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—Thermal metamorphism produced an aureole near the early Paleozoic Bayan-Kol gabbro–monzodiorite intrusion in the Erzin shear zone of western Sangilen (Tuva–Mongolia microcontinent, Central Asian Orogenic Belt). Field observation of intrusive contact, structure–textural and mineral transformations of metamorphic rocks, regular changes in the chemical composition of minerals with approaching the intrusive contact, and high temperature gradient from intrusive to wallrocks verified the occurrence of a contact aureole near the Bayan-Kol intrusion. The high-gradient thermal metamorphism (M2) affected garnet–staurolite–kyanite schists that formed during earlier regional metamorphism (M1) at 6.2–7.9 kbar and 600–670 ºC. The 0.5 km wide M2 metamorphic aureole mapped along the northwestern intrusion margin consists of a muscovite–sillimanite zone adjacent to the sedimentary country rocks and a cordierite–K-feldspar zone on the side of the intrusion. The M2 metamorphic reactions occurred within the granulite facies temperature range 880–910 ºC along the contact with monzodiorites and at ~950 ºC along the boundary with gabbronorites; the temperature on the aureole periphery was about 640 ºC. Pressure estimates indicate deep-seated high-grade metamorphism at 6.9–7.8 kbar, while the intrusion itself crystallized at 7.7–7.8 kbar. The suggested numerical model implying the formation of a thermal aureole at a depth of 26 km (7 kbar) in the lower crust is consistent with the temperature pattern determined by geothermobarometry for several key points of the metamorphic zoning and confirms its deep-level origin. Thus, the aureole near the Bayan-Kol intrusion represents a rare case of contact metamorphism in the lower continental crust. The obtained results, along with published petrological and geochronological evidence, reveal two depth levels of the early Paleozoic M2 metamorphism in the Sangilen area: upper (7–15 km, 2–4 kbar) and lower (26–30 km, 7–8 kbar) crust. The Bayan-Kol gabbro–monzodiorite intrusion is likely a small apophysis or a fragment of a deep-crust intermediate magma chamber, while the moderate-pressure (7–8 kbar) M2 granulites in the Erzin shear zone are products of high-gradient metamorphism related to the Cambrian–Ordovician collisional mafic magmatism in the Sangilen area.

For the first time, a thermomechanical model of a system of multilevel magma chambers above a mantle heat source has been developed to explain the formation mechanisms of intrusive complexes and metamorphic aureoles in Western Sangilen. A model of “thermal blur” at the collision stage and a model of a local magma reservoir at the transtension stage are proposed. The magmatic process was studied using a numerical thermomechanical model of the system magma reservoir–magma transport–formation of intermediate chambers–formation of metamorphic zonal complexes around intrusions at different depth levels. Modeling explains the mosaic distribution of granulite metamorphism zones in the Sangilen block. Model estimates of the duration of intrusive processes were obtained. The change in tectonic regimes in the evolution of Western Sangilen affects the depth of emplacement of gabbro–monzodiorite massifs and surrounding metamorphic aureoles.

—A model of the formation of the Teletskoe–Chulyshman metamorphic belt (TCMB) in Gorny Altai has been elaborated. The estimated pressure (not exceeding 3–4 kbar) and temperature (about 740 °C) indicate an increased regional crustal thermal gradient equal to 60–90 °C/km during the formation of the metamorphic belt. The age of migmatites of the Chulyshman complex has been evaluated at 483.9 ± 5.7 Ma (Early Ordovician) by U/Pb (SHRIMP) zircon dating. The paleogeodynamic setting of the TCMB formation and the protolith nature are identified based on the geochemical and petrochemical parameters of the metamorphic rocks. Structural parameters and numerical modeling show that the Chulyshman migmatite–gneiss complex is an apical part of the thermal-dome structure formed under the thermal impact of a magmatic basic heat source in the base of the crust and displaced to the relevant depths via thrusts and crustal extrusion during the Early Ordovician accretion–collision event. Matching the metamorphism parameters and the numerical-modeling results for the crustal thermal regime, we determined the rate of the anatectic front displacement along the thrust to be at least 6 cm/yr.

