Impact of mechanical anisotropy and power-law rheology on single layer folding

The infinitesimal and finite stages of folding in nonlinear viscous material with a layer-parallel anisotropy were investigated using numerical and analytical methods. Anisotropy was found to have a first-order effect on growth rate and wavelength selection, and these effects are already important for anisotropy values (normal viscosity/shear viscosity) < 10. The effect of anisotropy must therefore be considered when deducing viscosity contrasts from wavelength to thickness ratios of natural folds. Growth rates of single layer folds were found to increase and subsequently decrease during progressive deformation. This is due to interference between the single layer folds and chevron folds that form in the matrix as a result of instability caused by the anisotropic material behaviour. The wavelength of the chevron folds in the matrix is determined by the wavelength of the folded single layer, which can explain the high wavelength to thickness ratios that are sometimes found in multilayer sequences. Numerical models including anisotropic material properties allow the behaviour of multilayer sequences to be investigated without the need for resolution on the scale of individual layers. This is particularly important for large-scale models of layered lithosphere.     

Single layer folding in simple shear

Despite the common occurrence of simple shear deformation, laboratory and numerical simulations of folding have so far been almost exclusively in pure shear. Here we present a series of finite-element simulations of single layer folding in simple shear up to high shear strains (γ ≤ 4, and up to 75% shortening of the folding layer). In the simulations we vary the viscosity contrast between layer and its surroundings (25–100), the stress exponent (1 or 3) and the kinematics of deformation (pure- versus simple shear). In simple shear fold trains do not show a clear asymmetry, axial planes form perpendicular to the developing fold train and rotate along with the fold train. Differences in geometries between folds formed in simple and pure shear folds are thus difficult to distinguish visually, with simple shear folds slightly more irregular and with more variable axial plane orientation than in pure shear. Asymmetric refraction of an axial planar cleavage is a clearer indication of folding in simple shear. The main effect of an increase in stress exponent is an increase in effective viscosity contrast, with only a secondary effect on fold geometry. Naturally folded aplite dykes in a granodiorite are found in a shear zone in Roses, NE Spain. Comparison of the folded dykes with our numerical simulations indicates a viscosity contrast of around 25 and a stress exponent of 3. The natural folds confirm that at this moderate viscosity contrast, a significant amount of shortening (20–30%) is achieved by layer thickening instead of folding.     

Structural softening of the lithosphere

Structural softening is a decrease in the amount of stress needed to deform the lithosphere at a particular rate because of its structural reorganization while all true rheological properties remain constant. Structural softening is fundamentally different than material softening, where the decrease in stress is generated by a change in rheological properties with progressive deformation, such as grain size reduction resulting from large shearing strain. We study structural softening generated by folding of the crust-mantle boundary, which is a structural instability that inevitably develops during compression of the mechanically layered lithosphere. For ductile rheologies, the stress decrease represents a decrease of the effective lithospheric viscosity, which is proportional to the ratio of stress to lithospheric shortening strain rate. We present analytical and numerical results quantifying the decrease in stress and effective viscosity that occur during shortening at a constant rate. The decrease in effective viscosity can be up to 10-fold.     

Finite-element analysis of fold propagation — a problematic application?

Finite-element analysis has been used to simulate the progressive development of folds in a single layer of higher viscosity embedded in a matrix of lower viscosity and subjected to layer-parallel compression. In contrast with other studies of the problem, the layer is given an initial deflection which is not a periodic function of distance along the layer, but is instead localized and bell-shaped. The object is to see whether developing buckle folds will become periodic of their own accord.Two models have been studied, both with viscosity ratios of 10 : 1 between layer and matrix, and both with initial deflections of the same amplitude. In Model 1, however, the initial deflection has a greater span than in Model 2. During progressive deformation of the models, the initial deflections amplify, becoming buckle folds. The spans converge toward the same value, but the deflection in Model 1 amplifies faster than in Model 2. No new folds appear in Model 1, but in Model 2 new synclines appear to either side of the initial antiformal deflection. The zone of folding therefore propagates along the layering.The rate of propagation in the finite-element models is not as great as in corresponding models made from physical materials. It is suggested that this discrepancy may be due to cumulative systematic errors in the numerical method, which, in its present form, may not be entirely suitable for treating problems of instability and propagation during geological deformation.     

