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In [1]:



    


import SimPEG as simpeg
from scipy.constants import mu_0
def omega(freq):
    """Change frequency to angular frequency, omega"""
    return 2.*np.pi*freq



    


















    






Efficiency Warning: Interpolation will be slow, use setup.py!

            python setup.py build_ext --inplace
    

















In [2]:



    


%pylab inline



    


















    






Populating the interactive namespace from numpy and matplotlib

















In [3]:



    


np.sum(100*np.cumprod(np.ones(5)*1.6))



    


















    
Out[3]:








2529.536000000001

















In [4]:



    


# M = Mesh.TensorMesh([[(100.,32)],[(100.,34)],[(100.,18)]], x0='CCC')
M = simpeg.Mesh.TensorMesh([[(100,5,-1.5),(100.,10),(100,5,1.5)],[(100,5,-1.5),(100.,10),(100,5,1.5)],[(100,5,1.6),(100.,10),(100,3,2)]], x0=['C','C',-3529.5360])



    











In [5]:



    


print M.vectorNz



    


















    






[ -3.52953600e+03  -3.36953600e+03  -3.11353600e+03  -2.70393600e+03
  -2.04857600e+03  -1.00000000e+03  -9.00000000e+02  -8.00000000e+02
  -7.00000000e+02  -6.00000000e+02  -5.00000000e+02  -4.00000000e+02
  -3.00000000e+02  -2.00000000e+02  -1.00000000e+02   4.54747351e-13
   2.00000000e+02   6.00000000e+02   1.40000000e+03]

















In [1]:



    


# Setup the model
conds = [1e-2,1]
sig = simpeg.Utils.ModelBuilder.defineBlock(M.gridCC,[-200,-200,-400],[200,200,-200],conds)
sig[M.gridCC[:,2]>0] = 1e-8
sig[M.gridCC[:,2]<-600] = 1e-1
sigBG = np.zeros(M.nC) + conds[0]
sigBG[M.gridCC[:,2]>0] = 1e-8
colorbar(M.plotImage(log10(sig)))



    


















    






---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
<ipython-input-1-fe06aef8ad6f> in <module>()
      1 # Setup the model
      2 conds = [1e-2,1]
----> 3 sig = simpeg.Utils.ModelBuilder.defineBlock(M.gridCC,[-200,-200,-400],[200,200,-200],conds)
      4 sig[M.gridCC[:,2]>0] = 1e-8
      5 sig[M.gridCC[:,2]<-600] = 1e-1

NameError: name 'M' is not defined
















In [ ]:



    


# Receivers 
# 3D impedance at the surface (elevation 0)
rxList = []
for rxType in ['zxxr','zxxi','zxyr','zxyi','zyxr','zyxi','zyyr','zyyi',]:
    rxList.append(simpegmt.SurveyMT.RxMT(simpeg.mkvc(np.array([0.0]),2).T,rxType))
# Source list
srcList =[]
tD = False
if tD:
    for freq in freqs:
        srcList.append(simpegmt.SurveyMT.srcMT_polxy_1DhomotD(rxList,freq))
else:
    for freq in freqs:
        srcList.append(simpegmt.SurveyMT.srcMT_polxy_1Dprimary(rxList,freq,sigma_0))
# Make the survey
survey = simpegmt.SurveyMT.SurveyMT(srcList)
survey.mtrue = m_true
# Set the problem
problem = simpegmt.ProblemMT1D.eForm_psField(m1d,mapping=mappingExpAct)
from pymatsolver import MumpsSolver
problem.solver = MumpsSolver
problem.pair(survey)



    











In [10]:



    


# Make the data



    











In [11]:



    


# Setup y (north) polarization (_y)
ex_y = np.zeros(M.nEx, dtype='complex128')
ey_y = np.zeros((M.vnEy), dtype='complex128')
ez_y = np.zeros(M.nEz, dtype='complex128')
# Assign the source to ex_x
for i in arange(M.vnEy[0]):
    for j in arange(M.vnEy[1]):
        ey_y[i,j,:] = e0_1d        
# eBG_y = np.vstack((ex_y,Utils.mkvc(M.r(ey_y,'Ey','Ey','V'),2),ez_y))
# rhs_y = ABG.dot(eBG_y)



    











In [12]:



    


eBG_y = np.r_[ex_y,simpeg.Utils.mkvc(ey_y),ez_y]
rhs_y = ABG.dot(eBG_y)

We are using splu in scipy package. This is bit slow, but on the cluster you can use mumps, which might a lot faster. We can think about having better iterative solver.





In [13]:



    


%%time
# Solve the systems for each polarization
Ainv = simpeg.SolverLU(A)



    


















    






CPU times: user 1min 16s, sys: 761 ms, total: 1min 17s
Wall time: 1min 18s

















In [14]:



    


%%time
e_x = Ainv*rhs_x
e_y = Ainv*rhs_y



    


















    






CPU times: user 497 ms, sys: 1 ms, total: 498 ms
Wall time: 534 ms

I want to visualize electrical field, which is a vector, so I average them on to cell center. Also I want to see current density ($\vec{j} = \sigma \vec{e}$).





