4_Traveltime_inversion.ipynb

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    "<div>\n",
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    "        <h1>pyGIMLi Tutorial @ Transform 2021</h1>\n",
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    "# Introduction to method managers: Traveltime inversion\n",
    "\n",
    "## Objectives:\n",
    "1. Load travel time data from [third notebook](./3_Simulating_a_crosshole_traveltime_experiment)\n",
    "2. Learn about method managers and how they work\n",
    "3. Use the TravelTimeManager to invert the loaded data\n",
    "4. Analyze inversion results and play with inversion options"
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  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 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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  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pygimli as pg\n",
    "import pygimli.physics.traveltime as tt"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "### Load Data "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Data: Sensors: 20 data: 100, nonzero entries: ['err', 'g', 's', 't', 'valid']\n"
     ]
    }
   ],
   "source": [
    "data = tt.load(\"data/traveltime.dat\")\n",
    "print(data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define function to display data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
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      "text/plain": [
       "<Figure size 576x396 with 2 Axes>"
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     },
     "metadata": {
      "needs_background": "light"
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     "output_type": "display_data"
    }
   ],
   "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": "markdown",
   "metadata": {},
   "source": [
    "### Create 2D mesh"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
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    "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",
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  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "### Inversion"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We create an instance of the [`TravelTimeManager`](https://www.pygimli.org/pygimliapi/_generated/pygimli.physics.traveltime.html?highlight=traveltimemanager#pygimli.physics.traveltime.TravelTimeManager) class with the loaded data. Method Managers work as an interface for end-user interaction and can be seen as simple but complete application classes which manage all tasks of geophysical data processing. In this example we are using the TravelTimeManager from the TravelTime physics module where we use the `invert` method. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "mgr = tt.TravelTimeManager(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "28/04/21 - 16:41:21 - pyGIMLi - \u001b[0;32;49mINFO\u001b[0m - Found 1 regions.\n",
      "28/04/21 - 16:41:21 - pyGIMLi - \u001b[0;32;49mINFO\u001b[0m - Creating forward mesh from region infos.\n",
      "28/04/21 - 16:41:21 - pyGIMLi - \u001b[0;32;49mINFO\u001b[0m - Creating refined mesh (secnodes: 3) to solve forward task.\n",
      "28/04/21 - 16:41:21 - pyGIMLi - \u001b[0;32;49mINFO\u001b[0m - Startmodel set from given value. 0.001\n",
      "28/04/21 - 16:41:21 - pyGIMLi - \u001b[0;32;49mINFO\u001b[0m - Starting inversion.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "fop: <pygimli.physics.traveltime.TravelTimeManager.TravelTimeDijkstraModelling object at 0x7ffc885c6310>\n",
      "Data transformation: <pgcore._pygimli_.RTrans object at 0x7ffc885c69a0>\n",
      "Model transformation: <pgcore._pygimli_.RTransLog object at 0x7ffc885c64a0>\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 = 276.55 (dPhi = 66.76%) lam: 50.0\n",
      "--------------------------------------------------------------------------------\n",
      "inv.iter 3 ... chi² = 167.87 (dPhi = 39.12%) lam: 50.0\n",
      "--------------------------------------------------------------------------------\n",
      "inv.iter 4 ... chi² = 114.46 (dPhi = 31.42%) lam: 50.0\n",
      "--------------------------------------------------------------------------------\n",
      "inv.iter 5 ... chi² = 84.62 (dPhi = 25.9%) lam: 50.0\n",
      "--------------------------------------------------------------------------------\n",
      "inv.iter 6 ... chi² = 32.42 (dPhi = 60.53%) lam: 50.0\n",
      "--------------------------------------------------------------------------------\n",
      "inv.iter 7 ... chi² = 22.04 (dPhi = 31.24%) lam: 50.0\n",
      "--------------------------------------------------------------------------------\n",
      "inv.iter 8 ... chi² = 20.38 (dPhi = 7.33%) lam: 50.0\n",
      "--------------------------------------------------------------------------------\n",
      "inv.iter 9 ... chi² = 16.76 (dPhi = 17.1%) lam: 50.0\n",
      "--------------------------------------------------------------------------------\n",
      "inv.iter 10 ... chi² = 14.85 (dPhi = 10.9%) lam: 50.0\n",
      "--------------------------------------------------------------------------------\n",
      "inv.iter 11 ... chi² = 13.97 (dPhi = 5.57%) lam: 50.0\n",
      "--------------------------------------------------------------------------------\n",
      "inv.iter 12 ... chi² = 11.94 (dPhi = 13.57%) lam: 50.0\n",
      "--------------------------------------------------------------------------------\n",
      "inv.iter 13 ... chi² = 10.83 (dPhi = 8.6%) lam: 50.0\n",
      "--------------------------------------------------------------------------------\n",
      "inv.iter 14 ... chi² = 9.15 (dPhi = 13.99%) lam: 50.0\n",
      "--------------------------------------------------------------------------------\n",
      "inv.iter 15 ... chi² = 8.25 (dPhi = 8.85%) lam: 50.0\n",
      "--------------------------------------------------------------------------------\n",
      "inv.iter 16 ... chi² = 7.95 (dPhi = 3.13%) lam: 50.0\n",
      "--------------------------------------------------------------------------------\n",
      "inv.iter 17 ... chi² = 7.09 (dPhi = 9.56%) lam: 50.0\n",
      "--------------------------------------------------------------------------------\n",
      "inv.iter 18 ... chi² = 6.97 (dPhi = 1.52%) lam: 50.0\n",
      "################################################################################\n",
      "#                 Abort criteria reached: dPhi = 1.52 (< 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();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Method Manager also has `showResult()` and `drawRayPaths()` methods."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
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    "ax, cb = mgr.showResult();\n",
    "mgr.drawRayPaths(ax);"
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   "metadata": {},
   "source": [
    "Now we look at the simulated data (left) and inverted response (right)"
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  {
   "cell_type": "code",
   "execution_count": 18,
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     },
     "metadata": {
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     "output_type": "display_data"
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   ],
   "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": 19,
   "metadata": {},
   "outputs": [
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    "# 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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