O. P. Polyansky

Computer Modeling of Granite Gneiss Diapirism in the Earth's Crust: Controlling Factors, Duration, and Temperature Regime

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.

Formation and upwelling of mantle diapirs through the cratonic lithosphere: Numerical thermomechanical modeling

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.

Computer Modeling of Granite Magma Diapirism in the Earth's Crust

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.

Computer Modeling of Underthrusting and Subduction under Conditions of Gabbro-Eclogite Transition in the Mantle

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

Numerical modeling of mantle diapirism as a cause of intracontinental rifting

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.

The influence of crustal rheology on plate subduction based on numerical modeling results

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.

Mathematical modeling of magma fracturing and dike formation

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

A thermotectonic numerical model of collisional metamorphism in the Mongolian Altai

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.

Movement Rates of Metamorphic Fronts in Rocks near Magmatic Intrusive Bodies

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.

Reconstruction of the metamorphic P–T path from the garnet zoning in aluminous schists from the Tsogt Block, Mongolian Altai

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.