lmrRheologyLibrary.xml

<?xml version="1.0" encoding="UTF-8"?>
<StGermainData xmlns="http://www.vpac.org/StGermain/XML_IO_Handler/Jun2003">
    <struct name="components" mergeType="merge">
        <!-- ========================================================================= -->
        <!-- === Rheology library ==================================================== -->
        <!--
                The rheology library is a collection of pre-defined rheological parameters, including:
                    - viscous and brittle flow laws,
                    - densities,
                    - thermal properties (radiogenic heating, diffusivity, etc.),

                The best way to use this document is to:
                   1) Browse through the rheological parameters listed here, and pick the one you want to use,
                   2) Copy the name of the property,
                   3) Open your lmrMaterials.xml file, and find the material you are working on (for example, "lower_crust"),
                   4) Replace or create the name of the rheological property in the material definition.
                Looking through the default lmrMaterials.xml that comes with the LMR should make this obvious.

                The structure of the library is as such:
                    - Densities,
                    - Thermal properties,
                    - Partial melt functions,
                    - Flow laws
                        - Viscous laws:
                            - Isoviscous
                            - Temperature dependent
                            - Strain-rate/Temperature dependent
                            - Partial melt viscosity modifiers
                        - Brittle laws
                            - Drucker-Prager
                            - Stress Limiters

                 The document is also grouped into Earth-like layers: upper-crust, lower-crust, mantle, etc.

                 The naming format attempts to follow this style:
                        <category>_<description>_<author and year>
                 E.g. Dry Olivine dislocation creep viscous flow law from Korenaga and Karato, 2008 becomes
                        viscSRTdislocation_dry_olivine_Korenaga2008

                 Clearly this is not always an option, but names are generally as descriptive and concise as
                 possible. Rheologies with no references are derived from the authors.

                 These rheologies are purely meant to provide a collection of commonly used rheologies from the
                 literature - they are not the only option available. Please feel free to add or build your own
                 and add it to the collection.
        -->






        <!-- ======================================================================================= -->
        <!-- === Densities ========================================================================= -->
        <!-- NOTE: The LinearDensity function calculates:
                   rho = rhoRef * (1 + (beta * deltaP) - (alpha * deltaT))
                   where deltaP is the difference between P and the reference P, and deltaT
                   is the difference between T and the reference T. If either one is not
                   specified, it's term is ignored.

                   The Ppc_LinearDensityMelt function calculates the same as above, with an
                   extra term:
                   rho = rhoRef * (1 + (beta * deltaP) - (alpha * deltaT)
                                  - ( meltFraction * meltDensityChange ) )
        -->

        <!-- === Upper crustal ============== -->
        <struct name="densTemp_sediment">
            <param name="Type">Ppc_LinearDensity</param>
            <param name="ReferenceDensity" units="kg*m^-3">2500</param>

            <param name="Temperature"> temperature_ppc_wrapper </param>
            <param name="ReferenceTemperature" units="K"> 273.15 </param>
            <param name="ThermalExpansivity"> ThermalExpansivityProperty </param>
            <!-- Pressure dependent densities can be used by adding
                 the following params. -->
            <!--
            <param name="Pressure"> pressure_ppc_wrapper </param>
            <param name="ReferencePressure" units="MPa"> 0.0 </param>
            <param name="Compressibility"> <fill in your pressure property> </param>
            -->
        </struct>

        <struct name="densMelt_sediment">
            <param name="Type">Ppc_LinearDensityMelt</param>
            <param name="ReferenceDensity" units="kg*m^-3"> 2500 </param>

            <param name="Temperature"> temperature_ppc_wrapper </param>
            <param name="ReferenceTemperature" units="K"> 273.15 </param>
            <param name="ThermalExpansivity"> ThermalExpansivityProperty </param>

            <param name="MeltDensityChange"> MeltExpansionProperty </param>
            <param name="MeltFraction"> MeltFractionProperty </param>
        </struct>

        <struct name="densTemp_continental_upper_crust">
            <param name="Type">Ppc_LinearDensity</param>
            <param name="ReferenceDensity" units="kg*m^-3"> 2800 </param>

            <param name="Temperature"> temperature_ppc_wrapper </param>
            <param name="ReferenceTemperature" units="K"> 273.15 </param>
            <param name="ThermalExpansivity"> ThermalExpansivityProperty </param>
        </struct>

        <struct name="densMelt_continental_upper_crust">
            <param name="Type">Ppc_LinearDensityMelt</param>
            <param name="ReferenceDensity" units="kg*m^-3"> 2800 </param>

            <param name="Temperature"> temperature_ppc_wrapper </param>
            <param name="ReferenceTemperature" units="K"> 273.15 </param>
            <param name="ThermalExpansivity"> ThermalExpansivityProperty </param>

            <param name="MeltDensityChange"> MeltExpansionProperty </param>
            <param name="MeltFraction"> MeltFractionProperty </param>
        </struct>

        <struct name="densTemp_oceanic_crust">
            <param name="Type">Ppc_LinearDensity</param>
            <param name="ReferenceDensity" units="kg*m^-3"> 2900 </param>

            <param name="Temperature"> temperature_ppc_wrapper </param>
            <param name="ReferenceTemperature" units="K"> 273.15 </param>
            <param name="ThermalExpansivity"> ThermalExpansivityProperty </param>
        </struct>

        <struct name="densMelt_oceanic_crust">
            <param name="Type">Ppc_LinearDensityMelt</param>
            <param name="ReferenceDensity" units="kg*m^-3"> 2900 </param>

            <param name="Temperature"> temperature_ppc_wrapper </param>
            <param name="ReferenceTemperature" units="K"> 273.15 </param>
            <param name="ThermalExpansivity"> ThermalExpansivityProperty </param>

            <param name="MeltDensityChange"> MeltExpansionProperty </param>
            <param name="MeltFraction"> MeltFractionProperty </param>
        </struct>

        <struct name="densTemp_heavy_oceanic_crust">
            <param name="Type">Ppc_LinearDensity</param>
            <param name="ReferenceDensity" units="kg*m^-3"> 3200 </param>

