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Seogi's FDEM initial commit from SimPEG
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@@ -0,0 +1,489 @@
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{
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"metadata": {
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"name": "3DFDEM"
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},
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"nbformat": 3,
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"nbformat_minor": 0,
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"worksheets": [
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{
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"cells": [
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{
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"cell_type": "code",
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"collapsed": false,
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"input": [
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"import numpy as np\n",
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"from SimPEG import Solver, utils, TensorMesh\n",
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"from getInterpmat import getInterpmat\n",
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"from RHSem import path2edgeModel, MMRhalf"
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],
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"language": "python",
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"metadata": {},
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"outputs": [],
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"prompt_number": 1
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},
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{
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"cell_type": "heading",
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"level": 1,
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"metadata": {},
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"source": [
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"3D frequency domain EM code with wire source"
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]
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},
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{
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"cell_type": "heading",
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"level": 2,
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"metadata": {},
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"source": [
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"Step1: Generating mesh"
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]
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},
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{
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"cell_type": "code",
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"collapsed": false,
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"input": [
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"cs = 100\n",
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"ncore = 6\n",
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"pad = 5\n",
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"padfactor = 1.5\n",
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"cs = 100\n",
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"xpad = cs*(np.ones(pad)*padfactor)**np.arange(pad)\n",
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"ypad = cs*(np.ones(pad)*padfactor)**np.arange(pad)\n",
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"zpad = cs*(np.ones(pad)*padfactor)**np.arange(pad)\n",
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"\n",
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"xcore = cs*np.ones(ncore)\n",
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"ycore = cs*np.ones(ncore)\n",
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"zcore = cs*np.ones(ncore)\n",
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"\n",
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"hx = np.r_[xpad[::-1],xcore, cs, xcore, xpad]\n",
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"hy = np.r_[ypad[::-1],ycore, cs, ycore, ypad]\n",
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"hz = np.r_[zpad[::-1],zcore,zcore, zpad]\n",
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"\n",
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"x0 = np.array([-sum(hx)/2, -sum(hy)/2, -sum(hz)/2])\n",
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"mesh = TensorMesh([hx, hy, hz],x0)"
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],
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"language": "python",
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"metadata": {},
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"outputs": [],
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"prompt_number": 2
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},
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{
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"cell_type": "code",
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"collapsed": false,
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"input": [
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"mesh.plotGrid()"
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],
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"language": "python",
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"metadata": {},
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"outputs": [
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{
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"output_type": "stream",
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"stream": "stderr",
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"text": [
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"C:\\Users\\SEOGI\\AppData\\Local\\Enthought\\Canopy\\App\\appdata\\canopy-1.0.1.1189.win-x86_64\\lib\\site-packages\\matplotlib\\lines.py:483: RuntimeWarning: invalid value encountered in greater_equal\n",
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" return np.alltrue(x[1:]-x[0:-1]>=0)\n"
