Creep Rheology Research Articles

Progressive weakening within the overriding plate during dual inward dipping subduction

The evolution of dual inward dipping subduction (DIDS) is crucial to understand multiple slab interaction. Yet, how DIDS influences the thermo-mechanical behaviour of the overriding plate remains unclear, as previous DIDS investigations all applied a compositional or Newtonian rheology that excludes temperature dependency. Here we apply a composite rheology, including temperature dependent creep deformation mechanisms, in 2-D thermo-mechanical numerical modelling to investigate how DIDS modifies the rheological structure of the overriding plate. Three variables on plate sizes are investigated to understand what may control the maximum degree of plate weakening. We find that reducing the initial length or initial thickness of the overriding plate and increasing the initial thickness of the subducting plate can enhance the viscosity reduction within the overriding plate. The progressive weakening can result in a variety of stretching states ranging from 1) little or no lithosphere thinning and extension (<5% accumulation of strain), to 2) limited thermal lithosphere thinning (<30% accumulation of strain), and 3) localised rifting followed by spreading extension. Compared with single sided subduction, DIDS further reduces the magnitude of viscosity in the overriding plate. It does this by creating a dynamic fixed boundary condition for the overriding plate and forming a stronger upwelling mantle flow, both of which promote the progressive weakening in the overriding plate. The result implies that these generic DIDS effects are important aspects to consider to understand extension developed in natural DIDS cases. We also demonstrate that both temperature dependent creep rheologies and yielding deformation mechanism contribute significantly to the continuous viscosity reduction. The finding may also have a broader implication for more general processes that involve plate scale weakening, strain localisation and the formation of new plate boundaries.

Evolution of flow reversal and flow heterogeneities in high elasticity wormlike micelles (WLMs) with a yield stress

The formation and evolution of a heterogeneous flow and flow reversal are examined in highly elastic, gel-like wormlike micelles (WLMs) formed from an amphiphilic triblock poloxamer P234 in 2M NaCl. A combination of linear viscoelastic, steady shear, and creep rheology demonstrate that these WLMs have a yield stress and exhibit viscoelastic aging, similar to some soft glassy materials. Nonlinear shear rheology and rheoparticle tracking velocimetry reveal that these poloxamer WLMs undergo a period of strong elastic recoil and flow reversal after the onset of shear startup. As flow reversal subsides, a fluidized high shear rate region and a nearly immobile low shear rate region of fluid form, accompanied by wall slip and elastic instabilities. The features of this flow heterogeneity are reminiscent of those for aging yield stress fluids, where the heterogeneous flow forms during the initial stress overshoot and is sensitive to the inherent stress gradient of the flow geometry. Additionally, macroscopic bands that form transiently above a critical shear rate become “trapped” due to viscoelastic aging in the nearly immobile region. This early onset of the heterogeneous flow during the rapidly decreasing portion of the stress overshoot differs from that typically observed in shear banding WLMs and is proposed to be necessary for observing significant flow reversal. Exploring the early-time, transient behavior of this WLM gel with rheology similar to both WLM solutions and soft glassy materials provides new insights into spatially heterogeneous flows in both of these complex fluids.

Viscosity of Crystal‐Mushes and Implications for Compaction‐Driven Fluid Flow

AbstractCentrifuge experiments on olivine, chromite, and plagioclase aggregates saturated in basaltic liquid show evidence of viscous compaction by grain‐boundary diffusion‐controlled creep. The experiments confirm that the exponential dependence of shear viscosity on melt fraction, observed at low porosities in earlier shear deformation experiments, extends to sedimentary porosities. The compaction profiles are inconsistent with the porosity‐dependence commonly ascribed to viscosity in macroscopic compaction models, which underestimate the effect of matrix disaggregation and consequently overestimate the viscosities of crystal mushes by 1–2 orders of magnitude. The time to halve the porosity of natural olivine igneous sediments by compaction is estimated from the centrifuge experiments to be O(103)y. Half‐times for plagioclase and chromite layers are O(104–105)y, suggesting that such layers compact on magmatic time scales only if they are loaded by additional sedimentation. At conditions relevant to melt flow in asthenospheric settings and trans‐crustal magmatic systems, the bulk and shear viscosities inferred for olivine and plagioclase are O(1017)Pa s, 4 orders of magnitude less than inferred from earlier experimental studies of the diffusion creep rheology. The reduced viscosities imply time‐ and length‐scales for compaction processes that are substantially shorter than previously anticipated. Our analysis serendipitously reveals that the oft‐neglected solidity term of the Carman‐Kozeny porosity‐permeability relation is essential to prevent non‐physical behavior in models of cumulate compaction.