            <param name="Temperature"> temperature_ppc_wrapper </param>
            <param name="ReferenceTemperature" units="K"> 273.15 </param>
            <param name="ThermalExpansivity"> ThermalExpansivityProperty </param>
        </struct>

        <struct name="densMelt_heavy_oceanic_crustt">
            <param name="Type">Ppc_LinearDensityMelt</param>
            <param name="ReferenceDensity" units="kg*m^-3"> 3200 </param>

            <param name="Temperature"> temperature_ppc_wrapper </param>
            <param name="ReferenceTemperature" units="K"> 273.15 </param>
            <param name="ThermalExpansivity"> ThermalExpansivityProperty </param>

            <param name="MeltDensityChange"> MeltExpansionProperty </param>
            <param name="MeltFraction"> MeltFractionProperty </param>
        </struct>
        <!-- ================================ -->


        <!-- === Lower crustal ============== -->
        <struct name="densTemp_continental_lower_crust">
            <param name="Type">Ppc_LinearDensity</param>
            <param name="ReferenceDensity" units="kg*m^-3"> 2900 </param>

            <param name="Temperature"> temperature_ppc_wrapper </param>
            <param name="ReferenceTemperature" units="K"> 273.15 </param>
            <param name="ThermalExpansivity"> ThermalExpansivityProperty </param>
        </struct>

        <struct name="densMelt_continental_lower_crust">
            <param name="Type">Ppc_LinearDensityMelt</param>
            <param name="ReferenceDensity" units="kg*m^-3"> 2900 </param>

            <param name="Temperature"> temperature_ppc_wrapper </param>
            <param name="ReferenceTemperature" units="K"> 273.15 </param>
            <param name="ThermalExpansivity"> ThermalExpansivityProperty </param>

            <param name="MeltDensityChange"> MeltExpansionProperty </param>
            <param name="MeltFraction"> MeltFractionProperty </param>
        </struct>
        <!-- ================================ -->


        <!-- === Lithospheric Mantle ======== -->
        <struct name="densTemp_continental_litho_mantle">
            <param name="Type">Ppc_LinearDensity</param>
            <param name="ReferenceDensity" units="kg*m^-3"> 3300 </param>

            <param name="Temperature"> temperature_ppc_wrapper </param>
            <param name="ReferenceTemperature" units="K"> 273.15 </param>
            <param name="ThermalExpansivity"> ThermalExpansivityProperty </param>
        </struct>

        <struct name="densMelt_continental_litho_mantle">
            <param name="Type">Ppc_LinearDensityMelt</param>
            <param name="ReferenceDensity" units="kg*m^-3"> 3300 </param>

            <param name="Temperature"> temperature_ppc_wrapper </param>
            <param name="ReferenceTemperature" units="K"> 273.15 </param>
            <param name="ThermalExpansivity"> ThermalExpansivityProperty </param>

            <param name="MeltDensityChange"> MeltExpansionProperty </param>
            <param name="MeltFraction"> MeltFractionProperty </param>
        </struct>
        <!-- ================================ -->


        <!-- === Asthenospheric ============= -->
        <struct name="densTemp_asthenosphere">
            <param name="Type">Ppc_LinearDensity</param>
            <param name="ReferenceDensity" units="kg*m^-3"> 3360 </param>

            <param name="Temperature"> temperature_ppc_wrapper </param>
            <param name="ReferenceTemperature" units="K"> 273.15 </param>
            <param name="ThermalExpansivity"> ThermalExpansivityProperty </param>
        </struct>

        <struct name="densMelt_asthenosphere">
            <param name="Type">Ppc_LinearDensityMelt</param>
            <param name="ReferenceDensity" units="kg*m^-3"> 3360 </param>

            <param name="Temperature"> temperature_ppc_wrapper </param>
            <param name="ReferenceTemperature" units="K"> 273.15 </param>
            <param name="ThermalExpansivity"> ThermalExpansivityProperty </param>

            <param name="MeltDensityChange"> MeltExpansionProperty </param>
            <param name="MeltFraction"> MeltFractionProperty </param>
        </struct>
        <!-- ================================ -->

        <!-- === End of Densities ================================================================== -->
        <!-- ======================================================================================= -->










        <!-- ======================================================================================= -->
        <!-- === Thermal Properties ================================================================ -->

        <!-- NOTE: Certain parameters are fairly simialr across most materials, so we can approximate
                   that they are all the same. To do this, we just define constants, which are called
                   "global_<parameter>", and apply them to multiple materials in lmrMaterials.xml. -->

        <struct name="global_diffusivity">
            <param name="Type">Ppc_Constant</param>
            <param name="Value" units="m*m/s"> 1e-6 </param>
        </struct>

        <struct name="global_cp">
            <!-- Heat capacity -->
            <param name="Type">Ppc_Constant</param>
            <param name="Value" units="J/(K*kg)"> 1000 </param>
        </struct>

        <struct name="global_expansivity">
            <!-- Thermal expansivity -->
            <param name="Type">Ppc_Constant</param>
            <param name="Value" units="K^-1"> 3e-5 </param>
        </struct>

        <struct name="latentHeat_crust">
            <!-- Latent heat of fusion -->
            <param name="Type">Ppc_Constant</param>
            <param name="Value" units="kJ*kg^-1"> 300.0 </param>
        </struct>

        <struct name="latentHeat_mantle">
            <!-- Latent heat of fusion -->
            <param name="Type">Ppc_Constant</param>
            <param name="Value" units="kJ*kg^-1"> 300.0 </param>
        </struct>

        <!-- === Radiogenic heat production ============= -->
        <!-- NOTE: This is the value for the actual heat production. It gets divided
                   by rho*cp in the lmrNumerics.xml, to calculate the energy added into
                   the system. -->
        <struct name="radiogenic_upper_crust">
            <!-- Derived from Hasterok and Chapman, EPSL, 2011 -->
            <param name="Type">Ppc_Constant</param>
            <param name="Value" units="W/(m*m*m)"> 1.2e-6 </param>
        </struct>

        <struct name="radiogenic_lower_crust">
            <!-- Derived from Hasterok and Chapman, EPSL, 2011 -->
            <param name="Type">Ppc_Constant</param>
            <param name="Value" units="W/(m*m*m)"> 0.6e-6 </param>
        </struct>