The heat release effect was estimated due to friction in faults under shear and thrust conditions by mathematical modeling, 3D and 2D thermomechanical numerical models were developed. The equations of solid mechanics in a coupled formulation were solved: the equations of mechanical equilibrium and the equation of heat transfer. The model of an elastic-plastic material with the Drucker-Prager and Huber-Mises yield function is used. For the 3D shear model, the heating was 100-110 °C for the value of the friction coefficient 0.3, 180-190 °C for 0.5, about 300 °C for 0.65. In models of horizontal thrust, the heating in the contact zone was 120-130 °C with a depth of shear plane of 20 km and 150-160 °C with a depth of shear plane of 30 km for a friction coefficient of 0.3. The results obtained can be considered as a lower estimate of the heating in the Yenisei collision-shear zone.

—Spurrite-merwinite marbles on the right bank of the Kochumdek River in the Podkamennaya Tunguska basin formed along the top margin of a flood basalt intrusion (Kuzmovka complex) from a marly limestone protolith of the Rhuddanian Lower Kochumdek Subformation, at a pressure of ~200 bars. The contact metamorphic aureole comprises four zones of successively decreasing temperatures marked by the respective mineral assemblages: T ≥ 900 °C (merwinite, spurrite and gehlenite (±rankinite, bredigite); T ≥ 750 °C (spurrite); T ≥ 700 °C (tilleyite, wollastonite, and melilite (Gehl 2/3 Tmelt) result from magma flow along a conduit. The temperature profiles for the Kochumdek metamorphic complex show good fit between measured and geothermometer-derived values at a magma temperature of 1200 °C, an intrusion thickness of ≥ 40 m, a heating time of six months, and a magma flow lifespan within one month. Stagnant magma in a conduit of any thickness cools down and crystallizes rapidly and fails to heat up sediments to the temperatures required for spurrite–merwinite metamorphism (above 790 °C).

Possible mechanisms of rifting and the thermal regime of the lithosphere beneath the rift zone of the Vilyui sedimentary basin are considered based on the available isotopic ages of dike swarms, rates of sedimentation, and results of numerical modeling. Temporal correlations between the intrusion of mafic magma and a sharp increase in the rate of subsidence and sedimentation in the rift basin prove the contribution of both plate-tectonic and magmatic factors to the formation of the Vilyui rift. The results show a relationship between the rapid extension of the lithosphere and the formation of mafic dike swarms in the Yakutsk–Vilyui Large Igneous Province of the Siberian Platform at the Frasnian–Famennian boundary, with a peak at ~ 374.1 Ma, and at the end of the Late Devonian, with a peak at ~ 363.4 Ma. There were two pulses of dike formation during rapid subsidence of the basin basement in the period 380–360 Ma, with a sedimentation rate of 100–130 m/Myr, at a background rate of 10–20 m/Myr. Analysis of numerical thermomechanical models revealed that the best-fit model is that combining the mechanisms of intraplate extension (passive rifting) and the ascent of a mantle magmatic diapir (active rifting). A conclusion about the nature of the heat source of trap magmatism has been drawn: The plume-driven regime of the lithosphere can better explain the dynamics of extension during rifting than the decompression melting mechanism.

This paper describes a thermomechanical mathematical model of magma mingling and mixing during the formation of complex intrusions and presents the first results of numerical modeling. The model considers one-pulse intrusion of mafic or intermediate melts into a granitoid magma chamber. The model is based on literature data on the composition and structure of two polychronous intrusions: the Burgas quartz syenite massif and the Magadan granitoid batholith. The modeling shows that the main parameter controlling the convection regime is the density difference. The density and viscosity contrasts of interacting magmas during mingling and mixing are estimated. Depending on the density difference, one of the possible processes dominates: In the case of a small difference (less than 30–40 kg/m3), magma mixing and hybridization in a small contact zone takes place; in the case of a large difference (100 kg/m3 or more), magma mingling predominates. The viscosity contrast, in turn, determines whether interpenetration of melts or fragmentation of melts in the form of drops, spheres, etc. occurs. There is a limiting viscosity of salic magma (108 Pa⋅s) at which the flows freeze in the chamber and further cooling occurs with a slowly moving fluid. The time of formation of mingling structures is estimated to be several days to several hundred years, depending on the initial melt viscosity.