Fault‐bend folding as an end‐member solution of (double‐edge) fault‐propagation folding

Fault‐bend folding is the most commonly used kinematic mechanism to interpret the architecture and evolution of thrust‐related anticlines in thrust wedges. However, its basic requirement of an instantaneous propagation of the entire fault before hangingwall deformation, limits its kinematic effectiveness. To overcome this limitation, we used the interdependence between fold shape and fault slip vs. propagation rate (S/P ratio) implemented in double‐edge fault‐propagation folding. We show that very small S/P values produce fault‐propagation anticlines that, when transported forelandward along an upper décollement layer, closely resemble fault‐bend anticlines. Accordingly, if small geometric discrepancies between the two solutions are accepted, transported double‐edge fault‐propagation provides an effective kinematic alternative to fault‐bend folding. Even at very low S/P values, it in fact predicts a fast but finite propagation rate of the fault. We thus propose that double‐edge fault‐propagation folding provides a broadly applicable model of fault‐related folding that includes fault‐bend folding as an end‐member kinematic solution. Terra Nova, 18, 270–275, 2006     

The control of salt supply on entrainment of an anhydrite layer within a salt diapir

The influence of four parameters (sedimentation rate, viscosity of salt, stratigraphic location of the anhydrite layer within the salt layer, and the perturbation width) on salt supply to down-built diapirs and its entrainment capacity are studied systematically in numerical models. Model results show that these four parameters affect salt supply, and the evolution history of a salt diapir. As such, these parameters strongly influence the style and the amount of entrainment of dense inclusions into a diapir. In active diapirs (i.e. unburied diapirs), salt supply increases with increasing sedimentation rate whereas it decreases with an increase in salt viscosity. Diapirs initiating from wide perturbation provide more salt supply to feed the diapir. Presence and initial stratigraphic location of any denser layer (e.g. an anhydrite layer) within a salt layer also affects salt supply. When lateral forces are negligible, salt supply into a diapir depends on these four parameters, which directly control the entrainment of any embedded anhydrite layer into the diapir.     

Coalescence of fault‐bend and fault‐propagation folding in curved thrust systems: an insight from the Central Apennines,Italy

The coalescence and spatial variability of different thrust‐related folding mechanisms involving the same mechanical multilayer along a curved thrust system are documented in this study. The field‐based analysis of thrust‐related folds spectacularly exposed in the Gran Sasso thrust system, Central Apennines of Italy, allowed us to reconstruct the interference fold pattern between fault‐bend and fault‐propagation folding. These two thrust‐related folding mechanisms exhibit spatial variability along the differently oriented ramps of the curved Gran Sasso thrust system, passing from one style to the other. Their selective development is controlled by contrasting styles of compressional normal‐fault reactivation related to positive tectonic inversion. Fault‐bend and fault‐propagation folding interact with a characteristic interference fold pattern in the salient apex zone of the curved thrust system due to their synchronous/in‐sequence growth. This interference fold pattern might be helpful and predictive when reconstructing lateral variations in different thrust‐related folds in similar subaerial or submarine thrust belts.     

3D numerical modeling of forward folding and reverse unfolding of a viscous single-layer: Implications for the formation of folds and fold patterns

The main aims of this study are to show (i) that non-cylindrical three-dimensional (3D) fold shapes and patterns can form during a single, unidirectional shortening event and (ii) that numerical reverse modeling of 3D folding is a feasible method to reconstruct the formation of 3D buckle-folds. 3D viscous (Newtonian) single-layer folding is numerically simulated with the finite element method to investigate the formation of fold shapes during one shortening event. An initially flat layer rests on a matrix with smaller viscosity and is shortened in one direction parallel to the layering. Forward modeling with different initial geometrical perturbations on the flat layer and different lateral boundary conditions generates non-cylindrical 3D fold shapes and patterns. The simulations show that, in reality, the initial layer geometry and the boundary conditions strongly control the final fold geometry. Fold geometries produced from the forward folding models are used as initial setting in numerical reverse folding models with parameters identical to those of forward models. These reverse models accurately reconstruct the initial geometry of forward models with also only one extension event parallel to the previous shortening direction. The starting geometry of the forward models is inaccurately reconstructed by the reverse models if a significantly different viscosity ratio than in the forward models is used. This work demonstrates that reverse modeling has a high potential for reconstructing the deformation history of folded regions and rheological constraints such as viscosity ratio. Reverse models may be applied to natural 3D fold shapes and patterns in order to determine if they formed (i) during a single or multiple deformation events and (ii) as active buckle-folds with a viscosity ratio 1 or as passive, kinematic folds without buckling. This approach may find much application to fold interference patterns, in particular.     

