±  ∂ r± F 1 1 F 1 (+) − = ± = − , , u u(+)   y x 4πµ 4(1 − ν) ∂(±y)∂x 4πµ r± 4(1 − ν) ∂y2  

is given where r± = √  x + z + (y ± l) . The equation for by substitution of z for x in the latter equation. Omitting the derivation, 2

2

u(±) z

2

= − F 22 ; ε0yy 4πµ l x = y = z = 0

ε0xx x = y = z = 0

=

latter case. Using Hooke’s law, the strain ε′yy is expressed via stress as

ε′yy =

1 E

[σ′y − ν(σ′x + σ′z)],

where E is Young’s modulus. Substituting ε′yy = − ε0,

σ′z ≡ σz = − ρgz and σ′x = σ0 − βρgz into the latter equation gives σ′y = − Eε0 − νσ0 − ν(1 + β)ρgz. β is found assuming that both horizontal stresses change with depth at the same rate, as in the case of constrained compression. From β = ν(1 + β) we find that β = ν/(1 − ν) ≡ λ /(λ + 2µ) and σ′x = σ0 − λρgz ; σ′y = − Eε0 − νσ0 − λρgz . λ + 2µ

(9)

λ + 2µ

The strain along x is

ε′xx =

1 E

σ − ν ρgz − ν−Eε − νσ − ν ρgz − ρgz = 0 0 1−ν  0 1−ν      2

νε0 +

1 2 F ; 4πµ 4(1 − ν) l2

(1 + ν )σ0 E

,

and that along z is

2

1 4lx =− F ε0xx , x >> l, 4πµ 4(1 − ν) r5 y = z = 0 +

ε′zz = νε0 + (1 + ν2) νε0 + (1 + ν2)

and = − 2F2 λ(3λ + 4µ) ; σ0x  σ0y  = 2F µ . x = y = z = 0 x = y = z = 0 4πl2 λ + 2µ 4πl µ(λ + 2µ) According to these equations, 2

κ = − σ0x /σ0y = 3 µ . λ( λ + 4µ) At ν = 1 / 4 (λ = µ), κ = 1 / 7. Thus, although positive σx (extension stress) is possible, it is smaller than compression stress even in the ideal non-constrained conditions. On the contrary, the amount of extension strain is comparable to that of compression, and their ratio is 1/3 at ν = 1/4.

ε0xx

Note that the positive strain becomes negative as x increases, i.e., extension gives way to compression. This change means that material becomes extruded from the compression area into the ambient space. This effect is especially typical of convergent finite blocks (Fig. 9, b). Extrusion is a case typical of stress and strain in collisional regions, as well as constrained and non-constrained compression or strain shadow (see below). The extreme east of the Altai-Sayan area, especially the southern half coinciding with the eastern edge of the Hangayn, appears to be a good example of extrusion. Now we find stress and strain for non-constrained compression in a model for convergent infinite blocks. In order to discriminate between the cases of constrained and non-constrained compression, we hereafter prime the variables for the

σ0 E σ0 E

1 − 2λν  =  λ + 2µ   

−

ρgz E

−

ρgz . (λ + 2µ)

(10)

It is easy to calculate that ε′yy = −ε′0′ − νσ0 /E. As one could expect, ε′xx (extension) is positive at all depths. Its depth independence is the formal consequence of the assumption of equal depth-dependent increase in horizontal stresses, and thus has no physical significance. The strain εzz is positive at z < Z′ =

ν(λ + 2µ)ε0 ρg

(11)

(it is assumed that σ0 = 0). Z′ = (3/4)λε0 /ρg = (3/4)Z for Poisson’s ratio in block media at relatively small stress (λ = µ), where Z′ = 30 km at the conventional depth scale. The inequality Z > Z′ meaning a greater mountain growth potential in areas of constrained compression than in the non-constrained case appears to be realistic though the depth 30 km is as conventional as the above Z = 40 km. The depth dependence of stress in the non-constrained case is shown by dashed line in Fig. 10 (assuming σ0 = 0). In this case, the critical depth is outside the seismogenic layer (and, possibly, outside the crust). Therefore, σy < σz < σx throughout seismogenic crust (with regard to sign), i.e., strike slip along the vertical plane Pyx is the dominant mechanism in areas of non-constrained compression. Small variations of σ0 towards positive or negative stresses apparently cause no change. Our ideal elastic model fails to resolve the lower bound of

S.V. Gol’din and O.A. Kuchai / Russian Geology and Geophysics 48 (2007) 536–557

seismogenic depth, whereas the upper bound can be naturally inferred from τmax > τ∗. Having estimated τmax = (1 / 2)|σ′y − σ′x| = Eε0 = (5 / 2)µε0 >> τ∗, we see that earthquakes can, in principle, originate at any depth below the surface of consolidated crust, as in the case of constrained compression. Note that the predicted shear stress is higher than in the constrained case where τmax in seismogenic crust varies from (3 / 2)µε0 to (4 / 3)µε0. The non-constrained state, as we define it, is a very idealized situation. There is always some constraint, as well as many intermediate (moderately constrained) cases in which the curves σx(z) are between σ′x(z) (thin dashed line in Fig. 10) and σx(z) of constrained deformation. For instance, the stress σx(z) in the case of moderately constrained compression may coincide with σ1(x). Then, reverse earthquakes are most often as shallow as about the seismogenic layer surface while strike slip is the dominant mechanism in deeper crust. The Altai-Sayan area, which is “open” to the east, is subject to moderately constrained uniaxial compression, and the greatest part of large earthquakes reasonably have strike-slip mechanisms (Figs. 1, b and 5). Strain shadow. Crust, with its mosaic structure, always contains regions of strain shadow for σy (Fig. 9, d), where the vicinity of the middle rigid block is unloaded. Thereby ε0 decreases to some value ε′′0 << ε0, and the curve σy(z) in Fig. 10 can move down to σ1(x) or lower. At ε′′0 ≤ (ν/ 3)ε0, the critical point ∗∗

