State of the art numerical subduction modelling with ASPECT; thermo- mechanically coupled viscoplastic compressible rheology, free surface, phase changes, latent heat and open sidewalls A MSc. thesis by C.A.H. Blom Supervisors: C.A.P. Thieulot1, A.C. Glerum1, M.R.T. Fraters1, W. Spakman1 1Utrecht University, Department of Earth sciences, Mantle Dynamics Group July 2016 Abstract. Subduction dynamics exert great influence on surface processes, plate tectonics and mantle convection. Feedback between these processes in combination with the many parameters involved in numerical subduction modelling makes it a chal- lenge to find out how a single variable affects the system. In this study we focus on three problems. Firstly, we try to find out how boundary conditions (partic- ularly open boundary conditions) influence subduction evolution. Secondly, the effects of mantle phase transitions on subduction dynamics will be investigated. Thirdly, the role of compressibility in our models will be explored. Meanwhile, we try to find a relation between surface expressions and their causative mantle processes. Our research is performed in a two-dimensional domain with a free surface, either free slip, prescribed velocity or open sidewalls and a free slip bot- tom boundary. Up to seven compositional fields are involved which feature a thermo-mechanically coupled viscoplastic compressible rheology. Prescribed ve- locity boundaries are found to restrict the influences of the internal dynamics. As a result, the subduction geometry is largely defined by the boundary conditions. Open boundary conditions allow a multitude of new subduction geometries to evolve more naturally. The 410 km phase transition increases the slab pull force considerably and produces a surface depression. Open boundaries allow the slab to accelerate significantly after it has crossed the 410 km phase transition. Slabs in this study are probably too weak to penetrate through the 660 km phase transi- tion. Instead they buckle on the phase transition and high stresses cause elevated surface expressions. Compressibility is found to have a second order effect on subduction evolution. Contents Abstract 1 Introduction 1 1.1 Open boundary conditions...............................1 1.2 Slab morphology induced by mantle phase transitions...............2 1.3 Compressibility.....................................3 1.4 Surface expressions of subduction zones.......................4 2 Model description6 2.1 ASPECT........................................6 2.2 Model setup.......................................6 2.2.1 Governing equations..............................8 2.3 Rheology........................................8 3 Model adaptations 11 3.1 Material properties................................... 11 3.1.1 Viscosity.................................... 11 3.1.2 Density..................................... 13 3.2 Model extensions.................................... 14 3.2.1 The adiabatic mantle temperature...................... 14 3.2.2 The phase transition function......................... 14 3.2.3 The entropy derivative............................. 16 4 Results 19 4.1 Why a maximum number of nonlinear iterations increases model efficiency.... 19 4.2 Reducing the wall-time by material averaging.................... 19 4.3 How do free slip, free surface, prescribed velocity and open boundary conditions affect subduction evolution?.............................. 21 4.4 The combined effects of mantle phase transitions and sidewall boundary condi- tions on subduction evolution and surface topography............... 24 4.5 Testing the impact of compressibility on a model with phase transitions and a model without phase transitions........................... 28 5 Discussion 30 5.1 Reducing the computational time........................... 30 5.2 The effects of prescribed and open sidewalls..................... 31 5.3 The combined effects of mantle phase transitions and sidewall boundary condi- tions on subduction evolution............................. 32 5.4 Why compressibility can be ignored......................... 34 5.5 The combined effects of mantle phase transitions and sidewall boundary condi- tions on surface topography.............................. 34 6 Conclusion 36 Bibliography 36 Appendix A Derivation of the adiabatic temperature equationi Appendix B Benchmarking open boundaries in ELEFANT and ASPECT iii B.1 TEST OPENBC 1: 3D Sinking cube in ELEFANT and ASPECT ....... iii B.1.1 Compositional initial conditions........................ iii B.1.2 Velocity differences invoked by viscosity averaging schemes........ iv B.1.3 Zero velocity boundary conditions (1,2,3,4,5,6)/(0,1,2,3,4,5)........v B.1.4 Open boundary conditions (1,2)/(0,1), 48x48x48.............. viii B.1.5 Open boundary conditions (1,2,3,4)/(0,1,2,3), 48x48x48, No material av- eraging.....................................x B.2 TEST OPENBC 2: 2D simple lithospheric model.................. xii B.2.1 Compositional initial conditions........................ xii B.2.2 Free slip on the sidewalls........................... xiii B.2.3 Open boundary conditions on the sidewalls................. xv Appendix C Code xvii 1. Introduction Subduction zones are one of the most extensively studied terrestrial geodynamic areas because they affect human life by inducing seismicity and volcanic activity. Our inability to observe deep-subcrustal processes makes us dependent on numerical models to better understand what happens in subduction zones. Evermore complicated subduction models in combination with increasingly powerful computers allow us to study parameters that have been simplified or ignored in dated subduction setups. However, to effectively study the influences of individual parameters the total number of parameters should be limited, without over-simplification of the subduction physics (Gerya, 2011). 1.1 Open boundary conditions Regional subduction zones are modeled with a limited spatial extent, therefore, boundary con- ditions are required at the edges of the domain. The selected boundary conditions represent the mechanical and thermal state of the surrounding system and influence the evolution of the model (Quinquis et al., 2011). Free-slip boundary conditions are applied in most older and recent sub- duction models (e.g. Keppie et al., 2009, C´ı˘zkov´aet˘ al., 2012, Tosi et al., 2016). Impermeable boundary conditions, such as free-slip, are found to restrict slab rollback at subduction zones because of strong return flows. In addition, the aspect ratio of a domain with impermeable sidewalls affects slab evolution while a domain with open traction boundaries is less sensitive to its aspect ratio. Therefore, models with impermeable boundary conditions require larger aspect ratios than models with open traction sidewalls (Chertova et al., 2012). Permeable boundaries have proven to be a more realistic option than impermeable bound- aries because they do not inhibit lateral flow. However, most permeable boundaries are based on prescribed conditions such as prescribed velocities (e.g. Quinquis et al., 2011), prescribed stresses (other than the lithostatic pressure) or periodic boundaries (e.g. Ita and King, 1994, Capitanio et al., 2010, Crameri and Tackley, 2015). Prescribed conditions have been found to control trench motion and the geometry of the subducting slab. Quinquis et al.(2011) and van Hunen et al.(2001) for instance recognize that a slab subducting beneath a stationary over- riding plate often results in the slab folding on the ∼660 km discontinuity whereas subduction under an advancing overriding plate results in trench retreat and the slab resting on the lower mantle. Also, Ita and King(1994) recognized that the symmetry induced by periodic boundary conditions reduces the maximum wavelength in the mantle compared to free slip boundary con- ditions. Consequently, more and smaller convecting cells developed in domains with periodic sidewalls 1 Introduction 2 Furthermore, subduction is regarded as the main driving force for plate motion and mantle convection (Forsyth and Uyedat, 1975, Richter and McKenzie, 1978). So, a subducting system should be driven by lithosphere subduction and not by prescribed conditions. Self consistent lithosphere subduction has been modelled in high width to depth ratio box models with free slip boundary conditions (e.g. C´ı˘zkov´aet˘ al., 2012, Androvi˘cov´aet al., 2013, Tosi et al., 2016). Self consistent lithosphere subduction in which the flow through the sidewalls was completely determined by the model interior has only been described a few times (e.g. Quinteros et al. (2010), Chertova et al.(2012)). 1.2 Slab morphology induced by mantle phase transitions Tomographic studies show a diverse range of subducting slab types. Some slabs penetrate the phase transition zone almost vertically while others flatten out, bend or buckle on the 660 km phase transition and sink into the lower mantle after up to several 100 km of lateral movement (e.g. van der Hilst et al., 1997, Fukao et al., 2001, Zhao, 2004, Hayes et al., 2012). To distinguish between slab morphologies Garel et al.(2014) divided subducting slabs into four groups: (i) slabs which have a small dip in the upper mantle and flatten at the 660 km phase transition, (ii) slabs which are steep in the upper mantle and flatten at the 660 km transition zone, (iii) slabs with a constant dip from upper to lower mantle and (iv) near vertical slabs that get thicker at the base of the upper mantle. Previous research has demonstrated that some parameters have a larger effect on slab