mirror of
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Merge branch 'master' of https://github.com/simpeg/simpegMT into develop
Conflicts: simpegMT/Base.pyc simpegMT/Utils/MT1Danalytic.pyc simpegMT/Utils/MT1Dsolutions.pyc simpegMT/Utils/__init__.pyc simpegMT/__init__.pyc
This commit is contained in:
Rowan Cockett
+44
@@ -0,0 +1,44 @@
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*.py[cod]
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# C extensions
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*.so
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# Folders
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docs/build/*
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# Packages
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*.egg
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*.egg-info
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dist
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build
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eggs
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parts
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bin
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||||
var
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sdist
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develop-eggs
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.installed.cfg
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libgit
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lib64
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__pycache__
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# Installer logs
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pip-log.txt
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# Unit test / coverage reports
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.coverage
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.tox
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nosetests.xml
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# Translations
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*.mo
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# Mr Developer
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.mr.developer.cfg
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.project
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.pydevproject
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*.sublime-project
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*.sublime-workspace
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docs/_build/
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*.ipynb_checkpoints
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File diff suppressed because one or more lines are too long
@@ -1,101 +0,0 @@
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# Analytic solution of EM fields due to a plane wave
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import numpy as np, SimPEG as simpeg
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def getEHfields(m1d,sigma,freq,zd):
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'''Analytic solution for MT 1D layered earth. Returns E and H fields.
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:param SimPEG.mesh, object m1d: Mesh object with the 1D spatial information.
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:param numpy.array, vector sigma: Physical property of conductivity corresponding with the mesh.
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:param float, freq: Frequency to calculate data at.
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:param numpy array, vector zd: location to calculate EH fields at
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Assumes a halfspace with the same conductive as the last cell below.
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'''
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# Note add an error check for the mesh and sigma are the same size.
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# Need make the solution e^-iwt dependent
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# Constants: Assume constant
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mu = 4*np.pi*1e-7*np.ones((m1d.nC+1))
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eps = 8.85*1e-12*np.ones((m1d.nC+1))
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# Angular freq
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w = 2*np.pi*freq
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# Add the halfspace value to the property
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sig = np.concatenate((np.array([sigma[0]]),sigma))
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# Calculate the wave number
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k = np.sqrt(eps*mu*w**2-1j*mu*sig*w)
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# Initiate the propagation matrix, in the order down up.
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UDp = np.zeros((2,m1d.nC+1),dtype=complex)
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UDp[1,0] = 1 # Set the wave amplitude as 1 into the half-space at the bottom of the mesh
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# Loop over all the layers, starting at the bottom layer
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for lnr, h in enumerate(m1d.hx): # lnr-number of layer, h-thickness of the layer
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# Calculate
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yp1 = k[lnr]/(w*mu[lnr]) # Admittance of the layer below the current layer
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zp = (w*mu[lnr+1])/k[lnr+1] # Impedance in the current layer
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# Build the propagation matrix
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# Convert fields to down/up going components in layer below current layer
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Pj1 = np.array([[1,1],[yp1,-yp1]])
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# Convert fields to down/up going components in current layer
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Pjinv = 1./2*np.array([[1,zp],[1,-zp]])
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# Propagate down and up components through the current layer
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elamh = np.array([[np.exp(-1j*k[lnr+1]*h),0],[0,np.exp(1j*k[lnr+1]*h)]])
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# The down and up component in current layer.
