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   "source": [
    "# Calculate frictional slopes (part 3): The Anderson model\n",
    "\n",
    "Copyright 2022 Marco A. Lopez-Sanchez.  \n",
    "Content under [Creative Commons Attribution license CC-BY 4.0](https://creativecommons.org/licenses/by/4.0/), code under [Mozilla Public License 2.0](https://www.mozilla.org/en-US/MPL/2.0/).\n",
    "\n",
    "> **Goals**: Understand Anderson's model and plot our first brittle fault model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import the required Python scientific libraries\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# set a custom figure style (optional, you can comment on this whole block)\n",
    "import matplotlib as mpl\n",
    "mpl.style.use('fivethirtyeight')\n",
    "mpl.rcParams['figure.facecolor'] = 'white'\n",
    "mpl.rcParams['axes.facecolor'] = 'white'\n",
    "mpl.rcParams['axes.edgecolor'] = 'white'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Anderson model\n",
    "\n",
    "Anderson (1951) proposed a model for brittle fault failure within the crust making the following assumptions:\n",
    "\n",
    "- simplified the types of faults in three different cases (normal, inverse, and strike-slip)\n",
    "- brittle fractures occur according to the Coulomb criterion\n",
    "- assumed that two of the three principal stresses lies parallel to the earth's surface and the remaining one perpendicular to it (see figure below)\n",
    "\n",
    "![](https://raw.githubusercontent.com/marcoalopez/strength_envelopes/master/figures/Anderson.jpg)\n",
    "\n",
    "With these assumptions, Anderson recalculated the Coulomb fracture criterion in terms of differential stress $(\\sigma_d = \\sigma_1 - \\sigma_3)$ and lithostatic stress $(\\sigma_L = \\rho gh)$, being the lithostatic stress for the three different cases  \n",
    "- $\\sigma_L = \\sigma_1$ (normal),\n",
    "- $\\sigma_L = \\sigma_3$ (inverse),\n",
    "- $\\sigma_L = \\sigma_2$ (strike-slip).\n",
    "\n",
    "which by rearranging give (_disclaimer: Anderson did not consider the the fuid pore pressure but here it is included_)\n",
    "\n",
    "**Inverse fault**: $\\quad \\sigma_d = 2(\\sigma_0+\\mu \\sigma_L (1 - \\lambda)) / \\sqrt{\\mu^2 + 1}-\\mu \\quad (1)$\n",
    "\n",
    "**Strike-slip fault**: $\\quad \\sigma_d = 2(\\sigma_0+\\mu \\sigma_L (1 - \\lambda)) / \\sqrt{\\mu^2 + 1} \\quad (2)$\n",
    "\n",
    "**Normal (extensional) fault**: $\\quad \\sigma_d = -2(\\sigma_0-\\mu \\sigma_L (1 - \\lambda)) / \\sqrt{\\mu^2 + 1}+\\mu \\quad (3)$\n",
    "\n",
    "TODO"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Anderson_fault(fault_type, depths, pressure, mu=0.73, lamb=0.36, C0=0.0):\n",
    "    \"\"\" Returns the corresponding differential stress in MPa for a specific depth\n",
    "    based on the Anderson theory of faulting (Anderson, 1905) and the Coulomb–\n",
    "    Navier’s law of friction.\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    fault_type : string\n",
    "        the type of fault, either 'inverse', 'normal' or 'strike-slip'\n",
    "    depths : array-like\n",
    "        an array-like with the depths [km]\n",
    "    pressure : array-like\n",
    "        the lithostatic stress of pressure at different depths [GPa]\n",
    "    mu : scalar between 0 and 1, optional\n",
    "        Coefficient of friction. Default value 0.73; this is the Rutter\n",
    "        and Glover (2012) coefficient recalculated from Byerlee (1978) data\n",
    "    lamb : scalar between 0 and 1, optional\n",
    "        Hubbert-Rubbey coefficient of fluid pressure. Zero is for dry conditions.\n",
    "        Default = 0.36\n",
    "    C0 : positive scalar, optional\n",
    "        Internal cohesion of the rock [MPa]. Mostly negligible in nature, default\n",
    "        is zero. Alternatively, this parameter can be used as the frictional\n",
    "        cohesive strenght as well.\n",
    "    \"\"\"\n",
    "\n",
    "    depths = depths * 1000  # convert km to m\n",
    "    pressure = pressure * 1e9  # convert GPa to Pa\n",
    "\n",
    "    if fault_type == 'inverse':\n",
    "        diff_stress = (2 * (C0 + mu * pressure * (1 - lamb))) / (np.sqrt(mu**2 + 1) - mu)\n",
    "\n",
    "    elif fault_type == 'strike-slip':\n",
    "        diff_stress = (2 * (C0 + mu * pressure * (1 - lamb))) / (np.sqrt(mu**2 + 1))\n",
    "\n",
    "    elif fault_type == 'normal':\n",
    "        diff_stress = (- 2 * (C0 - mu * pressure * (1 - lamb))) / (np.sqrt(mu**2 + 1) + mu)\n",
    "    \n",
    "    else:\n",
    "        raise ValueError(\"fault type must be 'inverse', 'strike-slip' or 'normal'\")\n",
    "\n",
    "    return diff_stress / 10**6"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## First example of a frictional slope\n",