z

=

(λ + 2µ) (3λ + 2µ)ε′′0 2(λ + µ)ρg

,

which at λ = µ and ε′′0 = (ν/ 3)ε0 is (15/48)λε0 /ρg ≅ (2 / 3)z∗ (z∗∗ ≈ 13 km at the conventional depth scale), is located within seismogenic crust. Earthquakes that originate at depths z ≥ z∗∗ show normal slip on the plane Pzx parallel to the y axis (i.e., to regional compression), and shallower earthquakes have strike-slip mechanisms. These estimates generally fit the deformation pattern in the Baikal rift where crust is seismogenic to a depth of 42 km and most earthquakes are 15 to 20 km deep (Dévercherè et al., 2001). Note that the y axis in the Baikal rift must follow the NE direction. Dévercherè et al. (2001) report two remarkable hypocenter location histograms: one for the central Baikal rift and the other for its northeastern flank. Earthquakes that originate at depths of 15–20 km are from the central rift part, whereas those in the rift northeastern flank, mostly with strike-slip mechanisms, are between 0 and 28 km deep, most often at 7–11 km. These origin depths of mostly normal-slip events in the rift center and strike-slip earthquakes in the northeast appear quite natural. The rather low seismic activity of lower crust in the northeastern rift flank may be due to high rigidity. According to hypocenter locations correlated to a DSS profile (Suvorov et al., 2003), deep earthquakes in the NE rift flank are restricted to the Muya basin and the Muya tunnel while the lower crust farther to the east is aseismic.

549

Note that the model shows what can be called structural instability of mechanisms relative to the model parameters within some range of ε′′0: minor changes in the parameters change notably the proportion of slip mechanisms, as far as the appearance of reverse slip absent from the system {σ′x, σy = σ1, σz}. We can interpret in this context the compression episode of 1992–93 that interfered with extension in Lake Baikal (Dyad’kov et al., 2000). For about two years before that episode, earthquakes had mechanisms common of the local seismicity and released the causative shear stress. This stress at z ≥ z∗∗ is defined by the amount of the differential principal stresses σz − σ′x (both stresses are negative but |σz| > |σ′x|). The gravity remaining the same, the most natural way to decrease shear stress is to increase the amount of minimum horizontal stress. Assume that the new curve σx(z) coincides with σ2(z) shown by thin dashed line in Fig. 10. Then, constrained compression sets in above some depth z = ζ (σy < σx < σz < 0) with dominant reverse slip. Note that deformation remains the same at z > z** where normal slip still predominates! Unfortunately, the available data other than seismology in (Dyad’kov et al., 2000) were restricted to shallow effects: surface strain measurements at the Talaya station and data on tectonomagnetic anomalies produced by magnetostriction of magnetic basement rocks outside the lake. As for the series of reverse-slip earthquakes recorded during the episode, their hypocenters were not located. Of interest is the case of deep shadow with the two horizontal stresses coinciding and being σx = σy = σ0 − ν ρgz 1−ν

at σ0 < 0, where it is easy to see that εxx = εyy = (1 − ν)σ0 /E < 0. The three principal strain components correspond to shortening, but failure occurs as normal slip. We classify this case as constrained rupture. The slip plane has an unstable strike, and both horizontal axes plot as horizontal extension in the averaged-strain diagrams, though the actual strain is compression. According to data in Radziminovich et al. (2005), constrained rupture shows up in deformation of the eastern South Baikal basin. The situation is obviously the same at σ0 > 0. This does not mean there would be actually no extension on Baikal (more so, extension is indicated by GPS data), but one has to be aware of the possible ambiguity in seismic strain interpretation. Note also that structural instability may arise when compression is moderately constrained, but not in the ideal non-constrained case. As ε′′0 decreases, the depth range where the strain εzz is positive and corresponds to mountain growth reduces as well. Namely, at λ = µ and ε′′0 = (ν/ 3)ε0, the greatest depth where εzz is not negative is Z′′ =

ν(λ + 2µ)ε′′0 ρg

≅

λε0 12ρg

=

1 Z 12

(at the conventional depth scale Z′′ ≤ 2.5 km). The ratio

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_ Z′′/Z being small, subsidence and crust thinning dominates uplift (crust thickening). There are combinations of ε′′0 and σ0 (at 0 > −νκε′0′ /(1 + ν)σ0 /E < 0) in which εzz < 0 at any z ≥ 0, but in this case earthquakes have mostly strike-slip rather than normal mechanisms. The minimum possible depth (for brittle failure) is found from the inequality check of τmax = (1 / 2)|σ′y − σ′x| ≥ τ∗, and is calculated by substituting ε0 for ε′′0 as in the case of non-constrained compression. Multiplying that estimate by ν/ 3 = 1/12 gives the value (5/ 2)µε′′0 ≈ 2⋅10−3µ still greater than the real strength limit (µ/ 2πn)⋅10−3. In the normal-slip portion of seismogenic crust, τmax = (1 / 2)|σ′z − σ′x| = 1 ρgz − λρgz + σ0 = λ + 2µ 2   µε0