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UDp[:,lnr+1] = elamh.dot(Pjinv.dot(Pj1)).dot(UDp[:,lnr])
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# Calculate the fields
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Ed = np.zeros((zd.size,),dtype=complex)
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Eu = np.zeros((zd.size,),dtype=complex)
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Hd = np.zeros((zd.size,),dtype=complex)
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Hu = np.zeros((zd.size,),dtype=complex)
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# Loop over the layers and calculate the fields
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for ki,mui,epsi,dlow,dup,Up,Dp in zip(k[1::],mu[1::],eps[1::],m1d.vectorNx[:-1],m1d.vectorNx[1::],UDp[0,1::],UDp[1,1::]):
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dind = np.logical_and(dup >= zd, zd > dlow)
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Ed[dind] = Dp*np.exp(-1j*ki*(dup-zd[dind]))
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Eu[dind] = Up*np.exp(1j*ki*(dup-zd[dind]))
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Hd[dind] = (ki/(w*mui))*Dp*np.exp(-1j*ki*(dup-zd[dind]))
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Hu[dind] = -(ki/(w*mui))*Up*np.exp(1j*ki*(dup-zd[dind]))
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# Return return the fields
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return Ed, Eu, Hd, Hu
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def getImpedance(m1d,sigma,freq):
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"""Analytic solution for MT 1D layered earth. Returns the impedance at the surface.
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:param SimPEG.mesh, object m1d: Mesh object with the 1D spatial information.
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:param numpy.array, vector sigma: Physical property corresponding with the mesh.
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:param numpy.array, vector freq: Frequencies to calculate data at.
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"""
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# Define constants
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mu0 = 4*np.pi*1e-7
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eps0 = 8.85e-12
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# Initiate the impedances
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Z1d = np.empty(len(freq) , dtype='complex')
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h = m1d.hx #vectorNx[:-1]
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# Start the process
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for nrFr, fr in enumerate(freq):
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om = 2*np.pi*fr
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Zall = np.empty(len(h)+1,dtype='complex')
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# Calculate the impedance for the bottom layer
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Zall[0] = (mu0*om)/np.sqrt(mu0*eps0*(om)**2 - 1j*mu0*sigma[0]*om)
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for nr,hi in enumerate(h):
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# Calculate the wave number
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# print nr,sigma[nr]
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k = np.sqrt(mu0*eps0*om**2 - 1j*mu0*sigma[nr]*om)
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Z = (mu0*om)/k
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Zall[nr+1] = Z *((Zall[nr] + Z*np.tanh(1j*k*hi))/(Z + Zall[nr]*np.tanh(1j*k*hi)))
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#pdb.set_trace()
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Z1d[nrFr] = Zall[-1]
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return Z1d
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Binary file not shown.
@@ -1,43 +0,0 @@
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import numpy as np, SimPEG as simpeg
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from MT1Danalytic import getEHfields
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from scipy.constants import mu_0
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def get1DEfields(m1d,sigma,freq,sourceAmp=1.0):
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"""Function to get 1D electrical fields"""
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# Get the gradient
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G = m1d.nodalGrad
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# Mass matrices
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# Magnetic permeability
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Mmu = simpeg.Utils.sdiag(m1d.vol*(1.0/mu_0))
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# Conductivity
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Msig = m1d.getFaceInnerProduct(sigma)
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# Set up the solution matrix
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A = G.T*Mmu*G - 1j*2.*np.pi*freq*Msig
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# Define the inner part of the solution matrix
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Aii = A[1:-1,1:-1]
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# Define the outer part of the solution matrix
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Aio = A[1:-1,[0,-1]]
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# Set the boundary conditions
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Ed_low, Eu_low, Hd_low, Hu_low = getEHfields(m1d,sigma,freq,np.array([m1d.vectorNx[0]]))
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Etot_low = Ed_low + Eu_low
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## Note: need to use conjugate of the analytic solution. It is derived with e^iwt
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bc = np.r_[Etot_low.conj(),sourceAmp]
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# The right hand side
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rhs = -Aio*bc
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# Solve the system
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Aii_inv = simpeg.Solver(Aii)
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eii = Aii_inv*rhs
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# Assign the boundary conditions
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e = np.r_[bc[0],eii,bc[1]]
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# Return the electrical fields
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return e
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if __name__ == '__main__':
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hz = [(100.,18)]
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M = simpeg.Mesh.TensorMesh([hz],'C')
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sig = np.zeros(M.nC) + 1e-8
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sig[M.vectorCCx<=0] = sigHalf
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Binary file not shown.