        <struct name="radiogenic_lithospheric_mantle">
            <!-- Derived from Hasterok and Chapman, EPSL, 2011 -->
            <param name="Type">Ppc_Constant</param>
            <param name="Value" units="W/(m*m*m)"> 0.02e-6 </param>
        </struct>

        <struct name="radiogenic_no_heating">
            <param name="Type">Ppc_Constant</param>
            <param name="Value" units="W/(m*m*m)"> 0.0 </param>
        </struct>
        <!-- ============================================ -->

        <!-- === End of Thermal Properties ========================================================= -->
        <!-- ======================================================================================= -->










        <!-- ======================================================================================= -->
        <!-- === Partial Melt Functions ============================================================ -->

        <!-- The fraction of density decrease due to melting -->
        <struct name="melt_crustal_density_decrease">
            <param name="Type"> Ppc_Constant </param>
            <param name="Value"> 0.13 </param>
        </struct>

        <struct name="melt_mantle_density_decrease">
            <param name="Type"> Ppc_Constant </param>
            <param name="Value"> 0.13 </param>
        </struct>


        <!-- NOTE: The following solidus/liquidus functions are defined as:
                   T = term0 + term1*p + term2*p^2 + term3*p^3
                   Where p is Pressure. -->
        <struct name="melt_crustal_solidus">
            <param name="Type"> Ppc_Melt_Polynomial </param>
            <param name="Pressure"> pressure_ppc_wrapper </param>
            <param name="term0" units="K"> 993.0 </param>
            <param name="term1"> -1.2e-7 </param>
            <param name="term2"> 1.2e-16 </param>
            <param name="term3"> 0.0 </param>
        </struct>
        <struct name="melt_crustal_liquidus">
            <param name="Type"> Ppc_Melt_Polynomial </param>
            <param name="Pressure"> pressure_ppc_wrapper </param>
            <param name="term0" units="K"> 1493.0 </param>
            <param name="term1"> -1.2e-7 </param>
            <param name="term2"> 1.6e-16 </param>
            <param name="term3"> 0.0 </param>
        </struct>

        <struct name="melt_mantle_solidus">
            <param name="Type"> Ppc_Melt_Polynomial </param>
            <param name="Pressure"> pressure_ppc_wrapper </param>
            <param name="term0" units="K"> 1393.661 </param>
            <param name="term1"> 1.32899e-7 </param>
            <param name="term2"> -5.104e-18 </param>
            <param name="term3"> 0.0 </param>
        </struct>
        <struct name="melt_mantle_liquidus">
            <param name="Type"> Ppc_Melt_Polynomial </param>
            <param name="Pressure"> pressure_ppc_wrapper </param>
            <param name="term0" units="K"> 2013.0 </param>
            <param name="term1"> 6.15e-8 </param>
            <param name="term2"> -3.12e-18 </param>
            <param name="term3"> 0.0 </param>
        </struct>

        <!-- NOTE: The meltFraction functions are defined as:
                   supersolidus = ( ( T - solidusT ) / ( liquidusT - solidusT ) ) - 0.5
                   meltFraction = 0.5 + supersolidus + ( supersolidus^2 -0.25 ) *
                                                       ( 0.4256 + 2.988 * supersolidus )
                   As per McKenzie and Bickle, 1988.

                   This has been modified as part of the EarthByte_Additions toolbox, so
                   the melt fraction can be artificially limited. -->
        <struct name="melt_fraction">
            <param name="Type">Ppc_PartialMelt_Limited</param>
            <param name="LiquidusTag"> LiquidusProperty </param>
            <param name="SolidusTag">  SolidusProperty </param>
            <param name="TemperatureTag"> temperature_ppc_wrapper </param>
            <param name="MeltLimitTag"> MeltFractionLimitProperty </param>
        </struct>

        <struct name="melt_max_fraction_crust">
            <!-- The maximum fraction of melt possible -->
            <param name="Type"> Ppc_Constant </param>
            <param name="Value"> 0.3 </param>
        </struct>
        <struct name="melt_max_fraction_mantle">
            <param name="Type"> Ppc_Constant </param>
            <param name="Value"> 0.08 </param>
        </struct>
        <struct name="melt_max_no_limit">
            <param name="Type"> Ppc_Constant </param>
            <param name="Value"> 1.0 </param>
        </struct>



        <!-- === End of Partial Melt Functions ===================================================== -->
        <!-- ======================================================================================= -->











        <!-- ======================================================================================= -->
        <!-- === Viscous Rheologies ================================================================ -->


        <!-- === Isoviscous  ========================================= -->
        <struct name="viscIso_air_1e18">
            <param name="Type">MaterialViscosity</param>
            <param name="eta0" units="Pa*s"> 1e+18 </param>
        </struct>

        <struct name="viscIso_upper_crust_1e23">
            <param name="Type">MaterialViscosity</param>
            <param name="eta0" units="Pa*s"> 1e+23 </param>
        </struct>

        <struct name="viscIso_asthenosphere_1e20">
            <param name="Type">MaterialViscosity</param>
            <param name="eta0" units="Pa*s"> 1e+20 </param>
        </struct>
        <!-- ========================================================= -->


        <!-- === Temperature dependent =============================== -->
        <!-- NOTE: Underworld uses this equation for FrankKamenetskii:
                viscosity = eta0 * exp( -theta * temperature )
            -->
        <struct name="viscTemp_upper_crust">
            <param name="Type">FrankKamenetskii</param>
            <param name="TemperatureField">TemperatureField</param>
            <param name="eta0" units="Pa*s">5.35e23</param>
            <param name="theta">0.00632</param>
        </struct>

        <struct name="viscTemp_weak_lower_crust">
            <param name="Type">FrankKamenetskii</param>
            <param name="TemperatureField">TemperatureField</param>
            <param name="eta0" units="Pa*s">5.35e22</param>
            <param name="theta">0.00632</param>
        </struct>