λ ρg λ + 2µ λε0

z ⋅10−2 + σ0 / 2 z + σ0 / 2 = 13 µ 40

at z ≥ z∗∗. Neglecting σ0, for z ∈ (10, 20) km, τ∗ < µ⋅10−3 < τmax < 2µ⋅10−3. Thus, maximum stress and real strength hold their relationship all over the seismogenic depth within regions of strain shadow, and the two are of the same order of magnitude, unlike the cases of constrained and non-constrained compression. Therefore, ductile deformation plays a notably lesser part in conditions of strain shadow than elsewhere in a collisional region. This may be the reason for the relatively great thickness of the Baikal brittle crust, which is mostly cold according to Dévercherè et al. (2001). The possible collisional origin of the Baikal rift is supported by numerical modeling (Nazarova et al., 2002) showing change from normal to strike slip and back at minor rheology changes, and by modeling in (Polyansky, 2002). The same may be valid for the Mongolian Baikal region where the strike-slip Busiyngol earthquake occurred in place of a past normal-slip event (see above). Quasi-periodic intermittent fault activity found in the Baikal rift system and in the western Baikal region (Sherman and Savitsky, 2006) is evidence that both areas belong to a single zone of ductile deformation. Orientation of rupture planes. The orientation of rupture planes in an elastic model is identified to one angle and the choice between two conjugate planes, at any combination of σx, σy, and σz. Indeed, by the stress tensor symmetry, both conjugate planes are parallel to the intermediate stress direction and are at the angles β and −β to one remaining direction. The direction of strike slip is easy to identify by specifying the direction of maximum compression: it is right-lateral for one conjugate plane and left-lateral for the other. In the next section we are trying to justify the idea that the conjugate plane and the angle β are defined by superposition of the actual stress onto the existing plastic flow. Nevertheless, the purely elastic model is useful as well (together with failure criteria). After all, plastic flow is likewise controlled by stress. The elastic model is a good point of reference. A more serious

limitation is that the actual stress strongly departs from the ideal model because of basic strength inhomogeneity and quite a large contribution of ductile deformation. The best thing we may expect is to see some regularity in the depth dependence of β, etc. The failure criterion commonly has the form F(σ1, σ2, σ3) ≤ 0, and failure occurs if the inequality breaks down. (The equation corresponds to the critical state). σi is the principal stress in this formula. The strength of rocks is most often found using internal friction (the Mohr-Coulomb failure criterion), and the stability criteria is thus |τ| ≤ f (σn) = τc + fs |σn|,

(12)

where τ is the shear stress and σn is the normal stress applied to some plane P; τc and fs are the cohesion and internal friction coefficients, respectively. The straight line τc + fsσn (in the plane (σn, τ)) is tangent to the great Mohr circle given by τ=√ (1/4) (σ3 − σ1)2 − (σn − (1/ 2) (σ1 + σ3))2 .  Criterion (12) may seem invariant being dependent on the orientation of P, but each stress combination (σ1, σ2, σ3) uniquely defines the great Mohr circle and, hence, the probability of its tangency to |τ| = τc + fs|σn|. In fact, the Mohr-Coulomb intermediate stress σ2 does not influence the strength criterion, which does not quite agree with experiments. Note also that the Mohr-Coulomb criterion used in technical literature has the form σ1 − χσ3 ≤ σbp (χ = σbp/ σ comp ) (Levin et al., 2004) but it can be brought to (12). The b function f (σn) is not necessarily linear in the general case. In problems for strength of granular media (including rocks), the stress tensor T substitutes the effective stress tensor Te = T – paI, where I is the unit matrix and pa is the fluid pressure. The reason is that fluid pressure decreases the pressure at grain boundaries increasing the strength of material. In the system of open pores, pa = −ρagz, where ρa is the density of fluid (water). In closed pores, the magnitude of pressure pa can be much greater (because of fluid superheating). Shear stress remains the same (τe = τ) and the principal and normal stresses decrease for pa (with regard to sign). Consider a reverse slip under laterally constrained compression. The pairs (σy, σz) that define reverse slip at z ∈ (z1, z∗) make up a one-parameter set with z. If we express τ and σn in (12) via σy, σz and θ (see above), the criterion equation |τ| = τc + fs|σn| likewise defines a one-parameter set of stress pairs (σy, σz) with β. In both sets, σy and σz are linearly related, and the former thus defines a straight line segment and the latter a half-infinite straight line. In plane the two normally have no more than one common point corresponding to some depth zs. The existence of a single depth point at which stress fits the Mohr-Coulomb critical state is the consequence of idealization of both the stress and the strength criterion. In the general case, stress fields are three-dimensional and the critical state for the general criterion

