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1D DC examples

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seogi committed 2014-09-22 16:56:44 -07:00
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notebooks/DC_schumberger_FWD.ipynb
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{
"metadata": {
"name": "",
"signature": "sha256:4c81eac7c432b351e702d9aa1f39f2d14f9487903d874e4c95342ece5a8bb266"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "code",
"collapsed": false,
"input": [
"from SimPEG import *\n",
"import simpegDC as DC\n",
"from simpegem1d import Utils1D\n",
"import simpegEM.Utils as EMUtils\n",
"%pylab inline"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Populating the interactive namespace from numpy and matplotlib\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"DC Forward Modeling of Schlumber array"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here we test the accuracy of DC forward modeling using analytic solution."
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Step1: Generate mesh"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"cs = 25.\n",
"npad = 11\n",
"hx = [(cs,npad, -1.3),(cs,41),(cs,npad, 1.3)]\n",
"hy = [(cs,npad, -1.3),(cs,17),(cs,npad, 1.3)]\n",
"hz = [(cs,npad, -1.3),(cs,20)]"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 113
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"mesh = Mesh.TensorMesh([hx, hy, hz], 'CCN')"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 114
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"mesh.plotGrid()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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truncated
"text": [
"<matplotlib.figure.Figure at 0x4ecf510>"
]
}
],
"prompt_number": 115
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Step2: Generating model"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"sighalf = 1e-2\n",
"sigma = np.ones(mesh.nC)*sighalf"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 121
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Step3: Design survey: Schulumberger array"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<img src=\"http://www.landrinstruments.com/_/rsrc/1271695892678/home/ultra-minires/additional-information-1/schlumberger-soundings/schlum%20array.JPG\"> </img>"
]
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"$$ \\rho_a = \\frac{V}{I}\\pi\\frac{b(b+a)}{a}$$"
]
},
{
"cell_type": "heading",
"level": 4,
"metadata": {},
"source": [
"Let $b=na$, then we rewrite above equation as:"
]
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"$$ \\rho_a = \\frac{V}{I}\\pi na(n+1)$$"
]
},
{
"cell_type": "heading",
"level": 4,
"metadata": {},
"source": [
"Since AB/2 can be a good measure for depth of investigation, we express "
]
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"$$AB/2 = \\frac{(2n+1)a}{2}$$"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"matplotlib.rcParams.update({'font.size': 14, 'text.usetex': True, 'font.family': 'arial'})"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 140
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"ntx = 16"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 141
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"xtemp_txP = np.arange(ntx)*(25.)-500.\n",
"xtemp_txN = -xtemp_txP\n",
"ytemp_tx = np.zeros(ntx)\n",
"xtemp_rxP = -50.\n",
"xtemp_rxN = 50.\n",
"ytemp_rx = 0.\n",
"abhalf = abs(xtemp_txP-xtemp_txN)*0.5\n",
"a = xtemp_rxN-xtemp_rxP\n",
"b = ((xtemp_txN-xtemp_txP)-a)*0.5"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 142
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fig, ax = plt.subplots(1,1, figsize = (12,3))\n",
"for i in range(ntx):\n",
" ax.plot(np.r_[xtemp_txP[i], xtemp_txP[i]], np.r_[0., 0.4-0.01*(i-1)], 'k-', lw = 1)\n",
" ax.plot(np.r_[xtemp_txN[i], xtemp_txN[i]], np.r_[0., 0.4-0.01*(i-1)], 'k-', lw = 1)\n",
" ax.plot(xtemp_txP[i], ytemp_tx[i], 'bo')\n",
" ax.plot(xtemp_txN[i], ytemp_tx[i], 'ro')\n",
" ax.plot(np.r_[xtemp_txP[i], xtemp_txN[i]], np.r_[0.4-0.01*(i-1), 0.4-0.01*(i-1)], 'k-', lw = 1) \n",
"\n",
"ax.plot(np.r_[xtemp_rxP, xtemp_rxP], np.r_[0., 0.2], 'k-', lw = 1)\n",
"ax.plot(np.r_[xtemp_rxN, xtemp_rxN], np.r_[0., 0.2], 'k-', lw = 1)\n",
"ax.plot(xtemp_rxP, ytemp_rx, 'ko')\n",
"ax.plot(xtemp_rxN, ytemp_rx, 'go')\n",
"ax.plot(np.r_[xtemp_rxP, xtemp_rxN], np.r_[0.2, 0.2], 'k-', lw = 1) \n",
