{ "cells": [ { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ "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": 3, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] } ], "source": [ "%pylab inline" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "2529.536000000001" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.sum(100*np.cumprod(np.ones(5)*1.6))\n", "\n", " " ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# M = Mesh.TensorMesh([[(100.,32)],[(100.,34)],[(100.,18)]], x0='CCC')\n", "# M = simpeg.Mesh.TensorMesh([[(100,5,-1.5),(100.,5),(100,5,1.5)],[(100,5,-1.5),(100.,5),(100,5,1.5)],[(100,5,-1.5),(100.,10),(100,5,1.5)]], x0=['C','C','C'])\n", "M = simpeg.Mesh.TensorMesh([[(1000,6,-1.5),(1000.,6),(1000,6,1.5)],[(1000,6,-1.5),(1000.,2),(1000,6,1.5)],[(1000,10,-1.3),(1000.,2),(1000,10,1.3)]], x0=['C','C','C'])# Setup the model\n" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ -5.64053465e+04 -4.26194973e+04 -3.20149979e+04 -2.38576907e+04\n", " -1.75828390e+04 -1.27560300e+04 -9.04310000e+03 -6.18700000e+03\n", " -3.99000000e+03 -2.30000000e+03 -1.00000000e+03 7.27595761e-12\n", " 1.00000000e+03 2.30000000e+03 3.99000000e+03 6.18700000e+03\n", " 9.04310000e+03 1.27560300e+04 1.75828390e+04 2.38576907e+04\n", " 3.20149979e+04 4.26194973e+04 5.64053465e+04]\n" ] } ], "source": [ "print M.vectorNz" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAXkAAAEKCAYAAAD3tSVSAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAIABJREFUeJzt3Xl4FeX1wPHvySrIDhoWQZCiZd8EVGrBBUStKBUBrUAV\n", "64KKVftT0VZCFxVbtVqXSivWBURcEBFRUAmKCigCgoCAEEhCghDWiCwJ5/fHTOAm3DW5u+fzPPdh\n", "7sw7c8+5N5w79513ZkRVMcYYk5xSYh2AMcaYyLEib4wxScyKvDHGJDEr8sYYk8SsyBtjTBKzIm+M\n", "MUnMirwxxiQxK/ImoYnIVSLypYjsFZEtIvKuiPR2l50qIq+JyDYR2SUiy0XkdhGxv3vzk2F/7CZh\n", "icgdwGPAX4ETgebAU8BAEWkNLAI2AR1UtR5wBdAdqB2biI2JPrEzXk0iEpG6QD7wW1V9w8vyl4G6\n", "qnpJ1IMzJo7YnrxJVGcCxwHTfSw/D3g9euEYE5+syJtE1RDYrqqH/SwvjGI8xsQlK/ImURUDjfwc\n", "RC0GmkYxHmPikhV5k6g+Bw4Ag3ws/wC4PHrhGBOfrMibhKSqu4H7gadE5FIRqSki6SJyoYhMAMYB\n", "Z4nIwyKSBSAiPxORl9yDtsb8JFiRNwlLVR8F7gD+CHwPbAZGA9NVdQPOwdmWwDcisgvnQOwXwN6Y\n", 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The model\n", "Msig = M.getEdgeInnerProduct(sig)\n", "MsigBG = M.getEdgeInnerProduct(sigBG)\n", "Mmu = M.getFaceInnerProduct(mu_0, invProp=True)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [], "source": [ "freq = 1.0\n", "C = M.edgeCurl\n", "A = C.T*Mmu*C - 1j*omega(freq)*Msig\n", "ARH = -(C.T*Mmu*C - 1j*omega(freq)*MsigBG)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 2.46 s, sys: 24 ms, total: 2.49 s\n", "Wall time: 2.48 s\n" ] } ], "source": [ "%%time\n", "# Solve the systems for each polarization\n", "sys.path.append('/media/gudni/ExtraDrive1/Codes/python/pymatsolver/')\n", "from pymatsolver import MumpsSolver\n", "Ainv = MumpsSolver(A)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Need to solve x and y polarizations of the source.