The brittle‐ductile rheological behavior in subduction zones is commonly proposed to explain deep transient slips. Generally observed at large scales in tectonic “mélanges”, here we show that it is ...also observed at the grain scale in exhumed blueschist metagabbros. In these rocks, petrologic and microstructural observations show a bi‐phase material constituted by strong microfractured magmatic pyroxene clasts located in a weak and ductile lawsonite‐rich metamorphic matrix. To constrain the mechanical conditions allowing the brittle deformation of a clast in a ductile matrix, we used two‐dimensional simple shear numerical experiments. Results show four behaviors: (a) entirely brittle; (b) brittle‐ductile with clast fracturing in a ductile matrix; (c) ductile‐dominant with limited plastic deformation at clast edges; and (d) entirely ductile. We propose that the conditions of the brittle‐ductile behavior, commonly associated with deep transient slips, are controlled by the strength ratio between the strong brittle phase and the weak ductile phase.
Plain Language Summary
In subduction zones, brittle‐ductile behavior is commonly proposed to explain deep transient slips at the subduction interface. This particular behavior is generally characterized by the fracturing of strong pods located in a weak fluid‐like material. In this study, we observe this mixed rheological behavior at the mineral‐scale in oceanic rocks under deep transient slip conditions. We carry out petrological and microstructural observations that show micro‐fracturing of strong magmatic clasts and ductile deformation of a weak metamorphic hydrated matrix. Numerical experiments, inspired by these observations, are used to constrain the physical conditions for this brittle‐ductile behavior. Numerical results show four types of behavior: (a) both matrix and clast are brittle and fractured; (b) the clast is brittle and fractured and the matrix is ductilely deformed; (c) only the clast is brittle and fractures are localized at clast edges; and (d) both matrix and clast are ductile. This study demonstrates that the behavior of this bi‐phase material is controlled by the strength ratio between the brittle strong clast and the ductile weak matrix. These physical conditions significantly differ from the theoretical rheological prediction and may be the key to a better understanding of the mechanics of deep transient slips.
Key Points
The modeled brittle‐ductile rheological behavior occurs in a more limited temperature range than theoretically predicted
The strength ratio between the brittle yield stress and the dislocation creep stress predicts conditions for the brittle‐ductile behavior
The temperature, pressure and pore‐fluid pressure conditions for the brittle‐ductile behavior are those of the deep transient slips
To test Eastern Tibet crustal thickening modes, we compare 2‐D numerical models of two emblematic end‐member models, with either an obstacle in the low viscosity lower crust or a thrust embedded in ...the high viscosity one. We show that the obstacle halts the viscous lower crustal flow potentially initiated by the weight of the high Central Tibet, generating a smooth exhumation gradient at the edge of the plateau, not observed in Eastern Tibet. On the contrary, including a low viscosity discontinuity in the upper crust, mimicking a shallow steep listric fault as inferred in the region, reproduces a sharper exhumation profile, as constrained from thermo‐kinematic inversions of thermochronological data, and the lack of foreland basin, as observed in the field. Moreover, such fault drives deformation throughout the entire crust, suggesting a deep crustal ductile shear zone limiting the more ductile deformation in the lower crust although no discontinuity is imposed.
Plain Language Summary
The role of thrusting in crustal thickening during the formation of Tibet, the world's largest and highest orogenic plateau, constitutes one of the main controversies in earth sciences. In Eastern Tibet in particular, two end‐members based on two contrasting controversial hypotheses can be tested: the thickening is dominated either by the flow of the lower Tibetan crust halted by the hard Sichuan craton, or by thrusting of the Tibetan upper crust. Here, we present 2‐D crustal numerical models of a shallow steep listric thrust (as inferred in the region) embedded in the high viscosity upper crust, and we show that such model reproduces the exhumation profile constrained from thermochronological data and the lack of foreland basin observed in the field. Interestingly, we also show that such upper crustal thrust drives upward the more ductile lower crust albeit no discontinuity is imposed. On the contrary, by using a model driven by an overpressure in the lower crust, we show that the obstacle halts the viscous lower crustal flow and generates a smooth exhumation gradient at the edge of the plateau, not observed in Eastern Tibet.
