In [20]:

    

# Test 1D solution of MT problem and compare to a analytic solution
%pylab inline


    

    




Populating the interactive namespace from numpy and matplotlib

In [21]:

    

# import the simpegMT module
from simpegMT.Utils import MT1Danalytic, MT1Dsolutions
import SimPEG as simpeg
from scipy.constants import mu_0
def omega(freq):
    """Change frequency to angular frequency, omega"""
    return 2.*np.pi*freq


    

In [22]:

    

# Set up the mesh.
freq = 10
z = 100.
hz = [(z,10,-1.5),(z,10),(z,10,1.5)]
M = simpeg.Mesh.TensorMesh([hz],'C')
sig = np.zeros(M.nC) + 1e-8
sig[M.vectorCCx<=300] = 0.01


    

In [23]:

    

M.vectorNx


    

    
Out[23]:





array([-17499.51171875, -11733.0078125 ,  -7888.671875  ,  -5325.78125   ,
        -3617.1875    ,  -2478.125     ,  -1718.75      ,  -1212.5       ,
         -875.        ,   -650.        ,   -500.        ,   -400.        ,
         -300.        ,   -200.        ,   -100.        ,      0.        ,
          100.        ,    200.        ,    300.        ,    400.        ,
          500.        ,    650.        ,    875.        ,   1212.5       ,
         1718.75      ,   2478.125     ,   3617.1875    ,   5325.78125   ,
         7888.671875  ,  11733.0078125 ,  17499.51171875])

In [24]:

    

# Get the fields
anaEd, anaEu, anaHd, anaHu = MT1Danalytic.getEHfields(M,sig,freq,M.vectorNx)
anaEtemp = (anaEd+anaEu)
anaHtemp = (anaHd+anaHu)
# Scale the solution
anaZ = (anaEtemp/anaHtemp)[np.argmin(M.vectorNx**2)]
anaEcor = anaEtemp/anaEtemp[-1] #.real/np.abs(anaEtemp[-1].real)+1j*anaEtemp.imag/np.abs(anaEtemp[-1].imag)
anaHcor = anaHtemp/anaEtemp[-1] # .real/np.abs(anaEtemp[-1].real)+1j*anaHtemp.imag/np.abs(anaEtemp[-1].imag)

solE = MT1Dsolutions.get1DEfields(M,sig,freq,sourceAmp=1).conj()
solH = -M.nodalGrad*solE/(1j*omega(freq)*mu_0)


    

In [25]:

    

anaEtemp[-1]


    

    
Out[25]:





(922807.04800415318-689021.35510797054j)

In [26]:

    

np.hstack((simpeg.mkvc(anaEcor,2),simpeg.mkvc(solE,2)))


    

    
Out[26]:





array([[  6.95763292e-07 +5.19497296e-07j,
          6.95763292e-07 -5.19497296e-07j],
       [ -1.40834457e-05 -2.93173032e-05j,
          9.74760218e-06 -1.09092785e-05j],
       [  3.35815988e-04 +1.40732501e-04j,
          1.74907169e-04 +1.24344756e-04j],
       [ -7.70118008e-04 +1.65141317e-03j,
         -5.21083562e-04 +1.34839517e-03j],
       [ -5.32123445e-03 +3.24450003e-04j,
         -4.87010903e-03 +6.63069113e-04j],
       [ -8.64982593e-03 -6.64134560e-03j,
         -8.61854919e-03 -6.03020882e-03j],
       [ -7.46721859e-03 -1.59079740e-02j,
         -7.68552978e-03 -1.53974787e-02j],
       [ -2.91038457e-03 -2.39785146e-02j,
         -3.16876824e-03 -2.35863583e-02j],
       [  2.72167021e-03 -2.97359468e-02j,
          2.49400722e-03 -2.94018473e-02j],
       [  7.92975642e-03 -3.34680056e-02j,
          7.73825040e-03 -3.31542272e-02j],
       [  1.21356998e-02 -3.57924928e-02j,
          1.19706555e-02 -3.54839735e-02j],
       [  1.52903430e-02 -3.72269264e-02j,
          1.51424717e-02 -3.69189921e-02j],
       [  1.87388388e-02 -3.85404390e-02j,
          1.86057886e-02 -3.82344505e-02j],
       [  2.24915402e-02 -3.97057953e-02j,
          2.23709926e-02 -3.94030035e-02j],
       [  2.65576291e-02 -4.06933593e-02j,
          2.64473102e-02 -4.03949222e-02j],
       [  3.09448819e-02 -4.14710213e-02j,
          3.08425733e-02 -4.11780213e-02j],
       [  3.56594159e-02 -4.20041369e-02j,
          3.55629651e-02 -4.17175972e-02j],
       [  4.07054159e-02 -4.22554788e-02j,
          4.06127458e-02 -4.19763792e-02j],
       [  4.60848403e-02 -4.21852042e-02j,
          4.59939588e-02 -4.19144958e-02j],
       [  5.16310109e-02 -4.19401825e-02j,
          5.15406437e-02 -4.16710354e-02j],
       [  5.71771819e-02 -4.16951603e-02j,
          5.70873289e-02 -4.14275746e-02j],
       [  6.54964388e-02 -4.13276262e-02j,
          6.54073573e-02 -4.10623825e-02j],
       [  7.79753255e-02 -4.07763228e-02j,
          7.78874014e-02 -4.05145921e-02j],
       [  9.66936582e-02 -3.99493614e-02j,
          9.66074704e-02 -3.96929008e-02j],
       [  1.24771163e-01 -3.87089021e-02j,
          1.24687581e-01 -3.84603474e-02j],
       [  1.66887432e-01 -3.68481633e-02j,
          1.66807761e-01 -3.66114701e-02j],
       [  2.30061859e-01 -3.40569049e-02j,
          2.29988062e-01 -3.38380118e-02j],
       [  3.24823538e-01 -2.98695515e-02j,
          3.24758579e-01 -2.96773825e-02j],
       [  4.66966101e-01 -2.35870424e-02j,
          4.66914483e-01 -2.34350351e-02j],
       [  6.80179899e-01 -1.41584953e-02j,
          6.80148567e-01 -1.40669735e-02j],
       [  1.00000000e+00 +0.00000000e+00j,
          1.00000000e+00 -0.00000000e+00j]])

