4_Traveltime_inversion.ipynb

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    "<div>\n",
    "    <div style=\"float:left;width:50%;text-align:center\">\n",
    "        <h1>pyGIMLi Tutorial @ Transform 2021</h1>\n",
    "        <div>\n",
    "<table style=\"border-collapse:collapse;border-color:#ccc;border-spacing:0\" class=\"tg\"><thead><tr><th style=\"background-color:#f0f0f0;border-color:#ccc;border-style:solid;border-width:1px;color:#333;font-family:Arial, sans-serif;font-size:14px;font-weight:bold;overflow:hidden;padding:10px 5px;text-align:left;vertical-align:middle;word-break:normal\"></th><th style=\"background-color:#f0f0f0;border-color:#ccc;border-style:solid;border-width:1px;color:#333;font-family:Arial, sans-serif;font-size:14px;font-weight:bold;overflow:hidden;padding:10px 5px;text-align:left;vertical-align:middle;word-break:normal\">Info</th></tr></thead><tbody><tr><td style=\"background-color:#f9f9f9;border-color:#ccc;border-style:solid;border-width:1px;color:#333;font-family:Arial, sans-serif;font-size:14px;font-weight:bold;overflow:hidden;padding:10px 5px;text-align:left;vertical-align:middle;word-break:normal\">When</td><td style=\"background-color:#f9f9f9;border-color:#ccc;border-style:solid;border-width:1px;color:#333;font-family:Arial, sans-serif;font-size:14px;overflow:hidden;padding:10px 5px;text-align:left;vertical-align:middle;word-break:normal\">Monday, April 19 • 8:00 - 10:00 UTC (starts at 10.00 a.m. CET)</td></tr><tr><td style=\"background-color:#fff;border-color:#ccc;border-style:solid;border-width:1px;color:#333;font-family:Arial, sans-serif;font-size:14px;font-weight:bold;overflow:hidden;padding:10px 5px;text-align:left;vertical-align:middle;word-break:normal\">Slack (Q&amp;A)</td><td style=\"background-color:#fff;border-color:#ccc;border-style:solid;border-width:1px;color:#333;font-family:Arial, sans-serif;font-size:14px;overflow:hidden;padding:10px 5px;text-align:left;text-decoration:underline;vertical-align:top;word-break:normal\"><a href=\"https://softwareunderground.org/\">Software Underground</a> channel <a href=\"https://swung.slack.com/archives/C01T5V5S9EV\">#t21-mon-pygimli</a></td></tr><tr><td style=\"background-color:#f9f9f9;border-color:#ccc;border-style:solid;border-width:1px;color:#333;font-family:Arial, sans-serif;font-size:14px;font-weight:bold;overflow:hidden;padding:10px 5px;text-align:left;vertical-align:middle;word-break:normal\">Live stream</td><td style=\"background-color:#f9f9f9;border-color:#ccc;border-style:solid;border-width:1px;color:#333;font-family:Arial, sans-serif;font-size:14px;overflow:hidden;padding:10px 5px;text-align:left;text-decoration:underline;vertical-align:top;word-break:normal\"><a href=\"https://youtu.be/w3pu0H3dXe8\">https://youtu.be/w3pu0H3dXe8</a></td></tr><tr><td style=\"background-color:#fff;border-color:#ccc;border-style:solid;border-width:1px;color:#333;font-family:Arial, sans-serif;font-size:14px;font-weight:bold;overflow:hidden;padding:10px 5px;text-align:left;vertical-align:middle;word-break:normal\">pyGIMLi documentation</td><td style=\"background-color:#fff;border-color:#ccc;border-style:solid;border-width:1px;color:#333;font-family:Arial, sans-serif;font-size:14px;overflow:hidden;padding:10px 5px;text-align:left;text-decoration:underline;vertical-align:top;word-break:normal\"><a href=\"https://www.pygimli.org/documentation.html\">https://www.pygimli.org/documentation.html</a></td></tr></tbody></table>\n",
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    "# Introduction to method managers: Traveltime inversion\n",
    "\n",
    "## Objectives"
   ]
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    "# Just some plotting settings\n",
    "import matplotlib.pyplot as plt\n",
    "plt.style.use(\"seaborn-notebook\")\n",
    "%config InlineBackend.figure_format='svg' # Setting figure format for this notebook"
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   "source": [
    "import numpy as np\n",
    "import pygimli as pg\n",
    "import pygimli.physics.traveltime as tt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
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    {
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     "text": [
      "Data: Sensors: 20 data: 100, nonzero entries: ['err', 'g', 's', 't', 'valid']\n"
     ]
    }
   ],
   "source": [
    "data = tt.load(\"data/traveltime.dat\")\n",
    "print(data)"
   ]
  },
  {
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   "execution_count": 4,
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     "metadata": {
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     "output_type": "display_data"
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   ],
   "source": [
    "# For displaying data we define a function\n",
    "from pygimli.viewer.mpl import showVecMatrix\n",
    "def showCrossholeData(data, vals, **kwargs):\n",
    "    d = -pg.y(data)  # sensor depth\n",
    "    ds = d[data[\"s\"]]  # shot depth\n",
    "    dg = d[data[\"g\"]]  # geophone depth\n",
    "    ax, cb = showVecMatrix(ds, dg, vals, );\n",
    "    ax.set_xlabel(\"shot depth\");\n",
    "    ax.set_ylabel(\"geophone depth\");\n",
    "\n",
    "showCrossholeData(data, data[\"t\"], label=\"travel time (s)\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
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      "text/plain": [
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     "metadata": {
