Volterra_Exercise.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "<h1 id=\"Earthquake-Source-Physics Exercise\">Earthquake Source Physics Exercise<a class=\"anchor-link\" href=\"#Earthquake-Source-Physics Exercise\">¶</a></h1><h2 id=\"Interseismic-Deformation\">Interseismic Deformation<a class=\"anchor-link\" href=\"#Interseismic-Deformation\">¶</a></h2><p>This notebook illustrates the displacements and strains for interseismic deformation (i.e. a buried dislocation\n",
    "extending to $-\\infty$ in the $-x_2$ direction with a free surface).</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "s = 1.     # slip\n",
    "d = 2.     # depth of dislocation\n",
    "scale = 5. # spatial scale of plot\n",
    "mu = 1.    # shear modulus\n",
    "nx = 100   # number of grid points for making plots\n",
    "x1 = np.linspace(-scale, scale, 2*nx)\n",
    "x2 = np.linspace(-scale, 0., nx)\n",
    "x1grid, x2grid = np.meshgrid(x1, x2)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "<p>We will look at the displacements and the strains at the free surface. We found that the surface displacement is</p>\n",
    "$$ u_3 = \\frac{s}{\\pi}\\arctan\\left(\\frac{x_1}{d}\\right)$$<p>Differentiating with respect to $x_1$ gives us the surface strain</p>\n",
    "$$ \\epsilon_{13} = \\frac{1}{2}\\frac{\\partial u_3}{\\partial x_1} = \\frac{s}{2\\pi d}\\frac{1}{1+(x_1/d)^2} $$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "s = 1.     # slip\n",
    "d = 2.     # depth of dislocation\n",
    "scale = 5. # spatial scale of plot\n",
    "mu = 1.    # shear modulus\n",
    "nx = 100   # number of grid points for making plots\n",
    "x1 = np.linspace(-4.*scale, 4.*scale, 8*nx)\n",
    "u3 = s/np.pi*np.arctan(x1/d)\n",
    "e13 = s/2./np.pi/d/(1.+(x1/d)**2)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "def plot_surf(x, y, label, title):\n",
    "    \"helper function for making xy plots for surface data\"\n",
    "    plt.figure(figsize=(3.25, 2.75))\n",
    "    plt.plot(x, y)\n",
    "    plt.xlabel('$x_1$')\n",
    "    plt.ylabel(label)\n",
    "    plt.title(title)\n",
    "    plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 234x198 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 234x198 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "plot_surf(x1, u3, '$u_3$', 'Surface Displacements')\n",
    "plot_surf(x1, e13, '$\\epsilon_{13}$', 'Surface Strain')\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "<p>To get the surface stress field $\\sigma_{13}$, multiply by twice the shear modulus. Since it is a free surface, $\\sigma_{23} = 0$.</p>\n",
    "<p>Note that the strain is positive -- interseismic deformation <em>accumulates</em> strain. As we will see, shallow slip relieves this strain, leading to no net strain accumulation over the entire seismic cycle. This has motivated various models of strain accumulation and seismic gaps (places that show a slip deficit relative to its surroundings). However, this is an extremely simplified picture, and it remains an open question whether or not this idealized model has any use.</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "\n",
    " \n",
    "\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.7.6"
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 },
 "nbformat": 4,
 "nbformat_minor": 1
}