This paper presents results from new 40Ar/39Ar isotope dating of nine mafic dykes from three large dyke swarms (Vilyui–Markha, Kontai–Dzherba, and Chara–Sinsk) of the Yakutsk–Vilyui large igneous province (LIP), in addition to a reconstruction of the subsidence history of the middle Palaeozoic Vilyui paleorift basin (eastern Siberian platform). All previously published 40Ar/39Ar and U–Pb dates are summarized. Statistical analysis of the dyke ages reveals repeated magmatic events in the study area. Two major pulses of mafic magmatism are identified: one at the Frasnian–Famennian boundary, with a main peak at ca. 374.1 Ma, and another in the latest Devonian with a peak at ca. 363.4 Ma. The time of maximum intensity of dyke intrusion coincides (within uncertainty) with rapid subsidence in the Vilyui basin. The minimum total volume of middle Palaeozoic magmatism produced in the Yakutsk–Vilyui LIP is 100–215 K km3, which is much less than earlier estimates. Most of the mafic material within the Yakutsk–Vilyui LIP is related to the Vilyui basin and associated dyke swarms. Backstripping analysis of sedimentation in depressions of the Vilyui basin was carried out. Estimates were obtained for the spatial distribution of the stretching factor of the crust and mantle lithosphere, averaging 1.17 and 1.44, respectively. The amount of extension due to dyke intrusion is estimated to be ~ 6%. Backstripping analysis of sedimentation in the Vilyui basin was used to assess the effect of both intraplate far-field forces and upwelling magma flows initiated by a mantle plume. A numerical thermomechanical model was developed to investigate the relations between two possible mechanisms by which the Vilyui rift was initiated: intraplate extension (passive rifting) and the ascent of a mantle magmatic diapir (active rifting). A model considering both of these mechanisms shows the contribution of the far-field extension forces and the effect of convective flows around the mantle plume, assuming a temperature of 1500 °C for a heat source operating for ≥ 10 Myr. The best-fit model predicts the formation of the Vilyui basin under extensional conditions with a depth-integrated horizontal driving force of 2.0 × 1013 N/m, which corresponds to a lithostatic pressure of 0.73.

In situ Raman spectroscopy is used to study the layered mineral phengite K(Al, Mg)2(Si, Al)4O10(OH)2 in water under the high temperature and pressure conditions typical of cold subduction zones (T up to 373°C and P = 12.5 GPa). High pressure and temperature were created in a resistively heated diamond anvil cell. Raman spectra show the high P–T stability of phengite. No reversible polymorphic transitions (overhydration or notable amorphization) are observed.

The rate of mineral transformations in rocks near magmatic intrusions may be estimated using mathematical modeling for study of the duration of metamorphism and geological and mineralogical data. At the contacts of the Anakit trappean massif on the Nizhnyaya Tunguska River, where the temperature reached 900°C, the rate of growth of a wollastonite rim at the boundary between the limestone and the siliceous nodule was ∼3 × 10–10 cm/s. The zone of “spotted” hornfels with a width of 300‒400 m was formed during metamorphism of chlorite–sericite–epidote–albite–quartz schist near the Kharlov gabbro massif in the foothills of the Altai Mountains. The movement rate of the metamorphic front during the formation of rock may be estimated as ∼2 × 10–8 cm/s. It is suggested that the rate of metamorphism is controlled by the temperature and rock composition. As a whole, the rates of metamorphism of rocks near magmatic intrusive bodies exceed the rates of regional metamorphism. Upon accumulation of the actual data, this may be applied for diagnostics of the types of metamorphism.