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     "output_type": "display_data"
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   ],
   "source": [
    "x = np.linspace(min(pg.x(data)), max(pg.x(data)), 15)\n",
    "y = np.linspace(min(pg.y(data)), max(pg.y(data)), 19)\n",
    "grid = pg.meshtools.createMesh2D(x, y)\n",
    "ax, cb = pg.show(grid)\n",
    "ax.plot(pg.x(data), pg.y(data), \"ro\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
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   ],
   "source": [
    "# For displaying data we define a function\n",
    "from pygimli.viewer.mpl import showVecMatrix\n",
    "def showCrossholeData(data, vals, **kwargs):\n",
    "    d = -pg.y(data)  # sensor depth\n",
    "    ds = d[data[\"s\"]]  # shot depth\n",
    "    dg = d[data[\"g\"]]  # geophone depth\n",
    "    ax, cb = showVecMatrix(ds, dg, vals, label=\"apparent velocity (m/s)\", **kwargs);\n",
    "    ax.set_xlabel(\"shot depth\");\n",
    "    ax.set_ylabel(\"geophone depth\");\n",
    "\n",
    "showCrossholeData(data, data[\"t\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "mgr = tt.TravelTimeManager(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "19/04/21 - 00:11:52 - pyGIMLi - \u001b[0;32;49mINFO\u001b[0m - Found 1 regions.\n",
      "19/04/21 - 00:11:52 - pyGIMLi - \u001b[0;32;49mINFO\u001b[0m - Creating forward mesh from region infos.\n",
      "19/04/21 - 00:11:52 - pyGIMLi - \u001b[0;32;49mINFO\u001b[0m - Creating refined mesh (secnodes: 3) to solve forward task.\n",
      "19/04/21 - 00:11:52 - pyGIMLi - \u001b[0;32;49mINFO\u001b[0m - Startmodel set from given value. 0.001\n",
      "19/04/21 - 00:11:52 - pyGIMLi - \u001b[0;32;49mINFO\u001b[0m - Starting inversion.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "fop: <pygimli.physics.traveltime.TravelTimeManager.TravelTimeDijkstraModelling object at 0x000001B2A7A20A90>\n",
      "Data transformation: <pgcore._pygimli_.RTrans object at 0x000001B2A7A25220>\n",
      "Model transformation: <pgcore._pygimli_.RTransLog object at 0x000001B2A7A8C630>\n",
      "min/max (data): 0.019/0.038\n",
      "min/max (error): 0.13%/0.15%\n",
      "min/max (start model): 1.0e-03/1.0e-03\n",
      "--------------------------------------------------------------------------------\n",
      "--------------------------------------------------------------------------------\n",
      "inv.iter 2 ... chi² = 179.5 (dPhi = 75.23%) lam: 50.0\n",
      "--------------------------------------------------------------------------------\n",
      "inv.iter 3 ... chi² = 85.75 (dPhi = 52.08%) lam: 50.0\n",
      "--------------------------------------------------------------------------------\n",
      "inv.iter 4 ... chi² = 49.15 (dPhi = 41.88%) lam: 50.0\n",
      "--------------------------------------------------------------------------------\n",
      "inv.iter 5 ... chi² = 29.16 (dPhi = 39.87%) lam: 50.0\n",
      "--------------------------------------------------------------------------------\n",
      "inv.iter 6 ... chi² = 20.22 (dPhi = 29.47%) lam: 50.0\n",
      "--------------------------------------------------------------------------------\n",
      "inv.iter 7 ... chi² = 17.24 (dPhi = 14.19%) lam: 50.0\n",
      "--------------------------------------------------------------------------------\n",
      "inv.iter 8 ... chi² = 11.13 (dPhi = 32.61%) lam: 50.0\n",
      "--------------------------------------------------------------------------------\n",
      "inv.iter 9 ... chi² = 9.15 (dPhi = 16.63%) lam: 50.0\n",
      "--------------------------------------------------------------------------------\n",
      "inv.iter 10 ... chi² = 6.24 (dPhi = 28.43%) lam: 50.0\n",
      "--------------------------------------------------------------------------------\n",
      "inv.iter 11 ... chi² = 6.14 (dPhi = 1.38%) lam: 50.0\n",
      "################################################################################\n",
      "#                 Abort criteria reached: dPhi = 1.38 (< 2.0%)                 #\n",
      "################################################################################\n"
     ]
    },
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   "source": [
    "mgr.invert(data, mesh=grid, \n",
    "           startModel=0.001,\n",
    "           useGradient=False,\n",
    "           #zWeight=1,\n",
    "           secNodes=3,\n",
    "           lam=50,\n",
    "           verbose=True)\n",
    "mgr.showResult();"
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  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
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    "ax, cb = mgr.showResult();\n",
    "mgr.drawRayPaths(ax);"
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   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
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     },
     "metadata": {
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     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(ncols=2)\n",
    "showCrossholeData(data, data[\"t\"], ax=ax[0])\n",
    "showCrossholeData(data, mgr.inv.response, ax=ax[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
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   "source": [
    "# Have a look at the misfit\n",
    "misfit = data[\"t\"] - mgr.inv.response\n",
    "showCrossholeData(data, misfit, cMap=\"bwr\", cMin=-0.001, cMax=0.001)"
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