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Merge branch 'dcip/dev' of https://github.com/simpeg/simpeg into dcip/dev

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D Fournier
2016-02-19 16:42:13 -08:00
parent a7c35abd56 16239aa414
commit cd352dc5f7
51 changed files with 5336 additions and 887 deletions
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.travis.yml
+3
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@@ -20,6 +20,7 @@ env:
- TEST_DIR=tests/em/tdem
- TEST_DIR=tests/dcip
- TEST_DIR=tests/flow
- TEST_DIR=tests/mt
- TEST_DIR=tests/examples
- TEST_DIR=tests/em/fdem/inverse/adjoint
- TEST_DIR=tests/em/fdem/forward
@@ -55,3 +56,5 @@ notifications:
email:
- rowanc1@gmail.com
- lindseyheagy@gmail.com
- gkrosen@gmail.com
- sgkang09@gmail.com
SimPEG/Directives.py
+41 -45
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@@ -237,53 +237,49 @@ class SaveOutputDictEveryIteration(_SaveEveryIteration):
# Save the file as a npz
np.savez('{:03d}-{:s}'.format(self.opt.iter,self.fileName), iter=self.opt.iter, beta=self.invProb.beta, phi_d=self.invProb.phi_d, phi_m=self.invProb.phi_m, phi_ms=phi_ms, phi_mx=phi_mx, phi_my=phi_my, phi_mz=phi_mz,f=self.opt.f, m=self.invProb.curModel,dpred=self.invProb.dpred)
class SaveOutputDictEveryIteration(_SaveEveryIteration):
"""SaveOutputDictEveryIteration
A directive that saves some relevant information from the inversion run to a numpy .npz dictionary file (see numpy.savez function for further info).
"""
def initialize(self):
print "SimPEG.SaveOutputDictEveryIteration will save your inversion progress as dictionary: '%s-###.npz'"%self.fileName
def endIter(self):
# Save the data.
ms = self.reg.Ws * ( self.reg.mapping * (self.invProb.curModel - self.reg.mref) )
phi_ms = 0.5*ms.dot(ms)
if self.reg.smoothModel == True:
mref = self.reg.mref
else:
mref = 0
mx = self.reg.Wx * ( self.reg.mapping * (self.invProb.curModel - mref) )
phi_mx = 0.5 * mx.dot(mx)
if self.prob.mesh.dim==2:
my = self.reg.Wy * ( self.reg.mapping * (self.invProb.curModel - mref) )
phi_my = 0.5 * my.dot(my)
else:
phi_my = 'NaN'
if self.prob.mesh.dim==3 and 'CYL' not in self.prob.mesh._meshType:
mz = self.reg.Wz * ( self.reg.mapping * (self.invProb.curModel - mref) )
phi_mz = 0.5 * mz.dot(mz)
else:
phi_mz = 'NaN'
class update_IRLS(InversionDirective):
# Save the file as a npz
np.savez('{:s}-{:03d}'.format(self.fileName,self.opt.iter), iter=self.opt.iter, beta=self.invProb.beta, phi_d=self.invProb.phi_d, phi_m=self.invProb.phi_m, phi_ms=phi_ms, phi_mx=phi_mx, phi_my=phi_my, phi_mz=phi_mz,f=self.opt.f, m=self.invProb.curModel,dpred=self.invProb.dpred)
m = None
eps_min = None
factor = None
gamma = None
phi_m_last = None
def initialize(self):
# Scale the regularization for changes in norm
if getattr(self, 'phi_m_last', None) is not None:
self.reg.gamma = 1.
phim_new = self.reg.eval(self.invProb.curModel)
self.gamma = self.phi_m_last / phim_new
self.reg.gamma = self.gamma
def endIter(self):
# Cool the threshold parameter
if getattr(self, 'factor', None) is not None:
eps = self.reg.eps / self.factor
if getattr(self, 'eps_min', None) is not None:
self.reg.eps = np.max([self.eps_min,eps])
else:
self.reg.eps = eps
# Update the model used for the IRLS weights
if getattr(self, 'm', None) is None:
self.reg.m = self.invProb.curModel
# Update the pre-conditioner
diagA = np.sum(self.prob.G**2.,axis=0) + self.invProb.beta*(self.reg.W.T*self.reg.W).diagonal() * (self.reg.mapping * np.ones(self.prob.mesh.nC))**2.
PC = Utils.sdiag(diagA**-1.)
self.opt.approxHinv = PC
phim_new = self.reg.eval(self.invProb.curModel)
self.reg.gamma = self.reg.gamma * self.invProb.phi_m_last / phim_new
#==============================================================================
# import pylab as plt
# plt.figure()
# ax = plt.subplot(221)
# self.prob.mesh.plotSlice(self.invProb.curModel, ax = ax, normal = 'Z', ind=-5, clim = (0, 0.005))
#==============================================================================
# class UpdateReferenceModel(Parameter):
# mref0 = None
# def nextIter(self):
# mref = getattr(self, 'm_prev', None)
# if mref is None:
# if self.debug: print 'UpdateReferenceModel is using mref0'
# mref = self.mref0
# self.m_prev = self.invProb.m_current
# return mref
SimPEG/EM/FDEM/FDEM.py
+229 -97
View File
@@ -15,18 +15,20 @@ class BaseFDEMProblem(BaseEMProblem):
.. math ::
\mathbf{C} \mathbf{e} + i \omega \mathbf{b} = \mathbf{s_m} \\\\
{\mathbf{C}^T \mathbf{M_{\mu^{-1}}^f} \mathbf{b} - \mathbf{M_{\sigma}^e} \mathbf{e} = \mathbf{M^e} \mathbf{s_e}}
{\mathbf{C}^{\\top} \mathbf{M_{\mu^{-1}}^f} \mathbf{b} - \mathbf{M_{\sigma}^e} \mathbf{e} = \mathbf{s_e}}
if using the E-B formulation (:code:`Problem_e`
or :code:`Problem_b`) or the magnetic field
or :code:`Problem_b`). Note that in this case, :math:`\mathbf{s_e}` is an integrated quantity.
If we write Maxwell's equations in terms of
\\\(\\\mathbf{h}\\\) and current density \\\(\\\mathbf{j}\\\)
.. math ::
\mathbf{C}^T \mathbf{M_{\\rho}^f} \mathbf{j} + i \omega \mathbf{M_{\mu}^e} \mathbf{h} = \mathbf{M^e} \mathbf{s_m} \\\\
\mathbf{C}^{\\top} \mathbf{M_{\\rho}^f} \mathbf{j} + i \omega \mathbf{M_{\mu}^e} \mathbf{h} = \mathbf{s_m} \\\\
\mathbf{C} \mathbf{h} - \mathbf{j} = \mathbf{s_e}
if using the H-J formulation (:code:`Problem_j` or :code:`Problem_h`).
if using the H-J formulation (:code:`Problem_j` or :code:`Problem_h`). Note that here, :math:`\mathbf{s_m}` is an integrated quantity.
The problem performs the elimination so that we are solving the system for \\\(\\\mathbf{e},\\\mathbf{b},\\\mathbf{j} \\\) or \\\(\\\mathbf{h}\\\)
"""
@@ -36,7 +38,11 @@ class BaseFDEMProblem(BaseEMProblem):
def fields(self, m=None):
"""
Solve the forward problem for the fields.
Solve the forward problem for the fields.
:param numpy.array m: inversion model (nP,)
:rtype numpy.array:
:return F: forward solution
"""
self.curModel = m
@@ -55,7 +61,13 @@ class BaseFDEMProblem(BaseEMProblem):
def Jvec(self, m, v, u=None):
"""
Sensitivity times a vector
Sensitivity times a vector.
:param numpy.array m: inversion model (nP,)
:param numpy.array v: vector which we take sensitivity product with (nP,)
:param SimPEG.EM.FDEM.Fields u: fields object
:rtype numpy.array:
:return: Jv (ndata,)
"""
if u is None:
@@ -83,6 +95,7 @@ class BaseFDEMProblem(BaseEMProblem):
df_dmFun = getattr(u, '_%sDeriv_m'%rx.projField, None)
df_dm = df_dmFun(src, v, adjoint=False)
Df_Dm = np.array(df_dudu_dm + df_dm,dtype=complex)
P = lambda v: rx.projectFieldsDeriv(src, self.mesh, u, v) # wrt u, also have wrt m
@@ -94,7 +107,13 @@ class BaseFDEMProblem(BaseEMProblem):
def Jtvec(self, m, v, u=None):
"""
Sensitivity transpose times a vector
Sensitivity transpose times a vector
:param numpy.array m: inversion model (nP,)
:param numpy.array v: vector which we take adjoint product with (nP,)
:param SimPEG.EM.FDEM.Fields u: fields object
:rtype numpy.array:
:return: Jv (ndata,)
"""
if u is None:
@@ -133,6 +152,7 @@ class BaseFDEMProblem(BaseEMProblem):
du_dmT += dfT_dm
# TODO: this should be taken care of by the reciever
real_or_imag = rx.projComp
if real_or_imag is 'real':
Jtv += np.array(du_dmT,dtype=complex).real
@@ -147,11 +167,11 @@ class BaseFDEMProblem(BaseEMProblem):
def getSourceTerm(self, freq):
"""
Evaluates the sources for a given frequency and puts them in matrix form
Evaluates the sources for a given frequency and puts them in matrix form
:param float freq: Frequency
:rtype: numpy.ndarray (nE or nF, nSrc)
:return: S_m, S_e
:param float freq: Frequency
:rtype: (numpy.ndarray, numpy.ndarray)
:return: S_m, S_e (nE or nF, nSrc)
"""
Srcs = self.survey.getSrcByFreq(freq)
if self._eqLocs is 'FE':
@@ -175,20 +195,22 @@ class BaseFDEMProblem(BaseEMProblem):
class Problem_e(BaseFDEMProblem):
"""
By eliminating the magnetic flux density using
.. math ::
\mathbf{b} = \\frac{1}{i \omega}\\left(-\mathbf{C} \mathbf{e} + \mathbf{s_m}\\right)
we can write Maxwell's equations as a second order system in \\\(\\\mathbf{e}\\\) only:
By eliminating the magnetic flux density using
.. math ::
\\left(\mathbf{C}^T \mathbf{M_{\mu^{-1}}^f} \mathbf{C}+ i \omega \mathbf{M^e_{\sigma}} \\right)\mathbf{e} = \mathbf{C}^T \mathbf{M_{\mu^{-1}}^f}\mathbf{s_m} -i\omega\mathbf{M^e}\mathbf{s_e}
\mathbf{b} = \\frac{1}{i \omega}\\left(-\mathbf{C} \mathbf{e} + \mathbf{s_m}\\right)
which we solve for \\\(\\\mathbf{e}\\\).
we can write Maxwell's equations as a second order system in \\\(\\\mathbf{e}\\\) only:
.. math ::
\\left(\mathbf{C}^{\\top} \mathbf{M_{\mu^{-1}}^f} \mathbf{C}+ i \omega \mathbf{M^e_{\sigma}} \\right)\mathbf{e} = \mathbf{C}^{\\top} \mathbf{M_{\mu^{-1}}^f}\mathbf{s_m} -i\omega\mathbf{M^e}\mathbf{s_e}
which we solve for :math:`\mathbf{e}`.
:param SimPEG.Mesh mesh: mesh
"""
_fieldType = 'e'
@@ -200,13 +222,16 @@ class Problem_e(BaseFDEMProblem):
def getA(self, freq):
"""
.. math ::
\mathbf{A} = \mathbf{C}^T \mathbf{M_{\mu^{-1}}^f} \mathbf{C} + i \omega \mathbf{M^e_{\sigma}}
System matrix
.. math ::
\mathbf{A} = \mathbf{C}^{\\top} \mathbf{M_{\mu^{-1}}^f} \mathbf{C} + i \omega \mathbf{M^e_{\sigma}}
:param float freq: Frequency
:rtype: scipy.sparse.csr_matrix
:return: A
:param float freq: Frequency
:rtype: scipy.sparse.csr_matrix
:return: A
"""
MfMui = self.MfMui
MeSigma = self.MeSigma
C = self.mesh.edgeCurl
@@ -215,6 +240,20 @@ class Problem_e(BaseFDEMProblem):
def getADeriv_m(self, freq, u, v, adjoint=False):
"""
Product of the derivative of our system matrix with respect to the model and a vector
.. math ::
\\frac{\mathbf{A}(\mathbf{m}) \mathbf{v}}{d \mathbf{m}} = i \omega \\frac{d \mathbf{M^e_{\sigma}}\mathbf{v} }{d\mathbf{m}}
:param float freq: frequency
:param numpy.ndarray u: solution vector (nE,)
:param numpy.ndarray v: vector to take prodct with (nP,) or (nD,) for adjoint
:param bool adjoint: adjoint?
:rtype: numpy.ndarray
:return: derivative of the system matrix times a vector (nP,) or adjoint (nD,)
"""
dsig_dm = self.curModel.sigmaDeriv
dMe_dsig = self.MeSigmaDeriv(u)
@@ -225,26 +264,37 @@ class Problem_e(BaseFDEMProblem):
def getRHS(self, freq):
"""
.. math ::
\mathbf{RHS} = \mathbf{C}^T \mathbf{M_{\mu^{-1}}^f}\mathbf{s_m} -i\omega\mathbf{M_e}\mathbf{s_e}
Right hand side for the system
:param float freq: Frequency
:rtype: numpy.ndarray (nE, nSrc)
:return: RHS
.. math ::
\mathbf{RHS} = \mathbf{C}^{\\top} \mathbf{M_{\mu^{-1}}^f}\mathbf{s_m} -i\omega\mathbf{M_e}\mathbf{s_e}
:param float freq: Frequency
:rtype: numpy.ndarray
:return: RHS (nE, nSrc)
"""
S_m, S_e = self.getSourceTerm(freq)
C = self.mesh.edgeCurl
MfMui = self.MfMui
RHS = C.T * (MfMui * S_m) -1j * omega(freq) * S_e
return RHS
return C.T * (MfMui * S_m) -1j * omega(freq) * S_e
def getRHSDeriv_m(self, freq, src, v, adjoint=False):
"""
Derivative of the right hand side with respect to the model
:param float freq: frequency
:param SimPEG.EM.FDEM.Src src: FDEM source
:param numpy.ndarray v: vector to take product with
:param bool adjoint: adjoint?
:rtype: numpy.ndarray
:return: product of rhs deriv with a vector
"""
C = self.mesh.edgeCurl
MfMui = self.MfMui
S_mDeriv, S_eDeriv = src.evalDeriv(self, adjoint)
S_mDeriv, S_eDeriv = src.evalDeriv(self, adjoint=adjoint)
if adjoint:
dRHS = MfMui * (C * v)
@@ -256,20 +306,22 @@ class Problem_e(BaseFDEMProblem):
class Problem_b(BaseFDEMProblem):
"""
We eliminate \\\(\\\mathbf{e}\\\) using
We eliminate :math:`\mathbf{e}` using
.. math ::
.. math ::
\mathbf{e} = \mathbf{M^e_{\sigma}}^{-1} \\left(\mathbf{C}^T \mathbf{M_{\mu^{-1}}^f} \mathbf{b} - \mathbf{s_e}\\right)
\mathbf{e} = \mathbf{M^e_{\sigma}}^{-1} \\left(\mathbf{C}^{\\top} \mathbf{M_{\mu^{-1}}^f} \mathbf{b} - \mathbf{s_e}\\right)
and solve for \\\(\\\mathbf{b}\\\) using:
and solve for :math:`\mathbf{b}` using:
.. math ::
.. math ::
\\left(\mathbf{C} \mathbf{M^e_{\sigma}}^{-1} \mathbf{C}^T \mathbf{M_{\mu^{-1}}^f} + i \omega \\right)\mathbf{b} = \mathbf{s_m} + \mathbf{M^e_{\sigma}}^{-1}\mathbf{M^e}\mathbf{s_e}
\\left(\mathbf{C} \mathbf{M^e_{\sigma}}^{-1} \mathbf{C}^{\\top} \mathbf{M_{\mu^{-1}}^f} + i \omega \\right)\mathbf{b} = \mathbf{s_m} + \mathbf{M^e_{\sigma}}^{-1}\mathbf{M^e}\mathbf{s_e}
.. note ::
The inverse problem will not work with full anisotropy
.. note ::
The inverse problem will not work with full anisotropy
:param SimPEG.Mesh mesh: mesh
"""
_fieldType = 'b'
@@ -281,12 +333,14 @@ class Problem_b(BaseFDEMProblem):
def getA(self, freq):
"""
.. math ::
\mathbf{A} = \mathbf{C} \mathbf{M^e_{\sigma}}^{-1} \mathbf{C}^T \mathbf{M_{\mu^{-1}}^f} + i \omega
System matrix
:param float freq: Frequency
:rtype: scipy.sparse.csr_matrix
:return: A
.. math ::
\mathbf{A} = \mathbf{C} \mathbf{M^e_{\sigma}}^{-1} \mathbf{C}^{\\top} \mathbf{M_{\mu^{-1}}^f} + i \omega
:param float freq: Frequency
:rtype: scipy.sparse.csr_matrix
:return: A
"""
MfMui = self.MfMui
@@ -302,6 +356,20 @@ class Problem_b(BaseFDEMProblem):
def getADeriv_m(self, freq, u, v, adjoint=False):
"""
Product of the derivative of our system matrix with respect to the model and a vector
.. math ::
\\frac{\mathbf{A}(\mathbf{m}) \mathbf{v}}{d \mathbf{m}} = \mathbf{C} \\frac{\mathbf{M^e_{\sigma}} \mathbf{v}}{d\mathbf{m}}
:param float freq: frequency
:param numpy.ndarray u: solution vector (nF,)
:param numpy.ndarray v: vector to take prodct with (nP,) or (nD,) for adjoint
:param bool adjoint: adjoint?