Creep Rheology of Antigorite: Experiments at Subduction Zone Conditions

AbstractNovel fluid medium pressure cells were used to deform antigorite under constant stress creep conditions at low temperature, low strain rate (10−9 − 10−4 1/s), and high pressure (1 GPa) in a Griggs‐type apparatus. Antigorite cores were deformed at constant temperatures between 75°C and 550°C, by applying 8–12 stress‐strain steps per temperature. The microstructures of deformed samples share features documented in previous work (e.g., shear microcracks), and highlight the importance of basal shear and kinks to antigorite plasticity. Rheological data were fit with a low temperature plasticity law, consistent with a deformation mechanism involving large lattice resistance. When applied at geologic stresses and strain rates, the extrapolated viscosity agrees well with predictions based on subduction zone thermal models.

Fault Friction During Simulated Seismic Slip Pulses

AbstractTheoretical studies predict that during earthquake rupture faults slide at non‐constant slip velocity, however it is not clear which source time functions are compatible with the high velocity rheology of earthquake faults. Here we present results from high velocity friction experiments with non‐constant velocity history, employing a well‐known seismic source solution compatible with earthquake source kinematics. The evolution of friction in experiments shows a strong dependence on the applied slip history, and parameters relevant to the energetics of faulting scale with the impulsiveness of the applied slip function. When comparing constitutive models of strength against our experimental results we demonstrate that the evolution of fault strength is directly controlled by the temperature evolution on and off the fault. Flash heating predicts weakening behavior at short timescales, but at larger timescales strength is better predicted by a viscous creep rheology. We use a steady‐state slip pulse to test the compatibility of our strength measurements at imposed slip rate history with the stress predicted from elastodynamic equilibrium. Whilst some compatibility is observed, the strength evolution indicates that slip acceleration and deceleration might be more rapid than that imposed in our experiments.

Toward Constraining Mars' Thermal Evolution Using Machine Learning

AbstractThe thermal and convective evolution of terrestrial planets like Mars is governed by a number of initial conditions and parameters, which are poorly constrained. We use Mixture Density Networks (MDN) to invert various sets of synthetic present‐day observables and infer five parameters: reference viscosity, activation energy and activation volume of the diffusion creep rheology, an enrichment factor for radiogenic elements in the crust, and initial mantle temperature. The data set comes from 6,130 two‐dimensional simulations of the thermal evolution of Mars' interior. We quantify the possibility of constraining a parameter using the log‐likelihood value from the MDN. Reference viscosity can be constrained to within 32% of its entire range (1019 − 1022 Pa s), when all the observables are available: core‐mantle‐boundary heat flux, surface heat flux, radial contraction, melt produced, and duration of volcanism. Furthermore, crustal enrichment factor (1–50) can be constrained, at best, to within 15%, and the activation energy (105 − 5 × 105 J mol−1) to within 80%. Initial mantle temperature can be constrained to within 39% of its range (1,600–1,800 K). Using the full present‐day temperature profile or parts of it as an observable tightens the constraints further. The activation volume (4 × 10−6 − 10 × 10−6 m3 mol−1) cannot be constrained. We also tested different levels of uncertainty in the observables and found that constraints on different parameters loosen differently, with initial temperature being the most sensitive. Finally, we present how a joint probability model for all parameters can be obtained from the MDN.

A nonlinear and time‐dependent visco‐elasto‐plastic rheology model for studying shock‐physics phenomena

AbstractWe present a simple and efficient implementation of a viscous creep rheology based on diffusion creep, dislocation creep, and the Peierls mechanism in conjunction with an elasto‐plastic rheology model into a shock‐physics code, the iSALE impact code. Our approach is based on the calculation of an “effective viscosity” which is then used as a reference viscosity for any underlying viscoelastic (or even visco‐elasto‐plastic) model. Here we use a Maxwell‐model which best describes stress relaxation and is therefore likely most important for the formation of large meteorite impact basins. While common viscoelastic behavior during mantle convection or other slow geodynamic or geological processes is mostly controlled by diffusion and dislocation creep, we show that the Peierls mechanism dominates at the large strain rates that typically occur during meteorite impacts. Thus, the resulting visco‐elasto‐plastic rheology allows implementation of a more realistic mantle behavior in computer simulations, especially for those dealing with large meteorite impacts. The approach shown here opens the way to more faithful simulations of large impact basin formation, especially in elucidating the physics behind the formation of the external fault rings characteristic of large lunar basins.

