Files
simpeg/simpegPF/notebooks/tutorials/Tutorial_1_Mag forward modeling.ipynb
T
2015-10-23 12:08:19 -07:00

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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Populating the interactive namespace from numpy and matplotlib\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"WARNING: pylab import has clobbered these variables: ['linalg']\n",
"`%matplotlib` prevents importing * from pylab and numpy\n"
]
}
],
"source": [
"from SimPEG import *\n",
"from simpegPF.MagAnalytics import spheremodel, MagSphereAnaFun, CongruousMagBC, MagSphereAnaFunA\n",
"from simpegPF.Magnetics import MagneticsDiffSecondary, MagneticsDiffSecondaryInv, BaseMag\n",
"%pylab inline"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"import matplotlib\n",
"matplotlib.rcParams.update({'font.size': 16, 'text.usetex': True})"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Forward problem: Magnetics"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This is a tutorial for Mag forward problem using simpegPF package. We first start with analytic solution for susceptible sphere in a whole space. Then we solve steady-state Maxwell's equatoins for Mag problem (<a href=\"http://simpegpf.readthedocs.org/en/latest/api_PF.html\">See Doc</a>) using simpegPF package. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Step1: Discretize the earth"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We use TensorMesh class in SimPEG to discretize the 3D earth (<a href=\"http://docs.simpeg.xyz/en/latest/api_MeshCode.html?highlight=tensormesh#module-SimPEG.Mesh.TensorMesh\">See Doc</a>). Let's visualize discretized mesh on section views:"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x13415908>"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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HDDJSZ4TG+9bH9k89vzubZ84BYD545hwAsIGKhLljsmPnh/rb6vXxpr5QDxlk5JDRNR7b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\nnAMAAACZ4HAOAAAAZILDOQAAAJCJ/w+HnjcrUQNWeAAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x13302320>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"cs = 12.5\n",
"ncx, ncy, ncz, npad = 41, 41, 40, 5\n",
"hx = [(cs,npad,-1.4), (cs,ncx), (cs,npad,1.4)]\n",
"hy = [(cs,npad,-1.4), (cs,ncy), (cs,npad,1.4)]\n",
"hz = [(cs,npad,-1.4), (cs,ncz), (cs,npad,1.4)]\n",
"mesh = Mesh.TensorMesh([hx, hy, hz], 'CCC')\n",
"fig, ax = plt.subplots(1,2, figsize=(12, 5))\n",
"dat0 = mesh.plotSlice(np.zeros(mesh.nC), grid=True, ax=ax[0]); ax[0].set_title('XY plane')\n",
"dat1 = mesh.plotSlice(np.zeros(mesh.nC), grid=True, normal='X', ax=ax[1]); ax[1].set_title('YZ plane')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Step2: Compose suceptibility model: susceptible sphere in whole space"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"- $\\mu = \\mu_0(1+\\chi)$\n",
"- $\\mu$: magnetic permeability\n",
"- $\\mu_0$: magnetic permeability of vacuum space\n",
"- $\\chi$: magnetic susceptibility"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"from scipy.constants import mu_0\n",
"mu0 = 4*np.pi*1e-7\n",
"chibkg = 0. # Background susceptibility\n",
"chiblk = 0.01 # Susceptibility for a sphere\n",
"chi = np.ones(mesh.nC)*chibkg"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"sph_ind = spheremodel(mesh, 0, 0, -100, 80) # A sphere is located at (0, 0, 0) and radius of the sphere is 100 m\n",
"chi[sph_ind] = chiblk # Assign susceptibility value for the sphere\n",
"mu = (1.+chi)*mu0"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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8uni5PXbcpc/21Bh+FFmrrKU+HsupEWtvG++bP3R/AADSseg/Jhuxbp/aqf1j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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x13547e48>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(1,2, figsize=(12, 7))\n",
"indz = int(np.argmin(abs(mesh.vectorCCz-(-100.)))); indx = int(np.argmin(abs(mesh.vectorCCx-0.)))\n",
"dat0 = mesh.plotSlice(chi, grid=True, ind=indz, ax=ax[0]); ax[0].set_title(('XY plane at z=%5.2f')%(mesh.vectorCCz[indz]))\n",
"dat1 = mesh.plotSlice(chi, grid=True, normal='X', ind=indx, ax=ax[1]); ax[1].set_title(('YZ plane at x=%5.2f')%(mesh.vectorCCx[indx]))\n",
"cb0 = plt.colorbar(dat0[0], orientation='horizontal', ax=ax[0], ticks = linspace(0, 0.01, 5)); \n",
"cb1 = plt.colorbar(dat1[0], orientation='horizontal', ax=ax[1], ticks = linspace(0, 0.01, 5)); \n",
"cb0.set_label(\"Suceptibility\")\n",
"cb1.set_label(\"Suceptibility\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Step3: Set up an airborne MAG survey"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We have discretized 3D earth and generated suceptibility model, which means that we have discretized earth and physical property distribution. We can compute magnetic fields everywhere in our domain by solving parial differental equation (PDE), but our measurements are confined to finite locations. Therefore, we need to project computed fields $\\mathbf{u}$, which is defined everywhere in our domain to certain locations where we have receiving points. For instance in airborne mag survey these are the points where a plane or helicopter measure earth magnetic fields. This projection can be expressed as:\n",
"\n",
"$$ \\mathbf{d} = P(\\mathbf{u})$$\n",
"\n",
"where $P(\\cdot)$ is a projection from computed field to the measured data, and $d$ is the measure data. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's assume that we have a survey area: 400 m $\\times$ 400 m. We have 21 lines of airborne MAG survey, and we measure magnetic fields for every 20 m on each line. A pilot for this helicopter is really talented so that the flight height is constant for 30 m above the surface. "