        <struct name="viscTemp_strong_litho_mantle">
            <param name="Type">FrankKamenetskii</param>
            <param name="TemperatureField">TemperatureField</param>
            <param name="eta0" units="Pa*s">1e25</param>
            <param name="theta">0.0045</param>
        </struct>
        <!-- ========================================================= -->


        <!-- === Strain-rate/temperature dependent  ================== -->
        <!-- NOTE: Underworld uses this equation for HKViscousCreep:

            viscosity = 0.5 * pow( A, -1.0/n ) *
                        pow( eII, 1.0/n -1.0 ) *
                        pow( d, p/n ) * pow( fH2O, -r/n ) *
                        exp( (E + P*V) / ( n * R * T)
                where:
                A is PreExponentialFactor,
                n is StressExponent,
                eII is strain-rate,
                d is GrainSize,
                p is GrainSizeExponent,
                fH2O is WaterFugacity,
                r is WaterFugacityExponent,
                E is ActivationEnergy,
                P is Pressure
                V is ActivationVolume,
                R is the gas constant,
                T is temperature
            -->
                <!-- === Upper crustal ====== -->
        <struct name="viscSRTdislocation_wet_quartzite_Goetze1978">
            <!-- Wet quartzite: Goetze, Philosophical Transactions of the Royal Society of London, 1978-->
            <param name="Type">HKViscousCreep</param>
            <param name="StrainRateInvariantField">StrainRateInvariantField</param>
            <param name="TemperatureField">TemperatureField</param>
            <param name="PressureField">PressureField</param>

            <param name="StressExponent">3</param>
            <param name="PreExponentialFactor" units="(MPa)^-3*s^-1">5e-06</param>
            <param name="DefaultStrainRateInvariant" units="s^-1">1.0e-15</param>

            <param name="ActivationEnergy" units="kJ/mol">190</param>
            <param name="ActivationVolume" units="m^3/mol"> 0.0</param>
        </struct>

        <struct name="viscSRTdislocation_dry_quartz_Koch1983">
            <!-- Dry quartz: Koch, PhD thesis, 1983-->
            <param name="Type">HKViscousCreep</param>
            <param name="StrainRateInvariantField">StrainRateInvariantField</param>
            <param name="TemperatureField">TemperatureField</param>
            <param name="PressureField">PressureField</param>

            <param name="StressExponent">3</param>
            <param name="PreExponentialFactor" units="(Pa)^-3*s^-1">5e-25</param>
            <param name="DefaultStrainRateInvariant" units="s^-1">1.0e-15</param>

            <param name="ActivationEnergy" units="kJ/mol">149</param>
            <param name="ActivationVolume" units="m^3/mol"> 0.0</param>
        </struct>

        <struct name="viscSRTdislocation_wet_quartz_Kronenberg1984">
            <!-- Wet quartz: Kronenberg and Tullis, JGR, 1984-->
            <param name="Type">HKViscousCreep</param>
            <param name="StrainRateInvariantField">StrainRateInvariantField</param>
            <param name="TemperatureField">TemperatureField</param>
            <param name="PressureField">PressureField</param>

            <param name="StressExponent">2.4</param>
            <param name="PreExponentialFactor" units="(Pa)^-2.4*s^-1">1.3e-20</param>
            <param name="DefaultStrainRateInvariant" units="s^-1">1.0e-15</param>

            <param name="ActivationEnergy" units="kJ/mol">134</param>
            <param name="ActivationVolume" units="m^3/mol"> 0.0</param>
        </struct>

        <struct name="viscSRTdislocation_wet_quartzite_Paterson1990">
            <!-- Wet quartzite: Paterson and Luan, GeoSoc London SP, 1990-->
            <param name="Type">HKViscousCreep</param>
            <param name="StrainRateInvariantField">StrainRateInvariantField</param>
            <param name="TemperatureField">TemperatureField</param>
            <param name="PressureField">PressureField</param>

            <param name="StressExponent">3.1</param>
            <param name="PreExponentialFactor" units="(MPa)^-3.1*s^-1">6.60693448e-8</param>
            <param name="DefaultStrainRateInvariant" units="s^-1">1.0e-15</param>

            <param name="ActivationEnergy" units="kJ/mol">135</param>
            <param name="ActivationVolume" units="m^3/mol"> 0.0</param>
        </struct>


        <!-- === Lower crustal ====== -->
        <struct name="viscSRTdislocation_dry_mafic_granulite_Wang2012">
            <!-- Dry Mafic granulite: Wang et al., EPSL 2012 -->
            <param name="Type">HKViscousCreep</param>
            <param name="StrainRateInvariantField">StrainRateInvariantField</param>
            <param name="TemperatureField">TemperatureField</param>
            <param name="PressureField">PressureField</param>

            <param name="StressExponent">3.2</param>
            <param name="PreExponentialFactor" units="(MPa)^-3.2*s^-1">10e-2</param>
            <param name="DefaultStrainRateInvariant" units="s^-1">1.0e-15</param>

            <param name="ActivationEnergy" units="kJ/mol">244</param>
            <param name="ActivationVolume" units="m^3/mol"> 0.0</param>
        </struct>

        <struct name="viscSRTdislocation_dry_diabase_Mackwell1998">
            <!-- Dry diabase : Mackwell et al., JGR 1998 -->
            <param name="Type">HKViscousCreep</param>
            <param name="StrainRateInvariantField">StrainRateInvariantField</param>
            <param name="TemperatureField">TemperatureField</param>
            <param name="PressureField">PressureField</param>

            <param name="StressExponent">4.7</param>
            <param name="PreExponentialFactor" units="(MPa)^-4.7*s^-1">8</param>
            <param name="DefaultStrainRateInvariant" units="s^-1">1.0e-15</param>

            <param name="ActivationEnergy" units="kJ/mol">485</param>
            <param name="ActivationVolume" units="m^3/mol"> 0.0</param>
        </struct>

        <struct name="viscSRTdislocation_wet_anorthite_Rybacki2000">
            <!--  Wet anorthite dislocation: Rybacki, JGR, 2000 -->
            <param name="Type">HKViscousCreep</param>
            <param name="StrainRateInvariantField">StrainRateInvariantField</param>
            <param name="TemperatureField">TemperatureField</param>
            <param name="PressureField">PressureField</param>