@@ -1 +0,0 @@
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from MT1Dsolutions import * # Add the names of the functions
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Binary file not shown.
Binary file not shown.
Binary file not shown.
@@ -3,98 +3,99 @@
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import numpy as np, SimPEG as simpeg
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def getEHfields(m1d,sigma,freq,zd):
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'''Analytic solution for MT 1D layered earth. Returns E and H fields.
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||||
'''Analytic solution for MT 1D layered earth. Returns E and H fields.
|
||||
|
||||
:param SimPEG.mesh, object m1d: Mesh object with the 1D spatial information.
|
||||
:param numpy.array, vector sigma: Physical property of conductivity corresponding with the mesh.
|
||||
:param float, freq: Frequency to calculate data at.
|
||||
:param numpy array, vector zd: location to calculate EH fields at
|
||||
:param SimPEG.mesh, object m1d: Mesh object with the 1D spatial information.
|
||||
:param numpy.array, vector sigma: Physical property of conductivity corresponding with the mesh.
|
||||
:param float, freq: Frequency to calculate data at.
|
||||
:param numpy array, vector zd: location to calculate EH fields at
|
||||
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Assumes a halfspace with the same conductive as the last cell below.
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Assumes a halfspace with the same conductive as the last cell below.
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'''
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# Note add an error check for the mesh.
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'''
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# Note add an error check for the mesh and sigma are the same size.
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# Need make the solution e^-iwt dependent
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||||
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||||
# Constants: Assume constant
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mu = 4*np.pi*1e-7*np.ones((m1d.nC+1))
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eps = 8.85*1e-12*np.ones((m1d.nC+1))
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# Angular freq
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w = 2*np.pi*freq
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# Add the halfspace value to the property
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sig = np.concatenate((np.array([sigma[0]]),sigma))
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# Calculate the wave number
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k = np.sqrt(eps*mu*w**2-1j*mu*sig*w)
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# Constants: Assume constant
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mu = 4*np.pi*1e-7*np.ones((m1d.nC+1))
|
||||
eps = 8.85*1e-12*np.ones((m1d.nC+1))
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# Angular freq
|
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w = 2*np.pi*freq
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# Add the halfspace value to the property
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sig = np.concatenate((np.array([sigma[0]]),sigma))
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# Calculate the wave number
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k = np.sqrt(eps*mu*w**2-1j*mu*sig*w)
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# Initiate the propagation matrix, in the order down up.
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UDp = np.zeros((2,m1d.nC+1),dtype=complex)
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UDp[1,0] = 1 # Set the wave amplitude as 1 into the half-space at the bottom of the mesh
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# Loop over all the layers, starting at the bottom layer
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for lnr, h in enumerate(m1d.hx): # lnr-number of layer, h-thickness of the layer
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# Calculate
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yp1 = k[lnr]/(w*mu[lnr]) # Admittance of the layer below the current layer
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zp = (w*mu[lnr+1])/k[lnr+1] # Impedance in the current layer
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# Build the propagation matrix
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# Convert fields to down/up going components in layer below current layer
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Pj1 = np.array([[1,1],[yp1,-yp1]])
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# Convert fields to down/up going components in current layer
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Pjinv = 1./2*np.array([[1,zp],[1,-zp]])
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# Propagate down and up components through the current layer
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elamh = np.array([[np.exp(-1j*k[lnr+1]*h),0],[0,np.exp(1j*k[lnr+1]*h)]])
|
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# Initiate the propagation matrix, in the order down up.