Key Points
2‐D numerical models of thrusts embedded in the high viscosity upper crust, to test thermo‐kinematic models based on thermochronology data
accommodation in the lower crust by ductile flow of the deformation induced by the high angle thrust in the upper crust
predicting exhumation rates and subsidence patterns that are compatible with the measured ones in Eastern Tibet
SUMMARY
Many problems in geodynamic modelling result in a non-linear Stokes problem in which the viscosity depends on the strain rate and pressure (in addition to other variables). After ...discretization, the resulting non-linear system is most commonly solved using a Picard fixed-point iteration. However, it is well understood that Newton’s method – when augmented by globalization strategies to ensure convergence even from points far from the solution – can be substantially more efficient and accurate than a Picard solver. In this contribution, we evaluate how a straightforward Newton method must be modified to allow for the kinds of rheologies common in geodynamics. Specifically, we show that the Newton step is not actually well posed for strain rate-weakening models without modifications to the Newton matrix. We derive modifications that guarantee well posedness and that also allow for efficient solution strategies by ensuring that the top left block of the Newton matrix is symmetric and positive definite. We demonstrate the applicability and relevance of these modifications with a sequence of benchmarks and a test case of realistic complexity.
As several modeling studies indicate, the structural expression and dynamic behavior of orogenic mountain belts are dictated not only by their rheological properties or by far‐field tectonic motion, ...but also by the efficiency of erosion and sedimentation acting on its surface. Until recently, numerical investigations have been mainly limited to 2‐D studies because of the high computational cost required by 3‐D models. Here, we have efficiently coupled the landscape evolution model Cascade with the 3‐D thermomechanically coupled tectonics code FANTOM. Details of the coupling algorithms between both codes are given. We present results of numerical experiments designed to study the response of viscous‐plastic crustal materials subjected to convergence and to surface processes including both erosion and sedimentation. In particular, we focus on the equilibration of both the tectonic structures and on the surface morphology of the orogen. We show that increasing the efficiency of fluvial erosion increases the frontal thrust angle, which in turn decreases the width of the orogen. In addition, the maximum summit elevation of the orogen during transient evolution is significantly higher in those models showcasing surface processes than those that do not. This illustrates the strong coupling between tectonics and surface processes. We also demonstrate that an along‐strike gradient of erosion efficiency can have a major impact upon the landscape morphology and the tectonic structure and deformation of the orogen, in both the across‐strike and along‐strike directions. Overall, our results suggest that surface processes, by enhancing localization of deformation, can act as a positive forcing to topographic building.
Key Points:
Orogen asymmetry is enhanced by the erosion efficiency
The fault dip angle is the result of tectonics and erosion efficiency
The localization of deformation increases as a function of erosion efficiency
Thrusting implication in the crustal thickening history of eastern Tibet is highly debated. The ∼250 km‐long Muli thrust of the Yalong thrust belt in SE Tibet is a major Miocene structure with a ...pronounced topographic step (∼2,000 m). Using thermo‐kinematic modeling based on thermochronology data, we constrain the crustal geometry of the thrust as being steep (>70°) at the surface, in agreement with field observations, and flattening at depth (≥20 km) on an intra‐crustal décollement. Thrusting motion on the fault shows a velocity of 0.2 ± 0.06 km/Ma since 50 Ma, followed by an acceleration at a rate of 0.6 ± 0.08 km/Ma starting at 12.5 ± 1 Ma, yielding a total of ∼15 km of exhumed crust. Deeper, deformation may be localized through a ductile shear zone, and be related to the ∼15 km Moho step and shear wave velocity contrast imaged by tomography beneath the Yalong thrust belt.
Plain Language Summary
The India‐Eurasia collision (∼50 million years ago Ma) led to the formation of the Tibetan Plateau, the world's largest and highest orogenic plateau. The formation and evolution of such a unique geological feature has been one of the main controversies in Earth Sciences for decades, especially regarding the role of faulting in the thickening of the crust. Here, we present 3D thermo‐kinematic models of thermochronology data allowing to constrain the exhumation history of the Muli thrust fault, a ∼250 km‐long major structure of the SE Tibetan margin, linked to significant steps in surface topography and in crustal boundary at depth (Moho). We constrain a steep fault (>70°) within the upper crust, consistent with field observations, that flattens at depth (≥20 km). The Muli thrust presents rapid thrusting motion (0.6 ± 0.08 km/Ma) that initiated at ∼12.5 Ma, following a slower phase (0.2 ± 0.06 km/Ma) since 50 Ma, with total rock exhumation of ∼15 km. This underlines the important role of thrust faulting in the thickening of the SE Tibetan crust.