:rtype: numpy.ndarray
:return: derivative of the system matrix times a vector (nP,) or adjoint (nD,)
"""
MfMui = self.MfMui
C = self.mesh.edgeCurl
MeSigmaIDeriv = self.MeSigmaIDeriv
@@ -321,12 +389,14 @@ class Problem_b(BaseFDEMProblem):
def getRHS(self, freq):
"""
.. math ::
\mathbf{RHS} = \mathbf{s_m} + \mathbf{M^e_{\sigma}}^{-1}\mathbf{s_e}
Right hand side for the system
:param float freq: Frequency
:rtype: numpy.ndarray (nE, nSrc)
:return: RHS
.. math ::
\mathbf{RHS} = \mathbf{s_m} + \mathbf{M^e_{\sigma}}^{-1}\mathbf{s_e}
:param float freq: Frequency
:rtype: numpy.ndarray
:return: RHS (nE, nSrc)
"""
S_m, S_e = self.getSourceTerm(freq)
@@ -342,6 +412,17 @@ class Problem_b(BaseFDEMProblem):
return RHS
def getRHSDeriv_m(self, freq, src, v, adjoint=False):
"""
Derivative of the right hand side with respect to the model
:param float freq: frequency
:param SimPEG.EM.FDEM.Src src: FDEM source
:param numpy.ndarray v: vector to take product with
:param bool adjoint: adjoint?
:rtype: numpy.ndarray
:return: product of rhs deriv with a vector
"""
C = self.mesh.edgeCurl
S_m, S_e = src.eval(self)
MfMui = self.MfMui
@@ -350,7 +431,7 @@ class Problem_b(BaseFDEMProblem):
v = self.MfMui * v
MeSigmaIDeriv = self.MeSigmaIDeriv(S_e)
S_mDeriv, S_eDeriv = src.evalDeriv(self, adjoint)
S_mDeriv, S_eDeriv = src.evalDeriv(self, adjoint=adjoint)
if not adjoint:
RHSderiv = C * (MeSigmaIDeriv * v)
@@ -373,21 +454,22 @@ class Problem_b(BaseFDEMProblem):
class Problem_j(BaseFDEMProblem):
"""
We eliminate \\\(\\\mathbf{h}\\\) using
We eliminate \\\(\\\mathbf{h}\\\) using
.. math ::
.. math ::
\mathbf{h} = \\frac{1}{i \omega} \mathbf{M_{\mu}^e}^{-1} \\left(-\mathbf{C}^T \mathbf{M_{\\rho}^f} \mathbf{j} + \mathbf{M^e} \mathbf{s_m} \\right)
\mathbf{h} = \\frac{1}{i \omega} \mathbf{M_{\mu}^e}^{-1} \\left(-\mathbf{C}^{\\top} \mathbf{M_{\\rho}^f} \mathbf{j} + \mathbf{M^e} \mathbf{s_m} \\right)
and solve for \\\(\\\mathbf{j}\\\) using
and solve for \\\(\\\mathbf{j}\\\) using
.. math ::
.. math ::
\\left(\mathbf{C} \mathbf{M_{\mu}^e}^{-1} \mathbf{C}^T \mathbf{M_{\\rho}^f} + i \omega\\right)\mathbf{j} = \mathbf{C} \mathbf{M_{\mu}^e}^{-1} \mathbf{M^e} \mathbf{s_m} -i\omega\mathbf{s_e}
\\left(\mathbf{C} \mathbf{M_{\mu}^e}^{-1} \mathbf{C}^{\\top} \mathbf{M_{\\rho}^f} + i \omega\\right)\mathbf{j} = \mathbf{C} \mathbf{M_{\mu}^e}^{-1} \mathbf{M^e} \mathbf{s_m} -i\omega\mathbf{s_e}
.. note::
This implementation does not yet work with full anisotropy!!
.. note::
This implementation does not yet work with full anisotropy!!
:param SimPEG.Mesh mesh: mesh
"""
_fieldType = 'j'
@@ -399,12 +481,14 @@ class Problem_j(BaseFDEMProblem):
def getA(self, freq):
"""
.. math ::
\\mathbf{A} = \\mathbf{C} \\mathbf{M^e_{mu^{-1}}} \\mathbf{C}^T \\mathbf{M^f_{\\sigma^{-1}}} + i\\omega
System matrix
:param float freq: Frequency
:rtype: scipy.sparse.csr_matrix
:return: A
.. math ::
\\mathbf{A} = \\mathbf{C} \\mathbf{M^e_{\\mu^{-1}}} \\mathbf{C}^{\\top} \\mathbf{M^f_{\\sigma^{-1}}} + i\\omega
:param float freq: Frequency
:rtype: scipy.sparse.csr_matrix
:return: A
"""
MeMuI = self.MeMuI
@@ -421,12 +505,20 @@ class Problem_j(BaseFDEMProblem):
def getADeriv_m(self, freq, u, v, adjoint=False):
"""
In this case, we assume that electrical conductivity, \\\(\\\sigma\\\) is the physical property of interest (i.e. \\\(\\\sigma\\\) = model.transform). Then we want
Product of the derivative of our system matrix with respect to the model and a vector
.. math ::
In this case, we assume that electrical conductivity, :math:`\sigma` is the physical property of interest (i.e. :math:`\sigma` = model.transform). Then we want
\\frac{\mathbf{A(\sigma)} \mathbf{v}}{d \\mathbf{m}} &= \\mathbf{C} \\mathbf{M^e_{mu^{-1}}} \\mathbf{C^T} \\frac{d \\mathbf{M^f_{\\sigma^{-1}}}}{d \\mathbf{m}}
&= \\mathbf{C} \\mathbf{M^e_{mu}^{-1}} \\mathbf{C^T} \\frac{d \\mathbf{M^f_{\\sigma^{-1}}}}{d \\mathbf{\\sigma^{-1}}} \\frac{d \\mathbf{\\sigma^{-1}}}{d \\mathbf{\\sigma}} \\frac{d \\mathbf{\\sigma}}{d \\mathbf{m}}
.. math ::
\\frac{\mathbf{A(\sigma)} \mathbf{v}}{d \mathbf{m}} = \mathbf{C} \mathbf{M^e_{mu^{-1}}} \mathbf{C^{\\top}} \\frac{d \mathbf{M^f_{\sigma^{-1}}}\mathbf{v} }{d \mathbf{m}}
:param float freq: frequency
:param numpy.ndarray u: solution vector (nF,)
:param numpy.ndarray v: vector to take prodct with (nP,) or (nD,) for adjoint
:param bool adjoint: adjoint?
:rtype: numpy.ndarray
:return: derivative of the system matrix times a vector (nP,) or adjoint (nD,)
"""
MeMuI = self.MeMuI
@@ -446,12 +538,15 @@ class Problem_j(BaseFDEMProblem):
def getRHS(self, freq):
"""
.. math ::
Right hand side for the system
\mathbf{RHS} = \mathbf{C} \mathbf{M_{\mu}^e}^{-1}\mathbf{s_m} -i\omega \mathbf{s_e}
:param float freq: Frequency
:rtype: numpy.ndarray (nE, nSrc)
:return: RHS
.. math ::
\mathbf{RHS} = \mathbf{C} \mathbf{M_{\mu}^e}^{-1}\mathbf{s_m} -i\omega \mathbf{s_e}
:param float freq: Frequency
:rtype: numpy.ndarray (nE, nSrc)
:return: RHS
"""
S_m, S_e = self.getSourceTerm(freq)
@@ -466,9 +561,20 @@ class Problem_j(BaseFDEMProblem):
return RHS
def getRHSDeriv_m(self, freq, src, v, adjoint=False):
"""
Derivative of the right hand side with respect to the model
:param float freq: frequency
:param SimPEG.EM.FDEM.Src src: FDEM source
:param numpy.ndarray v: vector to take product with
:param bool adjoint: adjoint?
:rtype: numpy.ndarray
:return: product of rhs deriv with a vector
"""
C = self.mesh.edgeCurl
MeMuI = self.MeMuI
S_mDeriv, S_eDeriv = src.evalDeriv(self, adjoint)
S_mDeriv, S_eDeriv = src.evalDeriv(self, adjoint=adjoint)
if adjoint:
if self._makeASymmetric:
@@ -489,18 +595,19 @@ class Problem_j(BaseFDEMProblem):
class Problem_h(BaseFDEMProblem):
"""
We eliminate \\\(\\\mathbf{j}\\\) using
We eliminate \\\(\\\mathbf{j}\\\) using
.. math ::
.. math ::
\mathbf{j} = \mathbf{C} \mathbf{h} - \mathbf{s_e}
\mathbf{j} = \mathbf{C} \mathbf{h} - \mathbf{s_e}
and solve for \\\(\\\mathbf{h}\\\) using
and solve for \\\(\\\mathbf{h}\\\) using
.. math ::
.. math ::
\\left(\mathbf{C}^T \mathbf{M_{\\rho}^f} \mathbf{C} + i \omega \mathbf{M_{\mu}^e}\\right) \mathbf{h} = \mathbf{M^e} \mathbf{s_m} + \mathbf{C}^T \mathbf{M_{\\rho}^f} \mathbf{s_e}
\\left(\mathbf{C}^{\\top} \mathbf{M_{\\rho}^f} \mathbf{C} + i \omega \mathbf{M_{\mu}^e}\\right) \mathbf{h} = \mathbf{M^e} \mathbf{s_m} + \mathbf{C}^{\\top} \mathbf{M_{\\rho}^f} \mathbf{s_e}
:param SimPEG.Mesh mesh: mesh
"""
_fieldType = 'h'
@@ -512,13 +619,14 @@ class Problem_h(BaseFDEMProblem):
def getA(self, freq):
"""
.. math ::
System matrix
\mathbf{A} = \mathbf{C}^T \mathbf{M_{\\rho}^f} \mathbf{C} + i \omega \mathbf{M_{\mu}^e}
.. math::
\mathbf{A} = \mathbf{C}^{\\top} \mathbf{M_{\\rho}^f} \mathbf{C} + i \omega \mathbf{M_{\mu}^e}
:param float freq: Frequency
:rtype: scipy.sparse.csr_matrix
:return: A
:param float freq: Frequency
:rtype: scipy.sparse.csr_matrix
:return: A
"""
MeMu = self.MeMu
@@ -528,6 +636,19 @@ class Problem_h(BaseFDEMProblem):
return C.T * (MfRho * C) + 1j*omega(freq)*MeMu
def getADeriv_m(self, freq, u, v, adjoint=False):
"""
Product of the derivative of our system matrix with respect to the model and a vector
.. math::
\\frac{\mathbf{A}(\mathbf{m}) \mathbf{v}}{d \mathbf{m}} = \mathbf{C}^{\\top}\\frac{d \mathbf{M^f_{\\rho}}\mathbf{v} }{d\mathbf{m}}
:param float freq: frequency
:param numpy.ndarray u: solution vector (nE,)
:param numpy.ndarray v: vector to take prodct with (nP,) or (nD,) for adjoint
:param bool adjoint: adjoint?
:rtype: numpy.ndarray
:return: derivative of the system matrix times a vector (nP,) or adjoint (nD,)
"""
MeMu = self.MeMu
C = self.mesh.edgeCurl
@@ -539,24 +660,35 @@ class Problem_h(BaseFDEMProblem):
def getRHS(self, freq):
"""
.. math ::
Right hand side for the system
\mathbf{RHS} = \mathbf{M^e} \mathbf{s_m} + \mathbf{C}^T \mathbf{M_{\\rho}^f} \mathbf{s_e}
.. math ::
:param float freq: Frequency
:rtype: numpy.ndarray (nE, nSrc)
:return: RHS
\mathbf{RHS} = \mathbf{M^e} \mathbf{s_m} + \mathbf{C}^{\\top} \mathbf{M_{\\rho}^f} \mathbf{s_e}
:param float freq: Frequency
:rtype: numpy.ndarray
:return: RHS (nE, nSrc)
"""
S_m, S_e = self.getSourceTerm(freq)
C = self.mesh.edgeCurl
MfRho = self.MfRho
RHS = S_m + C.T * ( MfRho * S_e )
return RHS
return S_m + C.T * ( MfRho * S_e )
def getRHSDeriv_m(self, freq, src, v, adjoint=False):
"""
Derivative of the right hand side with respect to the model
:param float freq: frequency
:param SimPEG.EM.FDEM.Src src: FDEM source
:param numpy.ndarray v: vector to take product with
:param bool adjoint: adjoint?
:rtype: numpy.ndarray
:return: product of rhs deriv with a vector
"""
_, S_e = src.eval(self)
C = self.mesh.edgeCurl
MfRho = self.MfRho
@@ -567,7 +699,7 @@ class Problem_h(BaseFDEMProblem):
elif adjoint:
RHSDeriv = MfRhoDeriv.T * (C * v)
S_mDeriv, S_eDeriv = src.evalDeriv(self, adjoint)
S_mDeriv, S_eDeriv = src.evalDeriv(self, adjoint=adjoint)
return RHSDeriv + S_mDeriv(v) + C.T * (MfRho * S_eDeriv(v))
SimPEG/EM/FDEM/FieldsFDEM.py
+512 -9
View File
@@ -7,11 +7,39 @@ from SimPEG.Utils import Zero, Identity
class Fields(SimPEG.Problem.Fields):
"""Fancy Field Storage for a FDEM survey."""
"""
Fancy Field Storage for a FDEM survey. Only one field type is stored for
each problem, the rest are computed. The fields obejct acts like an array and is indexed by
.. code-block:: python
f = problem.fields(m)
e = f[srcList,'e']
b = f[srcList,'b']
If accessing all sources for a given field, use the :code:`:`
.. code-block:: python
f = problem.fields(m)
e = f[:,'e']
b = f[:,'b']
The array returned will be size (nE or nF, nSrcs :math:`\\times` nFrequencies)
"""
knownFields = {}
dtype = complex
class Fields_e(Fields):
"""
Fields object for Problem_e.
:param Mesh mesh: mesh
:param Survey survey: survey
"""
knownFields = {'eSolution':'E'}
aliasFields = {
'e' : ['eSolution','E','_e'],
@@ -30,6 +58,15 @@ class Fields_e(Fields):
self._edgeCurl = self.survey.prob.mesh.edgeCurl
def _ePrimary(self, eSolution, srcList):
"""
Primary electric field from source
:param numpy.ndarray eSolution: field we solved for
:param list srcList: list of sources
:rtype: numpy.ndarray
:return: primary electric field as defined by the sources
"""
ePrimary = np.zeros_like(eSolution)
for i, src in enumerate(srcList):
ep = src.ePrimary(self.prob)
@@ -37,19 +74,67 @@ class Fields_e(Fields):
return ePrimary
def _eSecondary(self, eSolution, srcList):
"""
Secondary electric field is the thing we solved for
:param numpy.ndarray eSolution: field we solved for
:param list srcList: list of sources
:rtype: numpy.ndarray
:return: secondary electric field
"""
return eSolution
def _e(self, eSolution, srcList):
"""
Total electric field is sum of primary and secondary
:param numpy.ndarray eSolution: field we solved for
:param list srcList: list of sources
:rtype: numpy.ndarray
:return: total electric field
"""
return self._ePrimary(eSolution,srcList) + self._eSecondary(eSolution,srcList)
def _eDeriv_u(self, src, v, adjoint = False):
"""
Derivative of the total electric field with respect to the thing we
solved for
:param SimPEG.EM.FDEM.Src src: source
:param numpy.ndarray v: vector to take product with
:param bool adjoint: adjoint?