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F(σ1(x), σ2(x), σ3(x)) ≤ 0 defines the surface in a physical space. However, we show below that the resulting “criterion depth” is an important characteristic of seismogenic crust, if viewed outside the limits of a purely elastic model. Another problem resolvable using the Mohr-Coulomb criterion is to find the angle β∗ (for each depth) corresponding to the minimum ratio σn /τ. The angle β∗(z) is presumably the most favorable for brittle fracture as well as for quasi-plastic flow along faults. Intuitively it is obvious that, according to the failure criterion, the slip plane would tend to become orthogonal to the minimum compression and turn correspondingly. A strike slip plane (under non-constrained and moderately constrained compression) would turn toward the N-S plane. We begin with the more simple latter problem for the case of reverse slip on the plane P, with the unit vector n of the form (0, sin β, cos β) normal to it (β is the angle of P to z = 0). The total stress vector corresponding to a surface with the normal n is t = (0, σey sin β, σez cos β). The normal stress equals the “length” of the t projection onto n: σn = σey sin2β + σez cos2β = 1 2

(σey + σez ) + 1 (σez − σey) cos 2β. 2

(13)

In the case of normal slip (in strain shadow), β∗ (again the dip of the plane P) is found in the same way: σez / σex . β∗ = arctg √  In this case |σex| < |σez |, and, hence, β∗ > π/4. Therefore, normal slip occurs on steeper planes than reverse slip. If, in the case of non-constrained compression, the normal to P is (sin β, cos β, 0), where β is the angle of the x axis to the vertical plane P, σey /σex . β∗ = arctg √  Since σex < σey, β∗ > π / 2. According to (9), at σ0 = 0, e

σy e σx

=

(λ + 2µ) (Eε0 − pa) + λρgz λρgz − pa

It is clear that β∗(z) decreases and tends to π / 4 as z increases. Near the day surface the plane P is roughly parallel to the direction of compression. The depth of the critical state is defined by the Mohr-Coulomb criterion |τ| = τc + fs |σen|

(0, σey sin β − sin β(σey sin2β + σez cos2β), β(σey

cos β − cos

2

sin β +

σez

e

cos β)).

e

b=±

2

sin β cos β

σz

tg β

.

b=−

Calculating the β derivative and bringing it to zero gives σez /σey .

(14)

Inasmuch as |σey| > |σez | for reverse slip, the most favorable plane for strike slip at any depth dips at the angle β∗ < π/4. Since e

σz (z) e

σy(z)

=

(ρ − ρa)gz ν  2µ  ε + ρgz − ρa gz 1 − ν  ν 0 

(17)

fs 1   √

2 + fs

1 2

(σey − σez ) = ±

fs

1

2 1 +fs 2  √

(σy − σz).

fs 1 +  √

2 fs

1 2

(σez − σey)

and

β = ± arctg √  ∗

= − fs.

According to (15), b < 0. Inasmuch as σy − σz < 0 (with regard to sign), b is negative if

e

= σey tg β +

e

Solving (17) with respect to b = σen − (1 / 2)(σey + σez ) gives

Thus, we are to minimize 2

e

e e e e 2 e2 (1 / 4) (σy − σz ) − (σn − (1 / 2) (σy + σz ))  √

2

τ = (σey − σez ) sin β cos β.

e

(16)

σn − (1 / 2) (σy + σz )

Straightforward calculation gives

σy sin β + σz cos β

.

and the condition of the tangency of (12) to the great Mohr circle. The latter condition in the case of reverse slip is

The shear stress vector t − σnn has the components

σez

(15)

,

β∗(z) is a monotone increasing function of z. The least dip is near the day surface (case of thrust). Note that at ν = 1 / 4 ν/(l − ν) = 1/ 3 and ρa ≈ ρ/ 3, hence, σey(z) ≈ const. In this case sudden fluid pressure change comparable with the matrix pressure can cause strong changes to the pattern which differs considerably from the depthward gradual flattening usually assumed for thrusts. The controversy is discussed below.

σn = 1 (σey + σez ) − 2

fs

1

2 1 +fs 2  √

(σez − σey).

Comparing with (13) gives cos 2β = −

fs 2 1 +fs  √

.

(18)

Equation (18) was first obtained by Anderson but in the context of a different problem (Turcotte and Schubert, 1982). This equation is valid for any slip (reverse, normal, or strike slip) if the angle β is found correspondingly. At the friction fs = 0, the dip of the rupture plane is π / 4, and at fs → 1 it is β → π / 2. Note that β depends uniquely on friction and is independent of depth. The depth of the critical state is found from the criterion equation in which fs and β are assumed known. When substituting into (16) it is convenient to reset the sign of all stress components assuming that

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S.V. Gol’din and O.A. Kuchai / Russian Geology and Geophysics 48 (2007) 536–557

compression is positive. This changes nothing but liberates us from the sign of µ λ + 2µ

[2(λ + µ)ε0 − ρgz]

1 2 1 +fs  √

=

τc + fs  2(λ + µ) (µε0 + ~ ρgz) −  λ + 2µ

fs µ  (2(λ + µ)ε0 − ρgz) , 2  λ + 2µ 1 +f   √

(19)

s

ρ = ρ − ρa. After transformation, zc is found as where ~ −1

2[(λ + µ) / λ] [√ 1 +fs − fs] − [(λ + 2µ) / λ] [τc / µ]ε0  2

zc = Z

2 1 +fs + 2fs [(λ + µ) / µ] [(ρ − ρs)/ρ]  √

.