Study on Effects of Low Viscosity Fluid Pre-injection on Hydraulic Fracture Complexity in Tight Heterogeneous Glutenite Reservoirs

Tight heterogeneous glutenite reservoir is typically not easy to form complex hydraulic fracture (HF) due to its poor physical properties, poor matrix seepage capacity, and small limit discharge radius and undeveloped natural fracture system. To improve the HF complexity and the stimulated reservoir volume (SRV), a novel stimulation technology called CO₂ miscible fracturing has been introduced and its fracturing mechanism has been studied. The CO₂ miscible fracturing modifies the in situ stress field by injecting low viscosity fluid to increase the HF complexity and SRV. Therefore, a series of numerical simulations based on a hydro-mechanical-damage model were carried out to study the effects of low viscosity fluid pre-injection on pore pressure, stress field, and fracturing effect in tight heterogeneous glutenite reservoirs. The results indicate that the low viscosity fluid injection can effectively increase the pore pressure around the wellbore and reduce the effective stress of the glutenite. The FCI and SRV increase with the increase of the pre-injection amount of the low viscosity fluid. The HF complexity and SRV can be improved by pre-injecting low viscosity fluid to transform the in situ stress field. The field application of this technology in a well of Shengli Oilfield showed that low-viscosity fluid pre-injection can effectively increase the width of the fractured zone, improve the SRV, and optimize the fracturing effect.

     

Salt tectonism and the evolution of the Sigsbee Scarp,Gulf of Mexico

A sequence of thirteen seismic reflection profiles across the Sigsbee Scarp suggests that it is the surface expression of the most recent of a regular sequence of parallel salt ridges. The ridges are intruded vertically and in sequence, basinward from an extensive and deeply buried salt layer. The process is self-propagating, due to an inherent instability resulting from the low density of the salt and its reduced viscosity at increased temperatures.     

A finite-element study of fold propagation in a viscous layer

A finite-element model of a viscous layer contained in a viscous matrix and undergoing layer-parallel compression is used to examine the hypothesis that a long chain of folds, as found in real rocks, can originate from one initial perturbation to the layer geometry. This hypothesis is tested by determining the velocity with which a perturbation spreads along layers of various viscosities.An insight is gained into the roles played by local strain and local layer strength in the folding mechanism. The results show that for layers with viscosity ratios comparable with those of real rocks it is impossible for long chains of folds to originate from one perturbation. The authors conclude that rock layers contain many initial perturbations and folding originates at all perturbation sites simultaneously. The growth of such folds depends on the amplitude and shape of the initial perturbation and on subsequent interference between folds.     

Exhumation of the Dora Maira ultrahigh‐pressure unit by buoyant uprise within a low‐viscosity mantle oblique‐slip shear zone

The Brossasco‐Isasca subunit (BIU) of the Dora Maira massif is currently the only known continental crustal ultrahigh‐pressure (UHP) unit in the Western Alps. The peak pressure/temperature conditions are 3.5–4.5 GPa/~730 °C; exhumation from ~3.5 GPa to ~1 GPa occurred within 2.2 ± 1.8 Ma, but the exhumation mechanism is incompletely understood. We present a conceptual model for the buoyancy‐driven exhumation of the BIU inside a low‐viscosity, dense mantle shear zone weakened by increased strain rates due to simultaneous strike‐slip and subduction (oblique‐slip) of the European plate. Two‐dimensional thermo‐mechanical models simulate such a buoyant uprise of an ellipse inside an inclined layer. Simulations (i) show the feasibility of the conceptual model, (ii) fit the pressure/temperature/time record and (iii) constrain effective viscosities. The model is compatible with the (i) small volume of continental crustal UHP rock in the Western Alps, (ii) minor erosion during exhumation and (iii) strike‐slip deformation during the exhumation period.     

