A free surface capturing discretization for the staggered grid finite difference scheme

International audienceThe coupling that exists between surface processes and deformation within both the shallowcrust and the deeper mantle-lithosphere has stimulated the development of computationalgeodynamic models that incorporate a free surface boundary condition. We introduce a treatmentof this boundary condition that is suitable for staggered grid, finite difference schemesemploying a structured Eulerian mesh. Our interface capturing treatment discretizes the freesurface boundary condition via an interface that conforms with the edges of control volumes(e.g. a ‘staircase’ representation) and requires only local stencil modifications to be performed.Comparisons with analytic solutions verify that the method is first-order accurate. Additionalintermodel comparisons are performed between known reference models to further validateour free surface approximation. Lastly, we demonstrate the applicability of a multigrid solverto our free surface methodology and demonstrate that the local stencil modifications do notstrongly influence the convergence of the iterative solver

Tectonic inheritance controls nappe detachment, transport and stacking in the Helvetic Nappe System, Switzerland: insights from thermo-mechanical simulations

International audienceTectonic nappes are observed for more than a hundred years. Although geological studies often refer to a "nappe theory", the physical mechanisms of nappe formation are still incompletely understood. We apply two-dimensional numerical simulations of shortening of a passive margin, to investigate the thermo-mechanical processes of detachment, transport and stacking of nappes. We use a visco-elasto-plastic model with standard creep flow laws and Drucker-Prager yield criterion. We consider tectonic inheritance with two initial mechanical heterogeneities: (1) lateral heterogeneity of the basement-cover interface due to half-grabens and horsts and (2) vertical heterogeneities due to layering of mechanically strong and weak sedimentary units. The model shows detachment and horizontal transport of a thrust nappe and stacking of this thrust nappe above a fold nappe. The detachment of the thrust sheet is triggered by stress concentrations around the sediment-basement contact and the resulting brittle-plastic shear band formation. The horizontal transport is facilitated by a basal shear zone just above the basement-cover contact, composed of thin, weak sediments. Fold nappe formation occurs by a dominantly ductile closure of a half-graben and the associated extrusion of the half-graben fill. We apply our model to the Helvetic nappe system in Western Switzerland, which is characterized by stacking of the Wildhorn thrust nappe above the Morcles fold nappe. The modeled structures and temperature field agree with data from the Helvetic nappe system. The mechanical heterogeneities must generate contrasts in effective viscosity (i.e. ratio of stress to strain rate) of four orders of magnitude to model nappe structures similar to the ones of the Helvetic nappe system

Impact of upper mantle convection on lithosphere hyperextension and subsequent horizontally forced subduction initiation

Many plate tectonic processes, such as subduction initiation, are embedded in long-term (> 100 Myr) geodynamic cycles often involving subsequent phases of extension, cooling without plate deformation and convergence. However, the impact of upper mantle convection on lithosphere dynamics during such long-term cycles is still poorly understood. We have designed two-dimensional upper mantle- scale (down to a depth of 660 km) thermo-mechanical numerical models of coupled lithosphere–mantle deformation. We consider visco–elasto–plastic deformation including a combination of diffusion, dislocation and Peierls creep law mechanisms. Mantle densities are calculated from petrological phase diagrams (Perple_X) for a Hawaiian pyrolite. Our models exhibit realistic Rayleigh numbers between 1e6 and 1e7, and the model temperature, density and viscosity structures agree with geological and geophysical data and observations. We tested the impact of the viscosity structure in the asthenosphere on upper mantle convection and lithosphere dynamics. We also compare models in which mantle convection is explicitly modelled with models in which convection is parameterized by Nusselt number scaling of the mantle thermal conductivity. Further, we quantified the plate driving forces necessary for subduction initiation in 2D thermo- mechanical models of coupled lithosphere–mantle deformation. Our model generates a 120 Myr long geodynamic cycle of subsequent extension (30 Myr), cooling (70 Myr) and convergence (20 Myr) coupled to upper mantle convection in a single and continuous simulation. Fundamental features such as the formation of hyperextended margins, upper mantle convective flow and subduction initiation are captured by the simulations presented here. Compared to a strong asthenosphere, a weak asthenosphere leads to the following differences: smaller value of plate driving forces necessary for subduction initiation (15 TN/m instead of 22 TN/m) and locally larger suction forces. The latter assists in establishing single-slab subduction rather than double-slab subduction. Subduction initiation is horizontally forced, occurs at the transition from the exhumed mantle to the hyperextended passive margin and is caused by thermal softening. Spontaneous subduction initiation due to negative buoyancy of the 400 km wide, cooled, exhumed mantle is not observed after 100 Myr in model history. Our models indicate that long-term lithosphere dynamics can be strongly impacted by sub-lithosphere dynamics. The first-order processes in the simulated geodynamic cycle are applicable to orogenies that resulted from the opening and closure of embryonic oceans bounded by magma-poor hyperextended rifted margins, which might have been the case for the Alpine orogeny