If we assume that ν = 1 / 4 (λ = µ), fs = 0.85, ρa = ρ/3, and τc / µ = 10−3 and ε0 = 3⋅102, then, zc = 0.48Z. At the conventional scale, zc = z* = 20 km. A nontrivial question is which is the state of material above and below zc. Stress changing linearly with depth, we may confine ourselves to the case of z = 0. It is easy to check that the left-hand side of the equation is greater than the right-hand side at our assumptions, i.e., the depth of supercritical state is shallower and not greater, contrary to what we intuitively expect. In order to eliminate the contradiction, we place the model into a real context. Our model obviously works as a static one on condition of ideal strength. At the real strength, failure occurs continuously within the interval 0 < z < zc and releases shear stress, which maintains the subcritical and critical states in seismogenic crust. Then, shear stress again increases to approach that in the reference ideal elastic model, due to stress diffusion and solid-state viscosity, this again results in failure, and so on. To put it different, a self-maintaining dynamic regime sets up in seismogenic crust, which is responsible for the recorded seismicity. Below we show that the difference between the reference model stress and that of the critical state is not the only energy source that maintains seismicity under constrained compression. The position of zc relative to seismogenic depth is defined in the general case by the sign of the derivative of  σ3(z) − σ1(z)  ,  σ1(z) + σ3(z) 

R (z) = 

where σ1 and σ3 are the minimum and maximum principal stresses. Within the depth interval corresponding to reverse slip, the denominator increases (normal stress increases) while the numerator decreases (shear stress decreases). In the strike-slip interval, the curves σx(z) and σy(z) are parallel in the reference model, and shear stress is thus constant while normal stress increases. Thus, the depth zc again controls the seismogenic depth. In the case of strain shadow, seismogenic crust consists of two parts, with predominant reverse and strike slip above z** (or 0 < z < z**), at relatively large negative σ0, and most frequent normal slip below z**. For normal slip, at σ0 = 0, the ratio R(z) is constant, i.e., zc does not bound seismogenic crust from below. Actually, the lower bound exists but it has to be of purely physical origin. Shear stress

in the reference model grows infinitely in the case of strain shadow, and transition to plastic state is inevitable at some depth. Nevertheless, it is natural to expect the deepest earthquakes in regions of strain shadow. At σ0 ≠ 0, the normal-slip depth interval is bound by the condition z > max(z**, zc) from the side of shallower depths. Regard for contact conditions. The above equations are applicable, without correction, to non-contact (constrained or non-constrained) compression. Now we consider stress associated with a rigid contact in our ideal model, first in the case of constrained deformation. The rigid contact condition does not interfere with the model symmetry, and therefore, all shear stresses with the subscript y in the plane y = 0 (including τxy and τyz) are zero. In this case, it follows from the first equilibrium equation in (5) that τxz = const (taking into account x independence of all parameters). This constant can be only zero according to the free-boundary conditions. Thus, the stress tensor in the plane y = 0 is diagonal: T = diag(σx, σy, σz). Therefore, all inferences obtained without regard for contact conditions are valid near the plane y = 0. Namely, the fault plane dips at an angle smaller than π / 4. Near the contact the symmetry fails, and at y ≠ 0 σx 0 0    T =  0 σy τyz . 0 τ σ  yz z   Let z be equal to or less than z* and the slip be reverse. For each y ≠ 0 and z there is the rotation angle ϕ of the coordinates (x, y, z) about the x axis such that the stress tensor becomes diagonal again in the new coordinates (x, y′, z′) (ϕ is assumed positive if the z axis turns toward the former y direction). The angle ϕ found using the known equations for the rotation of coordinates is ϕ = 1 arctg 2

2τyz σy − σz

.

In these coordinates, the reverse slip plane is bisector between the planes y′ = 0 and z′ = 0. There are always two such planes: if one dips at π / 4 + ϕ to the positive y direction, the other (conjugate) plane dips at 3π / 4 + ϕ. The sign of ϕ depends on the sign of τyz = (µ / 2)∂uz / ∂y because τyy > τzz at z < z* (mind that ∂uy /∂z = 0 because always εyy = −ε0). Now we are to compare vertical displacement in not contacting soft and rigid blocks. The displacement can be counted from any reference depth, and we assume that the blocks extend upward from z = z*. Then, as it follows from (7), for any depth z ≤ z∗, z

uz (z) = ∫

∗

λε0 − ρgz

∗

λ + 2µ

z−z

dz = ∫

z 0 ∗

ρgζ

∫ λ + 2µ dζ = −

z −z

0

−ρgζ dζ = λ + 2µ

∗

2

ρg (z − z) 2(λ + 2µ)

.

Let the blocks be of proximal densities but differ strongly in

S.V. Gol’din and O.A. Kuchai / Russian Geology and Geophysics 48 (2007) 536–557

Fig. 11. Displacement and strain near contact of rigid and soft blocks. See text for explanation.

rigidity. Then, the soft block (at no contact) moves up higher than the rigid block. That is why the displacement uz depends on y as in Fig. 11, a (arrows). The displacement uz being negative, this behavior means that ∂uz / ∂y > 0. Hence, both τyz and ϕ are positive. Thus reverse slip occurs either on the plane that dips toward the contact at π / 4 + ϕ (nearly vertical conjugate plane) or on a nearly horizontal plane dipping toward the opposite contact at π − (3π / 4 + ϕ) = π / 4 − ϕ. The choice of the conjugate plane is made taking into account plastic flow. ϕ increases at y → 1 / 2 and at y ≠ 0, z → z∗ (as σz → σy). The dip change of the vertical plane is sketched in Fig. 11, b (dashed line). If the set of dips is considered as a vector field in the plane yz, the integral curves of this field define a depthward flattening cross section of a possible fault. This fact eliminates, to a certain extent, the contradiction between the geometry of real thrusts and the steeper reverse planes inferred at y = const. Oblique convergence. Role of plastic flow. Compressionorthogonal convergence of rigid blocks is the exception rather than the rule, so we investigate the case of oblique convergence (Fig. 12, a). The velocity vector of oblique convergence consists of two components: normal convergence (or convergence proper) and parallel relative displacement of the blocks. Normal convergence reduces to the above problem, but now