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]
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},
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{
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"output_type": "display_data",
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"png": 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truncated
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"text": [
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"<matplotlib.figure.Figure at 0x7d56f60>"
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]
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}
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],
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"prompt_number": 3
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": []
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},
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{
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"cell_type": "heading",
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"level": 2,
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"metadata": {},
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"source": [
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"Step2: Generate conductivity model"
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]
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},
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{
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"cell_type": "code",
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"collapsed": false,
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"input": [
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"sigma = 1e-8*np.ones(prod(mesh.nC))\n",
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"Ind = mesh.gridCC[:,2]<0\n",
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"sigma[Ind] = 1e-3\n",
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"mesh.plotImage(sigma)"
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],
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"language": "python",
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"metadata": {},
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"outputs": [
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{
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"output_type": "pyout",
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"prompt_number": 4,
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"text": [
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"<matplotlib.collections.QuadMesh at 0x8276080>"
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]
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},
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{
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"output_type": "display_data",
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||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x7dd8048>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 4
|
||||
},
|
||||
{
|
||||
"cell_type": "heading",
|
||||
"level": 2,
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"Step3: Genereate the system matrix A\n",
|
||||
" "
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"Here we use the time dependency $e^{-\\imath\\omega t}$. Thus, our system for frequency domain EM problem can be written as \n",
|
||||
"\\begin{eqnarray}\n",
|
||||
"\t\\nabla \\times E -\\imath\\omega B = 0,\\\\\n",
|
||||
"\t\\nabla \\times \\frac{1}{\\mu} B - \\sigma (\\omega)^* E = J^s, \\\\\n",
|
||||
"\t\\tilde{n} \\times \\frac{1}{\\mu} B |_{\\partial \\Omega} = 0.\n",
|
||||
"\\end{eqnarray}\n",
|
||||
"By using weak formultion we have,\n",
|
||||
"\\begin{eqnarray}\n",
|
||||
"\t<\\nabla \\times E, \\mathbf{F}> - <\\imath\\omega B, \\mathbf{F}> = 0, \\\\\n",
|
||||
"\t<\\nabla \\times \\frac{1}{\\mu}\\mathbf{B}, \\mathbf{W}>-<\\mathbf{\\sigma}(\\omega)^*\\mathbf{E}, \\mathbf{W}> = <\\mathbf{J}^s, \\mathbf{W}>.\n",
|
||||
"\\end{eqnarray}\n",
|
||||
"By using the same trick we used for MMR problem with boundary conditions, we have discretized system \n",
|
||||
"\\begin{eqnarray}\n",
|
||||
"\t\\mathbf{M}_f\\mathbf{Curl}\\mathbf{e} - \\imath\\omega\\mathbf{M}_f\\mathbf{b} = 0, \\\\\n",
|
||||
"\t\\mathbf{Curl}^T\\mathbf{M}_{\\frac{1}{\\mu}}\\mathbf{b} - \\mathbf{M}_{\\sigma}^*\\mathbf{e} \n",
|
||||
"\t=\\mathbf{M}_e\\mathbf{j}^s. \n",
|
||||
"\\end{eqnarray}\n",
|
||||
"Rearranging above equations in terms of $\\mathbf{e}$ gives\n",
|
||||
"\\begin{eqnarray}\n",
|
||||
"\t\\mathbf{Curl}^T\\mathbf{M}_{\\frac{1}{\\mu}}\\mathbf{Curl}\\mathbf{e} - \\imath\\omega\\mathbf{M}_{\\sigma}^*\\mathbf{e} \n",
|
||||
"\t = \\imath\\omega\\mathbf{M}_e\\mathbf{j}^s.\n",
|
||||
"\\end{eqnarray}\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"f = 1e-5\n",
|
||||
"w = 2*np.pi*f\n",
|
||||
"mu0 = 4*pi*1e-7\n",
|
||||
"C = mesh.edgeCurl\n",
|
||||
"Msig = mesh.getEdgeInnerProduct(sigma)\n",
|
||||
"Mf = mesh.getFaceInnerProduct()\n",
|
||||
"Me = mesh.getEdgeInnerProduct()\n",
|
||||
"A = C.T*1/mu0*Mf*C-1j*w*Msig"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 5
|
||||
},
|
||||
{
|
||||
"cell_type": "heading",
|
||||
"level": 2,
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"Step 4: Generate right hand side"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"pts = np.array([[550, 50, 0],\n",
|
||||
" [550, 550, 0],\n",
|
||||
" [-550, 550, 0],\n",
|
||||
" [-550, 50, 0]\n",
|
||||
" ])\n",
|
||||
"Js = path2edgeModel(mesh, pts)\n",
|
||||
"L = mesh.edge\n",
|
||||
"rhs = 1j*w*L*Js"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 6
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"plot(pts[:,0], pts[:,1])\n",
|
||||
"ylim ([-600, 600])"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"output_type": "pyout",
|
||||
"prompt_number": 22,
|
||||
"text": [
|
||||
"(-600, 600)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0xd85d518>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 22
|
||||
},
|
||||
{
|
||||
"cell_type": "heading",
|
||||
"level": 2,
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"Step 5: Solve the linear system "
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"from time import time\n",
|
||||
"tic = time()\n",
|
||||
"f = Solver(A)\n",
