The transition from an endogenous to an exogenous regime of lava dome growth must be achieved by the formation of discontinuities within the dome. Such transitions (and vice versa) are an important characteristic of most long-lived lava domes and often coincide with significant changes in the dynamics of magma supply and lava dome collapse events. For the purpose of this paper, following recent experimental and observational evidence, we assume that such a transition occurs when shear bands are generated. A model for the formation of shear bands, and therefore the growth transition within a dome and coupled conduit domain is presented. Shear bands are most likely to initiate at the junction of the conduit and base of the dome, where the shear stress experienced between new lava entering the dome and existing lava is greatest. Stress accumulation within the shear bands is likely to lead to brittle shear, resulting in the formation of fractures. Finite element modelling of lava flow shows that such shear bands only develop for certain extrusion rates and lava viscosities. Similarly, the growth regime of the lava dome will depend upon the extrusion rate and viscosity within the conduit, which is largely controlled by volatile loss and the growth of crystals in the upper part of the conduit. We consider a simplified rheology during lava dome growth considering isothermal conditions with crystal growth. The development of shear bands in the conduit is explored with a numerical model parameterized with values appropriate for Soufrière Hills Volcano, Montserrat. During October to December 1996 this lava dome-forming eruption experienced a transition from endogenous to exogenous growth as it grew in height by about 90 m. Modelling indicates that the observed fall in magma extrusion rate from about 2.0 m 3 s-1 to 0.5 m 3 s-1 , as a result of the increased pressure head from the dome and the evolution in viscosity, could have subsequently changed the dome growth regime due to the development of shear bands. Our models provide insight into the shear stress fields possible within the conduit and the shear stresses required for shear band development.

We use a finite element (FEM) formulation of the level set method to model geological fluid flow problems involving interface propagation. Interface problems are ubiquitous in geophysics. Here we focus on a Rayleigh-Taylor instability, namely mantel plumes evolution, and the growth of lava domes. Both problems require the accurate description of the propagation of an interface between heavy and light materials (plume) or between high viscous lava and low viscous air (lava dome), respectively. The implementation of the models is based on Escript which is a Python module for the solution of partial differential equations (PDEs) using spatial discretization techniques such as FEM. It is designed to describe numerical models in the language of PDEs while using computational components implemented in C and C++ to achieve high performance for time-intensive, numerical calculations. A critical step in the solution geological flow problems is the solution of the velocitypressure problem. We describe how the Escript module can be used for a high-level implementation of an efficient variant of the well-known Uzawa scheme (Arrow et al., 1958). We begin with a brief outline of the Escript modules and then present illustrations of its usage for the numerical solutions of the problems mentioned above.

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Tear resistance at the edge of a slab is an important parameter controlling the evolution of subduction zones. However, compared with other subduction parameters such as plate strength, plate viscosity, plate thickness and trench width, the dynamics of tearing are poorly understood. Here we obtain a first-order understanding of the dynamics and morphology of subduction zones to resistance during tear propagation, by developing and using a novel computational modelling technique for subducting slabs, with side boundaries described by visco-plastic weak zones, developing into tear faults. Our 3D model is based upon a visco-plastic slab that sinks into the less dense mantle, generating poloidal and toroidal flows. The asthenospheric mantle field is static and only develops flow due to the subducting slab. We use the finite element code eScript/Finley and the level set method to describe the lithosphere to solve this fluid dynamics problem. Our results show the importance of tear resistance for the speed of trench migration and for shaping the final geometry of subduction systems. We show that slab tearing along a weak layer can result in a relatively straight slab hinge shape, while increasing the strength in the weak layer results in the curvature of the hinge increasing substantially. High tear resistance at the slab edges may hinder rollback to the extent that the slab becomes stretched and recumbently folded at the base of the domain. Tear resistance also controls whether the subducting lithosphere can experience accelerating rollback velocities or a constant rollback velocity.