`andrade_psp`

Andrade Model with Pseudo-Period Scaling, following Jackson and Faul (2010), Phys. Earth Planet. Inter., DOI. This is a single-sample fit of Jackson and Faul (2010) sample 6585 (Table 1 in the reference).

Requires

The following state variable arrays are required:

VBR.in.SV.T_K % temperature [K]
VBR.in.SV.P_GPa % pressure [GPa]
VBR.in.SV.dg_um % grain size [um]
VBR.in.SV.sig_MPa % differential stress [MPa]
VBR.in.SV.phi % melt fraction / porosity
VBR.in.SV.rho % density in kg m<sup>-3</sup>

Additionally, andrade_psp relies on output from the elastic methods so anharmonic MUST be in the VBR.in.elastic.methods_list. If anh_poro is in the methods list then andrade_psp will use the unrelaxed moduli from anh_poro (which includes the P,T projection of anharmonic plus the poroelastic correction). See the section on elastic methods for more details.

Calling Procedure

% set required state variables
clear
VBR.in.SV.T_K=700:50:1200;
VBR.in.SV.T_K=VBR.in.SV.T_K+273;
sz=size(VBR.in.SV.T_K); % temperature [K]

% remaining state variables (ISV)
VBR.in.SV.dg_um=3.1*ones(sz);
VBR.in.SV.P_GPa = 0.2 * ones(sz); % pressure [GPa]
VBR.in.SV.rho = 3300 * ones(sz); % density [kg m^-3]
VBR.in.SV.sig_MPa = 10 * ones(sz); % differential stress [MPa]
VBR.in.SV.phi = 0.0 * ones(sz); % melt fraction

% set frequency range
VBR.in.SV.f = 1./logspace(-2,4,100);

% set elastic methods list (at least 'anharmonic' is required)
VBR.in.elastic.methods_list={'anharmonic';'anh_poro'};

% set anelastic methods list
VBR.in.anelastic.methods_list={'andrade_psp'};

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

Output

Output is stored in VBR.out.anelastic.andrade_psp:

>> disp(fieldnames(VBR.out.anelastic.andrade_psp))

{
  [1,1] = J1
  [2,1] = J2
  [3,1] = Q
  [4,1] = Qinv
  [5,1] = M
  [6,1] = V
  [7,1] = Vave
}

The following fields are frequency dependent: J1,J2,Q,Qinv,M and V.

Parameters

To view the full list of parameters,

VBR.in.anelastic.andrade_psp = Params_Anelastic('andrade_psp');
disp(VBR.in.anelastic.andrade_psp)

Any of these parameters can be set before calling VBR_spine.

on the reference modulus

The parameter fits include a value for the reference modulus, temperature and pressure:

G_UR =  62.2
TR =  1173
PR =  0.20000    

which reflect the experimental conditions.

It is important to stress that these values are not used by the anharmonic calculation (as a result the reference modulus here is not used anywhere). The reference temperature and pressure are only used in calculating maxwell times when calculating the effective diffusion creep viscosity and do not match the reference values used by the anharmonic methods. In order to use the exact unrelaxed reference modulus of Jackson and Faul, 2010, you must either (1) overwrite VBR.in.elastic.anharmonic.Gu_0_ol using the JF10 value projected to the surface, as done in Projects/1_LabData/1_Attenuation/FitData_FJ10_Andrade.m or (2) set VBR.in.elastic.anharmonic.Gu_0_ol to the exact JF10 value but then change VBR.in.elastic.anharmonic.T_K_ref and VBR.in.elastic.anharmonic.P_Pa_ref to match the the JF10 values.

Example at Laboratory Conditions

The script Projects/1_LabData/1_Attenuation/FitData_FJ10_Andrade.m calculates the modulus, M, and attenuation, Q^-1, for a temperature range of 700-1200^oC in 50^oC increments for periods in 10^-2 to 10⁴ s following Jackson and Faul (2010):

'andradeLab'

Data are from figure 1e-1f of Jackson and Faul 2010 and are not included in the present repository.