simpeg/notebooks/DCexample.ipynb

In [1]:

from SimPEG import *
import simpegDCIP as DC
%pylab inline

Populating the interactive namespace from numpy and matplotlib

WARNING: pylab import has clobbered these variables: ['linalg']
`%matplotlib` prevents importing * from pylab and numpy

In [2]:

cs = 25.
hx = [(cs,7, -1.3),(cs,21),(cs,7, 1.3)]
hy = [(cs,7, -1.3),(cs,21),(cs,7, 1.3)]
hz = [(cs,7, -1.3),(cs,20)]

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mesh = Mesh.TensorMesh([hx, hy, hz], 'CCN')

In [6]:

blk1 = Utils.ModelBuilder.getIndicesBlock(np.r_[-50, 75, -50], np.r_[75, -50, -150], mesh.gridCC)
sighalf = 1e-3
sigma = np.ones(mesh.nC)*sighalf
sigma[blk1] = 1e-1
sigmahomo = np.ones(mesh.nC)*sighalf

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mesh.plotSlice(sigma, normal='X', grid=True)

Out [8]:

(<matplotlib.collections.QuadMesh at 0x1077619d0>,
 <matplotlib.lines.Line2D at 0x107761e90>)

In [9]:

xtemp = np.linspace(-150, 150, 21)
ytemp = np.linspace(-150, 150, 21)
xyz_rxP = Utils.ndgrid(xtemp-10., ytemp, np.r_[0.])
xyz_rxN = Utils.ndgrid(xtemp+10., ytemp, np.r_[0.])
xyz_rxM = Utils.ndgrid(xtemp, ytemp, np.r_[0.])

In [10]:

fig, ax = plt.subplots(1,1, figsize = (5,5))
mesh.plotSlice(sigma, grid=True, ax = ax)
ax.plot(xyz_rxP[:,0],xyz_rxP[:,1], 'w.')
ax.plot(xyz_rxN[:,0],xyz_rxN[:,1], 'r.', ms = 3)

Out [10]:

[<matplotlib.lines.Line2D at 0x10820a490>]

In [11]:

rx = DC.RxDipole(xyz_rxP, xyz_rxN)
tx = DC.SrcDipole([rx], [-200, 0, -12.5],[+200, 0, -12.5])

In [12]:

survey = DC.SurveyDC([tx])
problem = DC.ProblemDC_CC(mesh)
problem.pair(survey)

In [13]:

try:
    from pymatsolver import MumpsSolver
    problem.Solver = MumpsSolver
except Exception, e:
    problem.Solver = SolverLU

In [16]:

%%time
data = survey.dpred(sigmahomo)

CPU times: user 1.15 s, sys: 155 ms, total: 1.3 s
Wall time: 941 ms

In [17]:

u1 = problem.fields(sigma)
u2 = problem.fields(sigmahomo)

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Msig1 = Utils.sdiag(1./(mesh.aveF2CC.T*(1./sigma)))
Msig2 = Utils.sdiag(1./(mesh.aveF2CC.T*(1./sigmahomo)))

In [19]:

j1 = Msig1*mesh.cellGrad*u1[tx, 'phi_sol']
j2 = Msig2*mesh.cellGrad*u2[tx, 'phi_sol']

In [21]:

# us = u1-u2
# js = j1-j2

In [22]:

mesh.plotSlice(mesh.aveF2CCV*j1, vType='CCv', normal='Y', view='vec', streamOpts={"density":3, "color":'w'})
xlim(-300, 300)
ylim(-300, 0)

Out [22]:

(-300, 0)

In [23]:

mesh.plotSlice(mesh.aveF2CCV*js, vType='CCv', normal='Y', view='vec', streamOpts={"density":3, "color":'w'})
xlim(-300, 300)
ylim(-300, 0)

---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
<ipython-input-23-575f23801c4a> in <module>()
----> 1 mesh.plotSlice(mesh.aveF2CCV*js, vType='CCv', normal='Y', view='vec', streamOpts={"density":3, "color":'w'})
      2 xlim(-300, 300)
      3 ylim(-300, 0)

NameError: name 'js' is not defined

In [ ]:

a = np.random.randn(3)

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print (a.reshape([1,-1])).repeat(3, axis = 0)
print (a.reshape([1,-1])).repeat(3, axis = 0).sum(axis=1)

In [ ]:

def DChalf(txlocP, txlocN, rxloc, sigma, I=1.):
    rp = (txlocP.reshape([1,-1])).repeat(rxloc.shape[0], axis = 0)
    rn = (txlocN.reshape([1,-1])).repeat(rxloc.shape[0], axis = 0)
    rP = np.sqrt(((rxloc-rp)**2).sum(axis=1))
    rN = np.sqrt(((rxloc-rn)**2).sum(axis=1))
    return I/(sigma*2.*np.pi)*(1/rP-1/rN)

In [ ]:

data_analP = DChalf(np.r_[-200, 0, 0.],np.r_[+200, 0, 0.], xyz_rxP, sighalf)
data_analN = DChalf(np.r_[-200, 0, 0.],np.r_[+200, 0, 0.], xyz_rxN, sighalf)
data_anal = data_analP-data_analN

In [ ]:

Data_anal = data_anal.reshape((21, 21), order = 'F')
Data = data.reshape((21, 21), order = 'F')
X = xyz_rxM[:,0].reshape((21, 21), order = 'F')
Y = xyz_rxM[:,1].reshape((21, 21), order = 'F')

In [ ]:

fig, ax = plt.subplots(1,2, figsize = (12, 5))
vmin = np.r_[data, data_anal].min()
vmax = np.r_[data, data_anal].max()
dat0 = ax[0].contourf(X, Y, Data, 60, vmin = vmin, vmax = vmax)
dat1 = ax[1].contourf(X, Y, Data_anal, 60, vmin = vmin, vmax = vmax)
cb0 = plt.colorbar(dat1, orientation = 'horizontal', ax = ax[0])
cb1 = plt.colorbar(dat1, orientation = 'horizontal', ax = ax[1])

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