Continental rifts: Complex dissipative patterns from simple boundary conditions

We present numerical models that investigate the development of crustal and mantle detachments during lithospheric extension. Our models, which consider an elasto-visco-plastic lithosphere, explore the relationship between stored and dissipated energies during deformation. We apply the fundamental thermodynamic assumptions of minimization of Helmholtz free energy (i.e. stored energy) and maximization of dissipated energy, and include in the models feedback effects modulated by temperature, such as shear heating, that lead to strain localization. Our models simulate a wide range of extensional systems with varying values of crustal thickness and heat flow, showing how strain localization in the mantle interacts with localization in the upper crust and controls the evolution of extensional systems. Model results reveal a richness of structures and deformation styles as a response to a self-organized mechanism that minimizes the internal stored energy of the system by localizing deformation. Crustal detachments, here referred as low-angle normal decoupling horizons, are well developed during extension of overthickened (60 km) continental crust, even when the initial heat flow is relatively low (50 mW m-2). In contrast, localized mantle deformation is most pronounced when the extended lithosphere has a normal crustal thickness (30–40 km) and an intermediate heat flow (60–70mWm-2). Results show a nonlinear response to subtle changes in crustal thickness or heat flow, characterized by abrupt and sometimes unexpected switches in extension modes (e.g., from diffuse extensional deformation to effective lithospheric-scale rupturing) or from mantleto crust-dominated strain localization. We interpret this nonlinearity to result from the interference of doming wavelengths in the presence of multiple necking instabilities. Disharmonic crust and mantle doming wavelengths results in efficient communication between shear zones at different lithospheric levels, leading to rupturing of the whole lithosphere. In contrast, harmonic crust and mantle doming inhibits interaction of shear zones across the lithosphere and results in a prolonged history of extension prior to continental breakup

Studying the influence of a solid shell on lava dome growth and evolution using the level set method

A finite element formulation of the level set method, a technique to trace flow fronts and interfaces without element distortion, is presented to model the evolution of the free surface of a spreading flow for a highly viscous medium on a horizontal surface. As an example for this class of problem we consider the evolution of an axisymmetric lava dome. Equilibrium configurations of lava domes have been modelled analytically as brittle shells enclosing pressurized magma. The existence of the brittle shell may be viewed as a direct consequence of the strong temperature dependence of the viscosity. The temperature dependence leads to the formation of a thin predominantly elastic-plastic boundary layer along the free surface and acts as a constraint for the shape and flow of the lava dome. In our model, we adopt Iverson's assumption that the thin boundary layer behaves like an ideal plastic membrane shell enclosing the ductile interior of the lava dome. The effect of the membrane shell is then formally identical to a surface tension-like boundary condition for the normal stress at the free surface. The interior of the dome is modelled as a Newtonian fluid and the axisymmetry equations of motion are formulated in a Eulerian framework. We show that the level set is an effective tool to trace and model deforming interfaces for the example of the free surface of a lava dome. We demonstrate that Iverson's equilibrium dome shapes are indeed steady states of a transient model. We also show how interface conditions in the form of surface tension involving higher order spatial derivative (curvature) can be considered within a standard finite element framework

An overview of numerical methods for earth simulations

International audienceGeological simulation problems are distinct from engineering problems in having a strongly evolving geometry which is often developed through non-linear interaction between structureand rheology. Engineeringsimulationcodesare thereforeoften, by design, unsuitable for geological applications. We summarize the important features of a small number of numerical methods which have been developed with geological and geotechnical simulations in mind, summarize the advantages and disadvantages of some of these methods and introduce the sorts of problems for which each method is best suited

Large scale shear banding in extension

In this paper, we will explore the role of non-coaxiality on shear banding in pure shear. We first outline the consitituve relations. The deformation and localization process is illustrated by results of large deformation finite element simulations on a rectangular domain in extension for different constitutive models. We also show the variation of the average horizontal stress (stress resultant) conjugate to the prescribed boundary velocity with a strain measure for the horizontal extension. We assume incompressible deformations since the emphasis in this study is on large deformations. The equations of motion are integrated using an updated Lagrangian scheme