|
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UDp = np.zeros((2,m1d.nC+1),dtype=complex)
|
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UDp[1,0] = 1 # Set the wave amplitude as 1 into the half-space at the bottom of the mesh
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# Loop over all the layers, starting at the bottom layer
|
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for lnr, h in enumerate(m1d.hx): # lnr-number of layer, h-thickness of the layer
|
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# Calculate
|
||||
yp1 = k[lnr]/(w*mu[lnr]) # Admittance of the layer below the current layer
|
||||
zp = (w*mu[lnr+1])/k[lnr+1] # Impedance in the current layer
|
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# Build the propagation matrix
|
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|
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# The down and up component in current layer.
|
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UDp[:,lnr+1] = elamh.dot(Pjinv.dot(Pj1)).dot(UDp[:,lnr])
|
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# Convert fields to down/up going components in layer below current layer
|
||||
Pj1 = np.array([[1,1],[yp1,-yp1]])
|
||||
# Convert fields to down/up going components in current layer
|
||||
Pjinv = 1./2*np.array([[1,zp],[1,-zp]])
|
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# Propagate down and up components through the current layer
|
||||
elamh = np.array([[np.exp(-1j*k[lnr+1]*h),0],[0,np.exp(1j*k[lnr+1]*h)]])
|
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|
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# Calculate the fields
|
||||
Ed = np.zeros((zd.size,),dtype=complex)
|
||||
Eu = np.zeros((zd.size,),dtype=complex)
|
||||
Hd = np.zeros((zd.size,),dtype=complex)
|
||||
Hu = np.zeros((zd.size,),dtype=complex)
|
||||
# The down and up component in current layer.
|
||||
UDp[:,lnr+1] = elamh.dot(Pjinv.dot(Pj1)).dot(UDp[:,lnr])
|
||||
|
||||
# Loop over the layers and calculate the fields
|
||||
for ki,mui,epsi,dlow,dup,Up,Dp in zip(k[1::],mu[1::],eps[1::],m1d.vectorNx[:-1],m1d.vectorNx[1::],UDp[0,1::],UDp[1,1::]):
|
||||
dind = np.logical_and(dup >= zd, zd > dlow)
|
||||
Ed[dind] = Dp*np.exp(-1j*ki*(dup-zd[dind]))
|
||||
Eu[dind] = Up*np.exp(1j*ki*(dup-zd[dind]))
|
||||
Hd[dind] = (ki/(w*mui))*Dp*np.exp(-1j*ki*(dup-zd[dind]))
|
||||
Hu[dind] = -(ki/(w*mui))*Up*np.exp(1j*ki*(dup-zd[dind]))
|
||||
# Calculate the fields
|
||||
Ed = np.zeros((zd.size,),dtype=complex)
|
||||
Eu = np.zeros((zd.size,),dtype=complex)
|
||||
Hd = np.zeros((zd.size,),dtype=complex)
|
||||
Hu = np.zeros((zd.size,),dtype=complex)
|
||||
|
||||
# Return return the fields
|
||||
return Ed, Eu, Hd, Hu
|
||||
# Loop over the layers and calculate the fields
|
||||
for ki,mui,epsi,dlow,dup,Up,Dp in zip(k[1::],mu[1::],eps[1::],m1d.vectorNx[:-1],m1d.vectorNx[1::],UDp[0,1::],UDp[1,1::]):
|
||||
dind = np.logical_and(dup >= zd, zd > dlow)
|
||||
Ed[dind] = Dp*np.exp(-1j*ki*(dup-zd[dind]))
|
||||
Eu[dind] = Up*np.exp(1j*ki*(dup-zd[dind]))
|
||||
Hd[dind] = (ki/(w*mui))*Dp*np.exp(-1j*ki*(dup-zd[dind]))
|
||||
Hu[dind] = -(ki/(w*mui))*Up*np.exp(1j*ki*(dup-zd[dind]))
|
||||
|
||||
# Return return the fields
|
||||
return Ed, Eu, Hd, Hu
|
||||
|
||||
def getImpedance(m1d,sigma,freq):
|
||||
"""Analytic solution for MT 1D layered earth. Returns the impedance at the surface.