            <param name="StressExponent">3.0</param>
            <param name="PreExponentialFactor" units="(Pa)^-3.0*s^-1">3.9810717e-16</param>
            <param name="DefaultStrainRateInvariant" units="s^-1">1.0e-15</param>

            <param name="ActivationEnergy" units="kJ/mol">356</param>
            <param name="ActivationVolume" units="m^3/mol"> 0.0</param>
        </struct>




        <!-- === Lithospheric mantle ====== -->
        <struct name="viscSRTdislocation_wet_dunite_Brace1980">
            <!-- Wet Dunite : Brace and Kohlstedt, JGR 1980-->
            <param name="Type">HKViscousCreep</param>
            <param name="StrainRateInvariantField">StrainRateInvariantField</param>
            <param name="TemperatureField">TemperatureField</param>
            <param name="PressureField">PressureField</param>

            <param name="StressExponent">3</param>
            <param name="PreExponentialFactor" units="(MPa)^-3*s^-1">7.0e4</param>
            <param name="DefaultStrainRateInvariant" units="s^-1">1.0e-15</param>

            <param name="ActivationEnergy" units="kJ/mol">520</param>
            <param name="ActivationVolume" units="m^3/mol"> 0.0</param>
        </struct>

        <struct name="viscSRTdislocation_dry_olivine_Korenaga2008">
            <!-- Dry Olivine : Korenaga and Karato, JGR 2008 -->
            <param name="Type">HKViscousCreep</param>
            <param name="StrainRateInvariantField">StrainRateInvariantField</param>
            <param name="TemperatureField">TemperatureField</param>
            <param name="PressureField">PressureField</param>

            <param name="StressExponent">4.94</param>
            <param name="PreExponentialFactor" units="(MPa)^-4.94*s^-1">10e6.09</param>
            <param name="DefaultStrainRateInvariant" units="s^-1">1.0e-15</param>

            <param name="ActivationEnergy" units="kJ/mol">610</param>
            <param name="ActivationVolume" units="m^3/mol"> 0.0</param>
        </struct>

        <struct name="viscSRTdislocation_olivine_Kirby1987">
            <!-- Olivine : Kirby and Kronenberg, Review of Geophysics 1987 -->
            <param name="Type">HKViscousCreep</param>
            <param name="StrainRateInvariantField">StrainRateInvariantField</param>
            <param name="TemperatureField">TemperatureField</param>
            <param name="PressureField">PressureField</param>

            <param name="StressExponent">3</param>
            <param name="PreExponentialFactor" units="Pa^-3*s^-1">1e-15</param>
            <param name="DefaultStrainRateInvariant" units="s^-1">1.0e-15</param>

            <param name="ActivationEnergy" units="kJ/mol">500</param>
            <param name="ActivationVolume" units="m^3/mol"> 0.0</param>
        </struct>

        <struct name="viscSRTdislocation_diffusion_dry_olivine_Hirth2003">
            <!-- Hirth and Kohlstedt, Geophysical Monograph 2003
                 as per Brune, Nat. Commun. 2014 -->
            <param name="Type"> ViscousCreep </param>
            <param name="StrainRateInvariantField"> StrainRateInvariantField </param>
            <param name="TemperatureField"> TemperatureField </param>
            <param name="PressureField"> PressureField </param>

            <param name="enable_limit_eta"> False </param>
            <param name="max_limit_eta" units="Pa*s"> 0 </param>
            <param name="min_limit_eta" units="Pa*s"> 0 </param>

            <param name="GrainSize"> 10000 </param>
            <param name="shear_modulus" units="Pa"> 1 </param>
            <param name="burgers_vector" units="m"> 1 </param>
            <param name="DefaultStrainRateInvariant" units="s^-1"> 5.370318e-16 </param>

            <param name="enable_diffusion"> True </param>
            <param name="diffusion_material_constant" units="s^-1"> 2.23872114e-9 </param>
            <param name="diffusion_activation_energy" units="kJ*mol^-1"> 375 </param>
            <param name="diffusion_activation_volume" units="m^3*mol^-1"> 6e-6 </param>
            <param name="diffusion_grainsize_exponent"> 0 </param>

            <param name="enable_dislocation"> True </param>
            <param name="dislocation_material_constant" units="s^-1"> 2.7542287e-16 </param>
            <param name="dislocation_activation_energy" units="kJ*mol^-1"> 530 </param>
            <param name="dislocation_activation_volume" units="m^3*mol^-1"> 13e-6 </param>
            <param name="dislocation_stress_exponent">3.5</param>
            <param name="dislocation_grainsize_exponent">0</param>

            <param name="enable_peierls">False</param>
        </struct>

        <struct name="viscSRTdislocation_dry_olivine_Hirth2003">
            <!-- Hirth and Kohlstedt, Geophysical Monograph 2003 -->
            <param name="Type">HKViscousCreep</param>
            <param name="StrainRateInvariantField">StrainRateInvariantField</param>
            <param name="TemperatureField">TemperatureField</param>
            <param name="PressureField">PressureField</param>
            <param name="GrainSize"> 10000 </param>

            <param name="GrainSizeExponent"> 0.0 </param>
            <param name="WaterFugacityExponent"> 0 </param>
            <param name="StressExponent"> 3.5 </param>
            <param name="PreExponentialFactor" units="(MPa)^-3.5*s^-1">1.1e5</param>
            <param name="DefaultStrainRateInvariant" units="s^-1">1.0e-15</param>

            <param name="ActivationEnergy" units="kJ/mol">530</param>
            <param name="ActivationVolume" units="m^3/mol">6e-6</param>
        </struct>

        <struct name="viscSRTdiffusion_dry_olivine_Hirth2003">
            <!-- Hirth and Kohlstedt, Geophysical Monograph 2003 -->
            <param name="Type">HKViscousCreep</param>
            <param name="StrainRateInvariantField">StrainRateInvariantField</param>
            <param name="TemperatureField">TemperatureField</param>
            <param name="PressureField">PressureField</param>
            <param name="GrainSize"> 10000 </param>
            <param name="WaterFugacity"> 1000 </param>