:rtype: numpy.ndarray
:return: product of the derivative of the electric field with respect to the field we solved for with a vector
"""
return Identity()*v
def _eDeriv_m(self, src, v, adjoint = False):
"""
Derivative of the total electric field with respect to the inversion model. Here, we assume that the primary does not depend on the model.
:param SimPEG.EM.FDEM.Src src: source
:param numpy.ndarray v: vector to take product with
:param bool adjoint: adjoint?
:rtype: SimPEG.Utils.Zero
:return: product of the electric field derivative with respect to the inversion model with a vector
"""
# assuming primary does not depend on the model
return Zero()
def _bPrimary(self, eSolution, srcList):
"""
Primary magnetic flux density from source
:param numpy.ndarray eSolution: field we solved for
:param list srcList: list of sources
:rtype: numpy.ndarray
:return: primary magnetic flux density as defined by the sources
"""
bPrimary = np.zeros([self._edgeCurl.shape[0],eSolution.shape[1]],dtype = complex)
for i, src in enumerate(srcList):
bp = src.bPrimary(self.prob)
@@ -57,6 +142,15 @@ class Fields_e(Fields):
return bPrimary
def _bSecondary(self, eSolution, srcList):
"""
Secondary magnetic flux density from eSolution
:param numpy.ndarray eSolution: field we solved for
:param list srcList: list of sources
:rtype: numpy.ndarray
:return: secondary magnetic flux density
"""
C = self._edgeCurl
b = (C * eSolution)
for i, src in enumerate(srcList):
@@ -66,29 +160,84 @@ class Fields_e(Fields):
return b
def _bSecondaryDeriv_u(self, src, v, adjoint = False):
"""
Derivative of the secondary magnetic flux density with respect to the thing we solved for
:param SimPEG.EM.FDEM.Src src: source
:param numpy.ndarray v: vector to take product with
:param bool adjoint: adjoint?
:rtype: numpy.ndarray
:return: product of the derivative of the secondary magnetic flux density with respect to the field we solved for with a vector
"""
C = self._edgeCurl
if adjoint:
return - 1./(1j*omega(src.freq)) * (C.T * v)
return - 1./(1j*omega(src.freq)) * (C * v)
def _bSecondaryDeriv_m(self, src, v, adjoint = False):
S_mDeriv, _ = src.evalDeriv(self.prob, adjoint)
S_mDeriv = S_mDeriv(v)
"""
Derivative of the secondary magnetic flux density with respect to the inversion model.
:param SimPEG.EM.FDEM.Src src: source
:param numpy.ndarray v: vector to take product with
:param bool adjoint: adjoint?
:rtype: numpy.ndarray
:return: product of the secondary magnetic flux density derivative with respect to the inversion model with a vector
"""
S_mDeriv, _ = src.evalDeriv(self.prob, v, adjoint)
return 1./(1j * omega(src.freq)) * S_mDeriv
def _b(self, eSolution, srcList):
"""
Total magnetic flux density is sum of primary and secondary
:param numpy.ndarray eSolution: field we solved for
:param list srcList: list of sources
:rtype: numpy.ndarray
:return: total magnetic flux density
"""
return self._bPrimary(eSolution, srcList) + self._bSecondary(eSolution, srcList)
def _bDeriv_u(self, src, v, adjoint=False):
"""
Derivative of the total magnetic flux density with respect to the thing we solved for
:param SimPEG.EM.FDEM.Src src: source
:param numpy.ndarray v: vector to take product with
:param bool adjoint: adjoint?
:rtype: numpy.ndarray
:return: product of the derivative of the magnetic flux density with respect to the field we solved for with a vector
"""
# Primary does not depend on u
return self._bSecondaryDeriv_u(src, v, adjoint)
def _bDeriv_m(self, src, v, adjoint=False):
"""
Derivative of the total magnetic flux density with respect to the inversion model.
:param SimPEG.EM.FDEM.Src src: source
:param numpy.ndarray v: vector to take product with
:param bool adjoint: adjoint?
:rtype: SimPEG.Utils.Zero
:return: product of the magnetic flux density derivative with respect to the inversion model with a vector
"""
# Assuming the primary does not depend on the model
return self._bSecondaryDeriv_m(src, v, adjoint)
class Fields_b(Fields):
"""
Fields object for Problem_b.
:param Mesh mesh: mesh
:param Survey survey: survey
"""
knownFields = {'bSolution':'F'}
aliasFields = {
'b' : ['bSolution','F','_b'],
@@ -111,6 +260,15 @@ class Fields_b(Fields):
self._Me = self.survey.prob.Me
def _bPrimary(self, bSolution, srcList):
"""
Primary magnetic flux density from source
:param numpy.ndarray bSolution: field we solved for
:param list srcList: list of sources
:rtype: numpy.ndarray
:return: primary electric field as defined by the sources
"""
bPrimary = np.zeros_like(bSolution)
for i, src in enumerate(srcList):
bp = src.bPrimary(self.prob)
@@ -118,19 +276,66 @@ class Fields_b(Fields):
return bPrimary
def _bSecondary(self, bSolution, srcList):
"""
Secondary magnetic flux density is the thing we solved for
:param numpy.ndarray bSolution: field we solved for
:param list srcList: list of sources
:rtype: numpy.ndarray
:return: secondary magnetic flux density
"""
return bSolution
def _b(self, bSolution, srcList):
"""
Total magnetic flux density is sum of primary and secondary
:param numpy.ndarray bSolution: field we solved for
:param list srcList: list of sources
:rtype: numpy.ndarray
:return: total magnetic flux density
"""
return self._bPrimary(bSolution, srcList) + self._bSecondary(bSolution, srcList)
def _bDeriv_u(self, src, v, adjoint=False):
"""
Derivative of the total magnetic flux density with respect to the thing we
solved for
:param SimPEG.EM.FDEM.Src src: source
:param numpy.ndarray v: vector to take product with
:param bool adjoint: adjoint?
:rtype: numpy.ndarray
:return: product of the derivative of the magnetic flux density with respect to the field we solved for with a vector
"""
return Identity()*v
def _bDeriv_m(self, src, v, adjoint=False):
"""
Derivative of the total magnetic flux density with respect to the inversion model. Here, we assume that the primary does not depend on the model.
:param SimPEG.EM.FDEM.Src src: source
:param numpy.ndarray v: vector to take product with
:param bool adjoint: adjoint?
:rtype: SimPEG.Utils.Zero
:return: product of the magnetic flux density derivative with respect to the inversion model with a vector
"""
# assuming primary does not depend on the model
return Zero()
def _ePrimary(self, bSolution, srcList):
"""
Primary electric field from source
:param numpy.ndarray bSolution: field we solved for
:param list srcList: list of sources
:rtype: numpy.ndarray
:return: primary electric field as defined by the sources
"""
ePrimary = np.zeros([self._edgeCurl.shape[1],bSolution.shape[1]],dtype = complex)
for i,src in enumerate(srcList):
ep = src.ePrimary(self.prob)
@@ -138,6 +343,15 @@ class Fields_b(Fields):
return ePrimary
def _eSecondary(self, bSolution, srcList):
"""
Secondary electric field from bSolution
:param numpy.ndarray bSolution: field we solved for
:param list srcList: list of sources
:rtype: numpy.ndarray
:return: secondary electric field
"""
e = self._MeSigmaI * ( self._edgeCurl.T * ( self._MfMui * bSolution))
for i,src in enumerate(srcList):
_,S_e = src.eval(self.prob)
@@ -145,12 +359,32 @@ class Fields_b(Fields):
return e
def _eSecondaryDeriv_u(self, src, v, adjoint=False):
"""
Derivative of the secondary electric field with respect to the thing we solved for
:param SimPEG.EM.FDEM.Src src: source
:param numpy.ndarray v: vector to take product with
:param bool adjoint: adjoint?
:rtype: numpy.ndarray
:return: product of the derivative of the secondary electric field with respect to the field we solved for with a vector
"""
if not adjoint:
return self._MeSigmaI * ( self._edgeCurl.T * ( self._MfMui * v) )
else:
return self._MfMui.T * (self._edgeCurl * (self._MeSigmaI.T * v))
def _eSecondaryDeriv_m(self, src, v, adjoint=False):
"""
Derivative of the secondary electric field with respect to the inversion model
:param SimPEG.EM.FDEM.Src src: source
:param numpy.ndarray v: vector to take product with
:param bool adjoint: adjoint?
:rtype: numpy.ndarray
:return: product of the derivative of the secondary electric field with respect to the model with a vector
"""
bSolution = self[[src],'bSolution']
_,S_e = src.eval(self.prob)
Me = self._Me
@@ -166,25 +400,60 @@ class Fields_b(Fields):
elif adjoint:
de_dm = self._MeSigmaIDeriv(w).T * v
_, S_eDeriv = src.evalDeriv(self.prob, adjoint)
Se_Deriv = S_eDeriv(v)
_, S_eDeriv = src.evalDeriv(self.prob, v, adjoint)
de_dm = de_dm - self._MeSigmaI * Se_Deriv
de_dm = de_dm - self._MeSigmaI * S_eDeriv
return de_dm
def _e(self, bSolution, srcList):
"""
Total electric field is sum of primary and secondary
:param numpy.ndarray eSolution: field we solved for
:param list srcList: list of sources
:rtype: numpy.ndarray
:return: total electric field
"""
return self._ePrimary(bSolution, srcList) + self._eSecondary(bSolution, srcList)
def _eDeriv_u(self, src, v, adjoint=False):
"""
Derivative of the total electric field with respect to the thing we solved for
:param SimPEG.EM.FDEM.Src src: source
:param numpy.ndarray v: vector to take product with
:param bool adjoint: adjoint?
:rtype: numpy.ndarray
:return: product of the derivative of the electric field with respect to the field we solved for with a vector
"""
return self._eSecondaryDeriv_u(src, v, adjoint)
def _eDeriv_m(self, src, v, adjoint=False):
"""
Derivative of the total electric field density with respect to the inversion model.
:param SimPEG.EM.FDEM.Src src: source
:param numpy.ndarray v: vector to take product with
:param bool adjoint: adjoint?
:rtype: numpy.ndarray
:return: product of the electric field derivative with respect to the inversion model with a vector
"""
# assuming primary doesn't depend on model
return self._eSecondaryDeriv_m(src, v, adjoint)
class Fields_j(Fields):
"""
Fields object for Problem_j.
:param Mesh mesh: mesh
:param Survey survey: survey
"""
knownFields = {'jSolution':'F'}
aliasFields = {
'j' : ['jSolution','F','_j'],
@@ -207,6 +476,15 @@ class Fields_j(Fields):
self._Me = self.survey.prob.Me
def _jPrimary(self, jSolution, srcList):
"""
Primary current density from source
:param numpy.ndarray jSolution: field we solved for
:param list srcList: list of sources
:rtype: numpy.ndarray
:return: primary current density as defined by the sources
"""
jPrimary = np.zeros_like(jSolution,dtype = complex)
for i, src in enumerate(srcList):
jp = src.jPrimary(self.prob)
@@ -214,19 +492,66 @@ class Fields_j(Fields):
return jPrimary
def _jSecondary(self, jSolution, srcList):
"""
Secondary current density is the thing we solved for
:param numpy.ndarray jSolution: field we solved for
:param list srcList: list of sources
:rtype: numpy.ndarray
:return: secondary current density
"""
return jSolution
def _j(self, jSolution, srcList):
"""
Total current density is sum of primary and secondary
:param numpy.ndarray jSolution: field we solved for
:param list srcList: list of sources
:rtype: numpy.ndarray
:return: total current density
"""
return self._jPrimary(jSolution, srcList) + self._jSecondary(jSolution, srcList)
def _jDeriv_u(self, src, v, adjoint=False):
"""
Derivative of the total current density with respect to the thing we
solved for
:param SimPEG.EM.FDEM.Src src: source
:param numpy.ndarray v: vector to take product with
:param bool adjoint: adjoint?
:rtype: numpy.ndarray
:return: product of the derivative of the current density with respect to the field we solved for with a vector
"""
return Identity()*v
def _jDeriv_m(self, src, v, adjoint=False):
"""
Derivative of the total current density with respect to the inversion model. Here, we assume that the primary does not depend on the model.
:param SimPEG.EM.FDEM.Src src: source
:param numpy.ndarray v: vector to take product with
:param bool adjoint: adjoint?
:rtype: SimPEG.Utils.Zero
:return: product of the current density derivative with respect to the inversion model with a vector
"""
# assuming primary does not depend on the model
return Zero()
def _hPrimary(self, jSolution, srcList):
"""
Primary magnetic field from source
:param numpy.ndarray hSolution: field we solved for
:param list srcList: list of sources
:rtype: numpy.ndarray
:return: primary magnetic field as defined by the sources
"""
hPrimary = np.zeros([self._edgeCurl.shape[1],jSolution.shape[1]],dtype = complex)
for i, src in enumerate(srcList):
hp = src.hPrimary(self.prob)
@@ -234,6 +559,15 @@ class Fields_j(Fields):
return hPrimary
def _hSecondary(self, jSolution, srcList):
"""
Secondary magnetic field from bSolution
:param numpy.ndarray jSolution: field we solved for
:param list srcList: list of sources
:rtype: numpy.ndarray
:return: secondary magnetic field
"""
h = self._MeMuI * (self._edgeCurl.T * (self._MfRho * jSolution) )
for i, src in enumerate(srcList):
h[:,i] *= -1./(1j*omega(src.freq))
@@ -242,12 +576,32 @@ class Fields_j(Fields):
return h
def _hSecondaryDeriv_u(self, src, v, adjoint=False):
"""
Derivative of the secondary magnetic field with respect to the thing we solved for
:param SimPEG.EM.FDEM.Src src: source
:param numpy.ndarray v: vector to take product with
:param bool adjoint: adjoint?
:rtype: numpy.ndarray
:return: product of the derivative of the secondary magnetic field with respect to the field we solved for with a vector
"""
if not adjoint:
return -1./(1j*omega(src.freq)) * self._MeMuI * (self._edgeCurl.T * (self._MfRho * v) )
elif adjoint:
return -1./(1j*omega(src.freq)) * self._MfRho.T * (self._edgeCurl * ( self._MeMuI.T * v))
def _hSecondaryDeriv_m(self, src, v, adjoint=False):
"""
Derivative of the secondary magnetic field with respect to the inversion model
:param SimPEG.EM.FDEM.Src src: source
:param numpy.ndarray v: vector to take product with
:param bool adjoint: adjoint?
:rtype: numpy.ndarray
:return: product of the derivative of the secondary magnetic field with respect to the model with a vector
"""
jSolution = self[[src],'jSolution']
MeMuI = self._MeMuI
C = self._edgeCurl
@@ -260,7 +614,7 @@ class Fields_j(Fields):
elif adjoint:
hDeriv_m = -1./(1j*omega(src.freq)) * MfRhoDeriv(jSolution).T * ( C * (MeMuI.T * v ) )
S_mDeriv,_ = src.evalDeriv(self.prob, adjoint)
S_mDeriv,_ = src.evalDeriv(self.prob, adjoint = adjoint)
if not adjoint:
S_mDeriv = S_mDeriv(v)
@@ -272,17 +626,53 @@ class Fields_j(Fields):
def _h(self, jSolution, srcList):
"""
Total magnetic field is sum of primary and secondary
:param numpy.ndarray eSolution: field we solved for
:param list srcList: list of sources
:rtype: numpy.ndarray
:return: total magnetic field
"""
return self._hPrimary(jSolution, srcList) + self._hSecondary(jSolution, srcList)
def _hDeriv_u(self, src, v, adjoint=False):
"""
Derivative of the total magnetic field with respect to the thing we solved for
:param SimPEG.EM.FDEM.Src src: source
:param numpy.ndarray v: vector to take product with
:param bool adjoint: adjoint?
:rtype: numpy.ndarray
:return: product of the derivative of the magnetic field with respect to the field we solved for with a vector
"""
return self._hSecondaryDeriv_u(src, v, adjoint)
def _hDeriv_m(self, src, v, adjoint=False):
"""
Derivative of the total magnetic field density with respect to the inversion model.
:param SimPEG.EM.FDEM.Src src: source
:param numpy.ndarray v: vector to take product with
:param bool adjoint: adjoint?
:rtype: numpy.ndarray
:return: product of the magnetic field derivative with respect to the inversion model with a vector
"""
# assuming the primary doesn't depend on the model
return self._hSecondaryDeriv_m(src, v, adjoint)
class Fields_h(Fields):
"""
Fields object for Problem_h.
