01_example_2D_MT_CSEM_modeling.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2-D modeling with GoFEM: a half-space example\n",
    "\n",
    "This notebook shows how to setup a simple halfs-space model and parameter files for GoFEM\n",
    "\n",
    "*Created by A. Grayver, 2019, Updated July 2024*\n",
    "\n",
    "Let us start by including some common packages\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import sys\n",
    "import math\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.colors as colors\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, let the python know where deal.II's python package lives and also include pyGoFEM tools:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "from gofem.parameter_handler import *\n",
    "from gofem.mesh_utils import *\n",
    "from gofem.data_utils import *\n",
    "\n",
    "module_path = os.path.abspath('/home/ag/lib/dealii-9.5.2/build/lib/python3.12/site-packages')\n",
    "if module_path not in sys.path:\n",
    "    sys.path.append(module_path)\n",
    "\n",
    "import PyDealII.Release as dealii"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Creating mesh and defining model properties\n",
    "\n",
    "Create an initial coarse mesh.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "dy = np.ones(shape=5) * 1e5\n",
    "dz = np.array([100, 80, 60, 60, 80, 100], dtype = np.float64) * 1000\n",
    "mesh_size = np.array([np.sum(dy), np.sum(dz)])\n",
    "\n",
    "p_origin = dealii.Point((-mesh_size / 2.).tolist())\n",
    "p_end = dealii.Point((mesh_size / 2.).tolist())\n",
    "\n",
    "triangulation = dealii.Triangulation('2D')\n",
    "triangulation.generate_subdivided_steps_hyper_rectangle([dy.tolist(), dz.tolist()], p_origin, p_end, False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can plot the mesh:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plot_2d_triangulation(triangulation)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This mesh is still rather coarse. Theory says, that in order to get an accurate solution, we need to refine at\n",
    "\n",
    "* Conductivity contrasts\n",
    "* Receiver locations\n",
    "\n",
    "We can address this problem by refining the mesh globally several times:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(<Figure size 640x480 with 1 Axes>, <Axes: xlabel='y (m)', ylabel='z (m)'>)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "triangulation.refine_global(1)\n",
    "plot_2d_triangulation(triangulation)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is very inefficient, because each time we refine globally, number of cells is multiplied by four.\n",
    "\n",
    "One of the most powerful features of GoFEM is locally refined meshes, which allow us to refine only in regions where it is needed. like at the air-ground interface. To do that, we first need to assign some physical properties to cells. We mark each cell with a material id. In particular, all cells above the ground are given material id one and the rest will have id two:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "for cell in triangulation.active_cells():\n",
    "    if cell.center().y < 0:\n",
    "        cell.material_id = 1\n",
    "    else:\n",
    "        cell.material_id = 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "Note that in the deal.II notation, the two dimensional coordinate system is (X,Y) and we cannot change it at this stage.\n",
    "\n",
    "However, the GoFEM convention is to use local NED coordinate system with Z pointing down, X pointing to the North and Y to the east. However, for 2D, the GoFEM takes X to be the strike direction, hence we are left with the (Y,Z) coordinate system. Therefore, we need to keep in mind that deal.II's (X,Y) system corresponds to the GoFEM's (Y,Z) system in 2D. GoFEM does this conversion internally, but here, for the mesh generation, we need to do it manually. This is the reason we invoke the Y coordinate of each cell's to check if the cell is in the air or under the surface.\n",
    "\n",
    "We now need to actually assign some physical conductivity values (and names, for that matter) to the used id numbers. Let us simply use a python dictionary for that\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "materials = {1: ('air', 1e-8), 2: ('ground', 0.01)}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Additionally, we will set electric permittivity to zero everywhere. However, this can be changed is displacement currents are required."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Switch to one if displacement currents are needed \n",
    "# (e.g., in case of RMT or GPR applications)\n",
    "permittivity = 0."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, each material id is linked to a pair of values, representing its name and conductivity value (in S/m). This allows us to plot the mesh with conductivity assigned to each cell"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x7fc53047ce30>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def color(cell):\n",
    "    return materials[cell.material_id][1]\n",
    "\n",