|
||||
"E = f.solve(rhs)\n",
|
||||
"B = 1/(1j*w)*C*E\n",
|
||||
"print time() - tic"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"output_type": "stream",
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
"86.271999836\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 8
|
||||
},
|
||||
{
|
||||
"cell_type": "heading",
|
||||
"level": 2,
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"Step 6: Project to receiver points"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"E = np.conj(E)\n",
|
||||
"B = -np.conj(B)\n",
|
||||
"xr = np.linspace(-400, 400, 21)\n",
|
||||
"yr = np.linspace(-400, 400, 21)"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 9
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"X, Y = np.meshgrid(xr, yr)\n",
|
||||
"Z = np.zeros((size(xr), size(yr)))"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 10
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"rxLoc = np.c_[utils.mkvc(X), utils.mkvc(Y), utils.mkvc(Z)]\n",
|
||||
"Qfx = getInterpmat(mesh, rxLoc, 'fx')\n",
|
||||
"Qfy = getInterpmat(mesh, rxLoc, 'fy')\n",
|
||||
"Qfz = getInterpmat(mesh, rxLoc, 'fz')\n",
|
||||
"Qex = getInterpmat(mesh, rxLoc, 'ex')\n",
|
||||
"Qey = getInterpmat(mesh, rxLoc, 'ey')"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 11
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"Bx = reshape(Qfx*B, (size(xr), size(yr)), order = 'F')\n",
|
||||
"By = reshape(Qfy*B, (size(xr), size(yr)), order = 'F')\n",
|
||||
"Bz = reshape(Qfz*B, (size(xr), size(yr)), order = 'F')\n",
|
||||
"Ex = reshape(Qex*E, (size(xr), size(yr)), order = 'F')\n",
|
||||
"Ey = reshape(Qey*E, (size(xr), size(yr)), order = 'F')"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 12
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"Bxa, Bya = MMRhalf([-550,50], [550, 50], X, Y)"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 13
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"subplot(121)\n",
|
||||
"contourf(X, Y, By.real, 20)\n",
|
||||
"plt.colorbar()\n",
|
||||
"plt.title('By 3DFDEM')\n",
|
||||
"subplot(122)\n",
|
||||
"contourf(X, Y, Bx.real, 20)\n",
|
||||
"plt.colorbar()\n",
|
||||
"plt.title('Bx 3DFDEM')"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"output_type": "pyout",
|
||||
"prompt_number": 25,
|
||||
"text": [
|
||||
"<matplotlib.text.Text at 0xe148ba8>"
|
||||
]
|
||||
},
|
||||
{
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0xd475fd0>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 25
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"subplot(121)\n",
|
||||
"contourf(X, Y, Bya, 20)\n",
|
||||
"plt.colorbar()\n",
|
||||
"plt.title('By analytic')\n",
|
||||
"subplot(122)\n",
|
||||
"contourf(X, Y, Bxa, 20)\n",
|
||||
"plt.colorbar()\n",
|
||||
"plt.title('Bx analytic')"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"output_type": "pyout",
|
||||
"prompt_number": 26,
|
||||
"text": [
|
||||
"<matplotlib.text.Text at 0xe737c50>"
|
||||
]
|
||||
},
|
||||
{
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0xd86f978>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 26
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"vec = np.linspace(0,size(Bya)-1,size(Bya)) \n",
|
||||
"plot(vec, utils.mkvc(Bya), vec, utils.mkvc(By))\n",
|
||||
"plt.legend(['Analytic', '3DFDEM'])"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"output_type": "stream",
|
||||
"stream": "stderr",
|
||||
"text": [
|
||||
"C:\\Users\\SEOGI\\AppData\\Local\\Enthought\\Canopy\\User\\lib\\site-packages\\numpy\\core\\numeric.py:320: ComplexWarning: Casting complex values to real discards the imaginary part\n",
|
||||
" return array(a, dtype, copy=False, order=order)\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"output_type": "pyout",
|
||||
"prompt_number": 16,
|
||||
"text": [
|
||||
"<matplotlib.legend.Legend at 0xb6e3470>"
|
||||
]
|
||||
},
|
||||
{
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0xb6e3588>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 16
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"subplot(121),\n",
|
||||
"quiver(X, Y, Bx, By)\n",
|
||||
"subplot(122),\n",
|
||||
"quiver(X, Y, Bxa, Bya)"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"output_type": "pyout",
|
||||
"prompt_number": 17,
|
||||
"text": [
|
||||
"<matplotlib.quiver.Quiver at 0xd280cc0>"
|
||||
]
|
||||
},
|
||||
{
|
||||
"output_type": "display_data",
|
||||
"png": "iVBORw0KGgoAAAANSUhEUgAAAYMAAAD9CAYAAABeOxsXAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x828ccc0>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 17
|
||||
}
|
||||
],
|
||||
"metadata": {}
|
||||
}
|
||||
]
|
||||
}
|
||||
@@ -0,0 +1,731 @@
|
||||
{
|
||||
"metadata": {
|
||||
"name": "GroundedSource"
|
||||
},
|
||||
"nbformat": 3,
|
||||
"nbformat_minor": 0,
|
||||
"worksheets": [
|
||||
{
|
||||
"cells": [
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"import numpy as np\n",
|
||||
"import matplotlib.pyplot as plt\n",
|
||||
"from SimPEG import TensorMesh"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 18
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"pad = 1\n",
|
||||
"padfactor = 1.5\n",
|
||||
"cs = 100\n",
|
||||
"xpad = cs*(np.ones(pad)*padfactor)**np.arange(pad)\n",
|
||||
"ypad = cs*(np.ones(pad)*padfactor)**np.arange(pad)\n",
|
||||
"zpad = cs*(np.ones(pad)*padfactor)**np.arange(pad)\n",
|
||||
"\n",
|
||||
"core = 10\n",
|
||||
"xcore = cs*np.ones(core)\n",
|
||||
"ycore = cs*np.ones(core)\n",
|
||||
"zcore = cs*np.ones(core)\n",
|
||||
"\n",
|
||||
"hx = np.r_[xpad[::-1],xcore, cs, xcore,xpad]\n",
|
||||
"hy = np.r_[ypad[::-1],ycore, cs, ycore, ypad]\n",
|
||||
"hz = np.r_[zpad[::-1],zcore,zcore, zpad]\n",
|
||||
"x0 = np.array([-np.sum(hx)/2, -np.sum(hy)/2, -np.sum(hz)/2], )\n",
|
||||
"mesh = TensorMesh([hx, hy, hz],x0)"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 19
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"print mesh"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"output_type": "stream",
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
" ---- 3-D TensorMesh ---- \n",
|
||||
" x0: -1150.00\n",
|
||||
" y0: -1150.00\n",
|
||||
" z0: -1100.00\n",
|
||||
" nCx: 23\n",
|
||||
" nCy: 23\n",
|
||||
" nCz: 22\n",
|
||||
" hx: 23*100.00\n",
|
||||
" hy: 23*100.00\n",
|
||||
" hz: 22*100.00\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 20