553

we take into account that the normal stress σn is less than the regional compressive stress (σn < σz). Then, we are to look into parallel counter motion of blocks as sketched in Fig. 12, b. From this point on (Fig. 12, b) we include the effect of plastic flow on the seismic process neglected before. Relative counter motion of two parallel rigid plates is known to produce the so-called Couette flow between the two surfaces (series of small arrows in Fig. 12, b) corresponding to simple shear, as it is confirmed, for instance, by experiments with friable materials (Revuzhenko, 2000). We hypothesize that Couette flow exists in the lower crust (below the seismogenic zone) where quasi-plastic flow is associated with repacking at the scale of grains and relatively small aggregates, in the same way as in the experiments of Revuzhenko (2000). However, the natural rheological and scale heterogeneity of seismogenic crust, where the hierarchy of blocks is more prominent at many scales, rules out the “soft” scenario of Couette flow, which is the basic cause of brittle failure. In fact, plastic flow in the lower crust, by continuity, controls the respective deformation in the upper crust. This deformation partly occurs as creep and local plastic flow, but large volumes of brittle material in the subcritical state are subject to shear elastic strain inevitably leading to rupture. It appears reasonable to call it the brittle-plastic flow. Brittle failure, whichever be its mechanism, always includes a strike-slip component controlled by Couette flow (right-lateral strike slip in the case of Fig. 12, b). The specific mechanism of brittle failure is defined by constrained or non-constrained conditions of compression (change of σn for σz). Due to Couette flow, the conjugate plane can be chosen unambiguously in the case of strike slip, and a strike-slip component appears in the case of reverse slip (reverse oblique slip). Note that a rigid block of a comparable scale existing within the zone of plastic deformation (like Couette flow) rotates clockwise. In terms of physical mesomechanics, real plastic flow (with mesostructure) does go by rotation of rigid blocks and fluid flow of softer material. Note that at least large rupture nucleated at 15–20 km is often driven by the energy of quasi-plastic flow in the lower and middle crust. The setting corresponding to Couette flow between nearly

Fig. 12. Strain in case of oblique convergence. See text for explanation.

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S.V. Gol’din and O.A. Kuchai / Russian Geology and Geophysics 48 (2007) 536–557

Fig. 14. Flow associated with lateral extrusion from between two convergent blocks. Fig. 13. Interpretation of right-lateral and left-lateral strike slip in two parts of Altai-Sayan area.

parallel obliquely convergent blocks within the Altai-Sayan area exists in the West Sayan, and in the Mongolian Altay and the neighbor Gorny (Russian) Altai. The Mongolian Altay is confined between the Great Lakes Basin in the east and the Dzungarian and Zaisan basins in the west (Fig. 13, a). The right-lateral strike slip in these regions is consistent with our interpretation (Fig. 13, a). The West Sayan lies between the roughly W-E edges of the Great Lakes Basin and Minusa basin (Fig. 13, b), where the convergence direction is at a very small but nonzero angle to the plate boundaries, which corresponds to the observed left-lateral strike slip. Our inference acquires a more solid ground with the assumption that compression is directed mainly from NEN to SWS, as is suggested by many workers. Deformation is similar in the case of a fault system striking at a sharp angle to compression taken instead of convergent blocks. (Now a rigid block between two faults rotates in the opposite sense, as in Fig. 13, c). Thus, plastic flow aligns with the subsystem of faults that strikes at the least angle to regional compression, unless there are other control factors. The final solution can be obtained only by solving the boundary-value problems in the elastoplastic model with regard to the rigidity-plasticity (rheological) and fault-block structures. The former dominates at the regional scale and the latter at the smaller (local) scale. Flows in which right-lateral Couette flow contacts left-lateral one can arise in regions of lateral extrusion between parallel convergent blocks, and the geometry of flow depends on spacing between the convergent blocks (Fig. 14). The same ideas are applicable to the choice of conjugate plane in the case of reverse slip attendant with ductile deformation leading to mountain growth. Plastic flow associated with mountain growth is known to be of different types, including folding (flexure instability) or vertical (upward) extrusion. A thrust-type plastic flow commonly occurs if a rigid block underthrusts a mountain system along a flat boundary, as in the case of the Tien Shan-Tarim contact. In all cases, fault planes are tangent to the sliding surfaces of the respective flow, which allows unambiguous choice of the conjugate plane and its dip correction. Flow in the case of a nearly vertical contact (near the surface z = 0) can occur as eruption.