Evolution of Hydrothermal System at the Dizon Porphyry Cu-Au Deposit, Zambales, Philippines

Abstract. Evolution of hydrothermal system from initial porphyry Cu mineralization to overlapping epithermal system at the Dizon porphyry Cu‐Au deposit in western central Luzon, Zambales, Philippines, is documented in terms of mineral paragen‐esis, fluid inclusion petrography and microthermometry, and sulfur isotope systematics. The paragenetic stages throughout the deposit are summarized as follows; 1) stockwork amethystic quartz veinlets associated with chalcopyrite, bornite, magnetite and Au enveloped by chlorite alteration overprinting biotite alteration, 2) stockwork quartz veinlets with chalcopyrite and pyrite associated with Au and chalcopyrite and pyrite stringers in sericite alteration, 3) stringer quartz veinlets associated with molybdenite in sericite alteration, and 4) WNW‐trending quartz veins associated with sphalerite and galena at deeper part, while enargite and stibnite at shallower levels associated with advanced argillic alteration. Chalcopyrite and bornite associated with magnetite in quartz veinlet stockwork (stage 1) have precipitated initially as intermediate solid solution (iss) and bornite solid solution (bnss), respectively. Fluid inclusions in the stockwork veinlet quartz consist of gas‐rich inclusions and polyphase inclusions. Halite in polyphase inclusions dissolves at temperatures ranging from 360d?C to >500d?C but liquid (brine) and gas (vapor) do not homogenize at <500d?C. The maximum pressure and minimum temperature during the deposition of iss and bnss with stockwork quartz veinlets are estimated to be 460 bars and 500d?C. Fluid inclusions in veinlet stockwork quartz enveloped in sericite alteration (stage 2) consist mainly of gas‐rich inclusions and polyphase inclusions. In addition to the possible presence of saturated NaCl crystals at the time of entrapment of fluid inclusions that exhibit the liquid‐vapor homogenization temperatures lower than the halite dissolution temperatures in some samples, wide range of temperatures of halite dissolution and liquid‐vapor homogenization of polyphase inclusions from 230d?C to >500d?C and from 270d?C to >500d?C, respectively, suggests heterogeneous entrapment of gaseous vapor and hypersaline brine. The minimum pressure and temperature are estimated to be about 25 bars and 245d?C. Fluid inclusions in veinlet quartz associated with molybdenite (stage 3) are dominated by gas‐rich inclusions accompanied with minor liquid‐rich inclusions that homogenize at temperatures between 350d?C and 490d?C. Fluid inclusions in vuggy veinlet quartz associated with stibnite (stage 4) consist mainly of gas‐rich inclusions with subordinate polyphase inclusions that do not homogenize below 500d?C. Fluid inclusions in veinlet quartz associated with galena and sphalerite (stage 4) are composed of liquid‐rich two‐phase inclusions, and they homogenize into liquid phase at temperatures ranging widely from 190d?C to 300d?C (suggesting boiling) and the salinity ranges from 1.0 wt% to 3.4 wt% NaCl equivalent. A pressure of about 15 bars is estimated for the dilute aqueous solution of 190d?C from which veinlet quartz associated with galena and sphalerite precipitated. In addition to a change in temperature‐pressure regime from lithostatic pressure during the deposition of iss and bnss with stockwork quartz veinlets to hydrostatic pressure during fracture‐controlled quartz veinlet associated with galena and sphalerite, a decrease in pressure is supposed to have occurred due to unroofing or removal of the overlying piles during the temperature decrease in the evolution of hydrothermal system. The majority of the sulfur isotopic composition of sulfides ranges from ±0 % to +5 %. Sulfur originated from an iso‐topically uniform and homogeneous source, and the mineralization occurred in a single hydrothermal system.     