            <param name="GrainSizeExponent"> 3.0 </param>
            <param name="WaterFugacityExponent"> 0 </param>
            <param name="StressExponent"> 1.0 </param>
            <param name="PreExponentialFactor" units="(MPa)^-1*s^-1"> 1.5e9 </param>
            <param name="DefaultStrainRateInvariant" units="s^-1">1.0e-15</param>

            <param name="ActivationEnergy" units="kJ/mol">375</param>
            <param name="ActivationVolume" units="m^3/mol">6e-6</param>
        </struct>

        <struct name="viscSRTdislocation_diffusion_wet_olivine_Hirth2003">
            <!-- Hirth and Kohlstedt, Geophysical Monograph 2003
                 as per Brune, Nat. Commun. 2014 -->
            <param name="Type"> ViscousCreep </param>
            <param name="StrainRateInvariantField"> StrainRateInvariantField </param>
            <param name="TemperatureField"> TemperatureField </param>
            <param name="PressureField"> PressureField </param>

            <param name="enable_limit_eta"> False </param>
            <param name="max_limit_eta" units="Pa*s"> 0 </param>
            <param name="min_limit_eta" units="Pa*s"> 0 </param>

            <param name="GrainSize"> 10000 </param>
            <param name="shear_modulus" units="Pa"> 1 </param>
            <param name="burgers_vector" units="m"> 1 </param>
            <param name="DefaultStrainRateInvariant" units="s^-1"> 5.370318e-16 </param>

            <param name="enable_diffusion"> True </param>
            <param name="diffusion_material_constant" units="s^-1"> 2.18776162e-9 </param>
            <param name="diffusion_activation_energy" units="kJ*mol^-1"> 335 </param>
            <param name="diffusion_activation_volume" units="m^3*mol^-1"> 4e-6 </param>
            <param name="diffusion_grainsize_exponent"> 0 </param>

            <param name="enable_dislocation"> True </param>
            <param name="dislocation_material_constant" units="s^-1"> 8.9125094e-16 </param>
            <param name="dislocation_activation_energy" units="kJ*mol^-1"> 480 </param>
            <param name="dislocation_activation_volume" units="m^3*mol^-1"> 10e-6 </param>
            <param name="dislocation_stress_exponent">3.5</param>
            <param name="dislocation_grainsize_exponent">0</param>

            <param name="enable_peierls">False</param>
        </struct>

        <struct name="viscSRTdislocation_wet_olivine_Hirth2003">
            <!-- Hirth and Kohlstedt, Geophysical Monograph 2003 -->
            <param name="Type">HKViscousCreep</param>
            <param name="StrainRateInvariantField">StrainRateInvariantField</param>
            <param name="TemperatureField">TemperatureField</param>
            <param name="PressureField">PressureField</param>
            <param name="GrainSize"> 10000 </param>
            <param name="WaterFugacity"> 1000 </param>

            <param name="GrainSizeExponent"> 0.0 </param>
            <param name="WaterFugacityExponent"> 1.2 </param>
            <param name="StressExponent"> 3.5 </param>
            <param name="PreExponentialFactor" units="(MPa)^-3.5*s^-1"> 1600 </param>
            <param name="DefaultStrainRateInvariant" units="s^-1">1.0e-15</param>

            <param name="ActivationEnergy" units="kJ/mol">520</param>
            <param name="ActivationVolume" units="m^3/mol">23e-6</param>
        </struct>

        <struct name="viscSRTdiffusion_wet_olivine_Hirth2003">
            <!-- Hirth and Kohlstedt, Geophysical Monograph 2003 -->
            <param name="Type">HKViscousCreep</param>
            <param name="StrainRateInvariantField">StrainRateInvariantField</param>
            <param name="TemperatureField">TemperatureField</param>
            <param name="PressureField">PressureField</param>
            <param name="GrainSize"> 10000 </param>
            <param name="WaterFugacity"> 1000 </param>

            <param name="GrainSizeExponent"> 3.0 </param>
            <param name="WaterFugacityExponent"> 1.0 </param>
            <param name="StressExponent"> 1.0 </param>
            <param name="PreExponentialFactor" units="(MPa)^-1*s^-1"> 2.5e7 </param>
            <param name="DefaultStrainRateInvariant" units="s^-1">1.0e-15</param>

            <param name="ActivationEnergy" units="kJ/mol">375</param>
            <param name="ActivationVolume" units="m^3/mol">10e-6</param>
        </struct>

        <struct name="viscSRTdiffusion_wet_olivine_Faul2007">
            <!-- Faul and Jackson, JGR 2007 -->
            <param name="Type">HKViscousCreep</param>
            <param name="StrainRateInvariantField">StrainRateInvariantField</param>
            <param name="TemperatureField">TemperatureField</param>
            <param name="PressureField">PressureField</param>
            <param name="GrainSize"> 5 </param>
            <param name="WaterFugacity"> 1000 </param>

            <param name="GrainSizeExponent"> 3.0 </param>
            <param name="WaterFugacityExponent"> 0.0 </param>
            <param name="StressExponent"> 1.3 </param>
            <param name="PreExponentialFactor" units="(MPa)^-1.3*s^-1"> 2.0e10 </param>
            <param name="DefaultStrainRateInvariant" units="s^-1">1.0e-15</param>

            <param name="ActivationEnergy" units="kJ/mol">484</param>
            <param name="ActivationVolume" units="m^3/mol">0</param>
        </struct>

        <struct name="viscSRTdislocation_dry_olivine_Petersen2010">
            <!--Petersen et al., Science 2010 -->
            <param name="Type">HKViscousCreep</param>
            <param name="StrainRateInvariantField">StrainRateInvariantField</param>
            <param name="TemperatureField">TemperatureField</param>
            <param name="PressureField">PressureField</param>

            <param name="StressExponent"> 3.5 </param>
            <param name="PreExponentialFactor" units="Pa^-3.5*s^-1"> 2.41e-16 </param>
            <param name="DefaultStrainRateInvariant" units="s^-1">1.0e-15</param>