|
||||
"""Analytic solution for MT 1D layered earth. Returns the impedance at the surface.
|
||||
|
||||
:param SimPEG.mesh, object m1d: Mesh object with the 1D spatial information.
|
||||
:param numpy.array, vector sigma: Physical property corresponding with the mesh.
|
||||
:param numpy.array, vector freq: Frequencies to calculate data at.
|
||||
:param SimPEG.mesh, object m1d: Mesh object with the 1D spatial information.
|
||||
:param numpy.array, vector sigma: Physical property corresponding with the mesh.
|
||||
:param numpy.array, vector freq: Frequencies to calculate data at.
|
||||
|
||||
|
||||
"""
|
||||
"""
|
||||
|
||||
# Define constants
|
||||
mu0 = 4*np.pi*1e-7
|
||||
eps0 = 8.85e-12
|
||||
# Define constants
|
||||
mu0 = 4*np.pi*1e-7
|
||||
eps0 = 8.85e-12
|
||||
|
||||
# Initiate the impedances
|
||||
Z1d = np.empty(len(freq) , dtype='complex')
|
||||
h = m1d.hx #vectorNx[:-1]
|
||||
# Start the process
|
||||
for nrFr, fr in enumerate(freq):
|
||||
om = 2*np.pi*fr
|
||||
Zall = np.empty(len(h)+1,dtype='complex')
|
||||
# Calculate the impedance for the bottom layer
|
||||
Zall[0] = (mu0*om)/np.sqrt(mu0*eps0*(om)**2 - 1j*mu0*sigma[0]*om)
|
||||
# Initiate the impedances
|
||||
Z1d = np.empty(len(freq) , dtype='complex')
|
||||
h = m1d.hx #vectorNx[:-1]
|
||||
# Start the process
|
||||
for nrFr, fr in enumerate(freq):
|
||||
om = 2*np.pi*fr
|
||||
Zall = np.empty(len(h)+1,dtype='complex')
|
||||
# Calculate the impedance for the bottom layer
|
||||
Zall[0] = (mu0*om)/np.sqrt(mu0*eps0*(om)**2 - 1j*mu0*sigma[0]*om)
|
||||
|
||||
for nr,hi in enumerate(h):
|
||||
# Calculate the wave number
|
||||
# print nr,sigma[nr]
|
||||
k = np.sqrt(mu0*eps0*om**2 - 1j*mu0*sigma[nr]*om)
|
||||
Z = (mu0*om)/k
|
||||
|
||||
Zall[nr+1] = Z *((Zall[nr] + Z*np.tanh(1j*k*hi))/(Z + Zall[nr]*np.tanh(1j*k*hi)))
|
||||
for nr,hi in enumerate(h):
|
||||
# Calculate the wave number
|
||||
# print nr,sigma[nr]
|
||||
k = np.sqrt(mu0*eps0*om**2 - 1j*mu0*sigma[nr]*om)
|
||||
Z = (mu0*om)/k
|
||||
|
||||
#pdb.set_trace()
|
||||
Z1d[nrFr] = Zall[-1]
|
||||
Zall[nr+1] = Z *((Zall[nr] + Z*np.tanh(1j*k*hi))/(Z + Zall[nr]*np.tanh(1j*k*hi)))
|
||||
|
||||
return Z1d
|
||||
#pdb.set_trace()
|
||||
Z1d[nrFr] = Zall[-1]
|
||||
|
||||
return Z1d
|
||||
|
||||
@@ -3,40 +3,41 @@ from MT1Danalytic import getEHfields
|
||||
from scipy.constants import mu_0
|
||||
|
||||
def get1DEfields(m1d,sigma,freq,sourceAmp=1.0):
|
||||
"""Function to get 1D electrical fields"""
|
||||
|
||||
# Get the gradient
|
||||
G = m1d.nodalGrad