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"pts = np.array([[950, 50, 0], \n",
|
||||
" [950, 950, 0],\n",
|
||||
" [-950, 950,0],\n",
|
||||
" [-950, 50, 0]])\n",
|
||||
"pts = np.array([[950, 50, -500], \n",
|
||||
" [950, 50, +500]])\n",
|
||||
"pts = np.array([[950, 50, -200],\n",
|
||||
"\t\t\t\t[950, 50, 0], \n",
|
||||
" [950, 950, 0],\n",
|
||||
" [-950, 950,0],\n",
|
||||
" [-950, 50, 0],\n",
|
||||
" [-950, 50, -200]])\n"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 21
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"print mesh.vectorCCx\n",
|
||||
"print mesh.vectorCCy\n",
|
||||
"print mesh.vectorCCz\n"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"output_type": "stream",
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
"[-1100. -1000. -900. -800. -700. -600. -500. -400. -300. -200.\n",
|
||||
" -100. 0. 100. 200. 300. 400. 500. 600. 700. 800.\n",
|
||||
" 900. 1000. 1100.]\n",
|
||||
"[-1100. -1000. -900. -800. -700. -600. -500. -400. -300. -200.\n",
|
||||
" -100. 0. 100. 200. 300. 400. 500. 600. 700. 800.\n",
|
||||
" 900. 1000. 1100.]\n",
|
||||
"[-1050. -950. -850. -750. -650. -550. -450. -350. -250. -150.\n",
|
||||
" -50. 50. 150. 250. 350. 450. 550. 650. 750. 850.\n",
|
||||
" 950. 1050.]\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 22
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 22
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"def ismember(a, b):\n",
|
||||
" tf = np.array([i in b for i in a])\n",
|
||||
" return tf"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 23
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"#def edgeModel = path2edgeModel\n",
|
||||
"edm_x = np.zeros(np.prod(mesh.nEx))\n",
|
||||
"edm_y = np.zeros(np.prod(mesh.nEy))\n",
|
||||
"edm_z = np.zeros(np.prod(mesh.nEz))\n",
|
||||
"\n",
|
||||
"for ii in range (pts.shape[0]-1):\n",
|
||||
" pt1 = pts[ii,:]\n",
|
||||
" pt2 = pts[ii+1,:]\n",
|
||||
" delta = pt2 - pt1\n",
|
||||
" deltaDim = np.argwhere(delta)\n",
|
||||
" #assert(np.size(deltaDim)==1), \"Path must be orthoginal to mesh\"\n",
|
||||
" if deltaDim == 0:\n",
|
||||
" xLoc = mesh.vectorCCx[(min(pt1[0],pt2[0]) < mesh.vectorCCx ) & (mesh.vectorCCx < max(pt1[0],pt2[0]))]\n",
|
||||
" yLoc = pts[ii,1]\n",
|
||||
" zLoc = pts[ii,2]\n",
|
||||
" delDir = np.sign(pt2[0]-pt1[0])\n",
|
||||
" xyz = np.c_[xLoc, np.ones(np.size(xLoc))*yLoc, np.ones(np.size(xLoc))*zLoc]\n",
|
||||
" edgeInd=ismember(map(tuple,mesh.gridEx),map(tuple,xyz))\n",
|
||||
" edm_x[edgeInd] = delDir\n",
|
||||
" print '>> x-direction', ii\n",
|
||||
" print mesh.gridEx[edgeInd]\n",
|
||||
" if deltaDim == 1: \n",
|
||||
" xLoc = pts[ii,0]\n",
|
||||
" yLoc = mesh.vectorCCy[(min(pt1[1],pt2[1]) < mesh.vectorCCy ) & (mesh.vectorCCy < max(pt1[1],pt2[1]))]\n",
|
||||
" zLoc = pts[ii,2]\n",
|
||||
" delDir = np.sign(pt2[1]-pt1[1])\n",
|
||||
" xyz = np.c_[np.ones(np.size(yLoc))*xLoc, yLoc, np.ones(np.size(yLoc))*zLoc]\n",
|
||||
" edgeInd=ismember(map(tuple,mesh.gridEy),map(tuple,xyz))\n",
|
||||
" edm_y[edgeInd] = delDir\n",
|
||||
" print '>> y-direction', ii\n",
|
||||
" print mesh.gridEy[edgeInd]\n",
|
||||
" if deltaDim == 2: \n",
|
||||
" xLoc = pts[ii,0]\n",
|
||||
" yLoc = pts[ii,1]\n",
|
||||
" zLoc = mesh.vectorCCz[(min(pt1[2],pt2[2]) < mesh.vectorCCz ) & (mesh.vectorCCz < max(pt1[2],pt2[2]))]\n",
|
||||
" delDir = np.sign(pt2[2]-pt1[2])\n",
|
||||
" xyz = np.c_[np.ones(np.size(zLoc))*xLoc, np.ones(np.size(zLoc))*yLoc, zLoc]\n",
|
||||
" edgeInd=ismember(map(tuple,mesh.gridEz),map(tuple,xyz))\n",
|
||||
" edm_z[edgeInd] = delDir\n",
|
||||
" print '>> z-direction', ii\n",
|
||||
" print mesh.gridEz[edgeInd]\n",
|
||||
" \n",
|
||||
" edgeModel = np.r_[edm_x, edm_y, edm_z]"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"output_type": "stream",
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
">> z-direction 0\n",
|
||||
"[[ 950. 50. -150.]\n",
|
||||
" [ 950. 50. -50.]]\n",
|
||||
">> y-direction 1\n",
|
||||
"[[ 950. 100. 0.]\n",
|
||||
" [ 950. 200. 0.]\n",
|
||||
" [ 950. 300. 0.]\n",
|
||||
" [ 950. 400. 0.]\n",
|
||||
" [ 950. 500. 0.]\n",
|
||||
" [ 950. 600. 0.]\n",
|
||||
" [ 950. 700. 0.]\n",
|
||||
" [ 950. 800. 0.]\n",
|
||||
" [ 950. 900. 0.]]\n",
|
||||
">> x-direction"
|
||||
]
|
||||
},
|
||||
{
|
||||
"output_type": "stream",
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
" 2\n",
|
||||
"[[-900. 950. 0.]\n",
|
||||
" [-800. 950. 0.]\n",
|
||||
" [-700. 950. 0.]\n",
|
||||
" [-600. 950. 0.]\n",
|
||||
" [-500. 950. 0.]\n",
|
||||
" [-400. 950. 0.]\n",
|
||||
" [-300. 950. 0.]\n",
|
||||
" [-200. 950. 0.]\n",
|
||||
" [-100. 950. 0.]\n",
|
||||
" [ 0. 950. 0.]\n",
|
||||
" [ 100. 950. 0.]\n",
|
||||
" [ 200. 950. 0.]\n",
|
||||
" [ 300. 950. 0.]\n",
|
||||
" [ 400. 950. 0.]\n",
|
||||
" [ 500. 950. 0.]\n",
|
||||
" [ 600. 950. 0.]\n",
|
||||
" [ 700. 950. 0.]\n",
|
||||
" [ 800. 950. 0.]\n",
|
||||
" [ 900. 950. 0.]]\n",
|
||||
">> y-direction"
|
||||
]
|
||||
},
|
||||
{
|
||||
"output_type": "stream",
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
" 3\n",
|
||||
"[[-950. 100. 0.]\n",
|
||||
" [-950. 200. 0.]\n",
|
||||
" [-950. 300. 0.]\n",
|
||||
" [-950. 400. 0.]\n",
|
||||
" [-950. 500. 0.]\n",
|
||||
" [-950. 600. 0.]\n",
|
||||
" [-950. 700. 0.]\n",
|
||||
" [-950. 800. 0.]\n",
|
||||
" [-950. 900. 0.]]\n",
|
||||
">> z-direction 4\n",
|
||||
"[[-950. 50. -150.]\n",
|
||||
" [-950. 50. -50.]]\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 24
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"print xyz\n",
|
||||
"print mesh.vectorNx\n",
|
||||
"print mesh.vectorNy\n",
|
||||
"print mesh.vectorNz"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"output_type": "stream",
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
"[[-950. 50. -150.]\n",
|
||||
" [-950. 50. -50.]]\n",
|
||||
"[-1150. -1050. -950. -850. -750. -650. -550. -450. -350. -250.\n",
|
||||
" -150. -50. 50. 150. 250. 350. 450. 550. 650. 750.\n",
|
||||
" 850. 950. 1050. 1150.]\n",
|
||||
"[-1150. -1050. -950. -850. -750. -650. -550. -450. -350. -250.\n",
|
||||
" -150. -50. 50. 150. 250. 350. 450. 550. 650. 750.\n",
|
||||
" 850. 950. 1050. 1150.]\n",
|
||||
"[-1100. -1000. -900. -800. -700. -600. -500. -400. -300. -200.\n",
|
||||
" -100. 0. 100. 200. 300. 400. 500. 600. 700. 800.\n",
