simpeg/MT 1D code_testLayered.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "# Test 1D solution of MT problem and compare to a analytic solution\n",
    "%pylab inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# import the simpegMT module\n",
    "from simpegMT.Utils import MT1Danalytic, MT1Dsolutions\n",
    "import SimPEG as simpeg\n",
    "from scipy.constants import mu_0\n",
    "def omega(freq):\n",
    "    \"\"\"Change frequency to angular frequency, omega\"\"\"\n",
    "    return 2.*np.pi*freq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Set up the mesh.\n",
    "freq = 10\n",
    "z = 100.\n",
    "hz = [(z,10,-1.5),(z,10),(z,10,1.5)]\n",
    "M = simpeg.Mesh.TensorMesh([hz],'C')\n",
    "# sig = np.zeros(M.nC) + 1e-8\n",
    "conds = [1,1e-2]\n",
    "elev = 300\n",
    "sig = np.zeros(M.nC) + conds[1]\n",
    "sig[np.logical_and(M.gridCC>-200,M.gridCC<0)] = conds[0]\n",
    "sig[M.gridCC>elev] = 1e-8\n",
    "sig[M.gridCC<-500] = 1e-1\n",
    "sig[M.gridCC<-900] = conds[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f28e1428f50>]"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f28e25e0050>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "M.plotImage(log10(sig))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-17499.51171875, -11733.0078125 ,  -7888.671875  ,  -5325.78125   ,\n",
       "        -3617.1875    ,  -2478.125     ,  -1718.75      ,  -1212.5       ,\n",
       "         -875.        ,   -650.        ,   -500.        ,   -400.        ,\n",
       "         -300.        ,   -200.        ,   -100.        ,      0.        ,\n",
       "          100.        ,    200.        ,    300.        ,    400.        ,\n",
       "          500.        ,    650.        ,    875.        ,   1212.5       ,\n",
       "         1718.75      ,   2478.125     ,   3617.1875    ,   5325.78125   ,\n",
       "         7888.671875  ,  11733.0078125 ,  17499.51171875])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M.vectorNx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Get the fields\n",
    "anaEd, anaEu, anaHd, anaHu = MT1Danalytic.getEHfields(M,sig,freq,M.vectorNx)\n",
    "anaEtemp = (anaEd+anaEu)\n",
    "anaHtemp = (anaHd+anaHu)\n",
    "# Scale the solution\n",
    "anaZ = (anaEtemp/anaHtemp)[np.argmin(M.vectorNx**2)]\n",
    "anaEcor = anaEtemp/anaEtemp[-1] #.real/np.abs(anaEtemp[-1].real)+1j*anaEtemp.imag/np.abs(anaEtemp[-1].imag)\n",
    "anaHcor = anaHtemp/anaEtemp[-1] # .real/np.abs(anaEtemp[-1].real)+1j*anaHtemp.imag/np.abs(anaEtemp[-1].imag)\n",
    "\n",
    "solE = MT1Dsolutions.get1DEfields(M,sig,freq,sourceAmp=1).conj()\n",
    "solH = -M.nodalGrad*solE/(1j*omega(freq)*mu_0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(12836609.712174654+24128916.329733729j)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "anaEtemp[-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  1.71846041e-08 -3.23018213e-08j,\n",
       "          1.71846041e-08 +3.23018213e-08j],\n",
       "       [ -1.13091973e-06 +7.74148973e-07j,\n",
       "         -5.08843373e-07 -3.09514912e-07j],\n",
       "       [  3.71261251e-06 -1.48868560e-05j,\n",
       "          3.65512026e-06 -7.95948811e-06j],\n",
       "       [  7.37072093e-05 +2.15078894e-05j,\n",
       "          5.80305408e-05 +1.06357942e-05j],\n",
       "       [  4.75612845e-05 +2.19547586e-04j,\n",
       "          6.36366910e-05 +1.90231770e-04j],\n",
       "       [ -2.21258264e-04 +4.02750922e-04j,\n",
       "         -1.76226223e-04 +3.91452069e-04j],\n",
       "       [ -6.14770210e-04 +4.12789798e-04j,\n",
       "         -5.58922388e-04 +4.25303107e-04j],\n",
       "       [ -9.80056634e-04 +2.74642565e-04j,\n",
       "         -9.21632381e-04 +3.06492631e-04j],\n",
       "       [ -1.25588450e-03 +7.69129746e-05j,\n",
       "         -1.19789524e-03 +1.23674848e-04j],\n",
       "       [ -1.43995677e-03 -3.53489427e-04j,\n",
       "         -1.41049571e-03 -2.73526014e-04j],\n",
       "       [ -1.49344998e-03 -9.54835366e-04j,\n",
       "         -1.49148850e-03 -8.51549869e-04j],\n",
       "       [ -1.48131966e-03 -1.44956637e-03j,\n",
       "         -1.49169515e-03 -1.33110967e-03j],\n",
       "       [ -1.45773633e-03 -1.95598586e-03j,\n",