"\n",
"ax.grid(True) \n",
"ax.set_ylim(-0.2,0.6)\n",
"ax.set_xlim(-600,600)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 124,
"text": [
"(-600, 600)"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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truncated
"text": [
"<matplotlib.figure.Figure at 0x65e8150>"
]
}
],
"prompt_number": 124
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fig, ax = plt.subplots(1,1, figsize = (5,3))\n",
"mesh.plotSlice(sigma, grid=True, ax = ax, pcolorOpts={'cmap':'binary'})\n",
"ax.plot(xtemp_txP, ytemp_tx, 'bo')\n",
"ax.plot(xtemp_txN, ytemp_tx, 'ro')\n",
"ax.plot(xtemp_rxP, ytemp_rx, 'ko')\n",
"ax.plot(xtemp_rxN, ytemp_rx, 'go')\n",
"ax.set_xlim(-600, 600)\n",
"ax.set_ylim(-200, 200)\n",
"ax.set_title('Survey geometry (Plan view)')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 144,
"text": [
"<matplotlib.text.Text at 0x62fa710>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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truncated
"text": [
"<matplotlib.figure.Figure at 0x4ec6210>"
]
}
],
"prompt_number": 144
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"txlist = []\n",
"rx = DC.DipoleRx(np.r_[xtemp_rxP, ytemp_rx, -12.5], np.r_[xtemp_rxN, ytemp_rx, -12.5])\n",
"for i in range(ntx): \n",
" tx = DC.DipoleTx([xtemp_txP[i], ytemp_tx[i], -12.5],[xtemp_txN[i], ytemp_tx[i], -12.5], [rx])\n",
" txlist.append(tx)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 129
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"survey = DC.SurveyDC(txlist)\n",
"problem = DC.ProblemDC(mesh)\n",
"problem.pair(survey)\n",
"problem.Solver = SolverWrapD(EMUtils.Solver.Mumps)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 133
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Step4: Run DC forward modeling"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"data = survey.dpred(sigma)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 134
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$ \\rho_a = \\frac{V}{I}\\pi\\frac{b(b+a)}{a}$$"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"appres = data*np.pi*b*(b+a)/a\n",
"\n",
"\n",
"fig, ax = plt.subplots(1,1, figsize = (6, 4))\n",
"ax.semilogx(np.r_[100., 500.], np.r_[100., 100.], 'k--')\n",
"ax.semilogx(abhalf, appres, 'k.-')\n",
"ax.set_ylim(90., 120.)\n",
"ax.set_xscale('log')\n",
"ax.set_xlabel('AB/2')\n",
"ax.set_ylabel('Apparent resistivity ($\\Omega m$)')\n",
"ax.grid(True)\n",
"ax.legend(('True', 'simpegDC'), loc = 1, fontsize = 14)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 148,
"text": [
"<matplotlib.legend.Legend at 0x9a06b90>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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truncated
"text": [
"<matplotlib.figure.Figure at 0x934c3d0>"
]
}
],
"prompt_number": 148
}
],
"metadata": {}
}
]
}
notebooks/DC_schumberger_Inv.ipynb
+753
View File
@@ -0,0 +1,753 @@
{
"metadata": {
"name": "",
"signature": "sha256:19c3127b59d003240c9fc3ef942fdeb1b3f06fc6f97ca83dc7d01ca16af87352"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "code",
"collapsed": false,
"input": [
"from SimPEG import *\n",
"import simpegDC as DC\n",
"from simpegem1d import Utils1D\n",
"import simpegEM.Utils as EMUtils\n",
"%pylab inline"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Populating the interactive namespace from numpy and matplotlib\n"
]
}
],
"prompt_number": 89
},
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"1D DC inversion of Schlumberger array"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This is an example for 1D DC Sounding inversion. This 1D inversion usually use analytic foward modeling, which is efficient. However, we choose different approach to show flexibility in geophysical inversion through mapping. Here mapping ($M$)indicates transformation of our model to a different space:\n",
"\n",
"$$\n",
" \\mathbf{m} = M(\\mathbf{\\sigma})\n",
"$$\n",
"\n",
"Now we consider a transformation, which maps 3D conductivity model to 1D layer model. That is, 3D distribution of conducitivity can be parameterized as 1D model. Once we can compute derivative of this transformation, we can change our model space, based on the transformation. \n",
"\n",
"Following example will show you how user can implement this set up with 1D DC inversion example. Note that we have 3D forward modeling mesh."