Buoyancy versus shear forces in building orogenic wedges

International audienceThe dynamics of growing collisional orogens are mainly controlled by buoyancy and shear forces. However, the relative importance of these forces, their temporal evolution and their impact on the tectonic style of orogenic wedges remain elusive. Here, we quantify buoyancy and shear forces during collisional orogeny and investigate their impact on orogenic wedge formation and exhumation of crustal rocks. We leverage two-dimensional petrological–thermomechanical numerical simulations of a long-term (ca. 170 Myr) lithosphere deformation cycle involving subsequent hyperextension, cooling, convergence, subduction and collision. Hyperextension generates a basin with exhumed continental mantle bounded by asymmetric passive margins. Before convergence, we replace the top few kilometres of the exhumed mantle with serpentinite to investigate its role during subduction and collision.We study the impact of three parameters: (1) shear resistance, or strength, of serpentinites, controlling the strength of the evolving subduction interface; (2) strength of the continental upper crust; and (3) density structure of the subducted material. Densities are determined by linearized equations of state or by petrological-phase equilibria calculations. The three parameters control the evolution of the ratio of upward-directed buoyancy force to horizontal driving force, FB/FD=ArF, which controls the mode of orogenic wedge formation: ArF≈0.5 causes thrust-sheet-dominated wedges, ArF≈0.75 causes minor wedge formation due to relamination of subducted crust below the upper plate, and ArF≈1 causes buoyancy-flow- or diapir-dominated wedges involving exhumation of crustal material from great depth (>80 km). Furthermore, employing phase equilibria density models reduces the average topography of wedges by several kilometres.We suggest that during the formation of the Pyrenees ArF⪅0.5 due to the absence of high-grade metamorphic rocks, whereas for the Alps ArF≈1 during exhumation of high-grade rocks and ArF⪅0.5 during the post-collisional stage. In the models, FD increases during wedge growth and subduction and eventually reaches magnitudes (≈18 TN m−1) which are required to initiate subduction. Such an increase in the horizontal force, required to continue driving subduction, might have “choked” the subduction of the European plate below the Adriatic one between 35 and 25 Ma and could have caused the reorganization of plate motion and subduction initiation of the Adriatic plate

Thinning mechanisms of heterogeneous continental lithosphere

The mechanisms responsible for the formation of extremely thinned continental crust (<10 km thick) and lithosphere during rifting remains debated. Observations from present-day and fossil passive margins highlight the role of deep-seated deformation, likely controlled by heterogeneities within the continental lithosphere, such as changing lithologies, mechanical anisotropies and inherited structures. We investigate the mechanisms of lithospheric thinning by exploring the role of pre-existing heterogeneities on the architecture and evolution of rifted margins. We estimate pre-rift pressure conditions (P0) vs. depth diagrams of crustal to lithospheric sections, to quantify rift-related modifications on inherited lithostatic pressure gradients. Two field examples from the Alpine Tethys margins in the Eastern and Southern Alps (SE Switzerland and N Italy) were selected to characterize: (1) the pre-rift architecture of the continental lithosphere; (2) the localization of rift-related deformation in distinct portions of the lithosphere; and (3) the interaction between pre-existing heterogeneities of the lithosphere and rift-related structures. These observations are compared with high-resolution, two-dimensional thermo-mechanical numerical models. The design of the models takes into account pre-existing mechanical heterogeneities representing the initial pre-rift architecture of the continental lithosphere. Extensional structures consist of high-angle and low-angle normal faults, anastomosing shear-zones and decoupling horizons. Such structures accommodate the lateral extraction of mechanically stronger levels derived from the middle to lower crust. As a result, the extremely thinned continental crust in Tethyan passive margins represents the juxtaposition and amalgamation of distinct strong levels of the crust separated by major extensional structures identified by sharp pressure gradients. Future work should determine the applicability of these results to other present-day and fossil rifted margins

The Benefits of Using a Consistent Tangent Operator for Viscoelastoplastic Computations in Geodynamics

Strain localization is ubiquitous in geodynamics and occurs at all scales within the lithosphere. How the lithosphere accommodates deformation controls, for example, the structure of orogenic belts and the architecture of rifted margins. Understanding and predicting strain localization is therefore of major importance in geodynamics. While the deeper parts of the lithosphere effectively deform in a viscous manner, shallower levels are characterized by an elastoplastic rheological behavior. Herein we propose a fast and accurate way of solving problems that involve elastoplastic deformations based on the consistent linearization of the time-discretized elastoplastic relation and the finite difference method. The models currently account for the pressure-insensitive Von Mises and the pressure-dependent Drucker-Prager yield criteria. Consistent linearization allows for resolving strain localization at kilometer scale while providing optimal, that is, quadratic convergence of the force residual. We have validated our approach by a qualitative and quantitative comparison with results obtained using an independent code based on the finite element method. We also provide a consistent linearization for a viscoelastoplastic framework, and we demonstrate its ability to deliver exact partitioning between the viscous, the elastic, and the plastic strain components. The results of the study are fully reproducible, and the codes are available as a subset of M2Di MATLAB routines

Strain localization in lithosphere dynamics models.

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Lithosphere dynamics and strain localisation

International audienceStrain localisation is an essential ingredient of plate tectonics that fosters mechanical decoupling and relativemotion of tectonic plates. Understanding strain localisation is thus necessary to unravel processes such as theinitiation of subduction, the growth of orogenic wedges, or the opening of rift basins.However, strain localisation in tectonics is reported on a wide range of spatio-temporal scales, occurs in boththe brittle and ductile regions of the lithosphere and is hence attributed to a variety of mechanisms. In general,strain localisation can result from both dynamic and kinematic processes. While dynamic causes involve differentkinds of material softening (e.g. thermal softening, grain size evolution, fluid flow and mineral reactions),kinematic strain localisation arise from specific initial material configuration and strength variations (e.g. tectonicinheritance).Here, I will first discuss fundamental properties of ductile strain localisation processes, with emphasis on thermalsoftening and tectonic inheritance.Then, I will demonstrate the role of both kinematic and dynamic strain localisation, as well as their interplay basedon different examples of tectonic processes (orogenic wedge growth, rifting) and using numerical simulations.Finally, I will further discuss current physical and technical challenges related to modelling lithosphere-scalestrain localisation and will highlight some future perspective

Lithospheric-scale shear zone development in convergent setting: time-evolution and switches in dominant rheological behaviour

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