Key Points
Thermo‐kinematic modeling of Muli thrust, a major thrust fault of SE Tibetan Plateau
15 km crust exhumation in 50 Ma on a high‐angle (>70°) ramp—décollement fault linked to thickening of SE Tibetan crust
Fault related to significant Moho step and shear wave velocity contrast in deep crust suggests entire crust implication
Numerical simulations of thermal convection in the Earth's mantle often employ a pseudoplastic rheology in order to mimic the plate‐like behavior of the lithosphere. Yet the benchmark tests available ...in the literature are largely based on simple linear rheologies in which the viscosity is either assumed to be constant or weakly dependent on temperature. Here we present a suite of simple tests based on nonlinear rheologies featuring temperature, pressure, and strain rate‐dependent viscosity. Eleven different codes based on the finite volume, finite element, or spectral methods have been used to run five benchmark cases leading to stagnant lid, mobile lid, and periodic convection in a 2‐D square box. For two of these cases, we also show resolution tests from all contributing codes. In addition, we present a bifurcation analysis, describing the transition from a mobile lid regime to a periodic regime, and from a periodic regime to a stagnant lid regime, as a function of the yield stress. At a resolution of around 100 cells or elements in both vertical and horizontal directions, all codes reproduce the required diagnostic quantities with a discrepancy of at most
∼3% in the presence of both linear and nonlinear rheologies. Furthermore, they consistently predict the critical value of the yield stress at which the transition between different regimes occurs. As the most recent mantle convection codes can handle a number of different geometries within a single solution framework, this benchmark will also prove useful when validating viscoplastic thermal convection simulations in such geometries.
Key Points:
First suite of benchmark tests for thermal convection of a viscoplastic fluid
Five benchmark cases, two resolution tests, and bifurcation analysis from 11 codes
Small influence of nonlinear rheology on the accuracy of numerical solutions
Our 3D modelling study shows that the presence of lithospheric plates around a subducting plate has a significant influence on subduction dynamics, in particular on trench retreat rate, slab dip, and ...lateral shortening of the subducting plate. Neighbouring plates prevent unrealistic plate behaviour with no need for complex rheologies. Because, at the Earth's surface, plates form a continuous shell, they should not be neglected.
In recent years, much has been done to develop numerical tools to study the three‐dimensional nature of the Earth's lithosphere deformation. DOUAR is one of them: it is a new ALE Finite Element code ...that is based on an adaptive grid, a key feature in the capture of localized deformation. In order to illustrate this, various simulations of punch experiments have been performed on rigid plastic materials with von Mises and Drucker‐Prager type of rheologies. We present the grid refinement algorithm based on strain rate measurements and rederive the plane strain punch analytical solution which allows us to test the accuracy of our results. Various 3‐D strip punches experiments with different aspect ratios show DOUAR's ability to capture complex fault patterns. We also discuss the degree to which the incompressibility and rigid plasticity constraints are satisfied. Finally, we show the results of a crustal‐scale deformation experiment demonstrating the potential of the octree‐based mesh refinement algorithm to solve complex three‐dimensional geodynamical problems with great efficiency and accuracy.
The level set method allows for tracking material surfaces in 2-D and 3-D flow modeling and is well suited for applications of multi-material flow modeling. The level set method utilizes smooth level ...set functions to define material interfaces, which makes the method stable and free of oscillations that are typically observed in case step-like functions parameterize interfaces. By design the level set function is a signed distance function and gives for each point in the domain the exact distance to the interface as well as on which side it is located. In this paper we present four benchmarks which show the validity, accuracy and simplicity of using the level set method for multi-material flow modeling. The benchmarks are simplified setups of dynamical geophysical processes such as the Rayleigh-Taylor instability, post-glacial rebound, subduction and slab detachment. We also demonstrate the benefit of using the level set method for modeling a free surface with the sticky air approach. Our results show that the level set method allows for accurate material flow modeling and that the combination with the sticky air approach works well in mimicking Earth's free surface. Since the level set method tracks material interfaces instead of materials themselves, it has the advantage that the location of these interfaces is accurately known and that it represents a viable alternative to the more commonly used tracer method.
I present in this work the GHOST (Geoscientific Hollow Sphere Tessellation) software which allows for the fast generation of computational meshes in hollow sphere geometries counting up to 100 ...million cells. Each mesh is composed of concentric spherical shells which are built out of quadrilaterals or triangles. I focus here on three commonly used meshes used in geodynamics/geophysics and demonstrate the accuracy of shell surfaces and mesh volume measurements as a function of resolution. I further benchmark the built-in gravity and gravitational potential procedures in the simple case of a constant density geometry and finally show how the produced meshes can be used to visualise the S40RTS mantle tomography model. The code is open source and is available on the GitHub sharing platform.
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