Microfabric of folded quartz veins in metagreywackes: dislocation creep and subgrain rotation at high stress

The microfabrics of folded quartz veins in fine‐grained high pressure–low temperature metamorphic greywackes of the Franciscan Subduction Complex at Pacheco Pass, California, were investigated by optical microscopy, scanning electron microscopy including electron backscatter diffraction, and transmission electron microscopy. The foliated host metagreywacke is deformed by dissolution–precipitation creep, as indicated by the shape preferred orientation of mica and clastic quartz without any signs of crystal‐plastic deformation. The absence of crystal‐plastic deformation of clastic quartz suggests that the flow stress in the host metagreywacke remained below a few tens of MPa at temperatures of 250–300 °C. In contrast, the microfabric of the folded quartz veins indicates deformation by dislocation creep accompanied by subgrain rotation recrystallization. For the small recrystallized grain size of ～8 ± 6 μm, paleopiezometers indicate differential stresses of a few hundred MPa. The stress concentration in the single phase quartz vein is interpreted to be due to its higher effective viscosity compared to the fine‐grained host metagreywacke deforming by dissolution–precipitation creep. The fold shape suggests a viscosity contrast of one to two orders of magnitude. Deformation by dissolution–precipitation creep is expected to be a continuous process. The same must hold for folding of the vein and deformation of the vein quartz by dislocation creep. The microfabric suggests dynamic recrystallization predominantly by subgrain rotation and only minor strain‐induced grain boundary migration, which requires low contrasts in dislocation density across high‐angle grain boundaries to be maintained during climb‐controlled creep at high differential stress. The record of quartz in these continuously deformed veins is characteristic and different from the record in metamorphic rocks exhumed in seismically active regions, where high‐stress deformation at similar temperatures is episodic and related to the seismic cycle.     

Fluid inclusion evidence for the physicochemical conditions of sulfide deposition in the Olympias carbonate-hosted Pb-Zn(Au, Ag) sulfide ore deposit, E. Chalkidiki peninsula, N. Greece

The Olympias Pb-Zn(Au, Ag) sulfide ore deposit, E. Chalkidiki, N. Greece, is hosted by marbles of the polymetamorphic Kerdilia Formation of Paleozoic or older age. The geologic environment of the ore also comprises biotite-hornblende gneisses and amphibolites intruded by Tertiary pegmatite-aplite dikes, lamprophyre dikes, the 30-Ma Stratoni granodiorite, and porphyritic stocks. Only limited parts of the deposit display shear folding and brecciation; most of it is undeformed. Microthermometry of fluid inclusions in gangue syn-ore quartz indicates three types of primary and pseudosecondary inclusions: (1) H₂O-rich, 1–18 wt.% NaCl equivalent, <3.6 mol% CO₂; (2) H₂O-CO₂ inclusions, <4wt.% NaCl equivalent, with variable CO₂ contents, coexisting in both undeformed and deformed ore; (3) aqueous, highsalinity (28–32 wt,% NaCl equivalent) inclusions found only in undeformed ore. Type 2 inclusions are differentiated into two sub-types: (2a) relatively constant CO₂ content in the narrow range of 8–15 mol% and homogenization to the liquid phase; (2b) variable CO₂ content between 18 and 50 mol% and homogenization to the vapor phase. Type 1 and 2b inclusions are consistent with trapping of two fluids by unmixing of a high-temperature, saline, aqueous, CO₂-bearing fluid of possible magmatic origin, probably trapped in type 2a inclusions. Fluid unmixing and concomitant ore mineralization took place at temperatures of 350 ± 30 °C and fluctuating pressures of less than 500 bar, for both undeformed and deformed ores. The wide salinity range of type 1 inclusions probably represents a complex effect of salinity increase, due to fluid unmixing and volatile loss, and dilution, due to mixing with low-salinity meteoric waters. High solute enrichment of the residual liquid, due to extreme volatile loss during unmixing, may account for high salinity type 3 inclusions. The Olympias fluid inclusion salinity-temperature gradients bear similarities to analogous gradients related to Pb-Zn ores formed in “granite”-hosted, low-T distalskarn, skarn-free carbonate-replacement and epithermal environments.     