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Step1: Generate mesh"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"cs = 25.\n",
"npad = 11\n",
"hx = [(cs,npad, -1.3),(cs,41),(cs,npad, 1.3)]\n",
"hy = [(cs,npad, -1.3),(cs,17),(cs,npad, 1.3)]\n",
"hz = [(cs,npad, -1.3),(cs,20)]"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 90
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"mesh = Mesh.TensorMesh([hx, hy, hz], 'CCN')"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 91
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"mesh.plotGrid()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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truncated
"text": [
"<matplotlib.figure.Figure at 0x4702410>"
]
}
],
"prompt_number": 92
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Step2: Generating model and mapping (1D to 3D)"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"mapping = Maps.ExpMap(mesh)*Maps.Vertical1DMap(mesh)\n",
"siglay1 = 1./(100.)\n",
"siglay2 = 1./(500.)\n",
"sighalf = 1./(100.)\n",
"sigma = np.ones(mesh.nCz)*siglay1\n",
"sigma[mesh.vectorCCz<=-100.] = siglay2\n",
"sigma[mesh.vectorCCz<-150.] = sighalf\n",
"mtrue = np.log(sigma)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 138
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"dat = mesh.plotImage(mapping*mtrue)\n",
"print (mapping*mtrue).min()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"0.002\n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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truncated
"text": [
"<matplotlib.figure.Figure at 0x5424110>"
]
}
],
"prompt_number": 139
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fig, ax = plt.subplots(1,1, figsize = (3, 6))\n",
"Utils1D.plotLayer(1./sigma, mesh.vectorCCz, 'log', ax = ax)\n",
"ax.set_ylim(-600, 0)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 140,
"text": [
"(-600, 0)"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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truncated
"text": [
"<matplotlib.figure.Figure at 0x4b9a090>"
]
}
],
"prompt_number": 140
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fig, ax = plt.subplots(1,1, figsize = (7, 5))\n",
"dat = mesh.plotSlice((mapping*mtrue), normal='Y', ind = 9, ax = ax)\n",
"cb = plt.colorbar(dat[0], ax =ax)\n",
"ax.set_title(\"Vertical section\")\n",
"cb.set_label(\"Conductivity (S/m)\")\n",
"ax.set_xlim(-1000., 1000.)\n",
"ax.set_ylim(-500., 0.)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 213,
"text": [
"(-500.0, 0.0)"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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truncated
"text": [
"<matplotlib.figure.Figure at 0x6cda950>"
]
}
],
"prompt_number": 213
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Step3: Design survey: Schulumberger array"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<img src=\"http://www.landrinstruments.com/_/rsrc/1271695892678/home/ultra-minires/additional-information-1/schlumberger-soundings/schlum%20array.JPG\"> </img>"
]
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"$$ \\rho_a = \\frac{V}{I}\\pi\\frac{b(b+a)}{a}$$"
]
},
{
"cell_type": "heading",
"level": 4,
"metadata": {},
"source": [
"Let $b=na$, then we rewrite above equation as:"
]
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"$$ \\rho_a = \\frac{V}{I}\\pi na(n+1)$$"
]
},
{
"cell_type": "heading",
"level": 4,
"metadata": {},
"source": [
"Since AB/2 can be a good measure for depth of investigation, we express "
]
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"$$AB/2 = \\frac{(2n+1)a}{2}$$"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"ntx = 16"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 142
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"xtemp_txP = np.arange(ntx)*(25.)-500.\n",
"xtemp_txN = -xtemp_txP\n",
"ytemp_tx = np.zeros(ntx)\n",
"xtemp_rxP = -50.\n",
"xtemp_rxN = 50.\n",
"ytemp_rx = 0.\n",
"abhalf = abs(xtemp_txP-xtemp_txN)*0.5\n",
"a = xtemp_rxN-xtemp_rxP\n",
"b = ((xtemp_txN-xtemp_txP)-a)*0.5"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 143
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print a\n",
"print b"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"100.0\n",
"[ 450. 425. 400. 375. 350. 325. 300. 275. 250. 225. 200. 175.\n",
" 150. 125. 100. 75.]\n"
]
}
],
"prompt_number": 144
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fig, ax = plt.subplots(1,1, figsize = (12,3))\n",
"for i in range(ntx):\n",
" ax.plot(np.r_[xtemp_txP[i], xtemp_txP[i]], np.r_[0., 0.4-0.01*(i-1)], 'k-', lw = 1)\n",
" ax.plot(np.r_[xtemp_txN[i], xtemp_txN[i]], np.r_[0., 0.4-0.01*(i-1)], 'k-', lw = 1)\n",
" ax.plot(xtemp_txP[i], ytemp_tx[i], 'bo')\n",
" ax.plot(xtemp_txN[i], ytemp_tx[i], 'ro')\n",
