Kinematically-driven 2d oceanic subduction

Kinematically-driven 2d oceanic subduction#

This section was contributed by Anne Glerum.

This subduction example is based on the benchmark effort of Quinquis et al., of which initial results were published in Quinquis [2014]. In four increasingly complex setups 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 of the most complex case is outlined in Fig. 123. The models are run for 15 My and slab tip depth, trench location, RMS velocity and temperature, and viscous dissipation are monitored. In addition, we discuss the effects of the element size of the subduction interface and crustal layers, viscosity averaging and the solver tolerance.


Fig. 123 Case 4 model setup. Copied from Quinquis [2014].#

Case 1: Simple geometry and rheology#

The Case 1 model setup considers three materials (compositional fields) apart from the background sublithospheric mantle (see Fig. 124):

  1. the lithosphere of the overriding plate (combining the BOC, SHB and thermal layer of the overriding plate in Fig. 123),

  2. the crust of the subducting plate (weak seed and BOC combined), and

  3. the mantle lithosphere of the subducting plate (SHB and thermal layer combined).

The geometry of these compositions is implemented as follows:

# We fix composition on the right boundary,
# because we have inflow there.
subsection Boundary composition model
  set Fixed composition boundary indicators = right
  set List of model names                   = initial composition

subsection Compositional fields
  set Number of fields = 3
  set Names of fields  = OP, ML_SP, crust_SP

subsection Initial composition model
  set List of model names = function

  subsection Function
    set Function constants  = Ax=1475600.0, Az=670000.0, \
                              Bx=1500000.0, Bz=670000.0, \
                              Cx=1358500.0, Cz=588000.0, \
                              Dx=1382900.0, Dz=588000.0, \
                              Ex=1530000.0, Ez=560000.0, \
                              Fz=663000.0, Gz=662000.0, \
                              Hz=631000.0, Iz=630000.0
    set Function expression = \
                              if(z>=Cz&z>=((Az-Cz)/(Ax-Cx)*(x-Cx)+Cz),1,0); \
                              if((x>=Ex&z>=Ez&z<Gz)|(x<Ex&z<=((Bz-Dz)/(Bx-Dx)*(x-Dx)+Dz)&z<Gz&z>=((Ez-Dz)/(Ex-Dx)*(x-Dx)+Dz)),1,0); \
    set Variable names      = x,z

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):

set Nonlinear solver scheme                = single Advection, single Stokes

subsection Material model
  set Model name = multicomponent

  subsection Multicomponent
    set Reference temperature         = 0.0
    set Viscosity averaging scheme    = maximum composition

    # background, OP, ML SP, crust SP
    set Viscosities                   = 1.e20, 1.e23, 1.e23, 1.e20
    set Densities                     = 3200.0, 3250.0, 3250.0, 3250.0
    set Thermal conductivities        = 1

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:

subsection Boundary velocity model
  set Tangential velocity boundary indicators = left, bottom, top
  set Prescribed velocity boundary indicators = right x:function

  subsection Function
    set Function constants  = cm=100.0
    set Function expression = if(z<540000.0, (600.0/550.0)/cm, \
                                 if(z>560000.0, -5.0/cm, \
                                    ((((-600.0/550.0)-5.0)/-20.0)*((z/1000.0)-560.0)+5.0)*(-1.0/cm))); \
    set Variable names      = x,z

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:

subsection Mesh refinement
  set Initial adaptive refinement              = 2
  set Initial global refinement                = 8
  set Minimum refinement level                 = 6
  set Normalize individual refinement criteria = true
  set Refinement criteria merge operation      = plus
  set Coarsening fraction                      = 0.01
  set Refinement fraction                      = 0.95
  set Run postprocessors on initial refinement = false
  set Skip solvers on initial refinement       = true
  set Skip setup initial conditions on initial refinement = true
  set Strategy                                 = minimum refinement function, viscosity
  set Time steps between mesh refinement       = 16

  subsection Minimum refinement function
    set Coordinate system = depth
    set Variable names = x,z,t
    set Function constants = vel=150e3, L=100e3, crust=10e3
    set Function expression = if(x<crust,10,if(x<L,9,if(x<vel,8,6)))

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 work done (viscous dissipation) in the slab and total model domain. The computation of these quantities in done in several new plugins:

subsection Postprocess
  set List of postprocessors = visualization, velocity statistics, heating statistics, maximum depth of field, composition velocity statistics, viscous dissipation statistics

  subsection Visualization
    set List of output variables      = density, viscosity, strain rate, error indicator
    set Time between graphical output = 5e5

Fig. 124 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 Fig. 125 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 Fig. 126.


Fig. 125 Case 1 diagnostic quantities of ASPECT, Sulec and Elefant results.#


Fig. 126 Case 1 viscosity snapshots at 8 and 15 My.#