:param Mesh mesh: mesh
:param Survey survey: survey
"""
knownFields = {'hSolution':'E'}
aliasFields = {
'h' : ['hSolution','E','_h'],
@@ -303,6 +693,15 @@ class Fields_h(Fields):
self._MfRho = self.survey.prob.MfRho
def _hPrimary(self, hSolution, srcList):
"""
Primary magnetic field from source
:param numpy.ndarray eSolution: field we solved for
:param list srcList: list of sources
:rtype: numpy.ndarray
:return: primary magnetic field as defined by the sources
"""
hPrimary = np.zeros_like(hSolution,dtype = complex)
for i, src in enumerate(srcList):
hp = src.hPrimary(self.prob)
@@ -310,19 +709,67 @@ class Fields_h(Fields):
return hPrimary
def _hSecondary(self, hSolution, srcList):
"""
Secondary magnetic field is the thing we solved for
:param numpy.ndarray hSolution: field we solved for
:param list srcList: list of sources
:rtype: numpy.ndarray
:return: secondary magnetic field
"""
return hSolution
def _h(self, hSolution, srcList):
"""
Total magnetic field is sum of primary and secondary
:param numpy.ndarray hSolution: field we solved for
:param list srcList: list of sources
:rtype: numpy.ndarray
:return: total magnetic field
"""
return self._hPrimary(hSolution, srcList) + self._hSecondary(hSolution, srcList)
def _hDeriv_u(self, src, v, adjoint=False):
"""
Derivative of the total magnetic field with respect to the thing we
solved for
:param SimPEG.EM.FDEM.Src src: source
:param numpy.ndarray v: vector to take product with
:param bool adjoint: adjoint?
:rtype: numpy.ndarray
:return: product of the derivative of the magnetic field with respect to the field we solved for with a vector
"""
return Identity()*v
def _hDeriv_m(self, src, v, adjoint=False):
"""
Derivative of the total magnetic field with respect to the inversion model. Here, we assume that the primary does not depend on the model.
:param SimPEG.EM.FDEM.Src src: source
:param numpy.ndarray v: vector to take product with
:param bool adjoint: adjoint?
:rtype: SimPEG.Utils.Zero
:return: product of the magnetic field derivative with respect to the inversion model with a vector
"""
# assuming primary does not depend on the model
return Zero()
def _jPrimary(self, hSolution, srcList):
"""
Primary current density from source
:param numpy.ndarray hSolution: field we solved for
:param list srcList: list of sources
:rtype: numpy.ndarray
:return: primary current density as defined by the sources
"""
jPrimary = np.zeros([self._edgeCurl.shape[0], hSolution.shape[1]], dtype = complex)
for i, src in enumerate(srcList):
jp = src.jPrimary(self.prob)
@@ -330,6 +777,15 @@ class Fields_h(Fields):
return jPrimary
def _jSecondary(self, hSolution, srcList):
"""
Secondary current density from eSolution
:param numpy.ndarray hSolution: field we solved for
:param list srcList: list of sources
:rtype: numpy.ndarray
:return: secondary current density
"""
j = self._edgeCurl*hSolution
for i, src in enumerate(srcList):
_,S_e = src.eval(self.prob)
@@ -337,22 +793,69 @@ class Fields_h(Fields):
return j
def _jSecondaryDeriv_u(self, src, v, adjoint=False):
"""
Derivative of the secondary current density with respect to the thing we solved for
:param SimPEG.EM.FDEM.Src src: source
:param numpy.ndarray v: vector to take product with
:param bool adjoint: adjoint?
:rtype: numpy.ndarray
:return: product of the derivative of the secondary current density with respect to the field we solved for with a vector
"""
if not adjoint:
return self._edgeCurl*v
elif adjoint:
return self._edgeCurl.T*v
def _jSecondaryDeriv_m(self, src, v, adjoint=False):
_,S_eDeriv = src.evalDeriv(self.prob, adjoint)
S_eDeriv = S_eDeriv(v)
"""
Derivative of the secondary current density with respect to the inversion model.
:param SimPEG.EM.FDEM.Src src: source
:param numpy.ndarray v: vector to take product with
:param bool adjoint: adjoint?
:rtype: numpy.ndarray
:return: product of the secondary current density derivative with respect to the inversion model with a vector
"""
_,S_eDeriv = src.evalDeriv(self.prob, v, adjoint)
return -S_eDeriv
def _j(self, hSolution, srcList):
"""
Total current density is sum of primary and secondary
:param numpy.ndarray eSolution: field we solved for
:param list srcList: list of sources
:rtype: numpy.ndarray
:return: total current density
"""
return self._jPrimary(hSolution, srcList) + self._jSecondary(hSolution, srcList)
def _jDeriv_u(self, src, v, adjoint=False):
"""
Derivative of the total current density with respect to the thing we solved for
:param SimPEG.EM.FDEM.Src src: source
:param numpy.ndarray v: vector to take product with
:param bool adjoint: adjoint?
:rtype: numpy.ndarray
:return: product of the derivative of the current density with respect to the field we solved for with a vector
"""
return self._jSecondaryDeriv_u(src,v,adjoint)
def _jDeriv_m(self, src, v, adjoint=False):
"""
Derivative of the total current density with respect to the inversion model.
:param SimPEG.EM.FDEM.Src src: source
:param numpy.ndarray v: vector to take product with
:param bool adjoint: adjoint?
:rtype: SimPEG.Utils.Zero
:return: product of the current density with respect to the inversion model with a vector
"""
# assuming the primary does not depend on the model
return self._jSecondaryDeriv_m(src,v,adjoint)
SimPEG/EM/FDEM/SrcFDEM.py
+274 -19
View File
@@ -1,55 +1,141 @@
from SimPEG import Survey, Problem, Utils, np, sp
from scipy.constants import mu_0
from SimPEG.EM.Utils import *
from SimPEG.Utils import Zero
# from SurveyFDEM import Rx
from SimPEG.Utils import Zero
class BaseSrc(Survey.BaseSrc):
"""
Base source class for FDEM Survey
"""
freq = None
# rxPair = Rx
# rxPair = RxFDEM
integrate = True
def eval(self, prob):
"""
Evaluate the source terms.
- :math:`S_m` : magnetic source term
- :math:`S_e` : electric source term
:param Problem prob: FDEM Problem
:rtype: (numpy.ndarray, numpy.ndarray)
:return: tuple with magnetic source term and electric source term
"""
S_m = self.S_m(prob)
S_e = self.S_e(prob)
return S_m, S_e
def evalDeriv(self, prob, v, adjoint=False):
return lambda v: self.S_mDeriv(prob,v,adjoint), lambda v: self.S_eDeriv(prob,v,adjoint)
def evalDeriv(self, prob, v=None, adjoint=False):
"""
Derivatives of the source terms with respect to the inversion model
- :code:`S_mDeriv` : derivative of the magnetic source term
- :code:`S_eDeriv` : derivative of the electric source term
:param Problem prob: FDEM Problem
:param numpy.ndarray v: vector to take product with
:param bool adjoint: adjoint?
:rtype: (numpy.ndarray, numpy.ndarray)
:return: tuple with magnetic source term and electric source term derivatives times a vector
"""
if v is not None:
return self.S_mDeriv(prob,v,adjoint), self.S_eDeriv(prob,v,adjoint)
else:
return lambda v: self.S_mDeriv(prob,v,adjoint), lambda v: self.S_eDeriv(prob,v,adjoint)
def bPrimary(self, prob):
"""
Primary magnetic flux density
:param Problem prob: FDEM Problem
:rtype: numpy.ndarray
:return: primary magnetic flux density
"""
return Zero()
def hPrimary(self, prob):
"""
Primary magnetic field
:param Problem prob: FDEM Problem
:rtype: numpy.ndarray
:return: primary magnetic field
"""
return Zero()
def ePrimary(self, prob):
"""
Primary electric field
:param Problem prob: FDEM Problem
:rtype: numpy.ndarray
:return: primary electric field
"""
return Zero()
def jPrimary(self, prob):
"""
Primary current density
:param Problem prob: FDEM Problem
:rtype: numpy.ndarray
:return: primary current density
"""
return Zero()
def S_m(self, prob):
"""
Magnetic source term
:param Problem prob: FDEM Problem
:rtype: numpy.ndarray
:return: magnetic source term on mesh
"""
return Zero()
def S_e(self, prob):
"""
Electric source term
:param Problem prob: FDEM Problem
:rtype: numpy.ndarray
:return: electric source term on mesh
"""
return Zero()
def S_mDeriv(self, prob, v, adjoint = False):
"""
Derivative of magnetic source term with respect to the inversion model
:param Problem prob: FDEM Problem
:param numpy.ndarray v: vector to take product with
:param bool adjoint: adjoint?
:rtype: numpy.ndarray
:return: product of magnetic source term derivative with a vector
"""
return Zero()
def S_eDeriv(self, prob, v, adjoint = False):
"""
Derivative of electric source term with respect to the inversion model
:param Problem prob: FDEM Problem
:param numpy.ndarray v: vector to take product with
:param bool adjoint: adjoint?
:rtype: numpy.ndarray
:return: product of electric source term derivative with a vector
"""
return Zero()
class RawVec_e(BaseSrc):
"""
RawVec electric source. It is defined by the user provided vector S_e
RawVec electric source. It is defined by the user provided vector S_e
:param numpy.array S_e: electric source term
:param float freq: frequency
:param rxList: receiver list
:param list rxList: receiver list
:param float freq: frequency
:param numpy.array S_e: electric source term
"""
def __init__(self, rxList, freq, S_e): #, ePrimary=None, bPrimary=None, hPrimary=None, jPrimary=None):
@@ -58,16 +144,17 @@ class RawVec_e(BaseSrc):
BaseSrc.__init__(self, rxList)
def S_e(self, prob):
return self._S_e
class RawVec_m(BaseSrc):
"""
RawVec magnetic source. It is defined by the user provided vector S_m
RawVec magnetic source. It is defined by the user provided vector S_m
:param numpy.array S_m: magnetic source term
:param float freq: frequency
:param rxList: receiver list
:param float freq: frequency
:param rxList: receiver list
:param numpy.array S_m: magnetic source term
"""
def __init__(self, rxList, freq, S_m, integrate = True): #ePrimary=Zero(), bPrimary=Zero(), hPrimary=Zero(), jPrimary=Zero()):
@@ -78,17 +165,24 @@ class RawVec_m(BaseSrc):
BaseSrc.__init__(self, rxList)
def S_m(self, prob):
"""
Magnetic source term
:param Problem prob: FDEM Problem
:rtype: numpy.ndarray
:return: magnetic source term on mesh
"""
return self._S_m
class RawVec(BaseSrc):
"""
RawVec source. It is defined by the user provided vectors S_m, S_e
RawVec source. It is defined by the user provided vectors S_m, S_e
:param numpy.array S_m: magnetic source term
:param numpy.array S_e: electric source term
:param float freq: frequency
:param rxList: receiver list
:param rxList: receiver list
:param float freq: frequency
:param numpy.array S_m: magnetic source term
:param numpy.array S_e: electric source term
"""
def __init__(self, rxList, freq, S_m, S_e, integrate = True):
self._S_m = np.array(S_m,dtype=complex)
@@ -109,6 +203,51 @@ class RawVec(BaseSrc):
class MagDipole(BaseSrc):
"""
Point magnetic dipole source calculated by taking the curl of a magnetic
vector potential. By taking the discrete curl, we ensure that the magnetic
flux density is divergence free (no magnetic monopoles!).
This approach uses a primary-secondary in frequency. Here we show the
derivation for E-B formulation noting that similar steps are followed for
the H-J formulation.
.. math::
\mathbf{C} \mathbf{e} + i \omega \mathbf{b} = \mathbf{s_m} \\\\
{\mathbf{C}^T \mathbf{M_{\mu^{-1}}^f} \mathbf{b} - \mathbf{M_{\sigma}^e} \mathbf{e} = \mathbf{s_e}}
We split up the fields and :math:`\mu^{-1}` into primary (:math:`\mathbf{P}`) and secondary (:math:`\mathbf{S}`) components
- :math:`\mathbf{e} = \mathbf{e^P} + \mathbf{e^S}`
- :math:`\mathbf{b} = \mathbf{b^P} + \mathbf{b^S}`
- :math:`\\boldsymbol{\mu}^{\mathbf{-1}} = \\boldsymbol{\mu}^{\mathbf{-1}^\mathbf{P}} + \\boldsymbol{\mu}^{\mathbf{-1}^\mathbf{S}}`
and define a zero-frequency primary problem, noting that the source is
generated by a divergence free electric current
.. math::
\mathbf{C} \mathbf{e^P} = \mathbf{s_m^P} = 0 \\\\
{\mathbf{C}^T \mathbf{{M_{\mu^{-1}}^f}^P} \mathbf{b^P} - \mathbf{M_{\sigma}^e} \mathbf{e^P} = \mathbf{M^e} \mathbf{s_e^P}}
Since :math:`\mathbf{e^P}` is curl-free, divergence-free, we assume that there is no constant field background, the :math:`\mathbf{e^P} = 0`, so our primary problem is
.. math::
\mathbf{e^P} = 0 \\\\
{\mathbf{C}^T \mathbf{{M_{\mu^{-1}}^f}^P} \mathbf{b^P} = \mathbf{s_e^P}}
Our secondary problem is then
.. math::
\mathbf{C} \mathbf{e^S} + i \omega \mathbf{b^S} = - i \omega \mathbf{b^P} \\\\
{\mathbf{C}^T \mathbf{M_{\mu^{-1}}^f} \mathbf{b^S} - \mathbf{M_{\sigma}^e} \mathbf{e^S} = -\mathbf{C}^T \mathbf{{M_{\mu^{-1}}^f}^S} \mathbf{b^P}}
:param list rxList: receiver list
:param float freq: frequency
:param numpy.ndarray loc: source location (ie: :code:`np.r_[xloc,yloc,zloc]`)
:param string orientation: 'X', 'Y', 'Z'
:param float moment: magnetic dipole moment
:param float mu: background magnetic permeability
"""
#TODO: right now, orientation doesn't actually do anything! The methods in SrcUtils should take care of that
def __init__(self, rxList, freq, loc, orientation='Z', moment=1., mu = mu_0):
@@ -121,6 +260,13 @@ class MagDipole(BaseSrc):
BaseSrc.__init__(self, rxList)
def bPrimary(self, prob):
"""
The primary magnetic flux density from a magnetic vector potential
:param Problem prob: FDEM problem
:rtype: numpy.ndarray
:return: primary magnetic field
"""
eqLocs = prob._eqLocs
if eqLocs is 'FE':
@@ -152,14 +298,37 @@ class MagDipole(BaseSrc):
return C*a
def hPrimary(self, prob):
"""
The primary magnetic field from a magnetic vector potential
:param Problem prob: FDEM problem
:rtype: numpy.ndarray
:return: primary magnetic field
"""
b = self.bPrimary(prob)
return h_from_b(prob,b)
def S_m(self, prob):
"""
The magnetic source term
:param Problem prob: FDEM problem
:rtype: numpy.ndarray
:return: primary magnetic field
"""
b_p = self.bPrimary(prob)
return -1j*omega(self.freq)*b_p
def S_e(self, prob):
"""
The electric source term
:param Problem prob: FDEM problem
:rtype: numpy.ndarray
:return: primary magnetic field
"""
if all(np.r_[self.mu] == np.r_[prob.curModel.mu]):
return Zero()
else:
@@ -179,6 +348,21 @@ class MagDipole(BaseSrc):
class MagDipole_Bfield(BaseSrc):
"""
Point magnetic dipole source calculated with the analytic solution for the
fields from a magnetic dipole. No discrete curl is taken, so the magnetic
flux density may not be strictly divergence free.
This approach uses a primary-secondary in frequency in the same fashion as the MagDipole.
:param list rxList: receiver list
:param float freq: frequency
:param numpy.ndarray loc: source location (ie: :code:`np.r_[xloc,yloc,zloc]`)
:param string orientation: 'X', 'Y', 'Z'
:param float moment: magnetic dipole moment
:param float mu: background magnetic permeability
"""
#TODO: right now, orientation doesn't actually do anything! The methods in SrcUtils should take care of that
#TODO: neither does moment
def __init__(self, rxList, freq, loc, orientation='Z', moment=1., mu = mu_0):
@@ -190,6 +374,14 @@ class MagDipole_Bfield(BaseSrc):
BaseSrc.__init__(self, rxList)
def bPrimary(self, prob):
"""
The primary magnetic flux density from the analytic solution for magnetic fields from a dipole
:param Problem prob: FDEM problem
:rtype: numpy.ndarray
:return: primary magnetic field
"""
eqLocs = prob._eqLocs
if eqLocs is 'FE':
@@ -221,14 +413,35 @@ class MagDipole_Bfield(BaseSrc):
return b
def hPrimary(self, prob):
"""
The primary magnetic field from a magnetic vector potential
:param Problem prob: FDEM problem
:rtype: numpy.ndarray
:return: primary magnetic field
"""
b = self.bPrimary(prob)
return h_from_b(prob, b)
def S_m(self, prob):
"""
The magnetic source term
:param Problem prob: FDEM problem
:rtype: numpy.ndarray
:return: primary magnetic field
"""
b = self.bPrimary(prob)
return -1j*omega(self.freq)*b
def S_e(self, prob):
"""
The electric source term
:param Problem prob: FDEM problem
:rtype: numpy.ndarray
:return: primary magnetic field
"""
if all(np.r_[self.mu] == np.r_[prob.curModel.mu]):
return Zero()
else:
@@ -247,6 +460,20 @@ class MagDipole_Bfield(BaseSrc):
class CircularLoop(BaseSrc):
"""
Circular loop magnetic source calculated by taking the curl of a magnetic
vector potential. By taking the discrete curl, we ensure that the magnetic
flux density is divergence free (no magnetic monopoles!).
