Fix rheology in continental extension (WIP)

cookbooks/continental_extension/continental_extension.prm

@@ -294,8 +294,8 @@ subsection Material model
     # values below, relative to previous versions of the cookbook, are now consistent with the correct
     # scaling procedure outlined in Dannberg et al. (2017).
     set Prefactors for dislocation creep          = background: 7.37e-15, \
-                                                    crust_upper: 1.37e-26, \
-                                                    crust_lower: 5.71e-23, \
+                                                    crust_upper: 8.57e-28, \
+                                                    crust_lower: 7.13e-18, \
                                                     mantle_lithosphere: 7.37e-15
 
     set Stress exponents for dislocation creep    = background: 3.5, \

cookbooks/continental_extension/continental_extension_rheology.ipynb

@@ -0,0 +1,165 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "956323c4",
+   "metadata": {},
+   "source": [
+    "# Conversion of Continental Material Flow-Law Prefactors from Experiments to ASPECT"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "a1c36c8f",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a45a578c",
+   "metadata": {},
+   "source": [
+    "# Wet Quartzite from Gleason and Tullis (1995)\n",
+    "\n",
+    "The total conversion factor includes two parts.\n",
+    "\n",
+    "First, the factor change due to unit conversion from the experimental formulation  \n",
+    "($\\mu$m → m and MPa → Pa):\n",
+    "\n",
+    "$$\n",
+    "F_{\\text{unit}} = 10^{-6n - 6p}\n",
+    "$$\n",
+    "\n",
+    "Second, the factor change due to the use of **shear strain rate** in the experiments\n",
+    "versus the **second invariant of the strain rate tensor** used in ASPECT:\n",
+    "\n",
+    "$$\n",
+    "F_{s} = \\frac{3^{\\frac{n+1}{2}}}{2}\n",
+    "$$\n",
+    "\n",
+    "Here, $n$ is the reported stress exponent and $p$ is the reported grain-size exponent.\n",
+    "\n",
+    "The prefactor used in ASPECT and the experimental prefactor are therefore related by\n",
+    "\n",
+    "$$\n",
+    "A_{\\text{ASPECT}} = F_{\\text{unit}} \\, F_{s} \\, A_{\\text{exp}}\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "ae6c84d6",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "\n",
+    "# Gleason and Tullis (1995) - Wet Quartzite - Dislocation Creep\n",
+    "pfct_gt95_wqtz_disl_rprt = 1.1e-4 # Original reported prefactor in units of MPa^-n micrometers^m\n",
+    "sexp_gt95_wqtz_disl_rprt = 4.0    # Original reported stress exponent\n",
+    "gexp_gt95_wqtz_disl_rprt = 0      # Original reported grain size exponent\n",
+    "\n",
+    "# Convert prefactor to units of Pa^-n meters^m s^-1\n",
+    "pfct_gt95_wqtz_disl_unit = (pfct_gt95_wqtz_disl_rprt) * \\\n",
+    "                           (1.e-6**sexp_gt95_wqtz_disl_rprt) * \\\n",
+    "                           (1.e-6**gexp_gt95_wqtz_disl_rprt)\n",
+    "\n",
+    "# Calculate prefactor scaling term\n",
+    "pfct_gt95_wqtz_disl_sfac = 3.**((sexp_gt95_wqtz_disl_rprt+1.)/2.) / 2\n",
+    "\n",
+    "\n",
+    "# Calculated modified prefactor term for ASPECT\n",
+    "pfct_gt95_wqtz_disl_aspt = pfct_gt95_wqtz_disl_unit * pfct_gt95_wqtz_disl_sfac\n",
+    "\n",
+    "print('')\n",
+    "print('Gleason and Tullis (1995) Wet Quarzite Dislocation Prefactor Scaling = ', pfct_gt95_wqtz_disl_sfac)\n",
+    "print('Gleason and Tullis (1995) Wet Quarzite Dislocation Prefactor ASPECT  = ', pfct_gt95_wqtz_disl_aspt)\n",
+    "print('')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "0c0bc1b5",
+   "metadata": {},
+   "source": [
+    "# Wet Anorthite from Rybacki et al. (2006)\n",
+    "\n",
+    "This study uses **water fugacity** explicitly in the original flow law formulation.  \n",
+    "Therefore, we need to include an additional factor associated with the water fugacity term.  \n",
+    "The simplest approach is to assume a constant water fugacity:\n",
+    "\n",
+    "$$\n",
+    "F_{H_2O} = f_{H_2O}^{\\,r}\n",
+    "$$\n",
+    "\n",
+    "Here, $f_{H_2O}$ is the water fugacity, taken as a constant value of **1 MPa**, and $r$ is the reported water fugacity exponent.\n",
+    "\n",
+    "The other two factors have the same formulation as in the previous case.  \n",
+    "Therefore, the prefactor used in ASPECT and the experimental prefactor are related by\n",
+    "\n",
+    "$$\n",
+    "A_{\\text{ASPECT}} = F_{H_2O} \\, F_{\\text{unit}} \\, F_s \\, A_{\\text{exp}}\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "336177d6",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Rybacki et al. (2006) - Wet Anorthite - Dislocation Creep\n",
+    "pfct_ry06_want_disl_rprt = 10.**(0.2) # Original reported log(prefactor) in units of MPa^(-n-r) micrometers^m\n",
+    "sexp_ry06_want_disl_rprt = 3.0        # Original reported stress exponent\n",
+    "gexp_ry06_want_disl_rprt = 0          # Original reported grain size exponent\n",
+    "wfug_ry06_want_disl_rprt = 1          # Original reported water fugacity\n",
+    "constant_fug = 1 # 1MPa\n",
+    "\n",
+    "# Convert prefactor to units of Pa^(-n-r) meters^m s^-1\n",
+    "pfct_ry06_want_disl_unit = pfct_ry06_want_disl_rprt * \\\n",
+    "                           (1.e-6**(sexp_ry06_want_disl_rprt)) * \\\n",
+    "                           (1.e-6**gexp_ry06_want_disl_rprt)\n",
+    "\n",
+    "# Calculate water fugacity term\n",
+    "pfct_ry06_want_disl_ffac = constant_fug**wfug_ry06_want_disl_rprt\n",
+    "\n",
+    "# Calculate prefactor scaling term\n",
+    "pfct_ry06_want_disl_sfac = 3.**((sexp_ry06_want_disl_rprt+1.)/2.) / 2.0\n",
+    "\n",
+    "# Calculated modified prefactor term for ASPECT\n",
+    "pfct_ry06_want_disl_aspt = pfct_ry06_want_disl_ffac * pfct_ry06_want_disl_unit * pfct_ry06_want_disl_sfac\n",
+    "\n",
+    "print('')\n",
+    "print('Rybacki et al. (2006) Wet Anorthite Dislocation Prefactor Scaling = ', pfct_ry06_want_disl_sfac)\n",
+    "print('Rybacki et al. (2006) Wet Anorthite Dislocation Prefactor ASPECT  = ', pfct_ry06_want_disl_aspt)\n",
+    "print('')"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "hmgeolib",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.9.23"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}