            <param name="ActivationEnergy" units="kJ/mol">540</param>
            <param name="ActivationVolume" units="m^3/mol">15e-6</param>
        </struct>

        <struct name="viscSRTdiffusion_dry_olivine_Petersen2010">
            <!--Petersen et al., Science 2010 -->
            <param name="Type">HKViscousCreep</param>
            <param name="StrainRateInvariantField">StrainRateInvariantField</param>
            <param name="TemperatureField">TemperatureField</param>
            <param name="PressureField">PressureField</param>

            <param name="StressExponent"> 1.0 </param>
            <param name="PreExponentialFactor" units="Pa^-1.0*s^-1"> 1.49e-9 </param>
            <param name="DefaultStrainRateInvariant" units="s^-1">1.0e-15</param>

            <param name="ActivationEnergy" units="kJ/mol">300</param>
            <param name="ActivationVolume" units="m^3/mol">6e-6</param>
        </struct>




        <!-- === Melts =============================================== -->
        <!-- NOTE: Melting is applied to an existing viscous rheology, and is calculated as such:
             aux = 1.0 + (meltFraction - lowerlimit) / (lowerlimit - upperlimit)
             meltVisc = viscosity * (1 * aux + max_linear_decrease * (1 - aux) )
        -->
        <struct name="viscMelt_crustal_Hirth2003">
            <!-- Crustal melt : Hirth and Kohlstedt, Geophysical Monograph 2003 -->
            <param name="Type">MeltViscosity</param>
            <param name="MeltFraction">MeltFractionProperty</param>
            <param name="MeltFraction_LowerLimit">0.20</param>
            <param name="MeltFraction_UpperLimit">0.30</param>
            <param name="max_linear_decrease">1e-3</param>
        </struct>

        <struct name="viscMelt_mantle_Hirth2003">
            <!-- Mantle melt : Hirth and Kohlstedt, Geophysical Monograph 2003 -->
            <param name="Type">MeltViscosity</param>
            <param name="MeltFraction">MeltFractionProperty</param>
            <param name="MeltFraction_LowerLimit">0.03</param>
            <param name="MeltFraction_UpperLimit">0.08</param>
            <param name="max_linear_decrease">1e-2</param>
        </struct>
        <!-- ========================================================= -->

        <!-- === End of Viscous Rheologies ========================================================= -->
        <!-- ======================================================================================= -->







        <!-- ======================================================================================= -->
        <!-- === Yielding Rheologies =============================================================== -->

        <!-- === Strain weakening =========================== -->
        <struct name="strainWeakening">
            <!-- NOTE: strain weakening allows "faults" to become mechanically weaker as they become
                       damaged. As strain is accumulated, yielding rheologies linearly interpolate
                       between their original values (e.g., cohesion) to their damaged values (e.g.,
                       cohesionAfterSoftening). softeningStrain defines the percentage of strain that
                       a material is fully weakened.
            -->
            <param name="Type">StrainWeakening</param>
            <param name="TimeIntegrator">timeIntegrator</param>
            <param name="MaterialPointsSwarm">materialSwarm</param>
            <param name="softeningStrain">0.2</param>
            <!-- Pecentage until fully softened. E.g. 0.2 = 20% strain -->
            <param name="initialDamageFraction">0.0</param>
            <param name="initialDamageWavenumber">2e-6</param>
            <param name="initialDamageFactor">0.7</param>
            <param name="healingRate">0</param>
        </struct>
        <!-- ================================================ -->


        <!-- === Upper crustal ====== -->
        <struct name="yield_upper_crust_Rey2010">
            <!-- Upper-crust : Rey and Muller, Nature 2010 -->
            <param name="Type">DruckerPrager</param>
            <param name="PressureField">PressureField</param>
            <param name="MaterialPointsSwarm">materialSwarm</param>
            <param name="StrainRateField">StrainRateField</param>
            <param name="StrainWeakening">strainWeakening</param>

            <param name="cohesion" units="MPa">10</param>
            <param name="cohesionAfterSoftening" units="MPa">2</param>
            <param name="frictionCoefficient">0.577</param>
            <param name="frictionCoefficientAfterSoftening">0.1154</param>
        </struct>

        <struct name="yield_upper_crust_Rey2014">
            <!-- Upper-crust : Rey, Coltice, and Flament;, Nature 2014 -->
            <param name="Type">DruckerPrager</param>
            <param name="PressureField">PressureField</param>
            <param name="MaterialPointsSwarm">materialSwarm</param>
            <param name="StrainRateField">StrainRateField</param>
            <param name="StrainWeakening">strainWeakening</param>

            <param name="cohesion" units="MPa"> 10 </param>
            <param name="cohesionAfterSoftening" units="MPa"> 0.4 </param>
            <param name="frictionCoefficient"> 0.577 </param>
            <param name="frictionCoefficientAfterSoftening"> 0.02308 </param>
        </struct>


        <struct name="yield_upper_crust_stronger">
            <param name="Type">DruckerPrager</param>
            <param name="PressureField">PressureField</param>
            <param name="MaterialPointsSwarm">materialSwarm</param>
            <param name="StrainRateField">StrainRateField</param>
            <param name="StrainWeakening">strainWeakening</param>

            <param name="cohesion" units="MPa">40</param>
            <param name="cohesionAfterSoftening" units="MPa">4</param>
            <param name="frictionCoefficient">0.577</param>
            <param name="frictionCoefficientAfterSoftening">0.0577</param>
        </struct>


        <!-- === Lower crustal ====== -->
        <struct name="yield_lower_crust_Rey2010">
            <!-- Lower-crust : Rey and Muller, Nature 2010 -->
            <param name="Type">DruckerPrager</param>
            <param name="PressureField">PressureField</param>
            <param name="MaterialPointsSwarm">materialSwarm</param>
            <param name="StrainRateField">StrainRateField</param>
            <param name="StrainWeakening">strainWeakening</param>

            <param name="cohesion" units="MPa">20</param>
            <param name="cohesionAfterSoftening" units="MPa">4</param>
            <param name="frictionCoefficient">0.577</param>
            <param name="frictionCoefficientAfterSoftening">0.1154</param>
        </struct>