Scaled amplification equation: A key to the folding history of buckled viscous single-layers

The presented equation describes amplitude growth during viscous single-layer folding (buckling) up to high amplitudes. The equation relates the dimensionless fold amplitude (i.e. ratio of amplitude to wavelength) to the stretch (ratio of initial wavelength to instantaneous wavelength) for given values of the viscosity contrast between layer and surrounding material and the initial ratio of amplitude to wavelength. The amplification equation is suitably scaled so that all amplitude versus stretch curves for different values of viscosity contrasts and initial amplitudes fall onto essentially a single curve. The scaled amplification equation allows for representing fold amplification of viscous single-layers by a singular curve. The scaling parameter is the crossover strain, which is an estimate for the amount of strain that is accumulated during the initial stages of folding where the amplitude grows exponentially with strain. The singular curve allows quantifying the universal boundaries between the three folding stages, namely nucleation, amplification and kinematic growth. The scaled amplification equation is verified by numerical (finite element method) simulations of folding of single layers with initial random perturbations of the layer interfaces. The amplification equation describes the amplification of single folds within fold trains successfully, although the folds are neither regular nor periodic and vary considerably in shape. The easily measurable parameters, vertical and horizontal hinge distance, are shown to be good approximations for the analytical parameters amplitude and wavelength, respectively.     

A stabilized extended finite element framework for hydraulic fracturing simulations

We present a stabilized extended finite element formulation to simulate the hydraulic fracturing process in an elasto‐plastic medium. The fracture propagation process is governed by a cohesive fracture model, where a trilinear traction‐separation law is used to describe normal contact, cohesion and strength softening on the fracture face. Fluid flow inside the fracture channel is governed by the lubrication equation, and the flow rate is related to the fluid pressure gradient by the ‘cubic’ law. Fluid leak off happens only in the normal direction and is assumed to be governed by the Carter's leak‐off model. We propose a ‘local’ U‐P (displacement‐pressure) formulation to discretize the fluid‐solid coupled system, where volume shape functions are used to interpolate the fluid pressure field on the fracture face. The ‘local’ U‐P approach is compatible with the extended finite element framework, and a separate mesh is not required to describe the fluid flow. The coupled system of equations is solved iteratively by the standard Newton‐Raphson method. We identify instability issues associated with the fluid flow inside the fracture channel, and use the polynomial pressure projection method to reduce the pressure oscillations resulting from the instability. Numerical examples demonstrate that the proposed framework is effective in modeling 3D hydraulic fracture propagation. Copyright © 2016 John Wiley & Sons, Ltd.     

Fluid Inclusions and C?H?O?S?Pb Isotopes: Implications for the Genesis of the Zhuanshanzi Gold Deposit on the Northern Margin of the North China Craton

The Zhuanshanzi gold deposit lies in the eastern section of the Xingmeng orogenic belt and the northern section of the Chifeng‐Chaoyang gold belt. The gold veins are strictly controlled by a NW‐oriented shear fault zone. Quartz veins and altered tectonic rock‐type gold veins are the main vein types. The deposits can be divided into four mineralization stages, and the second and third metallogenic stages are the main metallogenic stages. In this paper, based on the detailed field geological surveys, an analysis of the orebody and ore characteristics, microtemperature measurement of fluid inclusions, the Laser Raman spectrum of the inclusions, determination of C? H? O? S? Pb isotopic geochemical characteristics, and so on were carried out to explore the origin of the ore‐forming fluids, ore‐forming materials, and the genesis of the deposits. The results show that the fluid inclusions can be divided into four types: type I – gas–liquid two‐phase inclusions; type II – gas‐rich inclusions; type III– liquid inclusions; and type IV – CO₂‐containing three‐phase inclusions. However, they are dominated by type Ib – gas liquid inclusions and type IV – three‐phase inclusions containing CO₂. The gas compositions are mainly H₂O and CO₂, indicating that the metallogenic system is a CO₂? H₂O? NaCl system. The homogenization temperature of the ore‐forming fluid evolved from a middle temperature to a low temperature, and the temperature of the fluid was further reduced due to meteoric water mixing during the late stage, as well as a lack of CO₂ components, and eventually evolved into a simple NaCl? H₂O hydrothermal system. C? H? O? S? Pb isotope research proved that the ore‐forming fluids are mainly magmatic water during the early stage, with abundant meteoric water mixed in during the late stage. Ore‐forming materials originated mostly from hypomagma and were possibly influenced by the surrounding rocks, suggesting that the ore‐forming materials were mainly magmatic hydrothermal deposits, with a small amount of crustal component. The fluid immiscibility and the CO₂ and CH₄ gases in the fluids played an active and important role in the precipitation and enrichment of Au during different metallogenic stages. The deposit is considered a magmatic hydrothermal deposit of middle–low temperature.     