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"xr = np.linspace(-200, 200, 21)\n",
"yr = np.linspace(-200, 200, 21)\n",
"X, Y = np.meshgrid(xr, yr)\n",
"Z = np.ones((size(xr), size(yr)))*30."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x17706b70>]"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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wBEwawb0guBcEaQ/ngC04B0wI6QvOAUcx6sFfU5+xfUN2Pr0rS9nOKZecc8sp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\nAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x138492e8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(1,1, figsize=(5, 5))\n",
"indz = int(np.argmin(abs(mesh.vectorCCz-(0.))));\n",
"dat0 = mesh.plotSlice(chi, grid=True, ind=indz, ax=ax); ax.set_title(('XY plane at z=%5.2f')%(mesh.vectorCCz[indz]))\n",
"ax.plot(X.flatten(), Y.flatten(), 'w.', ms=5)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Step4: Analytic solution"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We have an analytic solution when we have a sphere in a whole-space. simpegPF provides this function so that you can compute magnetic field on your receiving locations. Another input you need to put is direction of the earth magnetic fieds, and the strength, you can easily get this information from <a href=\"http://www.ngdc.noaa.gov/geomag-web/\">NOAA's website</a>. We assume that we have veritcal earth fields and the strength is 1. "
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"Bxra, Byra, Bzra = MagSphereAnaFunA(X, Y, Z, 80., 0., 0., -100, chiblk, np.array([0., 0., 1.]), flag)\n",
"Bxra = np.reshape(Bxra, (size(xr), size(yr)), order='F')\n",
"Byra = np.reshape(Byra, (size(xr), size(yr)), order='F')\n",
"Bzra = np.reshape(Bzra, (size(xr), size(yr)), order='F')"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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ox6ZGePS9Gk2XgkjbfHPd/l0KJX0WYmWYwTMEQaSvZWtDnobGLILqU3yVAK9E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\nSZKUMEgAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x132b8d30>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(1,3, figsize=(18, 4))\n",
"dat0=ax[0].contourf(X, Y, Bxra, 30); ax[0].set_title('Bx'); cb0 = plt.colorbar(dat0, ax=ax[0])\n",
"dat1=ax[1].contourf(X, Y, Byra, 30); ax[1].set_title('By'); cb1 = plt.colorbar(dat0, ax=ax[1])\n",
"dat2=ax[2].contourf(X, Y, Bzra, 30); ax[2].set_title('Bz'); cb2 = plt.colorbar(dat0, ax=ax[2])\n",
"for i in range(3):\n",
" ax[i].plot(X.flatten(), Y.flatten(), 'k.', ms=3)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Step5: Solve PDE"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note that data for this case magnetic fields projected to earth field direction, which is typical data type for airborne mag survey. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"First, set survey class"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"survey = BaseMag.BaseMagSurvey() # survey class for mag problem\n",
"Inc = 90.\n",
"Dec = 0.\n",
"Btot = 1\n",
"survey.setBackgroundField(Inc, Dec, Btot) # set inclination, declination, and strength of magnetic field\n",
"rxLoc = np.c_[Utils.mkvc(X), Utils.mkvc(Y), Utils.mkvc(Z)]\n",
"survey.rxLoc = rxLoc # set receiver locations"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Second, set problem class then pair with survey"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"prob = MagneticsDiffSecondary(mesh)\n",
"prob.pair(survey)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Third, run forward modeling"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"data = survey.dpred(mu)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we viualize computed solution and compare with analytic solutions! Note that you may always need to make sure that your numerical solution is reasonable enough. "
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x13826278>"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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0V1O4vc3MP1evjzLzRyqv/wERHWHm26p70UWCUMpUzZSx6XXXBktfxspmaWop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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1a54e9e8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(1,3, figsize=(18, 4))\n",
"vmin = Bzra.min()\n",
"vmax = Bzra.max()\n",
"residual = data.reshape((xr.size, yr.size), order='F')-Bzra\n",
"dat0=ax[0].contourf(X, Y, Bzra, 30, vmin=vmin, vmax=vmax)\n",
"dat1=ax[1].contourf(X, Y, data.reshape((xr.size, yr.size), order='F'), 30, vmin=vmin, vmax=vmax)\n",
"dat2=ax[2].contourf(X, Y, residual, 30)\n",
"cb0 = plt.colorbar(dat0, ax=ax[0])\n",
"cb1 = plt.colorbar(dat0, ax=ax[1])\n",
"cb2 = plt.colorbar(dat2, ax=ax[2])\n",
"ax[0].set_title('Bz (analytic)')\n",
"ax[1].set_title('Bz (simpegPF)')\n",
"ax[2].set_title('Residual')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<a rel=\"license\" href=\"http://creativecommons.org/licenses/by/4.0/\"><img alt=\"Creative Commons License\" style=\"border-width:0\" src=\"https://i.creativecommons.org/l/by/4.0/88x31.png\" /></a><br />This work is licensed under a <a rel=\"license\" href=\"http://creativecommons.org/licenses/by/4.0/\">Creative Commons Attribution 4.0 International License</a>."
]
}
],
"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": "2.7.10"
}
},
"nbformat": 4,
"nbformat_minor": 0
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