        <struct name="yield_lower_crust_Rey2014">
            <!-- Lower-crust : Rey, Coltice and Flament, Nature 2014 -->
            <param name="Type">DruckerPrager</param>
            <param name="PressureField">PressureField</param>
            <param name="MaterialPointsSwarm">materialSwarm</param>
            <param name="StrainRateField">StrainRateField</param>
            <param name="StrainWeakening">strainWeakening</param>

            <param name="cohesion" units="MPa"> 20 </param>
            <param name="cohesionAfterSoftening" units="MPa"> 0.8 </param>
            <param name="frictionCoefficient"> 0.577 </param>
            <param name="frictionCoefficientAfterSoftening"> 0.02308 </param>
        </struct>


        <struct name="yield_lower_crust_stronger">
            <param name="Type">DruckerPrager</param>
            <param name="PressureField">PressureField</param>
            <param name="MaterialPointsSwarm">materialSwarm</param>
            <param name="StrainRateField">StrainRateField</param>
            <param name="StrainWeakening">strainWeakening</param>

            <param name="cohesion" units="MPa">60</param>
            <param name="cohesionAfterSoftening" units="MPa">6</param>
            <param name="frictionCoefficient">0.288</param>
            <param name="frictionCoefficientAfterSoftening">0.0288</param>
        </struct>


        <!-- === Lithospheric ======= -->
        <struct name="yield_litho_mantle_Rey2010">
            <!-- Lithospheric mantle : Rey and Muller, Nature 2010 -->
            <param name="Type">DruckerPrager</param>
            <param name="PressureField">PressureField</param>
            <param name="MaterialPointsSwarm">materialSwarm</param>
            <param name="StrainRateField">StrainRateField</param>
            <param name="StrainWeakening">strainWeakening</param>

            <param name="cohesion" units="MPa">10</param>
            <param name="cohesionAfterSoftening" units="MPa">2</param>
            <param name="frictionCoefficient">0.577</param>
            <param name="frictionCoefficientAfterSoftening">0.1154</param>
        </struct>

        <struct name="yield_litho_mantle_Rey2014">
            <!-- Lithospheric mantle : Rey, Coltice, and Flament, Nature 2014 -->
            <param name="Type">DruckerPrager</param>
            <param name="PressureField">PressureField</param>
            <param name="MaterialPointsSwarm">materialSwarm</param>
            <param name="StrainRateField">StrainRateField</param>
            <param name="StrainWeakening">strainWeakening</param>

            <param name="cohesion" units="MPa">10</param>
            <param name="cohesionAfterSoftening" units="MPa"> 0.4 </param>
            <param name="frictionCoefficient"> 0.577 </param>
            <param name="frictionCoefficientAfterSoftening"> 0.02308 </param>
        </struct>

        <struct name="yield_litho_mantle_Watremez2013">
            <!-- Lithospheric mantle : Watremex et. al., G^3 2013 -->
            <param name="Type">DruckerPrager</param>
            <param name="PressureField">PressureField</param>
            <param name="MaterialPointsSwarm">materialSwarm</param>
            <param name="StrainRateField">StrainRateField</param>

            <param name="cohesion" units="MPa">300</param>
            <param name="frictionCoefficient">0.0349</param>
        </struct>


        <!-- === Stress limiters ======= -->
        <struct name="stressLimiter_simple_300MPa">
            <!-- Simple stress limiter
                 Calculates sigma = 2*eta*epsilon,
                 where sigma = stress, eta = visc, and epsilon = strain-rate.
                 If sigma is > maxYieldStress, then the viscosity is set
                 to maxYieldStress/(2*epsilon) -->
            <param name="Type"> SimpleStressLimiter </param>
            <param name="StrainRateInvariantField"> StrainRateInvariantField </param>
            <param name="maxYieldStress" units="MPa"> 150 </param>
            <param name="referenceStrainRate" units="s^-1"> 1e-15 </param>
        </struct>

        <struct name="stressLimiter_vonmises_300MPa">
            <param name="Type"> VonMises </param>
            <param name="MaterialPointsSwarm"> materialSwarm </param>
            <param name="StrainRateField"> StrainRateField </param>
            <param name="strainRateSoftening"> False </param>

            <param name="cohesion" units="MPa"> 150 </param>
        </struct>

        <struct name="stressLimiter_vonmises_400MPa">
            <param name="Type"> VonMises </param>
            <param name="MaterialPointsSwarm"> materialSwarm </param>
            <param name="StrainRateField"> StrainRateField </param>
            <param name="strainRateSoftening"> False </param>

            <param name="cohesion" units="MPa"> 200 </param>
        </struct>

        <struct name="stressLimiter_vonmises_500MPa">
            <param name="Type"> VonMises </param>
            <param name="MaterialPointsSwarm"> materialSwarm </param>
            <param name="StrainRateField"> StrainRateField </param>
            <param name="strainRateSoftening"> False </param>

            <param name="cohesion" units="MPa"> 250 </param>
        </struct>

        <struct name="stressLimiter_vonmises_600MPa">
            <param name="Type"> VonMises </param>
            <param name="MaterialPointsSwarm"> materialSwarm </param>
            <param name="StrainRateField"> StrainRateField </param>
            <param name="strainRateSoftening"> False </param>

            <param name="cohesion" units="MPa"> 300 </param>
            <param name="minimumViscosity" units="Pa*s"> 1e+19 </param>
        </struct>

        <struct name="stressLimiter_vanHunen_300MPa">
            <!-- van Hunen et. al., Tectonophysics, 2002
                 max viscosity = yieldStress *
                                 referenceStrainRate^(-1/powerlawIndex) *
                                 eII^((1/powerlawIndex)-1)
             -->
            <param name="Type"> vanHunenStressLimiter </param>
            <param name="StrainRateInvariantField"> StrainRateInvariantField </param>
            <param name="yieldStress" units="MPa"> 300 </param>
            <param name="powerlawIndex"> 5.0 </param>
            <param name="referenceStrainRate" units="s^-1"> 1e-15 </param>
        </struct>

        <!-- === End of Yielding Rheologies ======================================================== -->
        <!-- ======================================================================================= -->


    </struct>
</StGermainData>