Contrasting tectono-metamorphic evolution of orogenic lower crust in the Bohemian Massif: A numerical model

The Bohemian Massif, located at the eastern margin of the European Variscan belt, is characterised by an exceptional accumulation of felsic high-pressure granulites. The petrological, structural and geochronological studies of this region revealed systematic differences between the tectonometamorphic evolution of the southern (Moldanubian) and northern (West Sudetes) parts of the orogen. Two contrasting tectonic scenarios have been proposed: gravity-driven vertical mass exchanges followed by continental indentation in the Moldanubian domain, and crustal-scale folding leading to gneiss dome formation in the West Sudetes. We present a numerical model in order to correlate the apparent differences between these two regions with the variations in the dynamics of the modelled system. We model two colliding blocks: an orogenic root, where a felsic lower crust is overlain by a mafic layer and a middle crust, and a continental indentor. We examine the role of the rate of convergence of the two blocks, radiogenic heat production within the felsic lower crust and efficiency of erosion. The prograde part of the metamorphic evolution is controlled by the rate of convergence and the peak temperature depends on the heat production. The retrograde evolution is controlled mostly by erosional processes. In the models, where the material is weakened due to the heating in the felsic lower crust, the gravitational instability of the mafic and felsic layers causes their complete vertical exchange followed by a flow above the indentor. In colder and/or faster models, the thickening is dominated by the buckling of the mafic layer. These two styles of deformation, i.e. gravity-dominated and fold-dominated models, correspond to the structures observed in the Moldanubian and the West Sudetes. Moreover, the calculated pressure–temperature paths of the felsic lower crust are in agreement with available data.     

Behaviour of an isolated rimmed elliptical inclusion in 2D slow incompressible viscous flow

For 2D linear viscous flow, it is shown that the rates of rotation and stretch of an isolated elliptical inclusion with a coaxial elliptical rim are fully determined by two corresponding scalar values. For power-law viscosity, effective viscosity ratios of the inclusion and rim to the matrix depend on orientation and the system is more complex but, in practice, the simplification with two scalar values still provides a good approximation. Finite-element modelling (FEM) is used to determine the two characteristic values across a wide parameter space for the linear viscous case, with a viscosity ratio (relative to the matrix) of the inclusion from 10⁶ to 1, of the rim from 10⁻⁶ to 1, axial ratios from 1.00025 to 20, and rim thicknesses relative to the inclusion axes of 5 to 20%. Results are presented in a multi-dimensional data table, allowing continuous interpolation over the investigated parameter range. Based on these instantaneous rates, the shape fabric of a population of inclusions is forward modelled using an initial value Ordinary Differential Equation (ODE) approach, with the simplifying but unrealistic assumption that the rim remains elliptical in shape and coaxial with respect to the inclusion. However, comparison with accurate large strain numerical experiments demonstrates that this simplified model gives qualitatively robust predictions and, for a range of investigated examples, also remarkably good quantitative estimates for shear strains up to at least γ = 5. A statistical approach, allowing random variation in the initial orientation, axial ratio and rim viscosity, can reproduce the characteristic shape preferred orientation (SPO) of natural porphyroclast populations. However, vorticity analysis based on the SPO or the interpreted stable orientation of inclusions is not practical. Varying parameters, such as inclusion and rim viscosity, rim thickness, and power law-exponents for non-linear viscosity, can reproduce the range of naturally observed behaviour (e.g., back-rotation, effectively stable orientations at back-rotated angles, a cut-off axial ratio separating rotating from stable inclusions) even for constant simple shear and these features are not uniquely characteristic of the vorticity of the background flow.