This approach uses a primary-secondary in frequency in the same fashion as the MagDipole.
:param list rxList: receiver list
:param float freq: frequency
:param numpy.ndarray loc: source location (ie: :code:`np.r_[xloc,yloc,zloc]`)
:param string orientation: 'X', 'Y', 'Z'
:param float moment: magnetic dipole moment
:param float mu: background magnetic permeability
"""
#TODO: right now, orientation doesn't actually do anything! The methods in SrcUtils should take care of that
def __init__(self, rxList, freq, loc, orientation='Z', radius = 1., mu=mu_0):
@@ -259,6 +486,13 @@ class CircularLoop(BaseSrc):
BaseSrc.__init__(self, rxList)
def bPrimary(self, prob):
"""
The primary magnetic flux density from a magnetic vector potential
:param Problem prob: FDEM problem
:rtype: numpy.ndarray
:return: primary magnetic field
"""
eqLocs = prob._eqLocs
if eqLocs is 'FE':
@@ -289,14 +523,35 @@ class CircularLoop(BaseSrc):
return C*a
def hPrimary(self, prob):
"""
The primary magnetic field from a magnetic vector potential
:param Problem prob: FDEM problem
:rtype: numpy.ndarray
:return: primary magnetic field
"""
b = self.bPrimary(prob)
return 1./self.mu*b
def S_m(self, prob):
"""
The magnetic source term
:param Problem prob: FDEM problem
:rtype: numpy.ndarray
:return: primary magnetic field
"""
b = self.bPrimary(prob)
return -1j*omega(self.freq)*b
def S_e(self, prob):
"""
The electric source term
:param Problem prob: FDEM problem
:rtype: numpy.ndarray
:return: primary magnetic field
"""
if all(np.r_[self.mu] == np.r_[prob.curModel.mu]):
return Zero()
else:
SimPEG/EM/FDEM/SurveyFDEM.py
+48 -9
View File
@@ -10,6 +10,12 @@ import SrcFDEM as Src
####################################################
class Rx(SimPEG.Survey.BaseRx):
"""
Frequency domain receivers
:param numpy.ndarray locs: receiver locations (ie. :code:`np.r_[x,y,z]`)
:param string rxType: reciever type from knownRxTypes
"""
knownRxTypes = {
'exr':['e', 'Ex', 'real'],
@@ -60,15 +66,33 @@ class Rx(SimPEG.Survey.BaseRx):
"""Component projection (real/imag)"""
return self.knownRxTypes[self.rxType][2]
def projectFields(self, src, mesh, u):
P = self.getP(mesh)
u_part_complex = u[src, self.projField]
# get the real or imag component
real_or_imag = self.projComp
def projectFields(self, src, mesh, f):
"""
Project fields to recievers to get data.
:param Source src: FDEM source
:param Mesh mesh: mesh used
:param Fields f: fields object
:rtype: numpy.ndarray
:return: fields projected to recievers
"""
P = self.getP(mesh) # get interpolation to recievers
u_part_complex = f[src, self.projField]
real_or_imag = self.projComp # get the real or imag component
u_part = getattr(u_part_complex, real_or_imag)
return P*u_part
def projectFieldsDeriv(self, src, mesh, u, v, adjoint=False):
def projectFieldsDeriv(self, src, mesh, f, v, adjoint=False):
"""
Derivative of projected fields with respect to the inversion model times a vector.
:param Source src: FDEM source
:param Mesh mesh: mesh used
:param Fields f: fields object
:param numpy.ndarray v: vector to multiply
:rtype: numpy.ndarray
:return: fields projected to recievers
"""
P = self.getP(mesh)
if not adjoint:
@@ -95,10 +119,13 @@ class Rx(SimPEG.Survey.BaseRx):
class Survey(SimPEG.Survey.BaseSurvey):
"""
docstring for SurveyFDEM
Frequency domain electromagnetic survey
:param list srcList: list of FDEM sources used in the survey
"""
srcPair = Src.BaseSrc
rxPaair = Rx
def __init__(self, srcList, **kwargs):
# Sort these by frequency
@@ -126,6 +153,7 @@ class Survey(SimPEG.Survey.BaseSurvey):
@property
def nSrcByFreq(self):
"""Number of sources at each frequency"""
if getattr(self, '_nSrcByFreq', None) is None:
self._nSrcByFreq = {}
for freq in self.freqs:
@@ -133,11 +161,22 @@ class Survey(SimPEG.Survey.BaseSurvey):
return self._nSrcByFreq
def getSrcByFreq(self, freq):
"""Returns the sources associated with a specific frequency."""
"""
Returns the sources associated with a specific frequency.
:param float freq: frequency for which we look up sources
:rtype: dictionary
:return: sources at the sepcified frequency
"""
assert freq in self._freqDict, "The requested frequency is not in this survey."
return self._freqDict[freq]
def projectFields(self, u):
"""
Project fields to receiver locations
:param Fields u: fields object
:rtype: numpy.ndarray
:return: data
"""
data = SimPEG.Survey.Data(self)
for src in self.srcList:
for rx in src.rxList:
@@ -145,4 +184,4 @@ class Survey(SimPEG.Survey.BaseSurvey):
return data
def projectFieldsDeriv(self, u):
raise Exception('Use Sources to project fields deriv.')
raise Exception('Use Receivers to project fields deriv.')
SimPEG/EM/TDEM/SurveyTDEM.py
+24 -5
View File
@@ -79,12 +79,32 @@ class SrcTDEM(Survey.BaseSrc):
class SrcTDEM_VMD_MVP(SrcTDEM):
def __init__(self,rxList,loc):
def __init__(self,rxList,loc,waveformType="STEPOFF"):
self.loc = loc
self.waveformType = waveformType
SrcTDEM.__init__(self,rxList)
def getInitialFields(self, mesh):
"""Vertical magnetic dipole, magnetic vector potential"""
if self.waveformType == "STEPOFF":
print ">> Step waveform: Non-zero initial condition"
if mesh._meshType is 'CYL':
if mesh.isSymmetric:
MVP = MagneticDipoleVectorPotential(self.loc, mesh, 'Ey')
else:
raise NotImplementedError('Non-symmetric cyl mesh not implemented yet!')
elif mesh._meshType is 'TENSOR':
MVP = MagneticDipoleVectorPotential(self.loc, mesh, ['Ex','Ey','Ez'])
else:
raise Exception('Unknown mesh for VMD')
return {"b": mesh.edgeCurl*MVP}
elif self.waveformType == "GENERAL":
print ">> General waveform: Zero initial condition"
return {"b": np.zeros(mesh.nF)}
else:
raise NotImplementedError("Only use STEPOFF or GENERAL")
def getMeS(self, mesh, MfMui):
if mesh._meshType is 'CYL':
if mesh.isSymmetric:
MVP = MagneticDipoleVectorPotential(self.loc, mesh, 'Ey')
@@ -93,13 +113,12 @@ class SrcTDEM_VMD_MVP(SrcTDEM):
elif mesh._meshType is 'TENSOR':
MVP = MagneticDipoleVectorPotential(self.loc, mesh, ['Ex','Ey','Ez'])
else:
raise Exception('Unknown mesh for VMD')
return {"b": mesh.edgeCurl*MVP}
raise Exception('Unknown mesh for VMD')
return mesh.edgeCurl.T*MfMui*mesh.edgeCurl*MVP
class SrcTDEM_CircularLoop_MVP(SrcTDEM):
def __init__(self,rxList,loc,radius,waveformType):
def __init__(self,rxList,loc,radius,waveformType="STEPOFF"):
self.loc = loc
self.radius = radius
self.waveformType = waveformType
SimPEG/Examples/MT_1D_ForwardAndInversion.py
+129
View File
@@ -0,0 +1,129 @@
import SimPEG as simpeg
import numpy as np
import SimPEG.MT as MT
from scipy.constants import mu_0
import matplotlib.pyplot as plt
def run(plotIt=True):
"""
MT: 1D: Inversion
=======================
Forward model 1D MT data.
Setup and run a MT 1D inversion.
"""
## Setup the forward modeling
# Setting up 1D mesh and conductivity models to forward model data.
# Frequency
nFreq = 31
freqs = np.logspace(3,-3,nFreq)
# Set mesh parameters
ct = 20
air = simpeg.Utils.meshTensor([(ct,16,1.4)])
core = np.concatenate( ( np.kron(simpeg.Utils.meshTensor([(ct,10,-1.3)]),np.ones((5,))) , simpeg.Utils.meshTensor([(ct,5)]) ) )
bot = simpeg.Utils.meshTensor([(core[0],10,-1.4)])
x0 = -np.array([np.sum(np.concatenate((core,bot)))])
# Make the model
m1d = simpeg.Mesh.TensorMesh([np.concatenate((bot,core,air))], x0=x0)
# Setup model varibles
active = m1d.vectorCCx<0.
layer1 = (m1d.vectorCCx<-500.) & (m1d.vectorCCx>=-800.)
layer2 = (m1d.vectorCCx<-3500.) & (m1d.vectorCCx>=-5000.)
# Set the conductivity values
sig_half = 2e-3
sig_air = 1e-8
sig_layer1 = .2
sig_layer2 = .2
# Make the true model
sigma_true = np.ones(m1d.nCx)*sig_air
sigma_true[active] = sig_half
sigma_true[layer1] = sig_layer1
sigma_true[layer2] = sig_layer2
# Extract the model
m_true = np.log(sigma_true[active])
# Make the background model
sigma_0 = np.ones(m1d.nCx)*sig_air
sigma_0[active] = sig_half
m_0 = np.log(sigma_0[active])
# Set the mapping
actMap = simpeg.Maps.ActiveCells(m1d, active, np.log(1e-8), nC=m1d.nCx)
mappingExpAct = simpeg.Maps.ExpMap(m1d) * actMap
## Setup the layout of the survey, set the sources and the connected receivers
# Receivers
rxList = []
for rxType in ['z1dr','z1di']:
rxList.append(MT.Rx(simpeg.mkvc(np.array([0.0]),2).T,rxType))
# Source list
srcList =[]
for freq in freqs:
srcList.append(MT.SrcMT.polxy_1Dprimary(rxList,freq))
# Make the survey
survey = MT.Survey(srcList)
survey.mtrue = m_true
## Set the problem
problem = MT.Problem1D.eForm_psField(m1d,sigmaPrimary=sigma_0,mapping=mappingExpAct)
problem.pair(survey)
## Forward model data
# Project the data
survey.dtrue = survey.dpred(m_true)
survey.dobs = survey.dtrue + 0.025*abs(survey.dtrue)*np.random.randn(*survey.dtrue.shape)
if plotIt:
fig = MT.Utils.dataUtils.plotMT1DModelData(problem)
fig.suptitle('Target - smooth true')
# Assign uncertainties
std = 0.05 # 5% std
survey.std = np.abs(survey.dobs*std)
# Assign the data weight
Wd = 1./survey.std
## Setup the inversion proceedure
# Define a counter
C = simpeg.Utils.Counter()
# Set the optimization
opt = simpeg.Optimization.InexactGaussNewton(maxIter = 30)
opt.counter = C
opt.LSshorten = 0.5
opt.remember('xc')
# Data misfit
dmis = simpeg.DataMisfit.l2_DataMisfit(survey)
dmis.Wd = Wd
# Regularization - with a regularization mesh
regMesh = simpeg.Mesh.TensorMesh([m1d.hx[problem.mapping.sigmaMap.maps[-1].indActive]],m1d.x0)
reg = simpeg.Regularization.Tikhonov(regMesh)
reg.smoothModel = True
reg.alpha_s = 1e-7
reg.alpha_x = 1.
# Inversion problem
invProb = simpeg.InvProblem.BaseInvProblem(dmis, reg, opt)
invProb.counter = C
# Beta cooling
beta = simpeg.Directives.BetaSchedule()
beta.coolingRate = 4
betaest = simpeg.Directives.BetaEstimate_ByEig(beta0_ratio=0.75)
targmis = simpeg.Directives.TargetMisfit()
targmis.target = survey.nD
saveModel = simpeg.Directives.SaveModelEveryIteration()
saveModel.fileName = 'Inversion_TargMisEqnD_smoothTrue'
# Create an inversion object
inv = simpeg.Inversion.BaseInversion(invProb, directiveList=[beta,betaest,targmis])
## Run the inversion
mopt = inv.run(m_0)
if plotIt:
fig = MT.Utils.dataUtils.plotMT1DModelData(problem,[mopt])
fig.suptitle('Target - smooth true')
plt.show()
if __name__ == '__main__':
run()
SimPEG/Examples/MT_3D_Foward.py
+64
View File
@@ -0,0 +1,64 @@
# Test script to use SimPEG.MT platform to forward model synthetic data.
# Import
import SimPEG as simpeg
from SimPEG import MT
import numpy as np
try:
from pymatsolver import MumpsSolver as Solver
except:
from SimPEG import Solver
def run(plotIt=True, nFreq=1):
"""
MT: 3D: Forward
=======================
Forward model 3D MT data.
"""
# Make a mesh
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])
# Setup the model
conds = [1e-2,1]
sig = simpeg.Utils.ModelBuilder.defineBlock(M.gridCC,[-1000,-1000,-400],[1000,1000,-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
## Setup the the survey object
# Receiver locations
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))))
# Make a receiver list
rxList = []
for loc in rx_loc:
# NOTE: loc has to be a (1,3) np.ndarray otherwise errors accure
for rxType in ['zxxr','zxxi','zxyr','zxyi','zyxr','zyxi','zyyr','zyyi','tzxr','tzxi','tzyr','tzyi']:
rxList.append(MT.Rx(simpeg.mkvc(loc,2).T,rxType))
# Source list
srcList =[]
for freq in np.logspace(3,-3,nFreq):
srcList.append(MT.SrcMT.polxy_1Dprimary(rxList,freq))
# Survey MT
survey = MT.Survey(srcList)
## Setup the problem object
problem = MT.Problem3D.eForm_ps(M, sigmaPrimary=sigBG)
problem.pair(survey)
problem.Solver = Solver
# Calculate the data
fields = problem.fields(sig)
dataVec = survey.projectFields(fields)
# Make the data
mtData = MT.Data(survey,dataVec)
# Add plots
if plotIt:
pass
if __name__ == '__main__':
run()
SimPEG/Examples/__init__.py
+3 -1
View File
@@ -16,8 +16,10 @@ import Mesh_QuadTree_Creation
import Mesh_QuadTree_FaceDiv
import Mesh_QuadTree_HangingNodes
import Mesh_Tensor_Creation
import MT_1D_ForwardAndInversion
import MT_3D_Foward
__examples__ = ["DC_Analytic_Dipole", "DC_Forward_PseudoSection", "EM_FDEM_1D_Inversion", "EM_FDEM_Analytic_MagDipoleWholespace", "EM_TDEM_1D_Inversion", "FLOW_Richards_1D_Celia1990", "Forward_BasicDirectCurrent", "Inversion_Linear", "Mesh_Basic_PlotImage", "Mesh_Basic_Types", "Mesh_Operators_CahnHilliard", "Mesh_QuadTree_Creation", "Mesh_QuadTree_FaceDiv", "Mesh_QuadTree_HangingNodes", "Mesh_Tensor_Creation"]
__examples__ = ["DC_Analytic_Dipole", "DC_Forward_PseudoSection", "EM_FDEM_1D_Inversion", "EM_FDEM_Analytic_MagDipoleWholespace", "EM_TDEM_1D_Inversion", "FLOW_Richards_1D_Celia1990", "Forward_BasicDirectCurrent", "Inversion_Linear", "Mesh_Basic_PlotImage", "Mesh_Basic_Types", "Mesh_Operators_CahnHilliard", "Mesh_QuadTree_Creation", "Mesh_QuadTree_FaceDiv", "Mesh_QuadTree_HangingNodes", "Mesh_Tensor_Creation", "MT_1D_ForwardAndInversion", "MT_3D_Foward"]
##### AUTOIMPORTS #####
SimPEG/MT/BaseMT.py
+132
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@@ -0,0 +1,132 @@
from SimPEG import SolverLU as SimpegSolver, PropMaps, Utils, mkvc, sp, np
from SimPEG.EM.FDEM.FDEM import BaseFDEMProblem
from SurveyMT import Survey, Data
from FieldsMT import BaseMTFields
class BaseMTProblem(BaseFDEMProblem):
"""
Base class for all Natural source problems.