In [27]:

    

plot(solE.real,M.vectorNx,'r*--',anaEcor.real,M.vectorNx,'b+:')
#axis([-.2,.2,-10000,10000])


    

    
Out[27]:





[<matplotlib.lines.Line2D at 0x7feb9a686510>,
 <matplotlib.lines.Line2D at 0x7feb9a686790>]






    

In [28]:

    

plot((abs(solE.real)-abs(anaEcor.real))/abs(anaEcor.real),M.vectorNx,'b+:')


    

    
Out[28]:





[<matplotlib.lines.Line2D at 0x7feb9981fad0>]






    

In [29]:

    

plot(solE.imag,M.vectorNx,'r*--',anaEcor.imag,M.vectorNx,'b+:')


    

    
Out[29]:





[<matplotlib.lines.Line2D at 0x7feb997604d0>,
 <matplotlib.lines.Line2D at 0x7feb99760750>]






    

In [30]:

    

plot((abs(solE.imag)-abs(anaEcor.imag))/abs(anaEcor.imag),M.vectorNx,'b+:')


    

    




/home/gudni/anaconda/lib/python2.7/site-packages/IPython/kernel/__main__.py:1: RuntimeWarning: invalid value encountered in divide
  if __name__ == '__main__':






    
Out[30]:





[<matplotlib.lines.Line2D at 0x7feb9970fad0>]






    

In [31]:

    

semilogx(abs(solE),M.vectorNx,'r*--',abs(anaEcor),M.vectorNx,'b+:')


    

    
Out[31]:





[<matplotlib.lines.Line2D at 0x7feb9967c590>,
 <matplotlib.lines.Line2D at 0x7feb99638890>]






    

In [32]:

    

plot((abs(solE)-abs(anaEcor))/abs(anaEcor),M.vectorNx,'b+:')


    

    
Out[32]:





[<matplotlib.lines.Line2D at 0x7feb993ce610>]






    

In [33]:

    

def appResPhs(freq,z):
    app_res = ((1./(8e-7*np.pi**2))/freq)*np.abs(z)**2
    app_phs = np.arctan2(z.imag,z.real)*(180/np.pi)
    return app_res, app_phs
app_rAna, app_pAna = appResPhs(freq,anaZ)
app_rSol, app_pSol = appResPhs(freq,solE[np.argmin(M.hx**2)]/solH[np.argmin(M.hx**2)])
print app_rAna, app_pAna
print app_rSol, app_pSol


    

    




100.0 44.999998407
91.3634893888 -137.014649098

In [34]:

    

M.nodalGrad.dot(solE).shape


    

    
Out[34]:





(30,)

In [35]:

    

M.nN


    

    
Out[35]:





31

In [36]:

    

plot(-solH.imag,M.vectorCCx,'r*--',anaHcor.imag,M.vectorNx,'b+:')


    

    
Out[36]:





[<matplotlib.lines.Line2D at 0x7feb99304550>,
 <matplotlib.lines.Line2D at 0x7feb993047d0>]






    

In [37]:

    

M.vectorCCx


    

    
Out[37]:





array([-14616.25976562,  -9810.83984375,  -6607.2265625 ,  -4471.484375  ,
        -3047.65625   ,  -2098.4375    ,  -1465.625     ,  -1043.75      ,
         -762.5       ,   -575.        ,   -450.        ,   -350.        ,
         -250.        ,   -150.        ,    -50.        ,     50.        ,
          150.        ,    250.        ,    350.        ,    450.        ,
          575.        ,    762.5       ,   1043.75      ,   1465.625     ,
         2098.4375    ,   3047.65625   ,   4471.484375  ,   6607.2265625 ,
         9810.83984375,  14616.25976562])

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