" ax.plot(np.r_[xtemp_txP[i], xtemp_txN[i]], np.r_[0.4-0.01*(i-1), 0.4-0.01*(i-1)], 'k-', lw = 1) \n",
"\n",
"ax.plot(np.r_[xtemp_rxP, xtemp_rxP], np.r_[0., 0.2], 'k-', lw = 1)\n",
"ax.plot(np.r_[xtemp_rxN, xtemp_rxN], np.r_[0., 0.2], 'k-', lw = 1)\n",
"ax.plot(xtemp_rxP, ytemp_rx, 'ko')\n",
"ax.plot(xtemp_rxN, ytemp_rx, 'go')\n",
"ax.plot(np.r_[xtemp_rxP, xtemp_rxN], np.r_[0.2, 0.2], 'k-', lw = 1) \n",
"\n",
"ax.grid(True) \n",
"ax.set_ylim(-0.2,0.6)\n",
"# ax.set_xlim(-600,600)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 145,
"text": [
"(-0.2, 0.6)"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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truncated
"text": [
"<matplotlib.figure.Figure at 0x4da7b90>"
]
}
],
"prompt_number": 145
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fig, ax = plt.subplots(1,1, figsize = (5,3))\n",
"mesh.plotSlice(np.log10(mapping*mtrue), grid=True, ax = ax, pcolorOpts={'cmap':'binary'})\n",
"ax.plot(xtemp_txP, ytemp_tx, 'bo')\n",
"ax.plot(xtemp_txN, ytemp_tx, 'ro')\n",
"ax.plot(xtemp_rxP, ytemp_rx, 'ko')\n",
"ax.plot(xtemp_rxN, ytemp_rx, 'go')\n",
"ax.set_xlim(-1000, 1000)\n",
"ax.set_ylim(-200, 200)\n",
"ax.set_title('Survey geometry (Plan view)')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 220,
"text": [
"<matplotlib.text.Text at 0xee2d3d0>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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truncated
"text": [
"<matplotlib.figure.Figure at 0x77ef110>"
]
}
],
"prompt_number": 220
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We generate tx and rx lists:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"txlist = []\n",
"rx = DC.DipoleRx(np.r_[xtemp_rxP, ytemp_rx, -12.5], np.r_[xtemp_rxN, ytemp_rx, -12.5])\n",
"for i in range(ntx): \n",
" tx = DC.DipoleTx([xtemp_txP[i], ytemp_tx[i], -12.5],[xtemp_txN[i], ytemp_tx[i], -12.5], [rx])\n",
" txlist.append(tx)\n",
"survey = DC.SurveyDC(txlist) "
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 147
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Step4: Set up problem and pair with survey"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"problem = DC.ProblemDC(mesh, mapping=mapping)\n",
"problem.pair(survey)\n",
"problem.Solver = SolverWrapD(EMUtils.Solver.Mumps)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 216
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Step5: Run survey.dpred to comnpute syntetic data"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"data = survey.dpred(mtrue)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 149
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$ \\rho_a = \\frac{V}{I}\\pi\\frac{b(b+a)}{a}$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To make synthetic example you can use survey.makeSyntheticData, which generates related setups"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"survey.makeSyntheticData(mtrue,std=0.01,force=True)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 217
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"appres = data*np.pi*b*(b+a)/a\n",
"appres_obs = survey.dobs*np.pi*b*(b+a)/a\n",
"fig, ax = plt.subplots(1,1, figsize = (6, 4))\n",
"ax.semilogx(abhalf, appres, '.-')\n",
"ax.semilogx(abhalf, appres_obs, '.-')\n",
"ax.set_xscale('log')\n",
"ax.set_ylim(100., 180.)\n",
"ax.set_xlabel('AB/2')\n",
"ax.set_ylabel('Apparent resistivity ($\\Omega m$)')\n",
"ax.grid(True)\n",
"ax.legend(('Observed', 'Predicted'), loc = 1)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 214,
"text": [
"<matplotlib.legend.Legend at 0xee25050>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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truncated
"text": [
"<matplotlib.figure.Figure at 0xe215c90>"
]
}
],
"prompt_number": 214
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Step6: Run inversion"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"dmis = DataMisfit.l2_DataMisfit(survey)\n",
"reg = Regularization.Tikhonov(mesh,mapping=mapping)\n",
"opt = Optimization.InexactGaussNewton(maxIter=7,tolX=1e-15)\n",
"opt.remember('xc')\n",
"invProb = InvProblem.BaseInvProblem(dmis, reg, opt)\n",
"beta = Directives.BetaEstimate_ByEig(beta0_ratio=1e1)\n",
"betaSched = Directives.BetaSchedule(coolingFactor=5, coolingRate=2)\n",
"inv = Inversion.BaseInversion(invProb, directiveList=[beta,betaSched])"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 162
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"m0 = np.log(np.ones(problem.mapping.nP)*sighalf)\n",
"mopt = inv.run(m0)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"SimPEG.InvProblem will set Regularization.mref to m0.\n",
"SimPEG.InvProblem is setting bfgsH0 to the inverse of the eval2Deriv.\n",
" ***Done using same solver as the problem***\n",
"SimPEG.l2_DataMisfit is creating default weightings for Wd."