Microphysical Model Predictions of Fault Restrengthening Under Room-Humidity and Hydrothermal Conditions: From Logarithmic to Power-Law Healing.

The maximum fault strength and rate of interseismic fault strengthening (“healing”) are of great interest to earthquake hazard assessment studies, as they directly relate to event magnitude and recurrence time. Previous laboratory studies have revealed two distinct frictional healing behaviors, referred to as Dieterich‐type and non‐Dieterich‐type healing. These are characterized by, respectively, log‐linear and power‐law increase in the strength change with time. To date, there is no physical explanation for the frictional behavior of fault gouges that unifies these seemingly inconsistent observations. Using a microphysical friction model previously developed for granular fault gouges, we investigate fault strengthening analytically and numerically under boundary conditions corresponding to laboratory slide‐hold‐slide tests. We find that both types of healing can be explained by considering the difference in grain contact creep rheology at short and long time scales. Under hydrothermal conditions favorable for pressure solution creep, healing exhibits a power‐law evolution with hold time, with an exponent of ~1/3, and an “apparent” cutoff time (α) of hundreds of seconds. Under room‐humidity conditions, where grain contact deformation exhibits only a weak strain‐rate dependence, the predicted healing also exhibits a power‐law dependence on hold time, but it can be approximated by a log‐linear relation with α of a few seconds. We derive analytical expressions for frictional healing parameters (i.e., healing rate, cutoff time, and maximum healing), of which the predictions are consistent with numerical implementation of the model. Finally, we apply the microphysical model to small fault patches on a natural carbonate fault and interpret the restrengthening during seismic cycles.

Numerical Modeling of Mantle Flow Beneath Madagascar to Constrain Upper Mantle Rheology Beneath Continental Regions

AbstractOver the past few decades, azimuthal seismic anisotropy measurements have been widely used proxy to study past and present‐day deformation of the lithosphere and to characterize convection in the mantle. Beneath continental regions, distinguishing between shallow and deep sources of anisotropy remains difficult due to poor depth constraints of measurements and a lack of regional‐scale geodynamic modeling. Here, we constrain the sources of seismic anisotropy beneath Madagascar where a complex pattern cannot be explained by a single process such as absolute plate motion, global mantle flow, or geology. We test the hypotheses that either Edge‐Driven Convection (EDC) or mantle flow derived from mantle wind interactions with lithospheric topography is the dominant source of anisotropy beneath Madagascar. We, therefore, simulate two sets of mantle convection models using regional‐scale 3‐D computational modeling. We then calculate Lattice Preferred Orientation that develops along pathlines of the mantle flow models and use them to calculate synthetic splitting parameters. Comparison of predicted with observed seismic anisotropy shows a good fit in northern and southern Madagascar for the EDC model, but the mantle wind case only fits well in northern Madagascar. This result suggests the dominant control of the measured anisotropy may be from EDC, but the role of localized fossil anisotropy in narrow shear zones cannot be ruled out in southern Madagascar. Our results suggest that the asthenosphere beneath northern and southern Madagascar is dominated by dislocation creep. Dislocation creep rheology may be dominant in the upper asthenosphere beneath other regions of continental lithosphere.

Subduction of non-Newtonian plates: Thin-sheet dynamics of slab necking and breakoff