"""
def __init__(self, mesh, **kwargs):
BaseFDEMProblem.__init__(self, mesh, **kwargs)
Utils.setKwargs(self, **kwargs)
# Set the default pairs of the problem
surveyPair = Survey
dataPair = Data
fieldsPair = BaseMTFields
# Set the solver
Solver = SimpegSolver
solverOpts = {}
verbose = False
# Notes:
# Use the forward and devs from BaseFDEMProblem
# Might need to add more stuff here.
## NEED to clean up the Jvec and Jtvec to use Zero and Identities for None components.
def Jvec(self, m, v, u=None):
"""
Function to calculate the data sensitivities dD/dm times a vector.
:param numpy.ndarray m (nC, 1) - conductive model
:param numpy.ndarray v (nC, 1) - random vector
:param MTfields object (optional) - MT fields object, if not given it is calculated
:rtype: MTdata object
:return: Data sensitivities wrt m
"""
# Calculate the fields
if u is None:
u = self.fields(m)
# Set current model
self.curModel = m
# Initiate the Jv object
Jv = self.dataPair(self.survey)
# Loop all the frequenies
for freq in self.survey.freqs:
dA_du = self.getA(freq) #
dA_duI = self.Solver(dA_du, **self.solverOpts)
for src in self.survey.getSrcByFreq(freq):
# We need fDeriv_m = df/du*du/dm + df/dm
# Construct du/dm, it requires a solve
# NOTE: need to account for the 2 polarizations in the derivatives.
u_src = u[src,:]
# dA_dm and dRHS_dm should be of size nE,2, so that we can multiply by dA_duI. The 2 columns are each of the polarizations.
dA_dm = self.getADeriv_m(freq, u_src, v) # Size: nE,2 (u_px,u_py) in the columns.
dRHS_dm = self.getRHSDeriv_m(freq, v) # Size: nE,2 (u_px,u_py) in the columns.
if dRHS_dm is None:
du_dm = dA_duI * ( -dA_dm )
else:
du_dm = dA_duI * ( -dA_dm + dRHS_dm )
# Calculate the projection derivatives
for rx in src.rxList:
# Get the projection derivative
# v should be of size 2*nE (for 2 polarizations)
PDeriv_u = lambda t: rx.projectFieldsDeriv(src, self.mesh, u, t) # wrt u, we don't have have PDeriv wrt m
Jv[src, rx] = PDeriv_u(mkvc(du_dm))
dA_duI.clean()
# Return the vectorized sensitivities
return mkvc(Jv)
def Jtvec(self, m, v, u=None):
"""
Function to calculate the transpose of the data sensitivities (dD/dm)^T times a vector.
:param numpy.ndarray m (nC, 1) - conductive model
:param numpy.ndarray v (nD, 1) - vector
:param MTfields object u (optional) - MT fields object, if not given it is calculated
:rtype: MTdata object
:return: Data sensitivities wrt m
"""
if u is None:
u = self.fields(m)
self.curModel = m
# Ensure v is a data object.
if not isinstance(v, self.dataPair):
v = self.dataPair(self.survey, v)
Jtv = np.zeros(m.size)
for freq in self.survey.freqs:
AT = self.getA(freq).T
ATinv = self.Solver(AT, **self.solverOpts)
for src in self.survey.getSrcByFreq(freq):
ftype = self._fieldType + 'Solution'
u_src = u[src, :]
for rx in src.rxList:
# Get the adjoint projectFieldsDeriv
# PTv needs to be nE,
PTv = rx.projectFieldsDeriv(src, self.mesh, u, mkvc(v[src, rx],2), adjoint=True) # wrt u, need possibility wrt m
# Get the
dA_duIT = ATinv * PTv
dA_dmT = self.getADeriv_m(freq, u_src, mkvc(dA_duIT), adjoint=True)
dRHS_dmT = self.getRHSDeriv_m(freq, mkvc(dA_duIT), adjoint=True)
# Make du_dmT
if dRHS_dmT is None:
du_dmT = -dA_dmT
else:
du_dmT = -dA_dmT + dRHS_dmT
# Select the correct component
# du_dmT needs to be of size nC,
real_or_imag = rx.projComp
if real_or_imag == 'real':
Jtv += du_dmT.real
elif real_or_imag == 'imag':
Jtv += -du_dmT.real
else:
raise Exception('Must be real or imag')
# Clean the factorization, clear memory.
ATinv.clean()
return Jtv
SimPEG/MT/FieldsMT.py
+351
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@@ -0,0 +1,351 @@
from SimPEG import Survey, Utils, Problem, np, sp, mkvc
from scipy.constants import mu_0
import sys
from numpy.lib import recfunctions as recFunc
from SimPEG.EM.Utils import omega
##############
### Fields ###
##############
class BaseMTFields(Problem.Fields):
"""Field Storage for a MT survey."""
knownFields = {}
dtype = complex
class Fields1D_e(BaseMTFields):
"""
Fields storage for the 1D MT solution.
"""
knownFields = {'e_1dSolution':'F'}
aliasFields = {
'e_1d' : ['e_1dSolution','F','_e'],
'e_1dPrimary' : ['e_1dSolution','F','_ePrimary'],
'e_1dSecondary' : ['e_1dSolution','F','_eSecondary'],
'b_1d' : ['e_1dSolution','E','_b'],
'b_1dPrimary' : ['e_1dSolution','E','_bPrimary'],
'b_1dSecondary' : ['e_1dSolution','E','_bSecondary']
}
def __init__(self,mesh,survey,**kwargs):
BaseMTFields.__init__(self,mesh,survey,**kwargs)
def _ePrimary(self, eSolution, srcList):
ePrimary = np.zeros_like(eSolution)
for i, src in enumerate(srcList):
ep = src.ePrimary(self.survey.prob)
if ep is not None:
ePrimary[:,i] = ep[:,-1]
return ePrimary
def _eSecondary(self, eSolution, srcList):
return eSolution
def _e(self, eSolution, srcList):
return self._ePrimary(eSolution,srcList) + self._eSecondary(eSolution,srcList)
def _eDeriv_u(self, src, v, adjoint = False):
return v
def _eDeriv_m(self, src, v, adjoint = False):
# assuming primary does not depend on the model
return None
def _bPrimary(self, eSolution, srcList):
bPrimary = np.zeros([self.survey.mesh.nE,eSolution.shape[1]], dtype = complex)
for i, src in enumerate(srcList):
bp = src.bPrimary(self.survey.prob)
if bp is not None:
bPrimary[:,i] += bp[:,-1]
return bPrimary
def _bSecondary(self, eSolution, srcList):
C = self.mesh.nodalGrad
b = (C * eSolution)
for i, src in enumerate(srcList):
b[:,i] *= - 1./(1j*omega(src.freq))
# There is no magnetic source in the MT problem
# S_m, _ = src.eval(self.survey.prob)
# if S_m is not None:
# b[:,i] += 1./(1j*omega(src.freq)) * S_m
return b
def _b(self, eSolution, srcList):
return self._bPrimary(eSolution, srcList) + self._bSecondary(eSolution, srcList)
def _bSecondaryDeriv_u(self, src, v, adjoint = False):
C = self.mesh.nodalGrad
if adjoint:
return - 1./(1j*omega(src.freq)) * (C.T * v)
return - 1./(1j*omega(src.freq)) * (C * v)
def _bSecondaryDeriv_m(self, src, v, adjoint = False):
# Doesn't depend on m
# _, S_eDeriv = src.evalDeriv(self.survey.prob, adjoint)
# S_eDeriv = S_eDeriv(v)
# if S_eDeriv is not None:
# return 1./(1j * omega(src.freq)) * S_eDeriv
return None
def _bDeriv_u(self, src, v, adjoint=False):
# Primary does not depend on u
return self._bSecondaryDeriv_u(src, v, adjoint)
def _bDeriv_m(self, src, v, adjoint=False):
# Assuming the primary does not depend on the model
return self._bSecondaryDeriv_m(src, v, adjoint)
def _fDeriv_u(self, src, v, adjoint=False):
"""
Derivative of the fields object wrt u.
:param MTsrc src: MT source
:param numpy.ndarray v: random vector of f_sol.size
This function stacks the fields derivatives appropriately
return a vector of size (nreEle+nrbEle)
"""
de_du = v #Utils.spdiag(np.ones((self.nF,)))
db_du = self._bDeriv_u(src, v, adjoint)
# Return the stack
# This doesn't work...
return np.vstack((de_du,db_du))
def _fDeriv_m(self, src, v, adjoint=False):
"""
Derivative of the fields object wrt m.
This function stacks the fields derivatives appropriately
"""
return None
class Fields3D_e(BaseMTFields):
"""
Fields storage for the 3D MT solution. Labels polarizations by px and py.
:param SimPEG object mesh: The solution mesh
:param SimPEG object survey: A survey object
"""
# Define the known the alias fields
# Assume that the solution of e on the E.
## NOTE: Need to make this more general, to allow for other solutions formats.
knownFields = {'e_pxSolution':'E','e_pySolution':'E'}
aliasFields = {
'e_px' : ['e_pxSolution','E','_e_px'],
'e_pxPrimary' : ['e_pxSolution','E','_e_pxPrimary'],
'e_pxSecondary' : ['e_pxSolution','E','_e_pxSecondary'],
'e_py' : ['e_pySolution','E','_e_py'],
'e_pyPrimary' : ['e_pySolution','E','_e_pyPrimary'],
'e_pySecondary' : ['e_pySolution','E','_e_pySecondary'],
'b_px' : ['e_pxSolution','F','_b_px'],
'b_pxPrimary' : ['e_pxSolution','F','_b_pxPrimary'],
'b_pxSecondary' : ['e_pxSolution','F','_b_pxSecondary'],
'b_py' : ['e_pySolution','F','_b_py'],
'b_pyPrimary' : ['e_pySolution','F','_b_pyPrimary'],
'b_pySecondary' : ['e_pySolution','F','_b_pySecondary']
}
def __init__(self,mesh,survey,**kwargs):
BaseMTFields.__init__(self,mesh,survey,**kwargs)
def _e_pxPrimary(self, e_pxSolution, srcList):
e_pxPrimary = np.zeros_like(e_pxSolution)
for i, src in enumerate(srcList):
ep = src.ePrimary(self.survey.prob)
if ep is not None:
e_pxPrimary[:,i] = ep[:,0]
return e_pxPrimary
def _e_pyPrimary(self, e_pySolution, srcList):
e_pyPrimary = np.zeros_like(e_pySolution)
for i, src in enumerate(srcList):
ep = src.ePrimary(self.survey.prob)
if ep is not None:
e_pyPrimary[:,i] = ep[:,1]
return e_pyPrimary
def _e_pxSecondary(self, e_pxSolution, srcList):
return e_pxSolution
def _e_pySecondary(self, e_pySolution, srcList):
return e_pySolution
def _e_px(self, e_pxSolution, srcList):
return self._e_pxPrimary(e_pxSolution,srcList) + self._e_pxSecondary(e_pxSolution,srcList)
def _e_py(self, e_pySolution, srcList):
return self._e_pyPrimary(e_pySolution,srcList) + self._e_pySecondary(e_pySolution,srcList)
#NOTE: For e_p?Deriv_u,
# v has to be u(2*nE) long for the not adjoint and nE long for adjoint.
# Returns nE long for not adjoint and 2*nE long for adjoint
def _e_pxDeriv_u(self, src, v, adjoint = False):
'''
Takes the derivative of e_px wrt u
'''
if adjoint:
# adjoint: returns a 2*nE long vector with zero's for py
return np.vstack((v,np.zeros_like(v)))
# Not adjoint: return only the px part of the vector
return v[:len(v)/2]
def _e_pyDeriv_u(self, src, v, adjoint = False):
'''
Takes the derivative of e_py wrt u
'''
if adjoint:
# adjoint: returns a 2*nE long vector with zero's for px
return np.vstack((np.zeros_like(v),v))
# Not adjoint: return only the px part of the vector
return v[len(v)/2::]
def _e_pxDeriv_m(self, src, v, adjoint = False):
# assuming primary does not depend on the model
return None
def _e_pyDeriv_m(self, src, v, adjoint = False):
# assuming primary does not depend on the model
return None
def _b_pxPrimary(self, e_pxSolution, srcList):
b_pxPrimary = np.zeros([self.survey.mesh.nF,e_pxSolution.shape[1]], dtype = complex)
for i, src in enumerate(srcList):
bp = src.bPrimary(self.survey.prob)
if bp is not None:
b_pxPrimary[:,i] += bp[:,0]
return b_pxPrimary
def _b_pyPrimary(self, e_pySolution, srcList):
b_pyPrimary = np.zeros([self.survey.mesh.nF,e_pySolution.shape[1]], dtype = complex)
for i, src in enumerate(srcList):
bp = src.bPrimary(self.survey.prob)
if bp is not None:
b_pyPrimary[:,i] += bp[:,1]
return b_pyPrimary
def _b_pxSecondary(self, e_pxSolution, srcList):
C = self.mesh.edgeCurl
b = (C * e_pxSolution)
for i, src in enumerate(srcList):
b[:,i] *= - 1./(1j*omega(src.freq))
# There is no magnetic source in the MT problem
# S_m, _ = src.eval(self.survey.prob)
# if S_m is not None:
# b[:,i] += 1./(1j*omega(src.freq)) * S_m
return b
def _b_pySecondary(self, e_pySolution, srcList):
C = self.mesh.edgeCurl
b = (C * e_pySolution)
for i, src in enumerate(srcList):
b[:,i] *= - 1./(1j*omega(src.freq))
# There is no magnetic source in the MT problem
# S_m, _ = src.eval(self.survey.prob)
# if S_m is not None:
# b[:,i] += 1./(1j*omega(src.freq)) * S_m
return b
def _b_px(self, eSolution, srcList):
return self._b_pxPrimary(eSolution, srcList) + self._b_pxSecondary(eSolution, srcList)
def _b_py(self, eSolution, srcList):
return self._b_pyPrimary(eSolution, srcList) + self._b_pySecondary(eSolution, srcList)
# NOTE: v needs to be length 2*nE to account for both polarizations
def _b_pxSecondaryDeriv_u(self, src, v, adjoint = False):
# C = sp.kron(self.mesh.edgeCurl,[[1,0],[0,0]])
C = sp.hstack((self.mesh.edgeCurl,Utils.spzeros(self.mesh.nF,self.mesh.nE))) # This works for adjoint = None
if adjoint:
return - 1./(1j*omega(src.freq)) * (C.T * v)
return - 1./(1j*omega(src.freq)) * (C * v)
def _b_pySecondaryDeriv_u(self, src, v, adjoint = False):
# C = sp.kron(self.mesh.edgeCurl,[[0,0],[0,1]])
C = sp.hstack((Utils.spzeros(self.mesh.nF,self.mesh.nE),self.mesh.edgeCurl)) # This works for adjoint = None
if adjoint:
return - 1./(1j*omega(src.freq)) * (C.T * v)
return - 1./(1j*omega(src.freq)) * (C * v)
def _b_pxSecondaryDeriv_m(self, src, v, adjoint = False):
# Doesn't depend on m
# _, S_eDeriv = src.evalDeriv(self.survey.prob, adjoint)
# S_eDeriv = S_eDeriv(v)
# if S_eDeriv is not None:
# return 1./(1j * omega(src.freq)) * S_eDeriv
return None
def _b_pySecondaryDeriv_m(self, src, v, adjoint = False):
# Doesn't depend on m
# _, S_eDeriv = src.evalDeriv(self.survey.prob, adjoint)
# S_eDeriv = S_eDeriv(v)
# if S_eDeriv is not None:
# return 1./(1j * omega(src.freq)) * S_eDeriv
return None
def _b_pxDeriv_u(self, src, v, adjoint=False):
# Primary does not depend on u
return self._b_pxSecondaryDeriv_u(src, v, adjoint)
def _b_pyDeriv_u(self, src, v, adjoint=False):
# Primary does not depend on u
return self._b_pySecondaryDeriv_u(src, v, adjoint)
def _b_pxDeriv_m(self, src, v, adjoint=False):
# Assuming the primary does not depend on the model
return self._b_pxSecondaryDeriv_m(src, v, adjoint)
def _b_pyDeriv_m(self, src, v, adjoint=False):
# Assuming the primary does not depend on the model
return self._b_pySecondaryDeriv_m(src, v, adjoint)
def _f_pxDeriv_u(self, src, v, adjoint=False):
"""
Derivative of the fields object wrt u.