In‐situ method of Raman spectroscopy was used to study the layered phengite compressed in water under simultaneously high P–T (up to 373 °С and 12.5 GPa). The implemented conditions were typical of modeling the “cold” subduction zones in lithospheric slabs. Raman spectra have demonstrated a high Р–Т stability of the mineral. No non‐quenchable phengite states were observed.

The paper presents original authors’ data on aluminous schists in the Tsogt tectonic plate in the Southern Altai Metamorphic Belt. The nappe includes a medium-temperature/medium-pressure zonal metamorphic complex, whose metamorphic grade varies from the greenschist to epidote-amphibolite facies. The garnet and garnet–staurolite schists contain three garnet generations of different composition and morphology. The P–T metamorphic parameters estimated by mineralogical geothermometers and geobarometers and by numerical modeling with the PERPLEX 668 software provide evidence of two successive metamorphic episodes: high-gradient (of the andalusite–sillimanite type, geothermal gradient approximately 40–50°/km) and low-gradient (kyanite–sillimanite type, geothermal gradient approximately 27°/km). The P-T parameters of the older episode are T = 545–575°C and P = 3.1–3.7 kbar. Metamorphism during the younger episode was zonal, and its peak parameters were T = 560–565°C, P = 6.4–7.2 kbar for the garnet zone and T = 585–615°C, P = 7.1–7.8 kbar for the staurolite zone. The metamorphism evolved according to a clockwise P–T path: the pressure increased during the first episode at a practically constant temperature, and then during the second episode, the temperature increased at a nearly constant pressure. Such trends are typical of metamorphism related to collisional tectonic settings and may be explained by crustal thickening due to overthrusting. The regional crustal thickening reached at least 15–18 km.

Diapirism can be regarded as the main mechanism of transport through the lithosphere for both felsic and mafic/ultramafic magmas. However, the lack of field observations makes it difficult to identify the key mechanism responsible for the formation of dome-shaped structures. In this study, emplacement of natural diapirs is reconstructed by numerical experiments handling realistic rheological and petrological models for the crust and mantle lithosphere. Three different regimes of diapiric ascent were established depending on the chosen model rheology: (1) single-stage diapir ascent; (2) pulsating ascent of successive batches of mantle-derived magma to the base of the crust with a periodicity of 2–3 Myr; (3) emplacement of extensive magma bodies in the form of sills either beneath the base of the crust (underplating) or to deeper mantle levels. The timescale of 30 Myr for a heat source at the base of the lithosphere is sufficient to initiate the ascent of a diapir through the mantle and crust. The study provides the estimates of rheological properties of the lithosphere and partially molten material at which diapiric ascent through the mantle and crust can occur.

This chapter is a brief account of the history of the ideas that provided the conceptual basis for metamorphic petrology, with a list of outstanding researchers who made the greatest contributions to the study of metamorphism mostly until the end of the last century. The main emphasis is on the evolution of views on mineral transformations in rocks, including the kinetics of metamorphism and metamorphic facies concepts in terms of the diversity of mineral assemblages. Such a retrospect takes the reader into a set of problems of metamorphic petrology and introduces the terms and concepts.

This chapter presents a generalized P-T-t diagram of the evolution of metamorphic complexes of different geodynamic nature that are characteristic of different types of metamorphism. This diagram was built using the most recent natural observations, which are characterized by the simultaneous presence of prograde and retrograde segments of a P-T path. This chapter discusses some of the ambiguous interpretations of P-T-t paths in areas with simultaneous manifestation of different metamorphic processes. Quantitative models for the analysis of different types of interaction of rocks undergoing metamorphism are exemplified using the following processes involved in the formation of distinctly expressed zoned reaction textures (coronites, kelyphites, symplectites, nodules, and segregations) and mineral transformations in texturally homogeneous rocks between matrix minerals and porphyroblasts. It was shown that mass transfer during metamorphic reactions occurs with the preservation of the material balance within very small local volumes of the rock, which increase from a few hundredths of a mm3 to a few cm3, depending on the duration of metamorphism, P-T parameters, strain intensity and a degree of fluid saturation of rocks. We also consider different kinetic parameters of diffusion-controlled metamorphic reactions, such as mineral reaction mechanisms and rates.