|
||||
" 900. 1000. 1100.]\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 25
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"mesh.plotImage(edm_x, imageType='Ex')"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"output_type": "pyout",
|
||||
"prompt_number": 26,
|
||||
"text": [
|
||||
"<matplotlib.collections.QuadMesh at 0xaad7588>"
|
||||
]
|
||||
},
|
||||
{
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0xaac2748>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 26
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"mesh.plotImage(edm_y, imageType='Ey')"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"output_type": "pyout",
|
||||
"prompt_number": 27,
|
||||
"text": [
|
||||
"<matplotlib.collections.QuadMesh at 0xafdf9e8>"
|
||||
]
|
||||
},
|
||||
{
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0xaac32e8>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 27
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"mesh.plotImage(edm_z, imageType='Ez')"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"output_type": "pyout",
|
||||
"prompt_number": 28,
|
||||
"text": [
|
||||
"<matplotlib.collections.QuadMesh at 0xad95e48>"
|
||||
]
|
||||
},
|
||||
{
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x796c630>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 28
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"subplot(131)\n",
|
||||
"plot(edm_x)\n",
|
||||
"subplot(132)\n",
|
||||
"plot(edm_y)\n",
|
||||
"subplot(133)\n",
|
||||
"plot(edm_z)"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"output_type": "pyout",
|
||||
"prompt_number": 29,
|
||||
"text": [
|
||||
"[<matplotlib.lines.Line2D at 0xb903588>]"
|
||||
]
|
||||
},
|
||||
{
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0xad85438>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 29
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"A = np.array([2,5,2,6,3,6,2,2,5])\n",
|
||||
"B = np.array([3,4,4,3,6])\n",
|
||||
"\n",
|
||||
"def ismember(a, b):\n",
|
||||
" tf = np.array([i in b for i in a])\n",
|
||||
" return tf\n",
|
||||
"\n",
|
||||
"temp=ismember(map(tuple,mesh.gridEx),map(tuple,xyz))\n"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 13
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"print [i in ['x', 'y', 'z'] for i in ['y','w']]"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"output_type": "stream",
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
"[True, False]\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 14
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 14
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"def path2edgeModel(mesh, pts):\n",
|
||||
" edm_x = np.zeros(np.prod(mesh.nEx))\n",
|
||||
" edm_y = np.zeros(np.prod(mesh.nEy))\n",
|
||||
" edm_z = np.zeros(np.prod(mesh.nEz))\n",
|
||||
" \n",
|
||||
" for ii in range (pts.shape[0]-1):\n",
|
||||
" pt1 = pts[ii,:]\n",
|
||||
" pt2 = pts[ii+1,:]\n",
|
||||
" delta = pt2 - pt1\n",
|
||||
" deltaDim = np.argwhere(delta)\n",
|
||||
" #assert(np.size(deltaDim)==1), \"Path must be orthoginal to mesh\"\n",
|
||||
" if deltaDim == 0:\n",
|
||||
" xLoc = mesh.vectorCCx[(min(pt1[0],pt2[0]) < mesh.vectorCCx ) & (mesh.vectorCCx < max(pt1[0],pt2[0]))]\n",
|
||||
" yLoc = pts[ii,1]\n",
|
||||
" zLoc = pts[ii,2]\n",
|
||||
" delDir = np.sign(pt2[0]-pt1[0])\n",
|
||||
" xyz = np.c_[xLoc, np.ones(np.size(xLoc))*yLoc, np.ones(np.size(xLoc))*zLoc]\n",
|
||||
" edgeInd=ismember(map(tuple,mesh.gridEx),map(tuple,xyz))\n",
|
||||
" edm_x[edgeInd] = delDir\n",
|
||||
" print '>> x-direction', ii\n",
|
||||
" print mesh.gridEx[edgeInd]\n",
|
||||
" if deltaDim == 1: \n",
|
||||
" xLoc = pts[ii,0]\n",
|
||||
" yLoc = mesh.vectorCCy[(min(pt1[1],pt2[1]) < mesh.vectorCCy ) & (mesh.vectorCCy < max(pt1[1],pt2[1]))]\n",
|
||||
" zLoc = pts[ii,2]\n",
|
||||
" delDir = np.sign(pt2[1]-pt1[1])\n",
|
||||
" xyz = np.c_[np.ones(np.size(yLoc))*xLoc, yLoc, np.ones(np.size(yLoc))*zLoc]\n",
|
||||
" edgeInd=ismember(map(tuple,mesh.gridEy),map(tuple,xyz))\n",
|
||||
" edm_y[edgeInd] = delDir\n",
|
||||
" print '>> y-direction', ii\n",
|
||||
" print mesh.gridEy[edgeInd]\n",
|
||||
" if deltaDim == 2: \n",
|
||||
" xLoc = pts[ii,0]\n",
|
||||
" yLoc = pts[ii,1]\n",
|
||||
" zLoc = mesh.vectorCCz[(min(pt1[2],pt2[2]) < mesh.vectorCCz ) & (mesh.vectorCCz < max(pt1[2],pt2[2]))]\n",
|
||||
" delDir = np.sign(pt2[2]-pt1[2])\n",
|
||||
" xyz = np.c_[np.ones(np.size(zLoc))*xLoc, np.ones(np.size(zLoc))*yLoc, zLoc]\n",
|
||||
" edgeInd=ismember(map(tuple,mesh.gridEz),map(tuple,xyz))\n",
|
||||
" edm_z[edgeInd] = delDir\n",
|
||||
" print '>> z-direction', ii\n",
|
||||
" print mesh.gridEz[edgeInd]\n",
|
||||
" \n",
|
||||
" \n",
|
||||
" edgeModel = np.r_[edm_x, edm_y, edm_z]"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 15
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"Js = path2edgeModel(mesh, pts)"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"output_type": "stream",
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
">> z-direction 0\n",
|
||||
"[[ 950. 50. -150.]\n",
|
||||
" [ 950. 50. -50.]]\n",
|
||||
">> y-direction"
|
||||
]
|
||||
},
|
||||
{
|
||||
"output_type": "stream",
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
" 1\n",
|
||||
"[[ 950. 100. 0.]\n",
|
||||
" [ 950. 200. 0.]\n",
|
||||
" [ 950. 300. 0.]\n",
|
||||
" [ 950. 400. 0.]\n",
|
||||
" [ 950. 500. 0.]\n",
|
||||
" [ 950. 600. 0.]\n",
|
||||
" [ 950. 700. 0.]\n",
|
||||
" [ 950. 800. 0.]\n",
|
||||
" [ 950. 900. 0.]]\n",
|
||||
">> x-direction"
|
||||
]
|
||||
},
|
||||
{
|
||||
"output_type": "stream",
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
" 2\n",
|
||||
"[[-900. 950. 0.]\n",
|
||||
" [-800. 950. 0.]\n",
|
||||
" [-700. 950. 0.]\n",
|
||||
" [-600. 950. 0.]\n",
|
||||
" [-500. 950. 0.]\n",
|
||||
" [-400. 950. 0.]\n",
|
||||
" [-300. 950. 0.]\n",
|
||||
" [-200. 950. 0.]\n",
|
||||
" [-100. 950. 0.]\n",
|
||||
" [ 0. 950. 0.]\n",
|
||||
" [ 100. 950. 0.]\n",
|
||||
" [ 200. 950. 0.]\n",
|
||||
" [ 300. 950. 0.]\n",
|
||||
" [ 400. 950. 0.]\n",
|
||||
" [ 500. 950. 0.]\n",
|
||||
" [ 600. 950. 0.]\n",
|
||||
" [ 700. 950. 0.]\n",
|
||||
" [ 800. 950. 0.]\n",
|
||||
" [ 900. 950. 0.]]\n",
|
||||
">> y-direction"
|
||||
]
|
||||
},
|
||||
{
|
||||
"output_type": "stream",
