```{tags} category:cookbook feature:2d feature:cartesian feature:compositional-fields ``` (sec:cookbooks:kinematic-2d-oceanic-subduction)= # Kinematically-driven 2d oceanic subduction *This section was contributed by Anne Glerum and Yingying Li.* This subduction example is based on the benchmark effort of Quinquis et al., of which initial results were published in {cite:t}`quinquis:2014`. In four increasingly complex cases we will go from isoviscous materials without any temperature effects to a fully thermo-mechanical, nonlinear, strain-weakened visco-plastic, externally-driven model of oceanic subduction. The setup is outlined in {numref}`fig:QQ_setup`. The models are run for 15 My and slab tip depth, trench location, root-mean-square (RMS) velocity and temperature, and viscous dissipation are monitored. In addition, we will discuss the effects of the element size of the subduction interface and crustal layers, viscosity averaging and the solver tolerance. ```{figure-md} fig:QQ_setup Case 4 model setup. Copied from {cite:t}`quinquis:2014`. ``` ## Case 1: Simple rheology The Case 1 model setup considers seven materials (compositional fields) apart from the background sublithospheric mantle (see {numref}`fig:QQ_case1_setup`), including (1) the Bulk Oceanic Composition (BOC), (2) Serpentinized HarzBurgite (SHB) and (3) "thermal" layer of the overriding plate (OP), (4) the BOC, (5) SHB and (6) "thermal" layer of the subducting plate (SP), and (7) the weak seed. The geometry of these compositions is implemented as follows: ```{literalinclude} Case1_compositions.prm ``` No differences in material properties exist, except for density and viscosity, so we use the multicomponent material model. To keep the boundaries between fields as sharp as possible in terms of viscosity, we use the maximum composition to determine the viscosity in each evaluation point (note that this can be harder on the solver): ```{literalinclude} Case1_materialmodel.prm ``` Temperature effects are ignored. Subduction is driven by prescribed in- and outflow through the right boundary (with a gradual transition of the flow direction), all other boundaries are free slip. The volume of material that flows in is balanced by the volume that is prescribed to flow out (this is important as the model is incompressible). A weak crust along the plate interface and the subducting lithosphere facilitates subduction. Through the function plugin, we prescribe the in- and outflow: ```{literalinclude} Case1_velocity.prm ``` To follow the slab on its descent into the mantle, we use adaptive mesh refinement based on viscosity in combination with the minimum refinement strategy to ensure sufficient resolution in the crust and weak zone that allow the slab to detach from the surface: ```{literalinclude} Case1_meshrefinement.prm ``` To monitor the model evolution, several diagnostic quantities are tracked over time: the depth of the tip of the slab, the position of the trench, the RMS velocity of the slab and the whole model domain, and the viscous dissipation in the slab and total model domain. The computation of trench position is through a plugin called 'trench_location'. It needs to be compiled as a shared library that can be called from the input file. ```{literalinclude} Case1_postprocessing.prm ``` ```{figure-md} fig:QQ_case1_setup Case 1 density, viscosity and velocity at time zero. ``` We run the Case 1 setup for 15 My of model time. The diagnostic quantities in {numref}`fig:QQ_case1_diagnostics` show three stages of model evolution: first trench advance (top right plot), then free subduction (increasing slab RMS velocity), and after about 13 My interaction between the slab and bottom boundary at 660 km depth, which slows down the slab. The slab then curves inward along the bottom boundary. This can also be seen in {numref}`fig:QQ_case1_results`. ```{figure-md} fig:QQ_case1_diagnostics Case 1 diagnostic quantities of ASPECT ``` ```{figure-md} fig:QQ_case1_results Case 1 viscosity snapshots at 8 and 15 My. ``` ## Case 2a: Model with thermal evolution Case 2a builds on Case 1 by including a heterogeneous initial temperature field that combines the plate cooling model for the temperature in the plates with an adiabatic temperature gradient below the plates. For the plate cooling model, we assume that the overriding plate is 40 My old and the subducting plate 70 My. The temperature function (including a summation term) is too complex to write out as a function expression in the input file, so it is put in a new initial temperature plugin called ’subduction plate cooling’. This plugin needs to be compiled as a shared library that can be called from the input file: ```{literalinclude} Case2a_temperatures.prm ``` The initial temperature distribution can be seen in {numref}`fig:QQ_case2a_temperature_t0` ```{figure-md} fig:QQ_case2a_temperature_t0 Case 2a temperature distribution at time 0 ``` The thermal expansivity is set to zero in Case 2a, so that the thermal evolution is not coupled to the mechanical evolution through the density. A high conductivity of k = 183.33 Wm-1K-1 is assigned to the upper mantle to maintain the mantle adiabat. ```{literalinclude} Case2a_materialmodel.prm ``` We monitor the temperature evolution by tracking the root-mean-square (RMS) temperature and the isotherm depth using two plugins called "composition_trms_statistics" and "isotherm depth". To this end, we add the postprocessors "composition RMS temperature statistics" and "isotherm depth" to the prm file. The RMS temperature of the subducting plate (comprising the BOC_SP, SHB_SP, thermal_SP) as well as the whole domain is tracked over time, as is the 800 degrees Celsius isotherm. ```{literalinclude} Case2a_postprocessing.prm ``` {numref}`fig:QQ_case2a_diagnostics` shows the RMS temperature, 800 degrees Celsius isotherm depth as well as the other diagnostics. For reference, results from the ELEFANT software {cite}`thieulot:2015` are also shown. The 800 degrees Celsius isotherm depth continuously increases over time, but towards the end at a slower rate. The RMS temperature of the whole domain keeps decreasing due to the cold subducting plate entering the model domain. The slab RMS temperature decreases at the initial stage, then it goes up due to the slab being warmed up by the mantle. Note that the other diagnostics are indeed the same as for Case 1. ```{figure-md} fig:QQ_case2a_diagnostics ASPECT Case 1 and Case 2a as well as Elefant Case 2a diagnostic quantities ``` ## Case 2b: Model with a temperature-dependent density Case 2b builds on Case 2a. Compared to Case 2a, the thermal expansivity in Case 2b is set to 2.5e-5 K-1 instead of 0 K-1. This renders the density (and therefore the Stokes equations) temperature dependent. In addition, the benchmark uses different reference temperatures for each composition, but only one value can be specified for the reference temperature in ASPECT. Therefore, we adapted the reference densities for the different compositional fields to reflect the different reference temperatures. All the other parameters are identical to Case 2a: ```{literalinclude} Case2b_materialmodel.prm ``` The density evolution can be seen in {numref}`fig:QQ_case2b_density_evolution`. As the slab is heated up by the surrounding mantle, its density contrast with the mantle decreases, and so does its negative buoyancy. ```{figure-md} fig:QQ_case2b_density_evolution Case2b density evolution ``` Therefore, subduction occurs at a slower pace than in Case 1 and 2a (see {numref}`fig:QQ_case2b_diagnostics`). The subducting plate does not reach the bottom in 15 Myr, i.e., the third stage of Case 1 and 2a is missing. ```{figure-md} fig:QQ_case2b_diagnostics ASPECT Case2b diagnostic quantities ``` The total RMS velocity is however higher than in the previous cases (see {numref}`fig:QQ_case2b_diagnostics`) as an additional convection cell to the left of the slab increases the sub-lithospheric velocities (see {numref}`fig:QQ_case2b_velocity_evolution`). ```{figure-md} fig:QQ_case2b_velocity_evolution Case2b velocity evolution ``` Case 2b remains relatively simple, as all materials are linear viscous. In Case 3 (to be added) we will address nonlinear viscoplastic rheologies.