Summary We use a hybrid boundary-integral/thin-sheet (‘BITS’) model to investigate the subduction of 2-D viscous sheets with composite diffusion creep/dislocation creep rheology, with a focus on the conditions required for slab necking and breakoff. To validate the model, we show that its predictions of the sinking speed of the slab follow a universal scaling law identical to one previously derived for purely Newtonian sheets. We obtain analytical expressions for the fiber stress resultant and bending moment of the sheet during deformation by pure stretching and pure bending, respectively, and show that the non-Newtonian dislocation creep component of the rheology significantly weakens the sheet for both types of deformation. We solve the BITS equations for two distinct situations: “free” subduction, in which the slab pulls an attached negatively buoyant plate without hindrance; and “arrested” subduction that slows or stops when a positively buoyant (continental) portion of the attached plate arrives at the trench. Strong lithospheric thinning is difficult to obtain in free subduction and requires dominantly non-Newtonian rheology, i.e. large (&gt;5) values of the characteristic ratio λ of the Newtonian to the non-Newtonian viscosity. However, during arrested subduction strong thinning leading to breakoff occurs for much lower values of λ, and the point of maximum thinning is at shallower depths. These results are explained by a one-dimensional viscous dripping model (‘DRIP’) of a vertical slab with a composite rheology and an arbitrary kinematically prescribed time-dependent convergence rate U0(t). By injecting into DRIP convergence histories predicted by BITS, we find that DRIP reproduces closely the results of the more complicated BITS model. The DRIP model shows that the convergence rate controls slab breakoff in two distinct ways. On the one hand, the rate of lithospheric thinning is proportional to the accumulated convergence, i.e., the time integral of U0(t). The breakoff depth, on the other hand, is controlled by the convergence rate history, being shallower when U0 rapidly decreases (arrested subduction) after an initial period of oceanic subduction.

Stagnant-lid convection with diffusion and dislocation creep rheology: Influence of a non-evolving grain size

SUMMARY Heat transfer in one-plate planets is governed by mantle convection beneath the stagnant lid. Newtonian diffusion creep and non-Newtonian dislocation creep are the main mechanisms controlling large-scale mantle deformation. Diffusion creep strongly depends on the grain size (d), which in turn controls the relative importance of the two mechanisms. However, dislocation creep is usually neglected in numerical models of convection in planetary mantles. These mostly assume linear diffusion creep rheologies, often based on reduced activation parameters (compared to experimental values) that are thought to mimic the effects of dislocation creep and, as a side benefit, also ease the convergence of linear solvers. Assuming Mars-like parameters, we investigated the influence of a non-evolving grain size on Rayleigh–Bénard convection in the stagnant lid regime. In contrast to previous studies based on the Frank–Kamentskii approximation, we used Arrhenius laws for diffusion and dislocation creep—including temperature as well as pressure dependence—based on experimental measurements of olivine deformation. For d ≲ 2.5 mm, convection is dominated by diffusion creep. We observed an approximately equal partitioning between the two mechanisms for d ≈ 5 mm, while dislocation creep dominates for d ≳ 8 mm. Independent estimates of an average grain size of few mm up to 1 cm or more for present-day Mars suggest thus that dislocation creep plays an important role and possibly dominates the deformation. Mimicking dislocation creep convection using an effective linear rheology with reduced activation parameters, as often done in simulations of convection and thermal evolution of Mars, has significant limitations. Although it is possible to mimic mean temperature, mean lid thickness and Nusselt number, there are important differences in the flow pattern, root mean square velocity, and lid shape. The latter in particular affects the amount and distribution of partial melt, suggesting that care should be taken upon predicting the evolution of crust production when using simplified rheologies. The heat transport efficiency expressed in terms of the Nusselt number as a function of the Rayleigh number is thought to depend on the deformation mechanisms at play. We show that the relative volume in which dislocation creep dominates has nearly no influence on the Nusselt–Rayleigh scaling relation when a mixed rheology is used. In contrast, the flow pattern influences the Nusselt number more strongly. We derived a scaling law for the Nusselt number based on the mean lid thickness (〈L〉) and on the effective Rayleigh number (Raeff) obtained by suitably averaging the viscosity beneath the stagnant lid. We found that the Nusselt number follows the scaling $\mathrm{Nu} = 0.37 \langle L \rangle ^{-0.666} \mathrm{Ra}_{\mathrm{eff}}^{0.071}$ regardless of the deformation mechanism.