    "fig, ax = plot_2d_triangulation(triangulation, color_scheme=color)\n",
    "fig.colorbar(ax.collections[0], ax=ax,\\\n",
    "             orientation = 'vertical',\\\n",
    "             label = r'$\\sigma$ (S/m)',\\\n",
    "             norm=colors.LogNorm(vmin = 1e-8, vmax = 1e-2),\\\n",
    "             extend='max')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we can call a convenience function to refine at the air-ground interface"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(<Figure size 640x480 with 1 Axes>, <Axes: xlabel='y (m)', ylabel='z (m)'>)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "refine_at_interface(triangulation, material_ids = [2], repeat = 2)\n",
    "plot_2d_triangulation(triangulation)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this case, we did it twice and we excluded the air itself from refinement since accuracy in the air is less important. We can further refine only the central part since our receivers will be placed there"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "refine_at_interface(triangulation, material_ids = [2], repeat = 2, center = [0,0], radii = [50000])\n",
    "fig, ax = plot_2d_triangulation(triangulation)\n",
    "ax.set_xlim([-60000, 60000])\n",
    "ax.set_ylim([-20000, 20000])\n",
    "ax.invert_yaxis()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us see how many cells we have now and what is the diameter of the smallest and largest cells"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "# of cells = 360\n",
      "smallest cell = 3644.3 m\n",
      "largest cell = 70710.7 m\n"
     ]
    }
   ],
   "source": [
    "print('# of cells = %d\\nsmallest cell = %0.1f m\\nlargest cell = %0.1f m' % (triangulation.n_active_cells(),\\\n",
    "                                                                      triangulation.minimal_cell_diameter(),\\\n",
    "                                                                      triangulation.maximal_cell_diameter()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is still very modest number of cells, but we are getting there. Now, we can place some receivers at the surface and refine around these points. Again, we can use a convenience function from pyGoFEM and exclude air:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "# of cells = 2904\n",
      "smallest cell = 227.8 m\n",
      "largest cell = 70710.7 m\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "r_y = np.arange(-40000.1, 40000, 4000)\n",
    "receivers = []\n",
    "for y in r_y:\n",
    "    receivers.append([y, 0.1])\n",
    "    \n",
    "refine_around_points(triangulation, points = receivers,\\\n",
    "                     center = [0, 0], radii = [2000, 2000],\\\n",
    "                     repeat = 2, exclude_materials = [1])\n",
    "\n",
    "refine_around_points(triangulation, points = receivers,\\\n",
    "                     center = [0, 0], radii = [1000, 1000],\\\n",
    "                     repeat = 2, exclude_materials = [1])\n",
    "\n",
    "fig, ax = plot_2d_triangulation(triangulation)\n",
    "ax.set_xlim([-50000, 50000])\n",
    "ax.set_ylim([-10000, 20000])\n",
    "ax.invert_yaxis()\n",
    "ax.scatter(r_y, r_y*0 + 0.1, color='r', marker='v')\n",
    "\n",
    "print('# of cells = %d\\nsmallest cell = %0.1f m\\nlargest cell = %0.1f m' % (triangulation.n_active_cells(),\\\n",
    "                                                                      triangulation.minimal_cell_diameter(),\\\n",
    "                                                                      triangulation.maximal_cell_diameter()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Creating input files for GoFEM"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we can save the mesh, material properties and receivers in files that will be read by GoFEM:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "# save the mesh\n",
    "triangulation.save('./01/model.tria')\n",
    "\n",
    "# save the material properties\n",
    "with open('./01/model.materials', 'w') as f:\n",
    "    f.write('# id name conductivity permitivitty\\n')\n",
    "    f.write('iso\\n')\n",
    "    for mid,properties in materials.items():\n",
    "        f.write(\"%d %s %0.6e %0.6e\\n\" % (mid, properties[0], properties[1], permittivity))\n",
    "\n",
    "# save receivers\n",
    "with open('./01/receivers', 'w') as f:\n",
    "    f.write('# type name number_of_points x y z\\n')\n",
    "    idx = 0\n",
    "    for rec in receivers:\n",
    "        f.write(\"Dipole R%d 1 0. %0.6e %0.6e\\n\" % (idx, rec[0], rec[1]))\n",
    "        idx += 1\n",
    "        \n",
    "# save frequencies\n",
    "frequencies = np.logspace(-2, 2, 33)\n",
    "np.savetxt('./01/frequencies', frequencies, header = '# frequency (Hz)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In case you work with CSEM, you have to also setup sources. Example below creates an inline unit current electric dipole source placed at (0,1):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "with open('./01/sources', 'w') as f:\n",
    "    f.write('# type name field n_parts x y z moment_x moment_y moment_z current_re current_im\\n')\n",
