simpeg/simpegPF/notebooks/tutorials/Tutorial_1_Mag forward modeling.ipynb

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 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from SimPEG import *\n",
      "from simpegPF.MagAnalytics import spheremodel, MagSphereAnalFun, CongruousMagBC, MagSphereAnalFunA\n",
      "from simpegPF.Magnetics import MagneticsDiffSecondary, MagneticsDiffSecondaryInv, BaseMag\n",
      "%pylab inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import matplotlib\n",
      "matplotlib.rcParams.update({'font.size': 16, 'text.usetex': True})"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 16
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Forward problem: Magnetics"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This is a tutorial for Mag forward problem using simpegPF package. We first start with analytic solution for susceptible sphere in a whole space. Then we solve steady-state Maxwell's equatoins for Mag problem (<a href=\"http://simpegpf.readthedocs.org/en/latest/api_PF.html\">See Doc</a>) using simpegPF package. "
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Step1: Discretize the earth"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We use TensorMesh class in SimPEG to discretize the 3D earth (<a href=\"http://docs.simpeg.xyz/en/latest/api_MeshCode.html?highlight=tensormesh#module-SimPEG.Mesh.TensorMesh\">See Doc</a>). Let's visualize discretized mesh on section views:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "cs = 12.5\n",
      "ncx, ncy, ncz, npad = 41, 41, 40, 5\n",
      "hx = [(cs,npad,-1.4), (cs,ncx), (cs,npad,1.4)]\n",
      "hy = [(cs,npad,-1.4), (cs,ncy), (cs,npad,1.4)]\n",
      "hz = [(cs,npad,-1.4), (cs,ncz), (cs,npad,1.4)]\n",
      "mesh = Mesh.TensorMesh([hx, hy, hz], 'CCC')\n",
      "fig, ax = plt.subplots(1,2, figsize=(12, 5))\n",
      "dat0 = mesh.plotSlice(np.zeros(mesh.nC), grid=True, ax=ax[0]); ax[0].set_title('XY plane')\n",
      "dat1 = mesh.plotSlice(np.zeros(mesh.nC), grid=True, normal='X', ax=ax[1]); ax[1].set_title('YZ plane')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 17,
       "text": [
        "<matplotlib.text.Text at 0x3a99ad0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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5M6zx2PrY/qnnW9kAgKXjcA4AWLCq4OzU+VZ/qO6Pd/VZPWSQUUJG33hqz5De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\n2gfe3Ob6RUQdAGAr/IbK561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       "text": [
        "<matplotlib.figure.Figure at 0x3b6b310>"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Step2: Compose suceptibility model: susceptible sphere in whole space"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "- $\\mu = \\mu_0(1+\\chi)$\n",
      "- $\\mu$: magnetic permeability\n",
      "- $\\mu_0$: magnetic permeability of vacuum space\n",
      "- $\\chi$: magnetic susceptibility"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from scipy.constants import mu_0\n",
      "mu0 = 4*np.pi*1e-7\n",
      "chibkg = 0.     # Background susceptibility\n",
      "chiblk = 0.01   # Susceptibility for a sphere\n",
      "chi = np.ones(mesh.nC)*chibkg"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 19
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sph_ind = spheremodel(mesh, 0, 0, -100, 80) # A sphere is located at (0, 0, 0) and radius of the sphere is 100 m\n",
      "chi[sph_ind] = chiblk # Assign susceptibility value for the sphere\n",
      "mu = (1.+chi)*mu0"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 20
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig, ax  =  plt.subplots(1,2, figsize=(12, 7))\n",
      "indz = int(np.argmin(abs(mesh.vectorCCz-(-100.)))); indx = int(np.argmin(abs(mesh.vectorCCx-0.)))\n",
      "dat0 = mesh.plotSlice(chi, grid=True, ind=indz, ax=ax[0]); ax[0].set_title(('XY plane at z=%5.2f')%(mesh.vectorCCz[indz]))\n",
      "dat1 = mesh.plotSlice(chi, grid=True, normal='X', ind=indx, ax=ax[1]); ax[1].set_title(('YZ plane at x=%5.2f')%(mesh.vectorCCx[indx]))\n",
      "cb0 = plt.colorbar(dat0[0], orientation='horizontal',  ax=ax[0], ticks = linspace(0, 0.01, 5)); \n",
      "cb1 = plt.colorbar(dat1[0], orientation='horizontal',  ax=ax[1], ticks = linspace(0, 0.01, 5)); \n",
      "cb0.set_label(\"Suceptibility\")\n",
      "cb1.set_label(\"Suceptibility\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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q5DGK4WsUP7ZMPZKpavjaQ+N984fu76u9FiLnbABAiNBF/5uSbkl6knAsKZxv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\nrOGqyzX9dfUF/7ak17U4gr+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       "text": [
        "<matplotlib.figure.Figure at 0x42450d0>"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Step3: Set up an airborne MAG survey"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We have discretized 3D earth and generated suceptibility model, which means that we have discretized earth and physical property distribution. We can compute magnetic fields everywhere in our domain by solving parial differental equation (PDE), but our measurements are confined to finite locations. Therefore, we need to project computed fields $\\mathbf{u}$, which is defined everywhere in our domain to certain locations where we have receiving points. For instance in airborne mag survey these are the points where a plane or helicopter measure earth magnetic fields. This projection can be expressed as:\n",
      "\n",
      "$$ \\mathbf{d} = P(\\mathbf{u})$$\n",
      "\n",