Overturn of Ilmenite‐Bearing Cumulates in a Rheologically Weak Lunar Mantle

AbstractThe crystallization of the lunar magma ocean (LMO) determines the initial structure of the solid Moon. Near the end of the LMO crystallization, ilmenite‐bearing cumulates (IBC) form beneath the plagioclase crust. Being denser than the underlying mantle, IBC are prone to overturn, a hypothesis that explains several aspects of the Moon's evolution. Yet the formation of stagnant lid due to the temperature dependence of viscosity can easily prevent IBC from sinking. To infer the rheological conditions allowing IBC to sink, we calculated the LMO crystallization sequence and performed high‐resolution numerical simulations of the overturn dynamics. We assumed a diffusion creep rheology and tested the effects of reference viscosity, activation energy, and compositional viscosity contrast between IBC and mantle. The overturn strongly depends on reference viscosity and activation energy and is facilitated by a low IBC viscosity. For a reference viscosity of 1021 Pa s, characteristic of a dry rheology, IBC overturn cannot take place. For a reference viscosity of 1020 Pa s, the overturn is possible if the activation energy is a factor of 2–3 lower than the values typically assumed for dry olivine. These low activation energies suggest a role for dislocation creep. For lower‐reference viscosities associated with the presence of water or trapped melt, more than 95% IBC can sink regardless of the activation energy. Scaling laws for Rayleigh‐Taylor instability confirmed these results but also showed the need of numerical simulations to accurately quantify the overturn dynamics. Whenever IBC sink, the overturn occurs via small‐scale diapirs.

Nonlinear viscoplasticity in ASPECT: benchmarking and applications to subduction

Abstract. ASPECT (Advanced Solver for Problems in Earth's ConvecTion) is a massively parallel finite element code originally designed for modeling thermal convection in the mantle with a Newtonian rheology. The code is characterized by modern numerical methods, high-performance parallelism and extensibility. This last characteristic is illustrated in this work: we have extended the use of ASPECT from global thermal convection modeling to upper-mantle-scale applications of subduction.Subduction modeling generally requires the tracking of multiple materials with different properties and with nonlinear viscous and viscoplastic rheologies. To this end, we implemented a frictional plasticity criterion that is combined with a viscous diffusion and dislocation creep rheology. Because ASPECT uses compositional fields to represent different materials, all material parameters are made dependent on a user-specified number of fields.The goal of this paper is primarily to describe and verify our implementations of complex, multi-material rheology by reproducing the results of four well-known two-dimensional benchmarks: the indentor benchmark, the brick experiment, the sandbox experiment and the slab detachment benchmark. Furthermore, we aim to provide hands-on examples for prospective users by demonstrating the use of multi-material viscoplasticity with three-dimensional, thermomechanical models of oceanic subduction, putting ASPECT on the map as a community code for high-resolution, nonlinear rheology subduction modeling.

A force-level theory of the rheology of entangled rod and chain polymer liquids. I. Tube deformation, microscopic yielding, and the nonlinear elastic limit.

We employ a first-principles-based, force-level approach to construct the anharmonic tube confinement field for entangled fluids of rigid needles, and also for chains described at the primitive-path (PP) level in two limiting situations where chain stretch is assumed to either be completely equilibrated or unrelaxed. The influence of shear and extensional deformation and polymer orientation is determined in a nonlinear elastic limit where dissipative relaxation processes are intentionally neglected. For needles and PP-level chains, a self-consistent analysis of transverse polymer harmonic dynamical fluctuations predicts that deformation-induced orientation leads to tube weakening or widening. In contrast, for deformed polymers in which chain stretch does not relax, we find tube strengthening or compression. For all three systems, a finite maximum transverse entanglement force localizing the polymers in effective tubes is predicted. The conditions when this entanglement force can be overcome by an externally applied force associated with macroscopic deformation can be crisply defined in the nonlinear elastic limit, and the possibility of a "microscopic absolute yielding" event destroying the tube confinement can be analyzed. For needles and contour-relaxed PP chains, this force imbalance occurs at a stress of order the equilibrium shear modulus and a strain of order unity, corresponding to a mechanically fragile entanglement tube field. However, for unrelaxed stretched chains, tube compression stabilizes transverse polymer confinement, and there appears to be no force imbalance. These results collectively suggest that the crossover from elastic to irreversible viscous response requires chain retraction to initiate disentanglement. We qualitatively discuss comparisons with existing phenomenological models for nonlinear startup shear, step strain, and creep rheology experiments.

Accumulation of elastic strains in the upper crust on the locked transform faults and the tectonomagnetic effect

Plate tectonics only allows small deformations in the lithospheric plates. The laboratory experiments with the rock specimens show that the creep is transient when the creep strain is at most 1%. Hence, if we assume that the creep strain in the lithospheric plates is below this threshold, the creep is transient. The present paper addresses the role of the elastic, brittle (pseudo-plastic), and creep rheology of the lithosphere during the accumulation of elastic shear strains on the locked faults in the Earth’s crust, i.e., during the process of preparation of the earthquakes. The effective viscosity characterizing the transient creep is lower than that under the steady-state creep and it depends on the characteristic time of a given process. The characteristic duration of the stress and strain accumulation process in the vicinity of the locked faults is a few dozen years. On these time intervals, the thin upper crustal layer behaves as brittle; the underlying layer behaves as elastic (it is just this layer which accommodates stress accumulation leading to the earthquake), whereas the transient creep is predominant in the lower crust and mantle lithosphere. Transient creep entails nonlinear time dependence of the strains arising in the vicinity of the locked fault in the elastic crust. The perturbations in the magnetic field induced by these strains can be treated as the magnetic precursor of the earthquake.