This chapter considers numerical model-based relationships between metamorphism and geodynamics, discusses tectonomagmatic causes and controls of metamorphism, and makes attempt to link the geological types of metamorphism to the specific Р-Т conditions and Р-Т-t paths. Three categories of metamorphism are distinguished based on the magnitude of the heat flux: (1) metamorphism induced by a thermal gradient close to the average continental values (metamorphism associated with crustal subsidence, in depressions during continental rifting, metamorphism caused by tectonic stacking in orogeny, and metamorphism associated with Archean crust formation), (2) by a higher thermal gradient caused by the supply of additional heat by magmatic intrusions (contact metamorphism, medium-pressure zonal metamorphism) and diapirism, (3) by a lower thermal gradient during the collision of lithospheric plates and crustal blocks (metamorphism associated with overthrusting, underthrusting and subduction). Different types of metamorphism are manifested in different geodynamic regimes over different time scales and can be correlated with a specific combination of metamorphic facies. Interpretation of geodynamic and magmatic causes of different types of metamorphism using thermomechanical numerical models accounting for variable rates and mechanisms of subsidence and exhumation can be used to solve many geodynamical problems. Analysis of the problem reveals that metamorphism is a consequence and an indicator of geodynamics.

A mathematical model based on thermomechanical equations of mechanics of deformable solids was suggested to study the mechanism of collision and metamorphism in rocks of the Mongolian Altai orogen. The problem of crust deformation and distribution of the P–T parameters of metamorphism in the Tsogt block in the course of convergence of the Edren island-arc terrane and the Gobi–Altai back-arc terrane was considered. The results of mathematical modeling explain the 1.5-fold thickening of the crust (rock subsidence by 15–18 km), which is consistent with pressure estimates of metamorphism obtained from the data of geothermobarometry. Modeling provides estimates of the plate convergence rate by comparison of the calculated temperatures with the data of thermobarometry for rocks of the Tsogt metamorphic complex within the Tseel terrane.

The numerical model of mantle diapirism and active rifting is developed. The model describes the possibility of extension and thinning of the Earth’s crust under the action of a local 100-km long heat source in the sublithospheric mantle, which causes melting and rising of the magmatic diapir through the cratonic lithosphere. The model combines the mechanisms of the uplifting of the anomalously hot material due to its gravitational instability, underplating of magma beneath the continental crust, and its extension by the forces of the convective flows at the base of the plate. The obtained results shed light on some geological features of the joint formation of the large Vilyui igneous province and Vilyui sedimentary basin.

Magmatic phenomena play an important role inmass and heat transport within the Earth’s shells.Transport of magma in the lithosphere is determinedto a great extent by the force of gravity. Intrusive magmatism and diapirism are one of the manifestations ofgravity instability and heat and mass transport, i.e.,lifting of lighter matter in a viscoplastic medium anddescending of heavy matter. Diapirism in the lithosphere has been investigated in detail within physical,experimental [1], and mathematical [2, 3] models.The cause of magmatic intrusions is the pressure,which is arised in the gravity field mainly by the density difference between the melt and the host rocks.Horizontal tectonic motions also play a specific role inthis process. Magma intrusions are controlled by the“magma fracturing” mechanism, which has much incommon with hydraulic fracturing [4]. Magma fracturing is the process of the destruction of rocks bymeans of a fissure filled with melt under pressure.Intrusive magmatic bodies are formed as a result ofmagma fracturing. Their formation depends on twofactors: the fissuring rate of the host rocks and the ability of the magma to fill the channel in the crack tip [5].Many publications are dedicated to the mechanism ofmagma fracturing, in which the authors use laboratorymodeling [6] and analytical and numerical methods ofmathematical modeling [5, 7–9]. The influence ofmagma in these mathematical models was described ina simplified form: an internal constant pressure wasspecified in the growing fissure, while the motion ofthe magma was not considered.We developed a model of magma fracturing, inwhich we emphasized the interaction between mediawith contrasting rheological and thermophysicalproperties: a lowviscosity hightemperature melt andbrittleelastic rock at a temperature below melting.The melt material is modeled by a Newtonian fluid,while the rock material is an elastic medium with thepossibility of brittle damage. The breaking occurswhen the maximum stress at the solid body point σ