    "    f.write(\"Dipole S1 E 1 0. 0. 1. 0. 1. 0. 1. 0.\\n\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we can create an input parameter file:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "prm = ParameterHandler(inversion = False, dim = 2)\n",
    "\n",
    "# Let's use quadratic elements for accuracy\n",
    "prm.setitem(section = 'Modeling',\\\n",
    "            parameter = 'Order',\\\n",
    "            value = 2)\n",
    "\n",
    "# Tell the code where to read all files from\n",
    "prm.setitem(section = 'Model',\\\n",
    "            parameter = 'Model definition file',\\\n",
    "            value = '../model.tria')\n",
    "prm.setitem(section = 'Model',\\\n",
    "            parameter = 'Materials definition file',\\\n",
    "            value = '../model.materials')\n",
    "\n",
    "prm.setitem(section = 'Survey',\\\n",
    "            parameter = 'Frequencies file',\n",
    "            value = '../frequencies')\n",
    "prm.setitem(section = 'Survey',\\\n",
    "            parameter = 'Stations file',\n",
    "            value = '../receivers')\n",
    "prm.setitem(section = 'Survey',\\\n",
    "            parameter = 'Sources file',\n",
    "            value = '../sources')\n",
    "\n",
    "prm.setitem(section = 'Output',\\\n",
    "            parameter = 'Type',\n",
    "            value = 'point')\n",
    "prm.setitem(section = 'Output',\\\n",
    "            parameter = 'Data file',\n",
    "            value = 'halfspace')\n",
    "\n",
    "prm.write('./01/input_modeling.prm')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Run the code"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since this is a simple 2-D problem, modeling will not take long and we can run it from here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "import subprocess,shlex\n",
    "\n",
    "f = open(\"output.txt\", \"w\")\n",
    "args = shlex.split(\"/home/ag/GoFEM/GOFEM/applications/emmod/build/Release/gofem --parameter_file ../input_modeling.prm --task modeling --dim 2 --method MT\")\n",
    "proc = subprocess.Popen(args, stdout=f, stderr=f, cwd = './01/results')\n",
    "f.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Reading and plotting results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Upon finishing, the GoFEM will output both the modelled fields at the receiver locations at all frequencies (and sources, for CSEM) as well as the VTU files with the model and its attributes (if this type of output is requested), such as conductivity, EM fields, etc. The former can be read using a pyGoFEM function, whereas the latter is a Paraview compatible format that you can visualize externally or, if you feel enthusiastic, you can also use the paraview from within the python. \n",
    "\n",
    "Below, we read the GoFEM modeling results at receivers by using the pandas:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")\n",
    "\n",
    "dfs = read_modeling_responses('./01/results/halfspace_c=0_f=%0.8e.txt', frequencies)\n",
    "\n",
    "rho_data = np.zeros(shape=(len(frequencies),len(receivers),2))\n",
    "phi_data = np.zeros(shape=(len(frequencies),len(receivers),2))\n",
    "for idx in range(len(frequencies)):\n",
    "    rho_data[idx] = dfs[idx][['rho_xy', 'rho_yx']]\n",
    "    phi_data[idx] = dfs[idx][['phi_xy', 'phi_yx']]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And finally plot TE and TM modes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1920x1440 with 8 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(2, 2)\n",
    "p = axes[0,0].pcolormesh(r_y, np.log10(frequencies), rho_data[:,:,0], vmin=98, vmax = 102)\n",
    "fig.colorbar(p, ax=axes[0,0], label=r'$\\rho^{app}$ (Ohm*m)')\n",
    "axes[0,0].set_title('TE'), axes[0,0].set_xlabel('y (m)'), axes[0,0].set_ylabel('log10 f(Hz)')\n",
    "p = axes[0,1].pcolormesh(r_y, np.log10(frequencies), rho_data[:,:,1], vmin=98, vmax = 102)\n",
    "fig.colorbar(p, ax=axes[0,1], label=r'$\\rho^{app}$ (Ohm*m)')\n",
    "axes[0,1].set_title('TM'), axes[0,1].set_xlabel('y (m)'), axes[0,1].set_ylabel('log10 f(Hz)')\n",
    "p = axes[1,0].pcolormesh(r_y, np.log10(frequencies), phi_data[:,:,0], vmin=44, vmax = 46)\n",
    "fig.colorbar(p, ax=axes[1,0], label=r'$\\phi (^\\circ)$')\n",
    "axes[1,0].set_title('TE'), axes[1,0].set_xlabel('y (m)'), axes[1,0].set_ylabel('log10 f(Hz)')\n",
    "p = axes[1,1].pcolormesh(r_y, np.log10(frequencies), phi_data[:,:,1], vmin=-136, vmax = -134)\n",
    "fig.colorbar(p, ax=axes[1,1], label=r'$\\phi (^\\circ)$')\n",
    "axes[1,1].set_title('TM'), axes[1,1].set_xlabel('y (m)'), axes[1,1].set_ylabel('log10 f(Hz)')\n",
    "fig.set_size_inches(np.array(fig.get_size_inches()) * 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As is anticipated, they look pretty boring, but match analytical values very well, confirming high accuracy. Note also that for the high frequencies wee see slight deviations from the theoretical values (visible in the phase plots). This can be fixed by adding one more refinement around receivers. "
   ]
  }
 ],
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