The abundance of thrusts in the southern Tien Shan is often attributed to a greater activity of Tarim relative to Kazakhstan, which obviously contradicts Newton’s third law. Note also that thrusts in the northern and southern Pamirs are almost symmetrical. The asymmetry of the Tien Shan thrust pattern may be due to difference in the geometry of boundaries or in rigidity between its northern and southern parts. On the other hand, it appears unreasonable to specify the position of blocks corresponding to each flow style. The pattern of elastoplastic deformation mainly follows the compatibility equation implying that new fragments of plastic flow in a broadening zone of ductile deformation fit the existing flow. This is most likely the reason for the large width of thrusting areas both in the southern Tien Shan and the Pamirs. Inasmuch as the depth potential of mountain growth apparently involves lower crust in the case of constrained compression, the energy of hot material extruded to the surface contributes a lot to seismicity within seismogenic crust. Deformation in the eastern Altai-Sayan area, where plastic flow associated with eastward extrusion inevitable in convergence of two superplates appears to be an important agent, is worth special consideration and is detailed below. The general idea would be that the direction and geometry of slip depend on the way the modern stress superposes the existing plastic flow. We stress that by plastic flow we mean only local mass transfer which, in terms of fluid dynamics, corresponds to boiling liquid or turbulent flow in a mountain stream with the subtracted total downstream transport of water. As many geologists are aware, saying India is thrusting over Eurasia makes sense only in the Eurasian frame of reference. However, when frequently used, the words can give rise to illusions, namely, one may think that the Tien Shan would experience a greater pressure from Tarim than from Kazakhstan.

Interpretation of local effects Stress concentrators. Large concentrators of elastic stress, which eventually command the location of potential earthquakes, are caused by local geodynamics at a source-area scale. Space variations of stress in the ideal elastic model are controlled by elastic moduli changes as well as the geometry of inner boundaries and boundary conditions. However, other factors come into play in areas of shear instability where

S.V. Gol’din and O.A. Kuchai / Russian Geology and Geophysics 48 (2007) 536–557

processes responsible for energy supply and dissipation are nearly in the dynamic equilibrium. For instance, locally lower dissipation or slower plastic strain rate inevitably causes local increase in elastic stress. We discuss two causes of stress concentration generally following the theory by Panin (2000). One cause is the existence of an interface between rigid and plastic domains (rheologically different media). The purely elastic model already implies that the strain εxx in the vicinity of a boundary defined by the equation y = 0 commands the shear stress σxy largely controlled by elastic contrasts. Yet, intense ductile deformation in one of two neighbor domains (i.e., the two are deformed in different ways) produces still higher stress by continuity. The fact that most of large earthquakes in the Altai-Sayan area occur at mountain-basin boundaries is solid evidence that this is the main (or one main) cause of large energy concentration in collisional regions subject to non-constrained compression. The contact of a rigid plate with a plastic collisional region induces active thrust flow of plastic material over the plate (with no constraints except gravity), as well as underthrusting of the rigid plate beneath the plastic region. This motion intensifies the seismic process in the vicinity of the contact. The flow being the most rapid at some distance off the boundary, there is a greater probability that a large earthquake occurs at a respective distance due the mesostructure of plastic flow. This idea more or less accounts for the observed seismicity in the Tien Shan. The other cause is associated with plastic flow. As we wrote, plastic flow involves rotation of rigid domains. However, rotation of a real rigid block inside a solid can be either elastic or cause discontinuity. Once the potentialities of elastic rotation become exhausted, first the strain changes because of intense flexure, and then accommodation and fatigue processes set into work (Gol’din, 2005). This all eventually ends in brittle failure. The two causes are not alternative and can interplay at different scales. There is some reason to think that of the two causes the latter one was of equal (or greater) importance in the Altai earthquake at the natural macroscale. The M = 6.9 Zaisan earthquake of 1990 at 47.9° N, 85.1° E (Lutikov et al., 2004) appears to mismatch the general pattern as it occurred near the center rather than on the periphery of the basin we interpreted as a rigid (low seismic) block. Note, however, that the earthquake originated at a great depth (30–40 km) where the geometry of the involved blocks in unknown. About a half of its aftershocks fall within the mountain system on the northern border of the Zaisan basin (southwestern edge of the Gorny Altai). Therefore, the boundary between the Zaisan block and the mountain system north of it is located under the basin at depths of 30–40 km and can dip either beneath the basin or beneath the mountains. The rupture orientation (120°) does not contradict this hypothesis. There is another alternative hypothesis: the earthquake may be evidence that the rigid block is beginning to crack. As we noted, partial cracking of basin edges is typical of the collisional region as a whole. In this case deformation can