The results of numerical mathematical modeling of rock deformations under compression are given. The numerical solutions are obtained using discretization of the equations of the solid mechanics with the finite element method. The model of an ideal elastic-plastic material with a Huber-Mises yield surface was used in the calculations. The layered medium structure is taken into account in modeling of the compression of layers of the lower/middle crust on a local scale. The natural folds in strongly deformed metamorphic sequences were reproduced by the mathematical deformation models. It is shown that folding in the lower part of the Earth’s crust is possible, when the yield stresses of the host rocks are approximately two orders of magnitude less than those of the hard layers. The effect of the boundary conditions and thickness of the compressed rocks on the folding is shown.

The Late Paleozoic and Mesozoic history of high-latitude petroleum and coal basins is investigated and compared with the history of plume magmatism in the same areas. The sedimentation rates in all discussed cases are proven to be the fastest (more than 100 m per 1 Myr) during rifting events. Other peaks of rapid deposition may be associated with collisional mountain growth and/or climate change.

Deformation patterns in subduction zones, feeder systems of volcanoes, and rifts are compared and investigated in terms of relations among elastoplastic strain, rheology, pore fluids, and temperature. Regional-scale subduction processes have been explored in segments of the Kuriles–Kamchatka, Izu-Bonin, and Mariana zones. Slab geometry constraints from the 3D velocity structure are used to model the balance of forces in the three subduction zones and to distinguish the regions of predominant push or pull. Stress and strain variations in suprasubduction crust are considered for the case of magma sources beneath the Klyuchevskoy group of volcanoes. Time-lapse (4D) seismic tomography shows crustal magma reservoirs to appear and disappear rapidly as the volcanoes become active or dormant, respectively. This behavior is due to rapid strain changes which cause fast flow of fluids and the ensuing decrease or increase of melting temperature in the magma reservoirs. In addition to subduction zones, stress-strain patterns are modeled for collisional (compressive) settings, with the example of the Altai–Sayan area and the Caucasus, and for the conditions of rifting (extension), in the case of the Vilyui basin. As the modeling shows, formation of a superdeep basin does not necessarily require the crust to stretch twice or more: only 20% stretching in the necking region is enough to produce a 10–15 km deep basin.

Results of modeling of the formation of the Vilyui sedimentary basin are presented. We combine backstripping reconstructions of sedimentation and thermal regime during the subsidence with a numerical simulation based on the deformable solid mechanics. Lithological data and stratigraphic sections were used to “strip” the sedimentary beds successively and calculate the depth of the stratigraphic units during the sedimentation. It is the first time that the evolution of sedimentation which is nonuniform over the basin area has been analyzed for the Vilyui basin. The rift origin of the basin is proven. We estimate the spatial distribution of the parameters of crustal and mantle-lithosphere extension as well as expansion due to dike intrusion. According to the reconstructions, the type of subsidence curves for the sedimentary rocks of the basin depends on the tectonic regime of sedimentation in individual basins. The backstripping analysis revealed two stages of extension (sediments 4–5 km thick) and a foreland stage (sediments > 2 km thick). With the two-layered lithosphere model, we conclude that the subcrustal layer underwent predominant extension (by a factor of 1.2–2.0 vs. 1.1–1.4 in the crust). The goal of numerical experiments is to demonstrate that deep troughs can form in the continental crust under its finite extension. Unlike the oceanic rifting models, this modeling shows no complete destruction or rupture of the continental crust during the extension. The 2D numerical simulation shows the possibility of considerable basement subsidence near the central axis and explains why mafic dikes are concentrated on the basin periphery.