Three-Dimensional Thermal Model of the Costa Rica-Nicaragua Subduction Zone

The thermal structure of a subduction zone controls many key processes, including subducting plate metamorphism and dehydration, the megathrust earthquake seismogenic zone and volcanic arc magmatism. Here, we present the first three-dimensional (3D), steady-state kinematic-dynamic thermal model for the Costa Rica-Nicaragua subduction zone. The model consists of the subducting Cocos plate, the overriding Caribbean Plate, and a viscous mantle wedge in which flow is driven by interactions with the downgoing slab. The Cocos plate geometry includes along-strike variations in slab dip, which induce along-strike flow in the mantle wedge. Along-strike flow occurs primarily below Costa Rica, with a maximum magnitude of 4 cm/year (~40 % of the convergence rate) for a mantle with a dislocation creep rheology; an isoviscous mantle has lower velocities. Along-margin flow causes temperatures variations of up to 80 °C in the subducting slab and mantle wedge at the volcanic arc and backarc. The 3D effects do not strongly alter the shallow (<35 km) thermal structure of the subduction zone. The models predict that the megathrust seismogenic zone width decreases from ~100 km below Costa Rica to just a few kilometers below Nicaragua; the narrow width in the north is due to hydrothermal cooling of the oceanic plate. These results are in good agreement with previous 2D models and with the rupture area of recent earthquakes. In the models, along-strike mantle flow is induced only by variations in slab dip, with flow directed toward the south where the dip angle is smallest. In contrast, geochemical and seismic observations suggest a northward flow of 6–19 cm/year. We do not observe this in our models, suggesting that northward flow may be driven by additional factors, such as slab rollback or proximity to a slab edge (slab window). Such high velocities may significantly affect the thermal structure, especially at the southern end of the subduction zone. In this area, 3D models that include slab rollback and a slab edge are needed to investigate the mantle structure and dynamics.

Ice-shelf fracture due to viscoelastic flexure stress induced by fill/drain cycles of supraglacial lakes

AbstractUsing a previously derived treatment of viscoelastic flexure of floating ice shelves, we simulated multiple years of evolution of a single, axisymmetric supraglacial lake when it is subjected to annual fill/drain cycles. Our viscoelastic treatment follows the assumptions of the well-known thin-beam and thin-plate analysis but, crucially, also covers power-law creep rheology. As the ice-shelf surface does not completely return to its un-flexed position after a 1-year fill/drain cycle, the lake basin deepens with each successive cycle. This deepening process is significantly amplified when lake-bottom ablation is taken into account. We evaluate the timescale over which a typical lake reaches a sufficient depth such that ice-shelf fracture can occur well beyond the lake itself in response to lake filling/drainage. We show that, although this is unlikely during one fill/drain cycle, fracture is possible after multiple years assuming surface meltwater availability is unlimited. This extended zone of potential fracture implies that flexural stresses in response to a single lake filling/drainage event can cause neighbouring lakes to drain, which, in turn, can cause lakes farther afield to drain. Such self-stimulating behaviour may have accounted for the sudden, widespread appearance of a fracture system that drove the Larsen B Ice Shelf to break-up in 2002.