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
" 3\n",
|
||||
"[[-950. 100. 0.]\n",
|
||||
" [-950. 200. 0.]\n",
|
||||
" [-950. 300. 0.]\n",
|
||||
" [-950. 400. 0.]\n",
|
||||
" [-950. 500. 0.]\n",
|
||||
" [-950. 600. 0.]\n",
|
||||
" [-950. 700. 0.]\n",
|
||||
" [-950. 800. 0.]\n",
|
||||
" [-950. 900. 0.]]\n",
|
||||
">> z-direction"
|
||||
]
|
||||
},
|
||||
{
|
||||
"output_type": "stream",
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
" 4\n",
|
||||
"[[-950. 50. -150.]\n",
|
||||
" [-950. 50. -50.]]\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 16
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"print pts"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"output_type": "stream",
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
"[[ 950 50 -200]\n",
|
||||
" [ 950 50 0]\n",
|
||||
" [ 950 950 0]\n",
|
||||
" [-950 950 0]\n",
|
||||
" [-950 50 0]\n",
|
||||
" [-950 50 -200]]\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 30
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 30
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 17
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 17
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 17
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 17
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 17
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 17
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 17
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 17
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 17
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 17
|
||||
}
|
||||
],
|
||||
"metadata": {}
|
||||
}
|
||||
]
|
||||
}
|
||||
@@ -0,0 +1,395 @@
|
||||
{
|
||||
"metadata": {
|
||||
"name": "InterpolationMatrix"
|
||||
},
|
||||
"nbformat": 3,
|
||||
"nbformat_minor": 0,
|
||||
"worksheets": [
|
||||
{
|
||||
"cells": [
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"import numpy as np\n",
|
||||
"import scipy.sparse as sp\n",
|
||||
"from SimPEG.utils import spzeros, mkvc"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 1
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"#x = unique(mesh.gridEx[:,0])\n",
|
||||
"#y = unique(mesh.gridEx[:,1])\n",
|
||||
"#z = unique(mesh.gridEx[:,2])\n",
|
||||
"x = np.linspace(-1000,1000,5)\n",
|
||||
"y = np.linspace(-1000,1000,5)\n",
|
||||
"z = np.linspace(-1000,1000,5)"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 2
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"xr1 = np.linspace(-500,500,5)\n",
|
||||
"yr1 = np.linspace(-500,500,5)\n",
|
||||
"zr1 = 0"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 3
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"xr, yr = meshgrid(xr1, yr1, indexing='ij')\n",
|
||||
"zr = np.ones((xr.shape[0],xr.shape[1]))*zr1"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 4
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"xr = mkvc(xr)\n",
|
||||
"yr = mkvc(yr)\n",
|
||||
"zr = mkvc(zr)"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 5
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"nx = max(x.shape)\n",
|
||||
"ny = max(y.shape)\n",
|
||||
"nz = max(z.shape)\n",
|
||||
"npts = max(xr.shape)\n",
|
||||
"\n",
|
||||
"Q = np.zeros((npts, nx*ny*nz))\n",
|
||||
"\n",
|
||||
"for i in range(npts):\n",
|
||||
"\t# in x-direction \n",
|
||||
" im = np.argmin(abs(x-xr[i]))\n",
|
||||
" if xr[i] - x[im] >= 0: # Point on the left\n",
|
||||
" ind_x1 = im\n",
|
||||
" ind_x2 = im+1\n",
|
||||
" elif xr[i] - x[im] < 0: # Point on the right\n",
|
||||
" ind_x1 = im-1\n",
|
||||
" ind_x2 = im \n",
|
||||
" dx1 = xr[i] - x[ind_x1]\n",
|
||||
" dx2 = x[ind_x2] - xr[i]\n",
|
||||
" # in y-direction\n",
|
||||
" im = np.argmin(abs(y-yr[i]))\n",
|
||||
" if yr[i] - y[im] >= 0: # Point on the left\n",
|
||||
" ind_y1 = im\n",
|
||||
" ind_y2 = im+1\n",
|
||||
" elif yr[i] - y[im] < 0: # Point on the right\n",
|
||||
" ind_y1 = im-1\n",
|
||||
" ind_y2 = im \n",
|
||||
" dy1 = yr[i] - y[ind_y1]\n",
|
||||
" dy2 = y[ind_y2] - yr[i] \n",
|
||||
" # in z-direction\n",
|
||||
" im = np.argmin(abs(z-zr[i]))\n",
|
||||
" if zr[i] - z[im] >= 0: # Point on the left\n",
|
||||
" ind_z1 = im\n",
|
||||
" ind_z2 = im+1\n",
|
||||
" elif zr[i] - z[im] < 0: # Point on the right\n",
|
||||
" ind_z1 = im-1\n",
|
||||
" ind_z2 = im \n",
|
||||
" dz1 = zr[i] - z[ind_z1]\n",
|
||||
" dz2 = z[ind_z2] - zr[i] \n",
|
||||
" dv = (x[ind_x2] - x[ind_x1]) * (y[ind_y2] - y[ind_y1]) *(z[ind_z2] - z[ind_z1])\n",
|
||||
"\n",
|
||||
" Dx = x[ind_x2] - x[ind_x1]\n",
|
||||
" Dy = y[ind_y2] - y[ind_y1]\n",
|
||||
" Dz = z[ind_z2] - z[ind_z1]\n",
|
||||
"\n",
|
||||
" # Get the row in the matrix\n",
|
||||
"\n",
|
||||
" v = np.zeros((nx,ny,nz));\n",
|
||||
" \n",
|
||||
" v[ ind_x1, ind_y1, ind_z1] = (1-dx1/Dx)*(1-dy1/Dy)*(1-dz1/Dz);\n",
|
||||
" v[ ind_x1, ind_y2, ind_z1] = (1-dx1/Dx)*(1-dy2/Dy)*(1-dz1/Dz);\n",
|
||||
" v[ ind_x2, ind_y1, ind_z1] = (1-dx2/Dx)*(1-dy1/Dy)*(1-dz1/Dz);\n",
|
||||
" v[ ind_x2, ind_y2, ind_z1] = (1-dx2/Dx)*(1-dy2/Dy)*(1-dz1/Dz);\n",
|
||||
" v[ ind_x1, ind_y1, ind_z2] = (1-dx1/Dx)*(1-dy1/Dy)*(1-dz2/Dz);\n",
|
||||
" v[ ind_x1, ind_y2, ind_z2] = (1-dx1/Dx)*(1-dy2/Dy)*(1-dz2/Dz);\n",
|
||||
" v[ ind_x2, ind_y1, ind_z2] = (1-dx2/Dx)*(1-dy1/Dy)*(1-dz2/Dz);\n",
|
||||
" v[ ind_x2, ind_y2, ind_z2] = (1-dx2/Dx)*(1-dy2/Dy)*(1-dz2/Dz);\n",
|
||||
" \n",
|
||||
" \n",
|
||||
" Q[i,:] = mkvc(v)\n",
|
||||
"Q = sp.csr_matrix(Q)"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 6
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"import scipy.io\n",
|
||||
"\n",
|
||||
"# import file into a dictionary\n",
|
||||
"f = scipy.io.loadmat('q.mat')\n",
|
||||
" \n",
|
||||
"# read in the structure\n",
|
||||
"Qmat= f['q']\n",
|
||||
"Qmat = Qmat.todense()\n",
|
||||
"Q = Q.todense()"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 7
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"norm(Q-Qmat)"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"output_type": "pyout",
|
||||
"prompt_number": 13,
|
||||
"text": [
|
||||
"0.0"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 13
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"plt.subplot(131)\n",
|
||||
"spy(Q)\n",
|
||||
"plt.subplot(132)\n",
|
||||
"spy(Qmat)\n",
|
||||
"plt.subplot(133)\n",
|
||||
"spy(Qmat-Q)"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"output_type": "pyout",