In [15]:



    


Meinv = M.getEdgeInnerProduct(np.ones_like(sig), invMat=True)



    











In [16]:



    


j_x = Meinv*Msig*e_x
j_y = Meinv*Msig*e_x



    











In [17]:



    


e_x_CC = M.aveE2CCV*e_x
e_y_CC = M.aveE2CCV*e_y
j_x_CC = M.aveE2CCV*j_x
j_y_CC = M.aveE2CCV*j_y
# j_x_CC = Utils.sdiag(np.r_[sig, sig, sig])*e_x_CC

Then use "plotSlice" function, to visualize 2D sections





In [18]:



    


fig, ax = plt.subplots(1,2, figsize = (12, 5))
dat0 = M.plotSlice(abs(e_x_CC), vType='CCv', view='vec', streamOpts={'color': 'k'}, normal='X', ax = ax[0])
cb0 = plt.colorbar(dat0[0], ax = ax[0])
dat1 = M.plotSlice(abs(j_x_CC), vType='CCv', view='vec', streamOpts={'color': 'k'}, normal='X', ax = ax[1])
cb1 = plt.colorbar(dat1[0], ax = ax[1])

Is it reasonable?: Based on that you put resistive target that makes sense to me; current does not want to flow on resistive target so they just do roundabout:). And see air interface. It is continuous on current but not on electric field, which looks reasonable.





In [19]:



    


# Calculate the data
rx_x, rx_y = np.meshgrid(np.arange(-500,501,50),np.arange(-500,501,50))
rx_loc = np.hstack((simpeg.Utils.mkvc(rx_x,2),simpeg.Utils.mkvc(rx_y,2),np.zeros((np.prod(rx_x.shape),1))))
# Get the projection matrices
Qex = M.getInterpolationMat(rx_loc,'Ex')
Qey = M.getInterpolationMat(rx_loc,'Ey')
Qez = M.getInterpolationMat(rx_loc,'Ez')
Qfx = M.getInterpolationMat(rx_loc,'Fx')
Qfy = M.getInterpolationMat(rx_loc,'Fy')
Qfz = M.getInterpolationMat(rx_loc,'Fz')



    











In [20]:



    


e_x_loc = np.hstack([simpeg.Utils.mkvc(Qex*e_x,2),simpeg.Utils.mkvc(Qey*e_x,2),simpeg.Utils.mkvc(Qez*e_x,2)])
e_y_loc = np.hstack([simpeg.Utils.mkvc(Qex*e_y,2),simpeg.Utils.mkvc(Qey*e_y,2),simpeg.Utils.mkvc(Qez*e_y,2)])
h_x_loc = np.hstack([simpeg.Utils.mkvc(Qfx*C*e_x,2),simpeg.Utils.mkvc(Qfy*C*e_x,2),simpeg.Utils.mkvc(Qfz*C*e_x,2)])
h_y_loc = np.hstack([simpeg.Utils.mkvc(Qfx*C*e_y,2),simpeg.Utils.mkvc(Qfy*C*e_y,2),simpeg.Utils.mkvc(Qfz*C*e_y,2)])



    











In [21]:



    


# Make a combined matrix
dt = np.dtype([('ex1',complex),('ey1',complex),('ez1',complex),('hx1',complex),('hy1',complex),('hz1',complex),('ex2',complex),('ey2',complex),('ez2',complex),('hx2',complex),('hy2',complex),('hz2',complex)])
combMat = np.empty((len(e_x_loc)),dtype=dt)
combMat['ex1'] = e_x_loc[:,0]
combMat['ey1'] = e_x_loc[:,1]
combMat['ez1'] = e_x_loc[:,2]
combMat['ex2'] = e_y_loc[:,0]
combMat['ey2'] = e_y_loc[:,1]
combMat['ez2'] = e_y_loc[:,2]
combMat['hx1'] = h_x_loc[:,0]
combMat['hy1'] = h_x_loc[:,1]
combMat['hz1'] = h_x_loc[:,2]
combMat['hx2'] = h_y_loc[:,0]
combMat['hy2'] = h_y_loc[:,1]
combMat['hz2'] = h_y_loc[:,2]



    











In [22]:



    


def calculateImpedance(fieldsData):
    ''' 
    Function that calculates MT impedance data from a rec array with E and H field data from both polarizations
    '''
    zxx = (fieldsData['ex1']*fieldsData['hy2'] - fieldsData['ex2']*fieldsData['hy1'])/(fieldsData['hx1']*fieldsData['hy2'] - fieldsData['hx2']*fieldsData['hy1'])
    zxy = (-fieldsData['ex1']*fieldsData['hx2'] + fieldsData['ex2']*fieldsData['hx1'])/(fieldsData['hx1']*fieldsData['hy2'] - fieldsData['hx2']*fieldsData['hy1'])
    zyx = (fieldsData['ey1']*fieldsData['hy2'] - fieldsData['ey2']*fieldsData['hy1'])/(fieldsData['hx1']*fieldsData['hy2'] - fieldsData['hx2']*fieldsData['hy1'])
    zyy = (-fieldsData['ey1']*fieldsData['hx2'] + fieldsData['ey2']*fieldsData['hx1'])/(fieldsData['hx1']*fieldsData['hy2'] - fieldsData['hx2']*fieldsData['hy1'])
    return zxx, zxy, zyx, zyy

zxx, zxy, zyx, zyy = calculateImpedance(combMat)



    











In [23]:



    


zxy



    


















    
Out[23]:








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        102.58986124+93.42601702j,  102.39619991+93.42582359j,
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In [24]:



    


zyx



    


















    
Out[24]:








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In [26]:



    


zxy + zyx



    


















    
Out[26]:








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In [ ]:

Content source: simpeg/simpegmt

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