       "         -1.48139177e-03 -1.82244743e-03j],\n",
       "       [ -1.41870158e-03 -2.47390502e-03j,\n",
       "         -1.45669893e-03 -2.32548179e-03j],\n",
       "       [ -2.90180962e-04 -3.48330897e-03j,\n",
       "         -5.04762046e-04 -3.40934866e-03j],\n",
       "       [  3.59895776e-03 -4.54053788e-03j,\n",
       "          3.13908864e-03 -4.89175966e-03j],\n",
       "       [  9.19763090e-03 -4.77509117e-03j,\n",
       "          8.73344053e-03 -5.12251551e-03j],\n",
       "       [  1.48339589e-02 -4.93699809e-03j,\n",
       "          1.43682382e-02 -5.28431488e-03j],\n",
       "       [  2.05091907e-02 -4.98175514e-03j,\n",
       "          2.00447591e-02 -5.33266719e-03j],\n",
       "       [  2.62040772e-02 -4.95302628e-03j,\n",
       "          2.57423326e-02 -5.30188588e-03j],\n",
       "       [  3.18989638e-02 -4.92429721e-03j,\n",
       "          3.14399061e-02 -5.27110437e-03j],\n",
       "       [  4.04412937e-02 -4.88120312e-03j,\n",
       "          3.99862664e-02 -5.22493164e-03j],\n",
       "       [  5.32547886e-02 -4.81656058e-03j,\n",
       "          5.28058071e-02 -5.15567122e-03j],\n",
       "       [  7.24750311e-02 -4.71959260e-03j,\n",
       "          7.20351186e-02 -5.05177662e-03j],\n",
       "       [  1.01305395e-01 -4.57412782e-03j,\n",
       "          1.00879087e-01 -4.89592257e-03j],\n",
       "       [  1.44550940e-01 -4.35589030e-03j,\n",
       "          1.44145040e-01 -4.66210323e-03j],\n",
       "       [  2.09419254e-01 -4.02840425e-03j,\n",
       "          2.09043975e-01 -4.31125116e-03j],\n",
       "       [  3.06721710e-01 -3.53675174e-03j,\n",
       "          3.06392386e-01 -3.78457151e-03j],\n",
       "       [  4.52675331e-01 -2.79787645e-03j,\n",
       "          4.52415018e-01 -2.99322787e-03j],\n",
       "       [  6.71605530e-01 -1.68492364e-03j,\n",
       "          6.71448995e-01 -1.80181306e-03j],\n",
       "       [  1.00000000e+00 +0.00000000e+00j,\n",
       "          1.00000000e+00 -0.00000000e+00j]])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.hstack((simpeg.mkvc(anaEcor,2),simpeg.mkvc(solE,2)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f28e1642950>,\n",
       " <matplotlib.lines.Line2D at 0x7f28e1642410>]"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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       "ThxmZlYrThxmZlYrThxmZlYr/x/lWzp+eZujggAAAABJRU5ErkJggg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f28e149ae50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(solE.real,M.vectorNx,'r*--',anaEcor.real,M.vectorNx,'b+:')\n",
    "#axis([-.2,.2,-10000,10000])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f28e24abf10>]"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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       "ZlYRFw4zM6uIC4eZmVXEhcPMzCriwmFmZhVx4TAzs4r8f6jZeSiIHLknAAAAAElFTkSuQmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f28e166af10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot((abs(solE.real)-abs(anaEcor.real))/abs(anaEcor.real),M.vectorNx,'b+:')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f28e13c1750>,\n",
       " <matplotlib.lines.Line2D at 0x7f28e13c19d0>]"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f28e1672450>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(solE.imag,M.vectorNx,'r*--',anaEcor.imag,M.vectorNx,'b+:')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/gudni/anaconda/lib/python2.7/site-packages/IPython/kernel/__main__.py:1: RuntimeWarning: invalid value encountered in divide\n",
      "  if __name__ == '__main__':\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f28e12fd450>]"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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       "rkJggg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f28e13589d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot((abs(solE.imag)-abs(anaEcor.imag))/abs(anaEcor.imag),M.vectorNx,'b+:')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f28e1261d50>,\n",