\n", "from simpegMT.Utils import get1DEfields\n", "# Get a 1d solution for a halfspace background\n", "mesh1d = simpeg.Mesh.TensorMesh([M.hz],np.array([M.x0[2]]))\n", "e0_1d = get1DEfields(mesh1d,M.r(sigBG,'CC','CC','M')[0,0,:],freq,sourceAmp=None).conj()\n", "# Setup the primary field (p) for the x (east) polarization (_px)\n", "ex_px = np.zeros((M.vnEx),dtype=complex)\n", "ey_px = np.zeros(M.nEy,dtype=complex)\n", "ez_px = np.zeros(M.nEz,dtype=complex)\n", "# Assign the source to ex_x\n", "for i in arange(M.vnEx[0]):\n", " for j in arange(M.vnEx[1]):\n", " ex_px[i,j,:] = -e0_1d\n", "ep_px = np.r_[simpeg.Utils.mkvc(ex_px),ey_px,ez_px]\n", "rhs_px = ARH.dot(ep_px)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Setup y (north) polarization (_y)\n", "ex_py = np.zeros(M.nEx, dtype='complex128')\n", "ey_py = np.zeros((M.vnEy), dtype='complex128')\n", "ez_py = np.zeros(M.nEz, dtype='complex128')\n", "# Assign the source to ey_y\n", "for i in arange(M.vnEy[0]):\n", " for j in arange(M.vnEy[1]):\n", " ey_py[i,j,:] = e0_1d \n", " \n", "ep_py = np.r_[ex_py,simpeg.Utils.mkvc(ey_py),ez_py]\n", "rhs_py = ARH.dot(ep_py)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We are using splu in scipy package. This is bit slow, but on the cluster you can use mumps, which might a lot faster. We can think about having better iterative solver. " ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 42.8 ms, sys: 0 ns, total: 42.8 ms\n", "Wall time: 43.6 ms\n" ] } ], "source": [ "%%time\n", "es_px = Ainv*rhs_px\n", "es_py = Ainv*rhs_py" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Need to sum the ep and es to get the total field.\n", "e_x = es_px #+ ep_px\n", "e_y = es_py #+ ep_py" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I want to visualize electrical field, which is a vector, so I average them on to cell center. Also I want to see current density ($\\vec{j} = \\sigma \\vec{e}$)." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [], "source": [ "Meinv = M.getEdgeInnerProduct(np.ones_like(sig), invMat=True)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [], "source": [ "j_x = Meinv*Msig*e_x\n", "j_y = Meinv*Msig*e_x" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "(18598,)" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "e_x.shape" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [], "source": [ "e_x_CC = M.aveE2CCV*e_x\n", "e_y_CC = M.aveE2CCV*e_y\n", "j_x_CC = M.aveE2CCV*j_x\n", "j_y_CC = M.aveE2CCV*j_y\n", "# j_x_CC = Utils.sdiag(np.r_[sig, sig, sig])*e_x_CC" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Then use \"plotSlice\" function, to visualize 2D sections" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAtUAAAFRCAYAAAC7elE4AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAIABJREFUeJzsvXe4JWWV7/8pmiwgOYMNgmQkJ0FAkCDBRDCgGO44V8c4\n", "6qijdxznN3NHvY5XnXEcZ8xxDIikJufc0EB3Q3fTTeecc/fJ9fvjU3XP7sPeZ9euXW+d3U19n6cf\n", "OOfsvd+q2lXrXeu7vmutKI5jKlSoUKFChQoVKlSokB9bjfQBVKhQoUKFChUqVKiwuaNyqitUqFCh\n", "QoUKFSpUaBOVU12hQoUKFSpUqFChQpuonOoKFSpUqFChQoUKFdpE5VRXqFChQoUKFSpUqNAmKqe6\n", "QoUKFSpUqFChQoU2UTnVFTZbRFH0gSiKHq75eW0URaNH7ogqVKhQoUIjVDa7wpaOyqmu0NGIoujs\n", "KIoei6JoVRRFy6MoeiSKolPqvTaO453jOJ5V8PrrEsOf/uuLouh7Ra5RoUKFClsKKptd4ZWMrUf6\n", "ACpUaIQoinYBbgX+Evg9sB1wDtBd1jHEcbxTzfG8CliUHEuFChUqVKhBZbMrvNJRMdUVOhmvA+I4\n", "jn8Xi644ju+O43hivRdHUTQQRdGhyf/vEEXRv0RRNCthTB6Oomj75G9nJEzKyiiKnoui6NyMx3MV\n", 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'k'}, normal='Y', ax = ax[0])\n", "cb0 = plt.colorbar(dat0[0], ax = ax[0])\n", "dat1 = M.plotSlice(np.log10(np.abs(e_y_CC)), vType='CCv', view='vec', streamOpts={'color': 'k'}, normal='Y', ax = ax[1])\n", "cb1 = plt.colorbar(dat1[0], ax = ax[1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Is it reasonable?: Based on that you put resistive target that makes sense to me; current does not want to flow on resistive target so they just do roundabout:). And see air interface. It is continuous on current but not on electric field, which looks reasonable. " ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Calculate the data\n", "rx_x, rx_y = np.meshgrid(np.arange(-3000,3001,500),np.arange(-1000,1001,500))\n", "rx_loc = np.hstack((simpeg.Utils.mkvc(rx_x,2),simpeg.Utils.mkvc(rx_y,2),elev+np.zeros((np.prod(rx_x.shape),1))))\n", "# Get the projection matrices\n", "Qex = M.getInterpolationMat(rx_loc,'Ex')\n", "Qey = M.getInterpolationMat(rx_loc,'Ey')\n", "Qez = M.getInterpolationMat(rx_loc,'Ez')\n", "Qfx = M.getInterpolationMat(rx_loc,'Fx')\n", "Qfy = M.getInterpolationMat(rx_loc,'Fy')\n", "Qfz = M.getInterpolationMat(rx_loc,'Fz')" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [], "source": [ "e_x_loc = np.hstack([simpeg.Utils.mkvc(Qex*e_x,2),simpeg.Utils.mkvc(Qey*e_x,2),simpeg.Utils.mkvc(Qez*e_x,2)])\n", "e_y_loc = np.hstack([simpeg.Utils.mkvc(Qex*e_y,2),simpeg.Utils.mkvc(Qey*e_y,2),simpeg.Utils.mkvc(Qez*e_y,2)])\n", "Ciw = -C/(1j*omega(freq)*mu_0)\n", "h_x_loc = np.hstack([simpeg.Utils.mkvc(Qfx*Ciw*e_x,2),simpeg.Utils.mkvc(Qfy*Ciw*e_x,2),simpeg.Utils.mkvc(Qfz*Ciw*e_x,2)])\n", "h_y_loc = np.hstack([simpeg.Utils.mkvc(Qfx*Ciw*e_y,2),simpeg.Utils.mkvc(Qfy*Ciw*e_y,2),simpeg.Utils.mkvc(Qfz*Ciw*e_y,2)])" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Make a combined matrix\n", "dt = np.dtype([('ex1',complex),('ey1',complex),('ez1',complex),('hx1',complex),('hy1',complex),('hz1',complex),('ex2',complex),('ey2',complex),('ez2',complex),('hx2',complex),('hy2',complex),('hz2',complex)])\n", "combMat = np.empty((len(e_x_loc)),dtype=dt)\n", "combMat['ex1'] = e_x_loc[:,0]\n", "combMat['ey1'] = e_x_loc[:,1]\n", "combMat['ez1'] = e_x_loc[:,2]\n", "combMat['ex2'] = e_y_loc[:,0]\n", "combMat['ey2'] = e_y_loc[:,1]\n", "combMat['ez2'] = e_y_loc[:,2]\n", "combMat['hx1'] = h_x_loc[:,0]\n", "combMat['hy1'] = h_x_loc[:,1]\n", "combMat['hz1'] = h_x_loc[:,2]\n", "combMat['hx2'] = h_y_loc[:,0]\n", "combMat['hy2'] = h_y_loc[:,1]\n", "combMat['hz2'] = h_y_loc[:,2]\n" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def calculateImpedance(fieldsData):\n", " ''' \n", " Function that calculates MT impedance data from a rec array with E and H field data from both polarizations\n", " '''\n", " zxx = (fieldsData['ex1']*fieldsData['hy2'] - fieldsData['ex2']*fieldsData['hy1'])/(fieldsData['hx1']*fieldsData['hy2'] - fieldsData['hx2']*fieldsData['hy1'])\n", " zxy = (-fieldsData['ex1']*fieldsData['hx2'] + fieldsData['ex2']*fieldsData['hx1'])/(fieldsData['hx1']*fieldsData['hy2'] - fieldsData['hx2']*fieldsData['hy1'])\n", " zyx = (fieldsData['ey1']*fieldsData['hy2'] - fieldsData['ey2']*fieldsData['hy1'])/(fieldsData['hx1']*fieldsData['hy2'] - fieldsData['hx2']*fieldsData['hy1'])\n", " zyy = (-fieldsData['ey1']*fieldsData['hx2'] + fieldsData['ey2']*fieldsData['hx1'])/(fieldsData['hx1']*fieldsData['hy2'] - fieldsData['hx2']*fieldsData['hy1'])\n", " return zxx, zxy, zyx, zyy\n", "\n", "zxx, zxy, zyx, zyy = calculateImpedance(combMat)" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# rx_loc" ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(array([ 2.58052711]), array([ 41.12190413]))\n", "(array([ 1.49556255]), array([-154.79729349]))\n" ] } ], "source": [ "ind = np.where(np.sum(np.power(rx_loc - np.array([-3000,0,elev]),2),axis=1)< 5)\n", "m\n", "print appResPhs(freq,zyx[ind])\n", "print appResPhs(freq,zxy[ind])" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 1.48260668e+48 +2.81495302e+48j] [ 4.12341913e+49 +9.25329081e+50j]\n", "(array([ 1.49426011]), array([ 149.6731804]))\n" ] } ], "source": [ "e0_1d = e0_1d.conj()\n", "Qex = mesh1d.getInterpolationMat(np.array([elev]),'Ex')\n", "Qfx = mesh1d.getInterpolationMat(np.array([elev]),'Fx')\n", "h0_1dC = -(mesh1d.nodalGrad*e0_1d)/(1j*omega(freq)*mu_0)\n", "h0_1d = mesh1d.getInterpolationMat(mesh1d.vectorNx,'Ex')*h0_1dC\n", "indSur = np.where(mesh1d.vectorNx==elev)\n", "\n", "print (Qfx*e0_1d),(Qex*h0_1dC)#e0_1d, h0_1d\n", "print appResPhs(freq,(Qfx*e0_1d)/(Qex*h0_1dC).conj())" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import simpegMT as simpegmt\n", "sig1D = M.r(sig,'CC','CC','M')[0,0,:]\n", "anaEd, anaEu, anaHd, anaHu = simpegmt.Utils.MT1Danalytic.getEHfields(mesh1d,sig1D,freq,mesh1d.vectorNx)\n", "anaEtemp = anaEd+anaEu\n", "anaHtemp = anaHd+anaHu\n", "# Scale the solution\n", "anaE = (anaEtemp/anaEtemp[-1])#.conj()\n", "anaH = (anaHtemp/anaEtemp[-1])#.conj()" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 0.00198692+0.00198692j 0.00198692+0.00198692j 0.00198692+0.00198692j\n", " 0.00198692+0.00198692j 0.00198692+0.00198692j 0.00198692+0.00198692j\n", " 0.00198692+0.00198692j 0.00198692+0.00198692j 0.00198692+0.00198692j\n", " 0.00198692+0.00198692j 0.00198692+0.00198692j 0.00198692+0.00198692j\n", " 0.00198692+0.0098826j 0.00198692+0.02014699j 0.00198693+0.03349069j\n", " 0.00198697+0.05083751j 0.00198708+0.07338836j 0.00198737+0.10270447j\n", " 0.00198810+0.14081541j 0.00198983+0.19035962j 0.00199390+0.25476708j\n", " 0.00200329+0.33849678j 0.00202471+0.44734538j]\n", "(array([], dtype=float64), array([], dtype=float64))\n", "(array([], dtype=float64), array([], dtype=float64))\n" ] } ], "source": [ "anaZ = anaE/anaH\n", "indSur = np.where(mesh1d.vectorNx==elev)\n", "print anaZ\n", "print appResPhs(freq,anaZ[indSur])\n", "print appResPhs(freq,-anaZ[indSur])" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([ -5.64053465e+04, -4.26194973e+04, -3.20149979e+04,\n", " -2.38576907e+04, -1.75828390e+04, -1.27560300e+04,\n", " -9.04310000e+03, -6.18700000e+03, -3.99000000e+03,\n", " -2.30000000e+03, -1.00000000e+03, 7.27595761e-12,\n", " 1.00000000e+03, 2.30000000e+03, 3.99000000e+03,\n", " 6.18700000e+03, 9.04310000e+03, 1.27560300e+04,\n", " 1.75828390e+04, 2.38576907e+04, 3.20149979e+04,\n", " 4.26194973e+04, 5.64053465e+04])" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mesh1d.vectorNx" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.9" } }, "nbformat": 4, "nbformat_minor": 0 }