This paper reports the results of the numerical modeling of gravitationally instable processes in the lithospheric mantle of ancient cratons. The gravitational instability is considered as a result of melting at the lithosphere base owing to its local heating by anomalous mantle. Modeling was based on a finite element method in 2D formulation and took into account the geological structure and thermomechanical parameters of the lithosphere of the Siberian platform. Numerical results revealed the main tendencies in the mantle diapirisim of the mafic and ultramafic magma ascending through the “cold” high-viscosity lithosphere. It was shown that the shape of diapiric magmatic bodies is controlled by realistic visco-elastic-plastic rheology of lithosphere. The ascent of diapir in lithosphere was modeled for diverse regimes differing in duration, temperature field, and upwelling depth. It was concluded that the ascent of melt through lithosphere to the crust-mantle boundary is mainly controlled by rheology, and conditions of oscillatory diapirism with recurrent magma replenishments were modeled. Modeling results may shed light on some features related to the trap magmatism of the Siberian igneous province. The duration and rate of magma upwelling as well as the parameters of periodical magma upwelling were estimated and attempt was made to explain the high-velocity seismic anomalies that were recorded in the subcrustal regions of the Siberian platform.

This paper is devoted to the modeling the granite gneiss formation by means of diapiric upwelling. The natural examples of granitic diapirism in the Precambrian granite-greenstone belts and complexes of metamorphic cores are described. A new approach is proposed to describe the partial melting and development of gravity instability in the crustal granitic layer, which experienced heat impact and melting during intrusion of basaltic melt. Rheology of partially melted material and surrounding medium is regarded to be temperature-dependent, following either plasticity or creep (non-Newtonian viscosity) law. Modeling results show that crustal rheology plays a significant role in the character of diapirism (shape of upwelling bodies, duration of the process, and width of thermal aureole). The rates of upwelling within the crust behaving as elastoplastic body are orders of magnitude higher (meters to tens meters per year) than those obtained for creep (viscous) liquid model (0.8 cm/yr). Modeling results revealed that the limiting depth of upwelling of partially crystallized melt, with allowance for temperature dependence of creep, corresponds to the isotherm of 400°C.

Computer simulation of subduction was performed using nonlinear equations of deformable solid mechanics encompassing all types of nonlinearity: geometric, physical, and contact. This study presents a numerical model of subduction with allowance for the gabbro-to-eclogite phase transition. The model rheology is a plastic compressible material (Mohr-Coulomb law for a deformed rock material). It was shown that deep subduction can be modeled well with the selection of appropriate parameters of rock plasticity providing the initial thickening in the subducting slab nose.

A new point of view describing processes of partial melting and development of gravitational instability in a thickening crust with increased thickness of the granite layer is suggested. Numeral experiments support the following main conclusions. The critical volume of partially melted material should be formed for the beginning of flotation in a gravitational field. Due to model estimations, the height of the melting area in the granite crust should be not less than 6–7 km. A mushroom-shaped form of the floating body was observed in all models regardless of the thermal source size (fixed or variable width): the high temperature channel (magma leader) and head body of the diapir are formed. The height of diapir floating depends on rheological features of the surrounding crust: 10 times increase in the yield strength (from 1 to 10 MPa) while temperature decrease confines the possible level of rising to a depth of 15–16 km. An elevation of about 750 m is formed in the day surface relief above the axis part of the diapir.

The Altai lithospheric structure has been generally understood due to available high-resolution digital models. As a further step in modeling, we have simulated the structure of southeastern Altai as interaction of eight blocks which comprise or surround the Chuya and Kurai basins, proceeding from the basic configuration of blocks and earthquake mechanisms. Should the stresses in the system remain invariable, the western periphery of the Kurai basin will deform to let the Uimen-Sumulta fault join the Chuya (western end of Tolbonur) fault and evolve further as a single shear zone. The best fit model was one with slip along a single border fault in the middle of the area between two rheologically different terranes. This setting corresponds to a fault boundary between the more plastic Gorny Altai and more rigid Teletskoe-Chulyshman domains, which is consistent with current crustal movements from GPS data. In addition to scientific significance, models of this kind have practical applications as they highlight areas of stress buildup prone to release in large earthquakes. The new approach was applied to simulate the stress and strain patterns of central and southeastern Gorny Altai, and the models were tested against available geomorphological and seismotectonic data.