    "\n",
    "To start simple, let's estimate at which differential stress brittle failure occurs as a function of lithostatic pressure and the type of fault. For this, let's assume that the internal cohesion of the rock is null (_Amontons' law_), that the coefficient of friction is that of the _Byerlee's law_ for low pressures $\\mu = 0.85$, and that the rocks are completely dry (i.e. coefficient of fluid pressure equals 0). We also assume that the rock density and gravitational acceleration do not vary in the first 15 km of the crust."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
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       "         depths  pressure\n",
       "0      0.000000  0.000000\n",
       "1      0.010007  0.000270\n",
       "2      0.020013  0.000540\n",
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       "\n",
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   "source": [
    "# set the required parameters \n",
    "ro_crust = 2750  # average rock density in the crust [kg/m**3]\n",
    "g = 9.80665      # average gravitational acceleration [m/s**2]\n",
    "\n",
    "# generate a linear spaced array of depths every 10 m from 0 to 15 km depth\n",
    "depths = np.linspace(start=0, stop=15, num=1500)\n",
    "\n",
    "# create a spreadsheet (DataFrame) containing the depths and corresponding lithostatic stresses\n",
    "data = pd.DataFrame({\n",
    "    'depths': depths,\n",
    "    'pressure': (ro_crust * g * depths) / 1e6})  # / 1e6 to obtain GPa\n",
    "data"
   ]
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  {
   "cell_type": "code",
   "execution_count": 4,
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      "text/plain": [
       "         depths  pressure       thrust      normal      strike\n",
       "0      0.000000  0.000000     0.000000   -0.000000    0.000000\n",
       "1      0.010007  0.000270     0.992056    0.212152    0.349552\n",
       "2      0.020013  0.000540     1.984111    0.424305    0.699105\n",
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       "4      0.040027  0.001079     3.968223    0.848609    1.398210\n",
       "...         ...       ...          ...         ...         ...\n",
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       "\n",
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     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data['thrust'] = Anderson_fault('inverse',\n",
    "                                data['depths'],\n",
    "                                data['pressure'],\n",
    "                                mu=0.85,\n",
    "                                lamb=0.0)\n",
    "\n",
    "data['normal'] = Anderson_fault('normal',\n",
    "                                data['depths'],\n",
    "                                data['pressure'],\n",
    "                                mu=0.85,\n",
    "                                lamb=0.0)\n",
    "\n",
    "data['strike'] = Anderson_fault('strike-slip',\n",
    "                                data['depths'],\n",
    "                                data['pressure'],\n",
    "                                mu=0.85,\n",
    "                                lamb=0.0)\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
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",
      "text/plain": [
       "<Figure size 324x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# initialize the plot\n",
    "fig2, ax = plt.subplots(figsize=(4.5, 6))\n",
    "\n",
    "# tweak the figure so that the depth is shown on the y-axis downwards\n",
    "ax.invert_yaxis()\n",
    "ax.xaxis.tick_top()\n",
    "ax.xaxis.set_label_position('top')\n",
    "\n",
    "# plot the frictional slopes\n",
    "ax.plot(data['thrust'], data['depths'], label='thrust fault')\n",
    "ax.plot(data['normal'], data['depths'], label='normal fault')\n",
    "ax.plot(data['strike'], data['depths'], label='strike-slip fault')\n",
    "\n",
    "ax.set(xlabel='Differential stress (MPa)', ylabel='Depth (km)')\n",
    "ax.legend(loc='best', fontsize=16)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Notebook tested in 2022-08-23 using:\n",
      "Python 3.9.12 (main, Apr  4 2022, 05:22:27) [MSC v.1916 64 bit (AMD64)]\n",
      "Numpy 1.23.1\n",
      "Matplotlib 3.5.1\n",
      "Pandas 1.4.3\n"
     ]
    }
   ],
   "source": [
    "import sys\n",
    "from datetime import date    \n",
    "today = date.today().isoformat()\n",
    "\n",
    "print(f'Notebook tested in {today} using:')\n",
    "print('Python', sys.version)\n",
    "print('Numpy', np.__version__)\n",
    "print('Matplotlib', mpl.__version__)\n",
    "print('Pandas', pd.__version__)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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