Boudinage as a material instability of elasto-visco-plastic rocks

Pinch-and-swell structures are commonly interpreted to evolve out of viscosity contrasts, which are induced by geometric interactions and material imperfections. From materials science an additional localization phenomenon is well established, where localization emerges out of steady state for critical material parameters and/or loading rates. Here we investigate the conditions under which this second type of instabilities prevails and whether geological materials necessarily require a trigger by imperfections in order to generate instability. We focus on imperfections in terms of grain size variations embedded in a deformation environment controlled by thermo-mechanical feedbacks. We introduce a random distribution of grain sizes over two orders of magnitude in a central layer embedded in a matrix with a diffusion creep rheology. The rheology of the layer evolves with dislocation and diffusion creep as end-member deformation mechanisms. Applying pure shear extension, the 3-layer model is subjected to natural deformation conditions. The central layer quickly establishes a viscous steady state as a natural response of the system due to relaxation and energy optimization. Upon continued loading, localization then intriguingly arises out of a homogeneous state. We present an analysis which confirms that this type of instability is indeed physically admissible. Using vibration analysis, we verify the robustness of the numerical solution by first identifying the natural mode shapes and frequencies of the simulated structure and material parameters, including geometric imperfections. In a second step, the eigenmodes are perturbed and superposed to the initial conditions. We conclude that this pattern of perturbations guides the onset of strain localization. Boudinage can therefore be seen both as a geometric problem and/or a material bifurcation, which evolves out of homogeneous state. The latter class offers the great possibility of extracting fundamental material parameters out of localized structures directly from field observations.

Strain heating in process zones; implications for metamorphism and partial melting in the lithosphere

Since the late 1970s, most earth scientists have discounted the plausibility of melting by shear–strain heating because temperature-dependent creep rheology leads to negative feedback and self-regulation. This paper presents a new model of distributed shear-strain heating that can account for the genesis of large volumes of magmas in both the crust and the mantle of the lithosphere. The kinematic (geometry and rates) frustration associated with incompatible fault junctions (e.g. triple-junction) prevents localisation of all strain on the major faults. Instead, deformation distributes off the main faults forming a large process zone that deforms still at high rates under both brittle and ductile conditions. The increased size of the shear-heated region minimises conductive heat loss, compared with that commonly associated with narrow shear zones, thus promoting strong heating and melting under reasonable rheological assumptions. Given the large volume of the heated zone, large volumes of melt can be generated even at small melt fractions.There are clear examples of volcanism correlated with fault complexities that remain enigmatic and that could be related to that mechanism of “process zone heating”. We propose here a simple dislocation model to define the process zones, determine off-fault strain rates and quantify how much plastic work can be dissipated as heat. To provide an example, we examine the case of the junction between the East and North Anatolian shear zones in eastern Turkey. This is chosen because the composition and age of emplacement of the quite extensive volcanics are well known, as are the rates of motion on the associated strike-slip faults. The geometry of the system also allows the dislocation method to be easily adopted. We conclude that melting of the crust and the lithospheric mantle could start only a few Myrs after the onset of deformation. Conservative assumptions for rheological parameters and melting points can explain both the timing and the bimodal nature of the volcanism. Predictions of melt volume are within the rheological uncertainties. While the current paper is focused on strike-slip faults, the approach can be applied to kinematic complexities associated with thrust faults as well, and, maybe more generally, to regions in the lithosphere where oblique boundary conditions force deformation to occur partly in a distributed manner, while still at high rates.

Numerical modelling of magma dynamics coupled to tectonic deformation of lithosphere and crust

Many unresolved questions in geodynamics revolve around the physical behaviour of the two-phase system of a silicate melt percolating through and interacting with a tectonically deforming host rock. Well-accepted equations exist to describe the physics of such systems and several previous studies have successfully implemented various forms of these equations in numerical models. To date, most such models of magma dynamics have focused on mantle flow problems and therefore employed viscous creep rheologies suitable to describe the deformation properties of mantle rock under high temperatures and pressures. However, the use of such rheologies is not appropriate to model melt extraction above the lithosphere–asthenosphere boundary, where the mode of deformation of the host rock transitions from ductile viscous to brittle elasto-plastic. Here, we introduce a novel approach to numerically model magma dynamics, focusing on the conceptual study of melt extraction from an asthenospheric source of partial melt through the overlying lithosphere and crust. To this end, we introduce an adapted set of two-phase flow equations, coupled to a visco-elasto-plastic rheology for both shear and compaction deformation of the host rock in interaction with the melt phase. We describe in detail how to implement this physical model into a finite-element code, and then proceed to evaluate the functionality and potential of this methodology using a series of conceptual model setups, which demonstrate the modes of melt extraction occurring around the rheological transition from ductile to brittle host rocks. The models suggest that three principal regimes of melt extraction emerge: viscous diapirism, viscoplastic decompaction channels and elasto-plastic dyking. Thus, our model of magma dynamics interacting with active tectonics of the lithosphere and crust provides a novel framework to further investigate magmato-tectonic processes such as the formation and geometry of magma chambers and conduits, as well as the emplacement of plutonic rock complexes.