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"============================ Inexact Gauss Newton ============================"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" # beta phi_d phi_m f |proj(x-g)-x| LS Comment \n",
"-----------------------------------------------------------------------------\n",
" 0 9.67e-02 6.33e+03 2.24e+04 8.50e+03 9.06e+03 0 "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" 1 9.67e-02 4.67e+02 7.43e+03 1.19e+03 2.80e+03 0 "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" 2 1.93e-02 1.95e+02 4.57e+03 2.84e+02 4.36e+02 0 "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" 3 1.93e-02 1.02e+02 7.15e+03 2.40e+02 1.26e+02 0 "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" 4 3.87e-03 1.11e+02 6.52e+03 1.37e+02 2.18e+02 0 "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" 5 3.87e-03 3.10e+01 1.73e+04 9.80e+01 1.06e+02 0 "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" 6 7.73e-04 3.94e+01 1.45e+04 5.07e+01 1.01e+02 0 "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" 7 7.73e-04 1.04e+01 3.03e+04 3.38e+01 3.64e+01 0 "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"------------------------- STOP! -------------------------\n",
"1 : |fc-fOld| = 1.6880e+01 <= tolF*(1+|f0|) = 8.5000e+02\n",
"0 : |xc-x_last| = 1.3315e+00 <= tolX*(1+|x0|) = 2.6641e-14\n",
"0 : |proj(x-g)-x| = 3.6437e+01 <= tolG = 1.0000e-01\n",
"0 : |proj(x-g)-x| = 3.6437e+01 <= 1e3*eps = 1.0000e-02\n",
"1 : maxIter = 7 <= iter = 7\n",
"------------------------- DONE! -------------------------\n"
]
}
],
"prompt_number": 163
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"matplotlib.rcParams.update({'font.size': 14, 'text.usetex': True, 'font.family': 'arial'})"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 207
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"appres = data*np.pi*b*(b+a)/a\n",
"appres_obs = survey.dobs*np.pi*b*(b+a)/a\n",
"appres_pred = invProb.dpred*np.pi*b*(b+a)/a\n",
"fig, ax = plt.subplots(1,1, figsize = (6, 4))\n",
"ax.plot(abhalf, appres_obs, 'k.-')\n",
"ax.plot(abhalf, appres_pred, 'r.-')\n",
"ax.set_xscale('log')\n",
"ax.set_ylim(100., 180.)\n",
"ax.set_xlabel('AB/2')\n",
"ax.set_ylabel('Apparent resistivity ($\\Omega m$)')\n",
"ax.grid(True)\n",
"ax.legend(('Observed', 'Predicted'), loc = 1)\n",
"fig.savefig('obspred_dc1d_dat.png')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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truncated
"text": [
"<matplotlib.figure.Figure at 0x6cbdf90>"
]
}
],
"prompt_number": 218
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fig, ax = plt.subplots(1,1, figsize = (3, 6))\n",
"ax.plot(1., 1., 'k', lw = 2)\n",
"ax.plot(1., 1., 'r', lw = 2)\n",
"ax.legend(('True', 'Recovered'), loc = 4, fontsize = 14)\n",
"Utils1D.plotLayer(1./(np.exp(mopt)), mesh.vectorCCz, 'log', ax = ax, **{'lw':2, 'color':'r'})\n",
"Utils1D.plotLayer(1./(np.exp(mtrue)), mesh.vectorCCz, 'log', ax = ax, **{'lw':2})\n",
"ax.set_ylim(-600, 0)\n",
"fig.savefig('obspred_dc1d_mod.png')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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truncated
"text": [
"<matplotlib.figure.Figure at 0xdbb1050>"
]
}
],
"prompt_number": 219
}
],
"metadata": {}
}
]
}
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