The rheology of Newton’s viscous or nonlinear liq-uid with viscosity dependent on the temperature anddeformation rate is often used in modeling of subduc-tion (see, for example, [1]). The temperature in the sub-ducted plate and accretionary and mantle wedge, aswell as the velocity of motion in the suprasubductionmantle wedge, is commonly calculated in this case [2].The motion of the plate itself is set with a constantvelocity [3] or is deduced from the convection of thelithospheric mantle [4, 5]. The subduction is oftenreproduced as plunging flow of viscous and cold mate-rial (see, for example, [6]). The interpretation of numer-ical modeling is based on the viscosity or temperaturefield. The region with elevated viscosity (lowered tem-perature) relative to the adjacent medium is regarded asa subducted material (see, for example, [7]). In suchmodels, the subducted plate has a typical shape of thesinking plume or drops [8].We used a different approach to modeling of geody-namic and tectonic processes elaborated previously in[9, 10]. A model with elastoplastic rheology of the sub-duction plate and lithospheric mantle with delineationof the slab boundary and the adjacent mantle is pro-posed in terms of the solid mechanics as an alternativeto models with viscous liquid. The conditions of fittingthe physicomechanical laws are strictly fulfilled at theplate–mantle interface: we set up the frictionless condi-tions in the case of serpentinization of the mantlewedge or friction conditions according to the Cou-lomb–Mohr law. The setting of the problem assumesthe existence of interacting geological bodies: subduc-tion slab, underlying mantle, and rigid continentalcrust. In contrast to the aforementioned models, inwhich the subduction plate may be determined at adepth only rather conditionally, the proposed approachallows exact location of all interfaces between geologi-cal bodies and provides tracing of their progressivedeformation. Thus, the problem of determining theshape of the plunging slab, its boundaries with the adja-cent mantle, and the stress state of the subducted mate-rial may be solved within the framework of the newapproach.We consider two (oceanic and continental) platesthat were in equilibrium with the mantle at the time ofcollision and have an inclined interface. The plates areequilibrated by contact forces owing to the pressure ofthe right plate on the left one (Fig. 1). It is suggestedthat the oceanic plate collides with the continental platewith a rate of

In the Transangarian region of the Yenisey Ridge in eastern Siberia (Russia), Fe- and Al-rich metapelitic schists of the Korda plate show field and petrological evidence of two superimposed metamorphic events. An early middle Proterozoic event with age of c.1100 Ma produced low-pressure, andalusite- bearing assemblages at c. 3.5-4 kbar and 540-560 � C. During a subsequent late Proterozoic event at c. 850 Ma, a medium-pressure, regional metamorphic overprint produced kyanite-bearing mineral assemblages that replaced minerals formed in the low-pressure event. Based on the results of geothermobarometry and P-T path calculations it can be shown that pressure increased from 4.5 to 6.7 kbar at a relatively constant temperature of 540-600 � C towards a major suture zone called the Panimba thrust. In order to produce such nearly isothermal loading of 1-7 � Ck m )1 , we propose a model for the tectono-metamorphic evolution of the study area based on crustal thickening caused by south-westward thrusting of the 5-7 km-thick upper-plate metacarbonates over lower-plate metapelites with velocity of c. 350 m Myr )1 . A small temperature increase (up to 20 ± 15 � C) of the upper part of the overlapped plate is explained by specific behaviour of steady-state geotherms calculated using lower radioactive heat production of metacarbonates as compared with metapelites. The suggested thermal- mechanical model corresponds well with P-T paths inferred from obtained thermobarometric data and correlates satisfactorily with P-T trajectories predicted by other two-dimensional thermal models for different crustal thickening and exhumation histories.