:param MTsrc src: MT source
:param numpy.ndarray v: random vector of f_sol.size
This function stacks the fields derivatives appropriately
return a vector of size (nreEle+nrbEle)
"""
de_du = v #Utils.spdiag(np.ones((self.nF,)))
db_du = self._b_pxDeriv_u(src, v, adjoint)
# Return the stack
# This doesn't work...
return np.vstack((de_du,db_du))
def _f_pyDeriv_u(self, src, v, adjoint=False):
"""
Derivative of the fields object wrt u.
:param MTsrc src: MT source
:param numpy.ndarray v: random vector of f_sol.size
This function stacks the fields derivatives appropriately
return a vector of size (nreEle+nrbEle)
"""
de_du = v #Utils.spdiag(np.ones((self.nF,)))
db_du = self._b_pyDeriv_u(src, v, adjoint)
# Return the stack
# This doesn't work...
return np.vstack((de_du,db_du))
def _f_pxDeriv_m(self, src, v, adjoint=False):
"""
Derivative of the fields object wrt m.
This function stacks the fields derivatives appropriately
"""
# The fields have no dependance to the model.
return None
def _f_pyDeriv_m(self, src, v, adjoint=False):
"""
Derivative of the fields object wrt m.
This function stacks the fields derivatives appropriately
"""
# The fields have no dependance to the model.
return None
SimPEG/MT/Problem1D/Probs.py
+291
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@@ -0,0 +1,291 @@
from SimPEG.EM.Utils import omega
from SimPEG import mkvc
from scipy.constants import mu_0
from SimPEG.MT.BaseMT import BaseMTProblem
from SimPEG.MT.SurveyMT import Survey, Data
from SimPEG.MT.FieldsMT import Fields1D_e
from SimPEG.MT.Utils.MT1Danalytic import getEHfields
import numpy as np
import multiprocessing, sys, time
class eForm_psField(BaseMTProblem):
"""
A MT problem soving a e formulation and primary/secondary fields decomposion.
By eliminating the magnetic flux density using
.. math ::
\mathbf{b} = \\frac{1}{i \omega}\\left(-\mathbf{C} \mathbf{e} \\right)
we can write Maxwell's equations as a second order system in \\\(\\\mathbf{e}\\\) only:
.. math ::
\\left(\mathbf{C}^T \mathbf{M^e_{\mu^{-1}}} \mathbf{C} + i \omega \mathbf{M^f_\sigma}] \mathbf{e}_{s} =& i \omega \mathbf{M^f_{\delta \sigma}} \mathbf{e}_{p}
which we solve for \\\(\\\mathbf{e_s}\\\). The total field \\\mathbf{e}\\ = \\\mathbf{e_p}\\ + \\\mathbf{e_s}\\.
The primary field is estimated from a background model (commonly half space ).
"""
# From FDEMproblem: Used to project the fields. Currently not used for MTproblem.
_fieldType = 'e_1d'
_eqLocs = 'EF'
_sigmaPrimary = None
def __init__(self, mesh, **kwargs):
BaseMTProblem.__init__(self, mesh, **kwargs)
self.fieldsPair = Fields1D_e
# self._sigmaPrimary = sigmaPrimary
@property
def MeMui(self):
"""
Edge inner product matrix
"""
if getattr(self, '_MeMui', None) is None:
self._MeMui = self.mesh.getEdgeInnerProduct(1.0/mu_0)
return self._MeMui
@property
def MfSigma(self):
"""
Edge inner product matrix
"""
if getattr(self, '_MfSigma', None) is None:
self._MfSigma = self.mesh.getFaceInnerProduct(self.curModel.sigma)
return self._MfSigma
@property
def sigmaPrimary(self):
"""
A background model, use for the calculation of the primary fields.
"""
return self._sigmaPrimary
@sigmaPrimary.setter
def sigmaPrimary(self, val):
# Note: TODO add logic for val, make sure it is the correct size.
self._sigmaPrimary = val
def getA(self, freq):
"""
Function to get the A matrix.
:param float freq: Frequency
:rtype: scipy.sparse.csr_matrix
:return: A
"""
# Note: need to use the code above since in the 1D problem I want
# e to live on Faces(nodes) and h on edges(cells). Might need to rethink this
# Possible that _fieldType and _eqLocs can fix this
MeMui = self.MeMui
MfSigma = self.MfSigma
C = self.mesh.nodalGrad
# Make A
A = C.T*MeMui*C + 1j*omega(freq)*MfSigma
# Either return full or only the inner part of A
return A
def getADeriv_m(self, freq, u, v, adjoint=False):
"""
The derivative of A wrt sigma
"""
dsig_dm = self.curModel.sigmaDeriv
MeMui = self.MeMui
#
u_src = u['e_1dSolution']
dMfSigma_dm = self.mesh.getFaceInnerProductDeriv(self.curModel.sigma)(u_src) * self.curModel.sigmaDeriv
if adjoint:
return 1j * omega(freq) * ( dMfSigma_dm.T * v )
# Note: output has to be nN/nF, not nC/nE.
# v should be nC
return 1j * omega(freq) * ( dMfSigma_dm * v )
def getRHS(self, freq):
"""
Function to return the right hand side for the system.
:param float freq: Frequency
:rtype: numpy.ndarray (nF, 1), numpy.ndarray (nF, 1)
:return: RHS for 1 polarizations, primary fields
"""
# Get sources for the frequncy(polarizations)
Src = self.survey.getSrcByFreq(freq)[0]
S_e = Src.S_e(self)
return -1j * omega(freq) * S_e
def getRHSDeriv_m(self, freq, v, adjoint=False):
"""
The derivative of the RHS wrt sigma
"""
Src = self.survey.getSrcByFreq(freq)[0]
S_eDeriv = Src.S_eDeriv_m(self, v, adjoint)
return -1j * omega(freq) * S_eDeriv
def fields(self, m):
'''
Function to calculate all the fields for the model m.
:param np.ndarray (nC,) m: Conductivity model
'''
# Set the current model
self.curModel = m
F = Fields1D_e(self.mesh, self.survey)
for freq in self.survey.freqs:
if self.verbose:
startTime = time.time()
print 'Starting work for {:.3e}'.format(freq)
sys.stdout.flush()
A = self.getA(freq)
rhs = self.getRHS(freq)
Ainv = self.Solver(A, **self.solverOpts)
e_s = Ainv * rhs
# Store the fields
Src = self.survey.getSrcByFreq(freq)[0]
# NOTE: only store the e_solution(secondary), all other components calculated in the fields object
F[Src, 'e_1dSolution'] = e_s[:,-1] # Only storing the yx polarization as 1d
# Note curl e = -iwb so b = -curl e /iw
# b = -( self.mesh.nodalGrad * e )/( 1j*omega(freq) )
# F[Src, 'b_1d'] = b[:,1]
if self.verbose:
print 'Ran for {:f} seconds'.format(time.time()-startTime)
sys.stdout.flush()
return F
# Note this is not fully functional.
# Missing:
# Fields class corresponding to the fields
# Update Jvec and Jtvec to include all the derivatives components
# Other things ...
class eForm_TotalField(BaseMTProblem):
"""
A MT problem solving a e formulation and a Total bondary domain decompostion.
Solves the equation:
Math:
"""
# From FDEMproblem: Used to project the fields. Currently not used for MTproblem.
_fieldType = 'e'
_eqLocs = 'EF'
def __init__(self, mesh, **kwargs):
BaseMTProblem.__init__(self, mesh, **kwargs)
@property
def MeMui(self):
"""
Edge inner product matrix
"""
if getattr(self, '_MeMui', None) is None:
self._MeMui = self.mesh.getEdgeInnerProduct(1.0/mu_0)
return self._MeMui
@property
def MfSigma(self):
"""
Edge inner product matrix
"""
if getattr(self, '_MfSigma', None) is None:
self._MfSigma = self.mesh.getFaceInnerProduct(self.curModel.sigma)
return self._MfSigma
def getA(self, freq, full=False):
"""
Function to get the A matrix.
:param float freq: Frequency
:param logic full: Return full A or the inner part
:rtype: scipy.sparse.csr_matrix
:return: A
"""
MeMui = self.MeMui
MfSigma = self.MfSigma
# Note: need to use the code above since in the 1D problem I want
# e to live on Faces(nodes) and h on edges(cells). Might need to rethink this
# Possible that _fieldType and _eqLocs can fix this
# MeMui = self.MfMui
# MfSigma = self.MfSigma
C = self.mesh.nodalGrad
# Make A
A = C.T*MeMui*C + 1j*omega(freq)*MfSigma
# Either return full or only the inner part of A
if full:
return A
else:
return A[1:-1,1:-1]
def getADeriv_m(self, freq, u, v, adjoint=False):
raise NotImplementedError('getADeriv is not implemented')
def getRHS(self, freq):
"""
Function to return the right hand side for the system.
:param float freq: Frequency
:rtype: numpy.ndarray (nE, 2), numpy.ndarray (nE, 2)
:return: RHS for both polarizations, primary fields
"""
# Get sources for the frequency
# NOTE: Need to use the source information, doesn't really apply in 1D
src = self.survey.getSrcByFreq(freq)
# Get the full A
A = self.getA(freq,full=True)
# Define the outer part of the solution matrix
Aio = A[1:-1,[0,-1]]
Ed, Eu, Hd, Hu = getEHfields(self.mesh,self.curModel.sigma,freq,self.mesh.vectorNx)
Etot = (Ed + Eu)
sourceAmp = 1.0
Etot = ((Etot/Etot[-1])*sourceAmp) # Scale the fields to be equal to sourceAmp at the top
## Note: The analytic solution is derived with e^iwt
eBC = np.r_[Etot[0],Etot[-1]]
# The right hand side
return -Aio*eBC, eBC
def getRHSderiv_m(self, freq, backSigma, u, v, adjoint=False):
raise NotImplementedError('getRHSDeriv not implemented yet')
return None
def fields(self, m):
'''
Function to calculate all the fields for the model m.
:param np.ndarray (nC,) m: Conductivity model
:param np.ndarray (nC,) m_back: Background conductivity model
'''
self.curModel = m
# RHS, CalcFields = self.getRHS(freq,m_back), self.calcFields
F = Fields1D_e(self.mesh, self.survey)
for freq in self.survey.freqs:
if self.verbose:
startTime = time.time()
print 'Starting work for {:.3e}'.format(freq)
sys.stdout.flush()
A = self.getA(freq)
rhs, e_o = self.getRHS(freq)
Ainv = self.Solver(A, **self.solverOpts)
e_i = Ainv * rhs
e = mkvc(np.r_[e_o[0], e_i, e_o[1]],2)
# Store the fields
Src = self.survey.getSrcByFreq(freq)
# NOTE: only store e fields
F[Src, 'e_1dSolution'] = e[:,0]
if self.verbose:
print 'Ran for {:f} seconds'.format(time.time()-startTime)
sys.stdout.flush()
return F
SimPEG/MT/Problem1D/__init__.py
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from Probs import eForm_TotalField, eForm_psField
SimPEG/MT/Problem2D/Probs.py
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SimPEG/MT/Problem2D/__init__.py
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pass
SimPEG/MT/Problem3D/Probs.py
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from SimPEG import Survey, Problem, Utils, Models, np, sp, mkvc, SolverLU as SimpegSolver
from SimPEG.EM.Utils import omega
from scipy.constants import mu_0
from SimPEG.MT.BaseMT import BaseMTProblem
from SimPEG.MT.SurveyMT import Survey, Data
from SimPEG.MT.FieldsMT import Fields3D_e
import multiprocessing, sys, time
class eForm_ps(BaseMTProblem):
"""
A MT problem solving a e formulation and a primary/secondary fields decompostion.
By eliminating the magnetic flux density using
.. math ::
\mathbf{b} = \\frac{1}{i \omega}\\left(-\mathbf{C} \mathbf{e} \\right)
we can write Maxwell's equations as a second order system in \\\(\\\mathbf{e}\\\) only:
.. math ::
\\left(\mathbf{C}^T \mathbf{M^f_{\mu^{-1}}} \mathbf{C} + i \omega \mathbf{M^e_\sigma}] \mathbf{e}_{s} =& i \omega \mathbf{M^e_{\delta \sigma}} \mathbf{e}_{p}
which we solve for \\\(\\\mathbf{e_s}\\\). The total field \\\mathbf{e}\\ = \\\mathbf{e_p}\\ + \\\mathbf{e_s}\\.
The primary field is estimated from a background model (commonly as a 1D model).
"""
# From FDEMproblem: Used to project the fields. Currently not used for MTproblem.
_fieldType = 'e'
_eqLocs = 'FE'
fieldsPair = Fields3D_e
_sigmaPrimary = None
def __init__(self, mesh, **kwargs):
BaseMTProblem.__init__(self, mesh, **kwargs)
@property
def sigmaPrimary(self):
"""
A background model, use for the calculation of the primary fields.
"""
return self._sigmaPrimary
@sigmaPrimary.setter
def sigmaPrimary(self, val):
# Note: TODO add logic for val, make sure it is the correct size.
self._sigmaPrimary = val
def getA(self, freq):
"""
Function to get the A system.
:param float freq: Frequency
:rtype: scipy.sparse.csr_matrix
:return: A
"""
Mmui = self.MfMui
Msig = self.MeSigma
C = self.mesh.edgeCurl
return C.T*Mmui*C + 1j*omega(freq)*Msig
def getADeriv_m(self, freq, u, v, adjoint=False):
"""
Calculate the derivative of A wrt m.
"""
# This considers both polarizations and returns a nE,2 matrix for each polarization
if adjoint:
dMe_dsigV = sp.hstack(( self.MeSigmaDeriv( u['e_pxSolution'] ).T, self.MeSigmaDeriv(u['e_pySolution'] ).T ))*v
else:
# Need a nE,2 matrix to be returned
dMe_dsigV = np.hstack(( mkvc(self.MeSigmaDeriv( u['e_pxSolution'] )*v,2), mkvc( self.MeSigmaDeriv(u['e_pySolution'] )*v,2) ))
return 1j * omega(freq) * dMe_dsigV
def getRHS(self, freq):
"""
Function to return the right hand side for the system.
:param float freq: Frequency
:rtype: numpy.ndarray (nE, 2), numpy.ndarray (nE, 2)
:return: RHS for both polarizations, primary fields
"""
# Get sources for the frequncy(polarizations)
Src = self.survey.getSrcByFreq(freq)[0]
S_e = Src.S_e(self)
return -1j * omega(freq) * S_e
def getRHSDeriv_m(self, freq, v, adjoint=False):
"""
The derivative of the RHS with respect to sigma
"""
Src = self.survey.getSrcByFreq(freq)[0]
S_eDeriv = Src.S_eDeriv_m(self, v, adjoint)
return -1j * omega(freq) * S_eDeriv
def fields(self, m):
'''
Function to calculate all the fields for the model m.
:param np.ndarray (nC,) m: Conductivity model
'''
# Set the current model
self.curModel = m
F = Fields3D_e(self.mesh, self.survey)
for freq in self.survey.freqs:
if self.verbose:
startTime = time.time()
print 'Starting work for {:.3e}'.format(freq)
sys.stdout.flush()
A = self.getA(freq)
rhs = self.getRHS(freq)
# Solve the system
Ainv = self.Solver(A, **self.solverOpts)
e_s = Ainv * rhs
# Store the fields
Src = self.survey.getSrcByFreq(freq)[0]
# Store the fieldss
F[Src, 'e_pxSolution'] = e_s[:,0]
F[Src, 'e_pySolution'] = e_s[:,1]
# Note curl e = -iwb so b = -curl/iw
if self.verbose:
print 'Ran for {:f} seconds'.format(time.time()-startTime)
sys.stdout.flush()
Ainv.clean()
return F
SimPEG/MT/Problem3D/__init__.py
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from Probs import eForm_ps
SimPEG/MT/SrcMT.py
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from SimPEG import Utils, Problem, Maps, np, sp, mkvc
from SimPEG.EM.FDEM.SrcFDEM import BaseSrc as FDEMBaseSrc
from SimPEG.EM.Utils import omega
from scipy.constants import mu_0
from numpy.lib import recfunctions as recFunc
from Utils.sourceUtils import homo1DModelSource
from Utils import rec2ndarr
import sys
#################
### Sources ###
#################
class BaseMTSrc(FDEMBaseSrc):
'''
Sources for the MT problem.