|
||||
"prompt_number": 15,
|
||||
"text": [
|
||||
"<matplotlib.image.AxesImage at 0x8469588>"
|
||||
]
|
||||
},
|
||||
{
|
||||
"output_type": "display_data",
|
||||
"png": "iVBORw0KGgoAAAANSUhEUgAAAXEAAAAuCAYAAADeKCkyAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n4gAAAABJRU5ErkJggg==\n",
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x84d4cc0>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 15
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"a = np.random.rand(5)\n",
|
||||
"ind = np.logical_and(a>0.1,a<0.5)\n",
|
||||
"print ind"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"output_type": "stream",
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
"[False False False False False]\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 10
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"def interpmat(x,y,z,xr,yr,zr):\n",
|
||||
"\n",
|
||||
" \"\"\" Local nterpolation computed for each receiver point in turn \"\"\"\n",
|
||||
"\n",
|
||||
" nx = max(x.shape)\n",
|
||||
" ny = max(y.shape)\n",
|
||||
" nz = max(z.shape)\n",
|
||||
" npts = max(xr.shape)\n",
|
||||
"\n",
|
||||
" Q = np.zeros((npts, nx*ny*nz))\n",
|
||||
"\n",
|
||||
" for i in range(npts):\n",
|
||||
" \t# in x-direction \n",
|
||||
" im = np.argmin(abs(x-xr[i]))\n",
|
||||
" if xr[i] - x[im] >= 0: # Point on the left\n",
|
||||
" ind_x1 = im\n",
|
||||
" ind_x2 = im+1\n",
|
||||
" elif xr[i] - x[im] < 0: # Point on the right\n",
|
||||
" ind_x1 = im-1\n",
|
||||
" ind_x2 = im \n",
|
||||
" dx1 = xr[i] - x[ind_x1]\n",
|
||||
" dx2 = x[ind_x2] - xr[i]\n",
|
||||
" # in y-direction\n",
|
||||
" im = np.argmin(abs(y-yr[i]))\n",
|
||||
" if yr[i] - y[im] >= 0: # Point on the left\n",
|
||||
" ind_y1 = im\n",
|
||||
" ind_y2 = im+1\n",
|
||||
" elif yr[i] - y[im] < 0: # Point on the right\n",
|
||||
" ind_y1 = im-1\n",
|
||||
" ind_y2 = im \n",
|
||||
" dy1 = yr[i] - y[ind_y1]\n",
|
||||
" dy2 = y[ind_y2] - yr[i] \n",
|
||||
" # in z-direction\n",
|
||||
" im = np.argmin(abs(z-zr[i]))\n",
|
||||
" if zr[i] - z[im] >= 0: # Point on the left\n",
|
||||
" ind_z1 = im\n",
|
||||
" ind_z2 = im+1\n",
|
||||
" elif zr[i] - z[im] < 0: # Point on the right\n",
|
||||
" ind_z1 = im-1\n",
|
||||
" ind_z2 = im \n",
|
||||
" dz1 = zr[i] - z[ind_z1]\n",
|
||||
" dz2 = z[ind_z2] - zr[i] \n",
|
||||
" dv = (x[ind_x2] - x[ind_x1]) * (y[ind_y2] - y[ind_y1]) *(z[ind_z2] - z[ind_z1])\n",
|
||||
"\n",
|
||||
" Dx = x[ind_x2] - x[ind_x1]\n",
|
||||
" Dy = y[ind_y2] - y[ind_y1]\n",
|
||||
" Dz = z[ind_z2] - z[ind_z1]\n",
|
||||
"\n",
|
||||
" # Get the row in the matrix\n",
|
||||
"\n",
|
||||
" v = np.zeros((nx,ny,nz));\n",
|
||||
" \n",
|
||||
" v[ ind_x1, ind_y1, ind_z1] = (1-dx1/Dx)*(1-dy1/Dy)*(1-dz1/Dz);\n",
|
||||
" v[ ind_x1, ind_y2, ind_z1] = (1-dx1/Dx)*(1-dy2/Dy)*(1-dz1/Dz);\n",
|
||||
" v[ ind_x2, ind_y1, ind_z1] = (1-dx2/Dx)*(1-dy1/Dy)*(1-dz1/Dz);\n",
|
||||
" v[ ind_x2, ind_y2, ind_z1] = (1-dx2/Dx)*(1-dy2/Dy)*(1-dz1/Dz);\n",
|
||||
" v[ ind_x1, ind_y1, ind_z2] = (1-dx1/Dx)*(1-dy1/Dy)*(1-dz2/Dz);\n",
|
||||
" v[ ind_x1, ind_y2, ind_z2] = (1-dx1/Dx)*(1-dy2/Dy)*(1-dz2/Dz);\n",
|
||||
" v[ ind_x2, ind_y1, ind_z2] = (1-dx2/Dx)*(1-dy1/Dy)*(1-dz2/Dz);\n",
|
||||
" v[ ind_x2, ind_y2, ind_z2] = (1-dx2/Dx)*(1-dy2/Dy)*(1-dz2/Dz);\n",
|
||||
" \n",
|
||||
" \n",
|
||||
" Q[i,:] = mkvc(v)\n",
|
||||
" Q = sp.csr_matrix(Q)\n",
|
||||
" return Q"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 16
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"Q = interpmat(x,y,z,xr,yr,zr)"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 17
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"Q = Q.todense()\n",
|
||||
"norm(Q-Qmat)"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"output_type": "pyout",
|
||||
"prompt_number": 18,
|
||||
"text": [
|
||||
"0.0"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 18
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"plt.subplot(131)\n",
|
||||
"plt.plot(mkvc(Qmat))\n",
|
||||
"plt.subplot(132)\n",
|
||||
"plt.plot(mkvc(Q))\n",
|
||||
"plt.subplot(133)\n",
|
||||
"plt.plot(mkvc(Qmat-Q))"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"output_type": "pyout",
|
||||
"prompt_number": 29,
|
||||
"text": [
|
||||
"[<matplotlib.lines.Line2D at 0xcfc4ef0>]"
|
||||
]
|
||||
},
|
||||
{
|
||||
"output_type": "display_data",
|
||||
"png": "iVBORw0KGgoAAAANSUhEUgAAAXsAAAD9CAYAAABdoNd6AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0xca3aac8>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 29
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 16
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": []
|
||||
}
|
||||
],
|
||||
"metadata": {}
|
||||
}
|
||||
]
|
||||
}
|
||||
@@ -0,0 +1,73 @@
|
||||
import numpy as np
|
||||
|
||||
def ismember(a, b):
|
||||
tf = np.array([i in b for i in a])
|
||||
return tf
|
||||
|
||||
def path2edgeModel(mesh, pts):
|
||||
edm_x = np.zeros(np.prod(mesh.nEx))
|
||||
edm_y = np.zeros(np.prod(mesh.nEy))
|
||||
edm_z = np.zeros(np.prod(mesh.nEz))
|
||||
|
||||
for ii in range (pts.shape[0]-1):
|
||||
pt1 = pts[ii,:]
|
||||
pt2 = pts[ii+1,:]
|
||||
delta = pt2 - pt1
|
||||
deltaDim = np.argwhere(delta)
|
||||
#assert(np.size(deltaDim)==1), "Path must be orthoginal to mesh"
|
||||
if deltaDim == 0:
|
||||
xLoc = mesh.vectorCCx[(min(pt1[0],pt2[0]) < mesh.vectorCCx ) & (mesh.vectorCCx < max(pt1[0],pt2[0]))]
|
||||
yLoc = pts[ii,1]
|
||||
zLoc = pts[ii,2]
|
||||
delDir = np.sign(pt2[0]-pt1[0])
|
||||
xyz = np.c_[xLoc, np.ones(np.size(xLoc))*yLoc, np.ones(np.size(xLoc))*zLoc]
|
||||
edgeInd=ismember(map(tuple,mesh.gridEx),map(tuple,xyz))
|
||||
edm_x[edgeInd] = delDir
|
||||
# print '>> x-direction', ii
|
||||
# print mesh.gridEx[edgeInd]
|
||||
if deltaDim == 1:
|
||||
xLoc = pts[ii,0]
|
||||
yLoc = mesh.vectorCCy[(min(pt1[1],pt2[1]) < mesh.vectorCCy ) & (mesh.vectorCCy < max(pt1[1],pt2[1]))]
|
||||
zLoc = pts[ii,2]
|
||||
delDir = np.sign(pt2[1]-pt1[1])
|
||||
xyz = np.c_[np.ones(np.size(yLoc))*xLoc, yLoc, np.ones(np.size(yLoc))*zLoc]
|
||||
edgeInd=ismember(map(tuple,mesh.gridEy),map(tuple,xyz))
|
||||
edm_y[edgeInd] = delDir
|
||||
# print '>> y-direction', ii
|
||||
# print mesh.gridEy[edgeInd]
|
||||
if deltaDim == 2:
|
||||
xLoc = pts[ii,0]
|
||||
yLoc = pts[ii,1]
|
||||