      "where $P(\\cdot)$ is a projection from computed field to the measured data, and $d$ is the measure data. "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's assume that we have a survey area: 400 m $\\times$ 400 m. We have 21 lines of airborne MAG survey, and we measure magnetic fields for every 20 m on each line. A pilot for this helicopter is really talented so that the flight height is constant for 30 m above the surface.  "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "xr = np.linspace(-200, 200, 21)\n",
      "yr = np.linspace(-200, 200, 21)\n",
      "X, Y = np.meshgrid(xr, yr)\n",
      "Z = np.ones((size(xr), size(yr)))*30."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig, ax  =  plt.subplots(1,1, figsize=(5, 5))\n",
      "indz = int(np.argmin(abs(mesh.vectorCCz-(0.))));\n",
      "dat0 = mesh.plotSlice(chi, grid=True, ind=indz, ax=ax); ax.set_title(('XY plane at z=%5.2f')%(mesh.vectorCCz[indz]))\n",
      "ax.plot(X.flatten(), Y.flatten(), 'w.', ms=5)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 24,
       "text": [
        "[<matplotlib.lines.Line2D at 0x56e54d0>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x482ae10>"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Step4: Analytic solution"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We have an analytic solution when we have a sphere in a whole-space. simpegPF provides this function so that you can compute magnetic field on your receiving locations. Another input you need to put is direction of the earth magnetic fieds, and the strength, you can easily get this information from <a href=\"http://www.ngdc.noaa.gov/geomag-web/\">NOAA's website</a>. We assume that we have veritcal earth fields and the strength is 1. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Bxra, Byra, Bzra = MagSphereAnalFunA(X, Y, Z, 80., 0., 0., -100, chiblk, np.array([0., 0., 1.]), flag)\n",
      "Bxra = np.reshape(Bxra, (size(xr), size(yr)), order='F')\n",
      "Byra = np.reshape(Byra, (size(xr), size(yr)), order='F')\n",
      "Bzra = np.reshape(Bzra, (size(xr), size(yr)), order='F')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 25
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig, ax = plt.subplots(1,3, figsize=(18, 4))\n",
      "dat0=ax[0].contourf(X, Y, Bxra, 30); ax[0].set_title('Bx'); cb0 = plt.colorbar(dat0, ax=ax[0])\n",
      "dat1=ax[1].contourf(X, Y, Byra, 30); ax[1].set_title('By'); cb1 = plt.colorbar(dat0, ax=ax[1])\n",
      "dat2=ax[2].contourf(X, Y, Bzra, 30); ax[2].set_title('Bz'); cb2 = plt.colorbar(dat0, ax=ax[2])\n",
      "for i in range(3):\n",
      "    ax[i].plot(X.flatten(), Y.flatten(), 'k.', ms=3)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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hOQQQyn5CRZKY6JEk4ggLI0z75BBF1gM4G8A7ATyjab8ZwFcAfL15vQ312sX3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\nD7zAAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x56f2150>"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Step5: Solve PDE"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Note that data for this case magnetic fields projected to earth field direction, which is typical data type for airborne mag survey. "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "First, set survey class"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "survey = BaseMag.BaseMagSurvey() # survey class for mag problem\n",
      "Inc = 90.\n",
      "Dec = 0.\n",
      "Btot = 1\n",
      "survey.setBackgroundField(Inc, Dec, Btot) # set inclination, declination, and strength of magnetic field\n",
      "rxLoc = np.c_[Utils.mkvc(X), Utils.mkvc(Y), Utils.mkvc(Z)]\n",
      "survey.rxLoc = rxLoc # set receiver locations"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 27
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Second, set problem class then pair with survey"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "prob = MagneticsDiffSecondary(mesh)\n",
      "prob.pair(survey)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 28
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Third, run forward modeling"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = survey.dpred(mu)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 29
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now we viualize computed solution and compare with analytic solutions! Note that you may always need to make sure that your numerical solution is reasonable enough. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig, ax = plt.subplots(1,3, figsize=(18, 4))\n",
      "vmin = Bzra.min()\n",
      "vmax = Bzra.max()\n",
      "residual = data.reshape((xr.size, yr.size), order='F')-Bzra\n",
      "dat0=ax[0].contourf(X, Y, Bzra, 30, vmin=vmin, vmax=vmax)\n",
      "dat1=ax[1].contourf(X, Y, data.reshape((xr.size, yr.size), order='F'), 30, vmin=vmin, vmax=vmax)\n",
      "dat2=ax[2].contourf(X, Y, residual, 30)\n",
      "cb0 = plt.colorbar(dat0, ax=ax[0])\n",
      "cb1 = plt.colorbar(dat0, ax=ax[1])\n",
      "cb2 = plt.colorbar(dat2, ax=ax[2])\n",
      "ax[0].set_title('Bz (analytic)')\n",
      "ax[1].set_title('Bz (simpegPF)')\n",
      "ax[2].set_title('Residual')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 30,
       "text": [
        "<matplotlib.text.Text at 0x4858f10>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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qZkoFE2VKOl3NyIbumtuHgS2aKgjlLO1/J/R+Ss81pqnSxUxZ2mftQowVYVz6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       "text": [
        "<matplotlib.figure.Figure at 0x6054210>"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<a rel=\"license\" href=\"http://creativecommons.org/licenses/by/4.0/\"><img alt=\"Creative Commons License\" style=\"border-width:0\" src=\"https://i.creativecommons.org/l/by/4.0/88x31.png\" /></a><br />This work is licensed under a <a rel=\"license\" href=\"http://creativecommons.org/licenses/by/4.0/\">Creative Commons Attribution 4.0 International License</a>."
     ]
    }
   ],
   "metadata": {}
  }
 ]
}