       " <matplotlib.lines.Line2D at 0x7f28e1238110>]"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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       "5P8DEIvS62qo2M0AAAAASUVORK5CYII=\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f28e1293c90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "semilogx(abs(solE),M.vectorNx,'r*--',abs(anaEcor),M.vectorNx,'b+:')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f28e1042c50>]"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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       "/4X2pwIryo67xt//a4Hvpd//g8AHy467xvh/mWxs6X6yhLcWWFR27LX8+wFuAbYCL5H10f92iTG/\n",
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       "rkJggg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f28e11d9d50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot((abs(solE)-abs(anaEcor))/abs(anaEcor),M.vectorNx,'b+:')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.849336540898 41.0291116761\n",
      "10.1269411518 -150.251552846\n"
     ]
    }
   ],
   "source": [
    "def appResPhs(freq,z):\n",
    "    app_res = ((1./(8e-7*np.pi**2))/freq)*np.abs(z)**2\n",
    "    app_phs = np.arctan2(z.imag,z.real)*(180/np.pi)\n",
    "    return app_res, app_phs\n",
    "app_rAna, app_pAna = appResPhs(freq,anaZ)\n",
    "app_rSol, app_pSol = appResPhs(freq,solE[np.argmin(M.hx**2)]/solH[np.argmin(M.hx**2)])\n",
    "print app_rAna, app_pAna\n",
    "print app_rSol, app_pSol"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(30,)"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M.nodalGrad.dot(solE).shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "31"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M.nN\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f28e0f08c90>,\n",
       " <matplotlib.lines.Line2D at 0x7f28e0f08f10>]"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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       "4Q7AZ4GXmkFMAdSmn9eIMsbTmJgAziDXFFvu2/WN+X16H9gvInYl9++2n6S9s44LWAN8LyJ2BEYB\n",
       "p0naIeOYAP5AGceCSWoL/CpdYyhw/Prft6TPA9ulAc+nkhsYXTYbExO5LoLvAD/fqJM25amqrBZg\n",
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       "r4hYmtaXAr3WrxARK4DLgH8Ci4CVETEl67jWMxYo9/iXjYlpIPC6pD9IekbSREmbZRwT5P6inyLp\n",
       "aUmnlDGexsR0BbmnCddtYH/FY5LURtJzqc60iJjVHOIqiG8AMIzcDBPNIqYy+mgwc9LQoOWG6vSj\n",
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       "dgO+HRFPSfovcn+VnJNhTAB7RcRiSVuSe3pvdkQ8klVMkr4IvBYRz6pE8w6V4ucUual/dlVuotG/\n",
       "SqqNiLqs40rn2Ry4DTgjIt5uDjGV2cZed/3hA+WMt+TnbraJIyIO3NC+1LnVOyKWKDcH1msNVNsd\n",
       "eCwilqdj7gA+BzQpcZQgrrxDgL9FxOtNiadEMS0EFkZE/rHn2/j0Nv5KxERELE5fX5f0F3ITXRad\n",
       "OEoQ0+eAw1IbdUegi6QbIqLoWZtL+PtERLwp6V5yv/t1xcZUqrgktSc399wfI+LOpsRTqpgqoB7o\n",
       "X7Ddn09Om9RQnX6pLMuYGqWlNlXlBwySvjb0SzkbGCWpkyQBB5Dr0Mw6rrzjgZvLHA9sREwRsQRY\n",
       "IGlwKjoAmJllTJI2k1Sd1juT6w8q25MwGxNTRJwdEf0jYiC5ZsYHm5I0ShGTpC3yTxBJ6kRukOyz\n",
       "ZYxpY+MSufFZsyLiv8ocz0bFVCFPk5v5e0BqVTguxVbobuAkAOWeXlxZ0MyWVUx5GzeQulwdMuVc\n",
       "yHV8TyE3nfskoFsq7wvcW1Dvx+Q+AGeQm323fTOJqzOwjNxswc3lZ7ULuY7V54E7gK5ZxgRsCzyX\n",
       "lheBs5rDz6mg/r7A3VnHRO5JqmfSz+kF4EfN4XcK2JtcP9Bz5BLZs8CYrP/9yP2xtghYTa7d/2tl\n",
       "iOUQcg/mzMv/3gLfAL5RUOdXaf/z5J78LPe/2afGRK4JcAG5Zv03yPUNb76h83kAoJmZNUpLbaoy\n",
       "M7OMOHGYmVmjOHGYmVmjOHGYmVmjOHGYmVmjOHGYmVmjOHGYmVmjOHGYmVmj/P+o5FkWr3OFFQAA\n",
       "AABJRU5ErkJggg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f28e0fdce10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(-solH.imag,M.vectorCCx,'r*--',anaHcor.imag,M.vectorNx,'b+:')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-14616.25976562,  -9810.83984375,  -6607.2265625 ,  -4471.484375  ,\n",
       "        -3047.65625   ,  -2098.4375    ,  -1465.625     ,  -1043.75      ,\n",
       "         -762.5       ,   -575.        ,   -450.        ,   -350.        ,\n",
       "         -250.        ,   -150.        ,    -50.        ,     50.        ,\n",
       "          150.        ,    250.        ,    350.        ,    450.        ,\n",
       "          575.        ,    762.5       ,   1043.75      ,   1465.625     ,\n",
       "         2098.4375    ,   3047.65625   ,   4471.484375  ,   6607.2265625 ,\n",
       "         9810.83984375,  14616.25976562])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M.vectorCCx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  }
 ],
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