zLoc = mesh.vectorCCz[(min(pt1[2],pt2[2]) < mesh.vectorCCz ) & (mesh.vectorCCz < max(pt1[2],pt2[2]))]
|
||||
delDir = np.sign(pt2[2]-pt1[2])
|
||||
xyz = np.c_[np.ones(np.size(zLoc))*xLoc, np.ones(np.size(zLoc))*yLoc, zLoc]
|
||||
edgeInd=ismember(map(tuple,mesh.gridEz),map(tuple,xyz))
|
||||
edm_z[edgeInd] = delDir
|
||||
# print '>> z-direction', ii
|
||||
# print mesh.gridEz[edgeInd]
|
||||
|
||||
|
||||
edgeModel = np.r_[edm_x, edm_y, edm_z]
|
||||
return edgeModel
|
||||
|
||||
def rho(x1, y1, x, y):
|
||||
r = np.sqrt((x-x1)**2+(y-y1)**2)
|
||||
return r
|
||||
|
||||
def MMRhalf(loc1, loc2, x, y):
|
||||
""" Anaytic function for MMR response (B^{1D})
|
||||
- loc1=(x1,y1): x, y location for (+) charge
|
||||
- loc2=(x2,y2): x, y1
|
||||
- x : observation points in x-direction
|
||||
- y : observation points in y-direction
|
||||
"""
|
||||
x1=loc1[0]
|
||||
x2=loc2[0]
|
||||
y1=loc1[1]
|
||||
y2=loc2[1]
|
||||
mu0 = 4*np.pi*1e-7
|
||||
I = 1
|
||||
By =mu0*I/(4*np.pi)*np.array((x-x1)/rho(x1,y1,x,y)**2-(x-x2)/rho(x2,y2,x,y)**2)
|
||||
Bx =mu0*I/(4*np.pi)*np.array(-(y-y1)/rho(x1,y1,x,y)**2+(y-y2)/rho(x2,y2,x,y)**2)
|
||||
|
||||
return Bx, By
|
||||
@@ -0,0 +1,156 @@
|
||||
import numpy as np
|
||||
import scipy.sparse as sp
|
||||
from SimPEG import utils, TensorMesh
|
||||
from SimPEG.utils import spzeros, mkvc
|
||||
|
||||
def interpmat(x,y,z,xr,yr,zr):
|
||||
|
||||
""" Local nterpolation computed for each receiver point in turn """
|
||||
|
||||
nx = max(x.shape)
|
||||
ny = max(y.shape)
|
||||
nz = max(z.shape)
|
||||
npts = max(xr.shape)
|
||||
|
||||
Q = sp.lil_matrix((npts, nx*ny*nz))
|
||||
|
||||
for i in range(npts):
|
||||
# in x-direction
|
||||
im = np.argmin(abs(x-xr[i]))
|
||||
if xr[i] - x[im] >= 0: # Point on the left
|
||||
ind_x1 = im
|
||||
ind_x2 = im+1
|
||||
elif xr[i] - x[im] < 0: # Point on the right
|
||||
ind_x1 = im-1
|
||||
ind_x2 = im
|
||||
dx1 = xr[i] - x[ind_x1]
|
||||
dx2 = x[ind_x2] - xr[i]
|
||||
# in y-direction
|
||||
im = np.argmin(abs(y-yr[i]))
|
||||
if yr[i] - y[im] >= 0: # Point on the left
|
||||
ind_y1 = im
|
||||
ind_y2 = im+1
|
||||
elif yr[i] - y[im] < 0: # Point on the right
|
||||
ind_y1 = im-1
|
||||
ind_y2 = im
|
||||
dy1 = yr[i] - y[ind_y1]
|
||||
dy2 = y[ind_y2] - yr[i]
|
||||
# in z-direction
|
||||
im = np.argmin(abs(z-zr[i]))
|
||||
if zr[i] - z[im] >= 0: # Point on the left
|
||||
ind_z1 = im
|
||||
ind_z2 = im+1
|
||||
elif zr[i] - z[im] < 0: # Point on the right
|
||||
ind_z1 = im-1
|
||||
ind_z2 = im
|
||||
dz1 = zr[i] - z[ind_z1]
|
||||
dz2 = z[ind_z2] - zr[i]
|
||||
dv = (x[ind_x2] - x[ind_x1]) * (y[ind_y2] - y[ind_y1]) *(z[ind_z2] - z[ind_z1])
|
||||
|
||||
Dx = x[ind_x2] - x[ind_x1]
|
||||
Dy = y[ind_y2] - y[ind_y1]
|
||||
Dz = z[ind_z2] - z[ind_z1]
|
||||
|
||||
# Get the row in the matrix
|
||||
|
||||
inds = utils.sub2ind((nx,ny,nz),[
|
||||
( ind_x1, ind_y2, ind_z1),
|
||||
( ind_x1, ind_y1, ind_z1),
|
||||
( ind_x2, ind_y1, ind_z1),
|
||||
( ind_x2, ind_y2, ind_z1),
|
||||
( ind_x1, ind_y1, ind_z2),
|
||||
( ind_x1, ind_y2, ind_z2),
|
||||
( ind_x2, ind_y1, ind_z2),
|
||||
( ind_x2, ind_y2, ind_z2)])
|
||||
|
||||
vals = [(1-dx1/Dx)*(1-dy2/Dy)*(1-dz1/Dz),
|
||||
(1-dx1/Dx)*(1-dy1/Dy)*(1-dz1/Dz),
|
||||
(1-dx2/Dx)*(1-dy1/Dy)*(1-dz1/Dz),
|
||||
(1-dx2/Dx)*(1-dy2/Dy)*(1-dz1/Dz),
|
||||
(1-dx1/Dx)*(1-dy1/Dy)*(1-dz2/Dz),
|
||||
(1-dx1/Dx)*(1-dy2/Dy)*(1-dz2/Dz),
|
||||
(1-dx2/Dx)*(1-dy1/Dy)*(1-dz2/Dz),
|
||||
(1-dx2/Dx)*(1-dy2/Dy)*(1-dz2/Dz)]
|
||||
|
||||
Q[i, mkvc(inds)] = vals
|
||||
Q = Q.tocsr()
|
||||
return Q
|
||||
|
||||
def getInterpmat(mesh, rxLoc, dataType):
|
||||
""" """
|
||||
xr = rxLoc[:,0]
|
||||
yr = rxLoc[:,1]
|
||||
zr = rxLoc[:,2]
|
||||
nrx = rxLoc.shape[0]
|
||||
if dataType == 'fx':
|
||||
Qx = interpmat(np.unique(mesh.gridFx[:,0]),
|
||||
np.unique(mesh.gridFx[:,1]),
|
||||
np.unique(mesh.gridFx[:,2]),
|
||||
xr,yr,zr)
|
||||
Q = sp.hstack([Qx,spzeros(nrx,mesh.nF[1]),spzeros(nrx,mesh.nF[2])])
|
||||
elif dataType == 'fy':
|
||||
Qy = interpmat(np.unique(mesh.gridFy[:,0]),
|
||||
np.unique(mesh.gridFy[:,1]),
|
||||
np.unique(mesh.gridFy[:,2]),
|
||||
xr,yr,zr)
|
||||
Q = sp.hstack([spzeros(nrx,mesh.nF[0]),Qy,spzeros(nrx,mesh.nF[2])])
|
||||
elif dataType == 'fz':
|
||||
Qz = interpmat(np.unique(mesh.gridFz[:,0]),
|
||||
np.unique(mesh.gridFz[:,1]),
|
||||
np.unique(mesh.gridFz[:,2]),
|
||||
xr,yr,zr)
|
||||
Q = sp.hstack([spzeros(nrx,mesh.nF[0]),spzeros(nrx,mesh.nF[1]),Qz])
|
||||
elif dataType == 'ex':
|
||||
Qx = interpmat(np.unique(mesh.gridEx[:,0]),
|
||||
np.unique(mesh.gridEx[:,1]),
|
||||
np.unique(mesh.gridEx[:,2]),
|
||||
xr, yr, zr)
|
||||
Q = sp.hstack([Qx,spzeros(nrx,mesh.nE[1]),spzeros(nrx,mesh.nE[2])])
|
||||
elif dataType == 'ey':
|
||||
Qy = interpmat(np.unique(mesh.gridEy[:,0]),
|
||||
np.unique(mesh.gridEy[:,1]),
|
||||
np.unique(mesh.gridEy[:,2]),
|
||||
xr, yr, zr)
|
||||
Q = sp.hstack([spzeros(nrx,mesh.nE[0]),Qy,spzeros(nrx,mesh.nE[2])])
|
||||
elif dataType == 'ez':
|
||||
Qz = interpmat(np.unique(mesh.gridEz[:,0]),
|
||||
np.unique(mesh.gridEz[:,1]),
|
||||
np.unique(mesh.gridEz[:,2]),
|
||||
xr,yr,zr)
|
||||
Q = sp.hstack([spzeros(nrx,mesh.nE[0]),spzeros(nrx,mesh.nE[1]),Qz])
|
||||
else:
|
||||
assert(True), "Input either face (fx, fy, fz) or edge (ex, ey, ez) option"
|
||||
return Q
|
||||
|
||||
if __name__ == '__main__':
|
||||
pad = 1
|
||||
padfactor = 1.5
|
||||
cs = 100
|
||||
xpad = cs*(np.ones(pad)*padfactor)**np.arange(pad)
|
||||
ypad = cs*(np.ones(pad)*padfactor)**np.arange(pad)
|
||||
zpad = cs*(np.ones(pad)*padfactor)**np.arange(pad)
|
||||
|
||||
core = 10
|
||||
xcore = cs*np.ones(core)
|
||||
ycore = cs*np.ones(core)
|
||||
zcore = cs*np.ones(core)
|
||||
|
||||
hx = np.r_[xpad[::-1],xcore, cs, xcore,xpad]
|
||||
hy = np.r_[ypad[::-1],ycore, cs, ycore, ypad]
|
||||
hz = np.r_[zpad[::-1],zcore,zcore, zpad]
|
||||
x0 = np.array([-np.sum(hx)/2, -np.sum(hy)/2, -np.sum(hz)/2], )
|
||||
mesh = TensorMesh([hx, hy, hz],x0)
|
||||
|
||||
xr1 = np.linspace(-500,500,5)
|
||||
yr1 = np.linspace(-500,500,5)
|
||||
zr1 = 0
|
||||
xr, yr = np.meshgrid(xr1, yr1, indexing='ij')
|
||||
zr = np.ones((xr.shape[0],xr.shape[1]))*zr1
|
||||
xr = mkvc(xr)
|
||||
yr = mkvc(yr)
|
||||
zr = mkvc(zr)
|
||||
rxLoc = np.c_[xr, yr, zr]
|
||||
Q = getInterpmat(mesh, rxLoc, 'ex')
|
||||
|
||||
print Q
|
||||
|
||||
Reference in new issue
Block a user