|
||||
# Mass matrices
|
||||
# Magnetic permeability
|
||||
Mmu = simpeg.Utils.sdiag(m1d.vol*(1.0/mu_0))
|
||||
# Conductivity
|
||||
Msig = m1d.getFaceInnerProduct(sigma)
|
||||
# Set up the solution matrix
|
||||
A = G.T*Mmu*G - 1j*2.*np.pi*freq*Msig
|
||||
# Define the inner part of the solution matrix
|
||||
Aii = A[1:-1,1:-1]
|
||||
# Define the outer part of the solution matrix
|
||||
Aio = A[1:-1,[0,-1]]
|
||||
"""Function to get 1D electrical fields"""
|
||||
|
||||
# Set the boundary conditions
|
||||
Ed_low, Eu_low, Hd_low, Hu_low = getEHfields(m1d,sigma,freq,np.array([m1d.vectorNx[0]]))
|
||||
Etot_low = Ed_low + Eu_low
|
||||
bc = np.r_[Etot_low,sourceAmp]
|
||||
# The right hand side
|
||||
rhs = -Aio*bc
|
||||
# Solve the system
|
||||
Aii_inv = simpeg.Solver(Aii)
|
||||
eii = Aii_inv*rhs
|
||||
# Assign the boundary conditions
|
||||
e = np.r_[bc[0],eii,bc[1]]
|
||||
# Return the electrical fields
|
||||
return e
|
||||
# Get the gradient
|
||||
G = m1d.nodalGrad
|
||||
# Mass matrices
|
||||
# Magnetic permeability
|
||||
Mmu = simpeg.Utils.sdiag(m1d.vol*(1.0/mu_0))
|
||||
# Conductivity
|
||||
Msig = m1d.getFaceInnerProduct(sigma)
|
||||
# Set up the solution matrix
|
||||
A = G.T*Mmu*G - 1j*2.*np.pi*freq*Msig
|
||||
# Define the inner part of the solution matrix
|
||||
Aii = A[1:-1,1:-1]
|
||||
# Define the outer part of the solution matrix
|
||||
Aio = A[1:-1,[0,-1]]
|
||||
|
||||
# Set the boundary conditions
|
||||
Ed_low, Eu_low, Hd_low, Hu_low = getEHfields(m1d,sigma,freq,np.array([m1d.vectorNx[0]]))
|
||||
Etot_low = Ed_low + Eu_low
|
||||
## Note: need to use conjugate of the analytic solution. It is derived with e^iwt
|
||||
bc = np.r_[Etot_low.conj(),sourceAmp]
|
||||
# The right hand side
|
||||
rhs = -Aio*bc
|
||||
# Solve the system
|
||||
Aii_inv = simpeg.Solver(Aii)
|
||||
eii = Aii_inv*rhs
|
||||
# Assign the boundary conditions
|
||||
e = np.r_[bc[0],eii,bc[1]]
|
||||
# Return the electrical fields
|
||||
return e
|
||||
|
||||
|
||||
if __name__ == '__main__':
|
||||
|
||||
hz = [(100.,18)]
|
||||
M = simpeg.Mesh.TensorMesh([hz],'C')
|
||||
sig = np.zeros(M.nC) + 1e-8
|
||||
sig[M.vectorCCx<=0] = sigHalf
|
||||
hz = [(100.,18)]
|
||||
M = simpeg.Mesh.TensorMesh([hz],'C')
|
||||
sig = np.zeros(M.nC) + 1e-8
|
||||
sig[M.vectorCCx<=0] = sigHalf
|
||||
|
||||
@@ -1,2 +1,2 @@
|
||||
from MT1Dsolutions import * # Add the names of the functions
|
||||
from MT1Danalytic import *
|
||||
from MT1Danalytic import *
|
||||
|
||||
Reference in New Issue
Block a user