555

involve the lower boundary of the rigid block. The earthquake mechanism (right-lateral strike slip) and its depth fit the cas of a moderately constrained compression but the presence oe a reverse slip component in the northwestern flank of thef causative fault indicates more constrained conditions near th Kazakhstan plate. Events with purely reverse mechanismse were recorded west of the Zaisan earthquake about 84° E (Fig. 2). Nontypical earthquake mechanisms. Strike-slip and re verse focal mechanisms in the Altai-Sayan area are nearlyequal in number (Fig. 1, b), which is consistent with moderately constrained regional compression. Our modelin predicts that reverse-slip earthquakes originate more often at g shallower and strike-slip ones at greater depths in seismogenic crust. Yet, the available hypocenter locations are of low quality insufficient to prove or disprove this prediction Rupture in many large events of the Altai-Sayan area occurs. on strike-slip planes parallel to the collisional directio (Fig. 5), except for the Ureg Nuur earthquake that originatedn at a depth of ∼10 km. Therefore, strike slip with collision-par allel compression is a typical mechanism of the area, whereasnon-sporadic reverse- and, especially, normal-slip mechanisms or strike slip off N-S compression must result from specifi causes that may be interesting. The existence of normal-slipc earthquakes in the eastern Altai-Sayan area where rift-related regime coexists with compression is worth a special discus sion, and we restrict ourselves to the western and central partsof the area. Reverse-slip events are typically shallow in th conditions of moderately constrained compression but ma e occur at any depth if compression is locally constrained. Note y in this respect the area of reverse mechanisms between 47 an 49° near the western edge of the Mongolian Altay. This narrow d neck between the Great Lakes Basin and the Dzungarian microplate is a perfect example of non-contact constraine compression (Fig. 15). The same reason may explain the d reverse-slip mechanism of the Ms = 7.0 Ureg Nuur earthquake of 15 May 1970. It occurred at the northern edge of an uplift inserted from the south into the eastern Ureg Nuur basin which, in turn, neighbors the large basin of Lake Uvs Nuur Therefore the epicenter is located between two closely spaced. rigid blocks that confine both eastward and westward lateral extrusion.

Fig. 15. Non-contact constrained compression.

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S.V. Gol’din and O.A. Kuchai / Russian Geology and Geophysics 48 (2007) 536–557

Seismic strain along the eastern edge of the Mongolian Altay near its border with the region of Great Lakes (between 48 and 50° N) and in the southernmost Mongolian Altay near its border with Dzungaria corresponds to principal compression and principal extension at 30–60° to the regional compression. On close examination, the same style of deformation appears elsewhere in the Altai-Sayan area but most often near contacts with aseismic blocks. A very likely explanation is the effect from a rigid contact. In this case we deal with continuity of horizontal displacement across a contact which gives rise to the shear stress τnl, in the coordinates of the contact (n is the normal to the contact and l is the contact-tangent direction). If the magnitude of this stress is comparable to regional compression, the predicted angles between the locally principal and regional strain directions are quite realistic. The symmetric pattern of anomalous principal strain directions everywhere within the narrow zone of Mongolian Altay between 46°30′ and 47°30′ would be evidence of Couette flow, had not the symmetry been partly due to smoothing. The presence of reverse-slip mechanisms along the East Sayan-West Sayan boundary between 94 and 96° E requires a more sophisticated explanation than that for the Mongolian Altay. This slip geometry might be due to shallow origin depths of earthquakes under moderately constrained compression, but no reliable hypocenter locations are available for the area, nor for the area north of the Hangayn fault about 98° E. Few normal-slip mechanisms in the western and central Altai-Sayan area may be associated with strain shadow of regional compression which typically produces normal slip (see above). Local extension is known to arise in inhomogeneous media even under uniform compression, and the absence of normal slip from the mosaic strain pattern of the AltaiSayan area would be surprising. A normal slip that belongs to a strain shadow region can be recognized from the principal extension direction across regional compression, for instance, in normal-slip earthquakes between 94 and 96° E and between 50 and 51°30′ N. Note also that Lake Teletskoye, Lake Baikal, and the Busiyngol basin strike parallel to regional compression in the respective parts of the Altai-Sayan area.

Conclusions 1. All main features of seismic strain in the Altai-Sayan area can be accounted for by N-S regional compression associated with the India-Eurasia collision. 2. The observed diversity of earthquake mechanisms and slip directions is largely due to the hierarchic systems of rigid and plastic blocks (rheological structure) and of blocks and their fault boundaries (fault block structure). The former controls the stress regime and the latter the details of earthquake rupture. Both systems consist of aseismic rigid blocks, soft blocks that lost shear stability with respect to the long-lived collisional stress, and faults. The type of stress depends on the kinematics and geometry of convergent rigid blocks. An important role belongs to the correspondence

between the modern stress in the brittle crust and the quasi-plastic flow in the lower crust. 3. Lateral constraint of regional compression and the origin depth of earthquakes are specific factors that define slip mechanisms (reverse, normal or strike slip). The constraint degree corresponds to possibility for lateral extrusion of soft material. Reverse slip occurs most often in constrained conditions and strike slip under non-constrained compression. In moderately constrained conditions, most of deep earthquakes have strike-slip mechanisms and shallow events most often show reverse slip. The sense (right- or left-lateral) of strike slip depends either on the direction of convergence relative to the block boundaries or on the respective Couette flow in the lower crust. The direction of slip also bears an effect of Coulomb stress. Normal slip occurs in regions of strain shadow where regional compression is weaker. Normal and strike-slip mechanisms can alternate in regions of transition from non-constrained compression to strain shadow, which is apparently the case of the eastern Altai-Sayan area that meets the Baikal rift. Earthquake mechanisms are finally defined by the correspondence between the orientation of conjugate planes, the existing plastic flow, and the condition of normal stress minimization. We wish to thank V.N. Nikolaevskiy, P.G. Dyad’kov, S.I. Sherman, B.P. Sibiryakov, V.Yu. Timofeev, V.A. San’kov, L.A. Nazarova, I.Yu. Kulakov, V.I. Budanov and many others for discussions, advice, and personal communications. The study was performed as part of Program 16 of the Presidium of the Russian Academy of Sciences (Project 3) and Integrate Project 116 of the Siberian Branch of the Russian Academy of Sciences and was partly supported by grant 07-05-00986a from the Russian Foundation for Basic Research.

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