Files
simpeg/notebooks/MT Script-3D_twoHalfspace-simpegMT.ipynb
T
GudniRos c4229b4906 Refactoring the MT code to relect on the FDEM parent.
The test work for FDEM branch feat/sourceRefactor commit 9eede4e840
2015-06-03 11:12:55 -07:00

2978 lines
218 KiB
Plaintext

{
"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": [
"<matplotlib.colorbar.Colorbar instance at 0x7fda385d5c20>"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
},
{
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],
"text/plain": [
"<matplotlib.figure.Figure at 0x7fda38893e90>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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],
"text/plain": [
"<matplotlib.figure.Figure at 0x7fda38893e50>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Setup the model\n",
"# conds = [1,1e-2]\n",
"# elev = 300\n",
"# sig = simpeg.Utils.ModelBuilder.defineBlock(M.gridCC,[-100000,-100000,-200],[100000,100000,0],conds)\n",
"# sig[M.gridCC[:,2]>elev] = 1e-8\n",
"# sig[M.gridCC[:,2]<-500] = 1e-1\n",
"# sig[M.gridCC[:,2]<-900] = 1e-2\n",
"elev=0\n",
"conds = [1,1e-2]\n",
"sig = np.ones(M.nC)*conds[0]\n",
"sig[M.gridCC[:,0]>0] = conds[1]\n",
"sig[M.gridCC[:,2]>elev] = 1e-8\n",
"# sigBG = np.zeros(M.nC) + conds[0]\n",
"# sigBG[M.gridCC[:,2]>0] = 1e-8\n",
"sigBG = np.ones(M.nC)*conds[0]\n",
"sigBG[M.gridCC[:,2]>elev] = 1e-8\n",
"colorbar(M.plotImage(log10(sig)))\n",
"colorbar(M.plotImage(log10(sigBG)))\n"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# Get the mass matrix \n",
"# 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": {
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"VjEAAAAASUVORK5CYII=\n"
],
"text/plain": [
"<matplotlib.figure.Figure at 0x7fda2780a550>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(1,2, figsize = (12, 5))\n",
"dat0 = M.plotSlice(np.log10(np.abs(e_x_CC)), vType='CCv', view='vec', streamOpts={'color': '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
}