xfit_premelt

Steady state flow law for pre-melting viscosity drop following Yamauchi and Takei (2016), J. Geophys. Res. Solid Earth, DOI. By default, this method uses flow law paramters (reference viscosity, activation energy, etc.) from a fit to the upper mantle.

Requires

In addition to the state variable arrays required by the other viscous methods (see HK2003, HZK2011), this method also requires a solidus:

VBR.in.SV.Tsolidus_K % solidus in degrees K

Calling Procedure

% set required state variables
clear
VBR.in.SV.T_K = linspace(800,1200,10)+273; % temperature [K]
VBR.in.SV.Tsolidus_K = (1200+273) * ones(size(VBR.in.SV.T_K)); % solidus [K]
VBR.in.SV.P_GPa = 2 * ones(size(VBR.in.SV.T_K)); % pressure [GPa]
VBR.in.SV.dg_um = 4 * ones(size(VBR.in.SV.T_K)); % grain size [um]
VBR.in.SV.sig_MPa = 10 *  ones(size(VBR.in.SV.T_K)); % differential stress [MPa]
VBR.in.SV.phi = 0.01 * ones(size(VBR.in.SV.T_K)); % melt fraction / porosity

% add to viscous methods list
VBR.in.viscous.methods_list={'xfit_premelt'};

% call VBR_spine
[VBR] = VBR_spine(VBR) ;

Parameters

Parameters, including flow law parameters can be explored by loading them into the workspace with

VBR.in.viscous.xfit_premelt = Params_Viscous('xfit_premelt');
disp(VBR.in.viscous.xfit_premelt)

eta_melt_free_method

The parameter, VBR.in.viscous.xfit_premelt.eta_melt_free_method, controls what viscosity method is used to calculate the melt free viscosity. By default, this is set to xfit_premelt, in which case it uses the upper mantle fit directly from Yamauchi and Takei (2016). If set to one of the other viscosity mtehods, HK2003 or HZK2011, then the melt free viscosity is calculated using those methods with melt fraction set to 0 and then the near-solidus pre-melting effect is then multiplied on.

Grain size dependence

Note that in section 4.4 of Yamauchi and Takei (2016), YT2016 fit for H, V following Priestly & McKenzie (2013) with dg_um = dg_um_r (i.e., the grain size is at the reference grain size). This results in a viscosity relationship independent of grain size. The VBRc sets dg_um_r to 4mm, the mean grain size of the upper mantle calculated in Priestly & McKenzie (2013). To exactly match Yamauchi and Takei (2016), you should set the grain size to the value of the reference grain size (e.g., VBR.in.SV.dg_um = 4000.).

Output

Output is stored in VBR.out.viscous.xfit_premelt. Unlike the other viscous methods, xfit_premelt only returns a diffusion creep viscosity sub-structure:

>> disp(fieldnames(VBR.out.viscous.xfit_premelt))

{
  [1,1] = diff
}
>> disp(fieldnames(VBR.out.viscous.xfit_premelt.diff))

{
  [1,1] = eta
  [2,1] = eta_meltfree
}

Note that eta_meltfree is both the melt-free and volatile-free viscosity: the pre-melting method incorprates weakening from volatiles in the solidus depression. To incorporate effects of volatiles, should calculate a volatile-dependent solidus.