Use the SimPEG BaseSrc, since the source fields share properties with the transmitters.
:param float freq: The frequency of the source
:param list rxList: A list of receivers associated with the source
'''
freq = None #: Frequency (float)
def __init__(self, rxList, freq):
self.freq = float(freq)
FDEMBaseSrc.__init__(self, rxList)
# 1D sources
class polxy_1DhomotD(BaseMTSrc):
"""
MT source for both polarizations (x and y) for the total Domain.
It calculates fields calculated based on conditions on the boundary of the domain.
"""
def __init__(self, rxList, freq):
BaseMTSrc.__init__(self, rxList, freq)
# TODO: need to add the primary fields calc and source terms into the problem.
# Need to implement such that it works for all dims.
class polxy_1Dprimary(BaseMTSrc):
"""
MT source for both polarizations (x and y) given a 1D primary models.
It assigns fields calculated from the 1D model as fields in the full space of the problem.
"""
def __init__(self, rxList, freq):
# assert mkvc(self.mesh.hz.shape,1) == mkvc(sigma1d.shape,1),'The number of values in the 1D background model does not match the number of vertical cells (hz).'
self.sigma1d = None
BaseMTSrc.__init__(self, rxList, freq)
# Hidden property of the ePrimary
self._ePrimary = None
def ePrimary(self,problem):
# Get primary fields for both polarizations
if self.sigma1d is None:
# Set the sigma1d as the 1st column in the background model
if len(problem._sigmaPrimary) == problem.mesh.nC:
if problem.mesh.dim == 1:
self.sigma1d = problem.mesh.r(problem._sigmaPrimary,'CC','CC','M')[:]
elif problem.mesh.dim == 3:
self.sigma1d = problem.mesh.r(problem._sigmaPrimary,'CC','CC','M')[0,0,:]
# Or as the 1D model that matches the vertical cell number
elif len(problem._sigmaPrimary) == problem.mesh.nCz:
self.sigma1d = problem._sigmaPrimary
if self._ePrimary is None:
self._ePrimary = homo1DModelSource(problem.mesh,self.freq,self.sigma1d)
return self._ePrimary
def bPrimary(self,problem):
# Project ePrimary to bPrimary
# Satisfies the primary(background) field conditions
if problem.mesh.dim == 1:
C = problem.mesh.nodalGrad
elif problem.mesh.dim == 3:
C = problem.mesh.edgeCurl
bBG_bp = (- C * self.ePrimary(problem) )*(1/( 1j*omega(self.freq) ))
return bBG_bp
def S_e(self,problem):
"""
Get the electrical field source
"""
e_p = self.ePrimary(problem)
Map_sigma_p = Maps.Vertical1DMap(problem.mesh)
sigma_p = Map_sigma_p._transform(self.sigma1d)
# Make mass matrix
# Note: M(sig) - M(sig_p) = M(sig - sig_p)
# Need to deal with the edge/face discrepencies between 1d/2d/3d
if problem.mesh.dim == 1:
Mesigma = problem.mesh.getFaceInnerProduct(problem.curModel.sigma)
Mesigma_p = problem.mesh.getFaceInnerProduct(sigma_p)
if problem.mesh.dim == 2:
pass
if problem.mesh.dim == 3:
Mesigma = problem.MeSigma
Mesigma_p = problem.mesh.getEdgeInnerProduct(sigma_p)
return (Mesigma - Mesigma_p) * e_p
def S_eDeriv_m(self, problem, v, adjoint = False):
'''
Get the derivative of S_e wrt to sigma (m)
'''
# Need to deal with
if problem.mesh.dim == 1:
# Need to use the faceInnerProduct
MsigmaDeriv = problem.mesh.getFaceInnerProductDeriv(problem.curModel.sigma)(self.ePrimary(problem)[:,1]) * problem.curModel.sigmaDeriv
# MsigmaDeriv = ( MsigmaDeriv * MsigmaDeriv.T)**2
if problem.mesh.dim == 2:
pass
if problem.mesh.dim == 3:
# Need to take the derivative of both u_px and u_py
ePri = self.ePrimary(problem)
# MsigmaDeriv = problem.MeSigmaDeriv(ePri[:,0]) + problem.MeSigmaDeriv(ePri[:,1])
# MsigmaDeriv = problem.MeSigmaDeriv(np.sum(ePri,axis=1))
if adjoint:
return sp.hstack(( problem.MeSigmaDeriv(ePri[:,0]).T, problem.MeSigmaDeriv(ePri[:,1]).T ))*v
else:
return np.hstack(( mkvc(problem.MeSigmaDeriv(ePri[:,0]) * v,2), mkvc(problem.MeSigmaDeriv(ePri[:,1])*v,2) ))
if adjoint:
#
return MsigmaDeriv.T * v
else:
# v should be nC size
return MsigmaDeriv * v
class polxy_3Dprimary(BaseMTSrc):
"""
MT source for both polarizations (x and y) given a 3D primary model. It assigns fields calculated from the 1D model
as fields in the full space of the problem.
"""
def __init__(self, rxList, freq):
# assert mkvc(self.mesh.hz.shape,1) == mkvc(sigma1d.shape,1),'The number of values in the 1D background model does not match the number of vertical cells (hz).'
self.sigmaPrimary = None
BaseMTSrc.__init__(self, rxList, freq)
# Hidden property of the ePrimary
self._ePrimary = None
def ePrimary(self,problem):
# Get primary fields for both polarizations
self.sigmaPrimary = problem._sigmaPrimary
if self._ePrimary is None:
self._ePrimary = homo3DModelSource(problem.mesh,self.sigmaPrimary,self.freq)
return self._ePrimary
def bPrimary(self,problem):
# Project ePrimary to bPrimary
# Satisfies the primary(background) field conditions
if problem.mesh.dim == 1:
C = problem.mesh.nodalGrad
elif problem.mesh.dim == 3:
C = problem.mesh.edgeCurl
bBG_bp = (- C * self.ePrimary(problem) )*(1/( 1j*omega(self.freq) ))
return bBG_bp
def S_e(self,problem):
"""
Get the electrical field source
"""
e_p = self.ePrimary(problem)
Map_sigma_p = Maps.Vertical1DMap(problem.mesh)
sigma_p = Map_sigma_p._transform(self.sigma1d)
# Make mass matrix
# Note: M(sig) - M(sig_p) = M(sig - sig_p)
# Need to deal with the edge/face discrepencies between 1d/2d/3d
if problem.mesh.dim == 1:
Mesigma = problem.mesh.getFaceInnerProduct(problem.curModel.sigma)
Mesigma_p = problem.mesh.getFaceInnerProduct(sigma_p)
if problem.mesh.dim == 2:
pass
if problem.mesh.dim == 3:
Mesigma = problem.MeSigma
Mesigma_p = problem.mesh.getEdgeInnerProduct(sigma_p)
return (Mesigma - Mesigma_p) * e_p
def S_eDeriv_m(self, problem, v, adjoint = False):
'''
Get the derivative of S_e wrt to sigma (m)
'''
# Need to deal with
if problem.mesh.dim == 1:
# Need to use the faceInnerProduct
MsigmaDeriv = problem.mesh.getFaceInnerProductDeriv(problem.curModel.sigma)(self.ePrimary(problem)[:,1]) * problem.curModel.sigmaDeriv
# MsigmaDeriv = ( MsigmaDeriv * MsigmaDeriv.T)**2
if problem.mesh.dim == 2:
pass
if problem.mesh.dim == 3:
# Need to take the derivative of both u_px and u_py
ePri = self.ePrimary(problem)
# MsigmaDeriv = problem.MeSigmaDeriv(ePri[:,0]) + problem.MeSigmaDeriv(ePri[:,1])
# MsigmaDeriv = problem.MeSigmaDeriv(np.sum(ePri,axis=1))
if adjoint:
return sp.hstack(( problem.MeSigmaDeriv(ePri[:,0]).T, problem.MeSigmaDeriv(ePri[:,1]).T ))*v
else:
return np.hstack(( mkvc(problem.MeSigmaDeriv(ePri[:,0]) * v,2), mkvc(problem.MeSigmaDeriv(ePri[:,1])*v,2) ))
if adjoint:
#
return MsigmaDeriv.T * v
else:
# v should be nC size
return MsigmaDeriv * v
SimPEG/MT/SurveyMT.py
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from SimPEG import Survey as SimPEGsurvey, Utils, Problem, Maps, np, sp, mkvc
from SimPEG.EM.FDEM.SrcFDEM import BaseSrc as FDEMBaseSrc
from SimPEG.EM.Utils import omega
from scipy.constants import mu_0
from numpy.lib import recfunctions as recFunc
from Utils import rec2ndarr
import SrcMT
import sys
#################
### Receivers ###
#################
class Rx(SimPEGsurvey.BaseRx):
"""
Class that defines natural source receivers.
See knownRxTypes for types of allowed receivers.
:param ndArray locs: Locations of the receivers
:param str rxType: The type of receiver
"""
knownRxTypes = {
# 3D impedance
'zxxr':['Z3D', 'real'],
'zxyr':['Z3D', 'real'],
'zyxr':['Z3D', 'real'],
'zyyr':['Z3D', 'real'],
'zxxi':['Z3D', 'imag'],
'zxyi':['Z3D', 'imag'],
'zyxi':['Z3D', 'imag'],
'zyyi':['Z3D', 'imag'],
# 2D impedance
# TODO:
# 1D impedance
'z1dr':['Z1D', 'real'],
'z1di':['Z1D', 'imag'],
# Tipper
'tzxr':['T3D','real'],
'tzxi':['T3D','imag'],
'tzyr':['T3D','real'],
'tzyi':['T3D','imag']
}
# TODO: Have locs as single or double coordinates for both or numerator and denominator separately, respectively.
def __init__(self, locs, rxType):
SimPEGsurvey.BaseRx.__init__(self, locs, rxType)
@property
def projType(self):
"""
Receiver type for projection.
"""
return self.knownRxTypes[self.rxType][0]
@property
def projComp(self):
"""Component projection (real/imag)"""
return self.knownRxTypes[self.rxType][1]
def projectFields(self, src, mesh, f):
'''
Project the fields to natural source data.
:param SrcMT src: The source of the fields to project
:param SimPEG.Mesh mesh:
:param FieldsMT f: Natural source fields object to project
'''
## NOTE: Assumes that e is on t
if self.projType is 'Z1D':
Pex = mesh.getInterpolationMat(self.locs[:,-1],'Fx')
Pbx = mesh.getInterpolationMat(self.locs[:,-1],'Ex')
ex = Pex*mkvc(f[src,'e_1d'],2)
bx = Pbx*mkvc(f[src,'b_1d'],2)/mu_0
# Note: Has a minus sign in front, to comply with quadrant calculations.
# Can be derived from zyx case for the 3D case.
f_part_complex = -ex/bx
# elif self.projType is 'Z2D':
elif self.projType is 'Z3D':
## NOTE: Assumes that e is on edges and b on the faces. Need to generalize that or use a prop of fields to determine that.
if self.locs.ndim == 3:
eFLocs = self.locs[:,:,0]
bFLocs = self.locs[:,:,1]
else:
eFLocs = self.locs
bFLocs = self.locs
# Get the projection
Pex = mesh.getInterpolationMat(eFLocs,'Ex')
Pey = mesh.getInterpolationMat(eFLocs,'Ey')
Pbx = mesh.getInterpolationMat(bFLocs,'Fx')
Pby = mesh.getInterpolationMat(bFLocs,'Fy')
# Get the fields at location
# px: x-polaration and py: y-polaration.
ex_px = Pex*f[src,'e_px']
ey_px = Pey*f[src,'e_px']
ex_py = Pex*f[src,'e_py']
ey_py = Pey*f[src,'e_py']
hx_px = Pbx*f[src,'b_px']/mu_0
hy_px = Pby*f[src,'b_px']/mu_0
hx_py = Pbx*f[src,'b_py']/mu_0
hy_py = Pby*f[src,'b_py']/mu_0
# Make the complex data
if 'zxx' in self.rxType:
f_part_complex = ( ex_px*hy_py - ex_py*hy_px)/(hx_px*hy_py - hx_py*hy_px)
elif 'zxy' in self.rxType:
f_part_complex = (-ex_px*hx_py + ex_py*hx_px)/(hx_px*hy_py - hx_py*hy_px)
elif 'zyx' in self.rxType:
f_part_complex = ( ey_px*hy_py - ey_py*hy_px)/(hx_px*hy_py - hx_py*hy_px)
elif 'zyy' in self.rxType:
f_part_complex = (-ey_px*hx_py + ey_py*hx_px)/(hx_px*hy_py - hx_py*hy_px)
elif self.projType is 'T3D':
if self.locs.ndim == 3:
horLoc = self.locs[:,:,0]
vertLoc = self.locs[:,:,1]
else:
horLoc = self.locs
vertLoc = self.locs
Pbx = mesh.getInterpolationMat(horLoc,'Fx')
Pby = mesh.getInterpolationMat(horLoc,'Fy')
Pbz = mesh.getInterpolationMat(vertLoc,'Fz')
bx_px = Pbx*f[src,'b_px']
by_px = Pby*f[src,'b_px']
bz_px = Pbz*f[src,'b_px']
bx_py = Pbx*f[src,'b_py']
by_py = Pby*f[src,'b_py']
bz_py = Pbz*f[src,'b_py']
if 'tzx' in self.rxType:
f_part_complex = (- by_px*bz_py + by_py*bz_px)/(bx_px*by_py - bx_py*by_px)
if 'tzy' in self.rxType:
f_part_complex = ( bx_px*bz_py - bx_py*bz_px)/(bx_px*by_py - bx_py*by_px)
else:
NotImplementedError('Projection of {:s} receiver type is not implemented.'.format(self.rxType))
# Get the real or imag component
real_or_imag = self.projComp
f_part = getattr(f_part_complex, real_or_imag)
# print f_part
return f_part
def projectFieldsDeriv(self, src, mesh, f, v, adjoint=False):
"""
The derivative of the projection wrt u
:param MTsrc src: MT source
:param TensorMesh mesh: Mesh defining the topology of the problem
:param MTfields f: MT fields object of the source
:param numpy.ndarray v: Random vector of size
"""
real_or_imag = self.projComp
if not adjoint:
if self.projType is 'Z1D':
Pex = mesh.getInterpolationMat(self.locs[:,-1],'Fx')
Pbx = mesh.getInterpolationMat(self.locs[:,-1],'Ex')
# ex = Pex*mkvc(f[src,'e_1d'],2)
# bx = Pbx*mkvc(f[src,'b_1d'],2)/mu_0
dP_de = -mkvc(Utils.sdiag(1./(Pbx*mkvc(f[src,'b_1d'],2)/mu_0))*(Pex*v),2)
dP_db = mkvc( Utils.sdiag(Pex*mkvc(f[src,'e_1d'],2))*(Utils.sdiag(1./(Pbx*mkvc(f[src,'b_1d'],2)/mu_0)).T*Utils.sdiag(1./(Pbx*mkvc(f[src,'b_1d'],2)/mu_0)))*(Pbx*f._bDeriv_u(src,v)/mu_0),2)
PDeriv_complex = np.sum(np.hstack((dP_de,dP_db)),1)
elif self.projType is 'Z2D':
raise NotImplementedError('Has not been implement for 2D impedance tensor')
elif self.projType is 'Z3D':
if self.locs.ndim == 3:
eFLocs = self.locs[:,:,0]
bFLocs = self.locs[:,:,1]
else:
eFLocs = self.locs
bFLocs = self.locs
# Get the projection
Pex = mesh.getInterpolationMat(eFLocs,'Ex')
Pey = mesh.getInterpolationMat(eFLocs,'Ey')
Pbx = mesh.getInterpolationMat(bFLocs,'Fx')
Pby = mesh.getInterpolationMat(bFLocs,'Fy')
# Get the fields at location
# px: x-polaration and py: y-polaration.
ex_px = Pex*f[src,'e_px']
ey_px = Pey*f[src,'e_px']
ex_py = Pex*f[src,'e_py']
ey_py = Pey*f[src,'e_py']
hx_px = Pbx*f[src,'b_px']/mu_0
hy_px = Pby*f[src,'b_px']/mu_0
hx_py = Pbx*f[src,'b_py']/mu_0
hy_py = Pby*f[src,'b_py']/mu_0
# Derivatives as lambda functions
# The size of the diratives should be nD,nU
ex_px_u = lambda vec: Pex*f._e_pxDeriv_u(src,vec)
ey_px_u = lambda vec: Pey*f._e_pxDeriv_u(src,vec)
ex_py_u = lambda vec: Pex*f._e_pyDeriv_u(src,vec)
ey_py_u = lambda vec: Pey*f._e_pyDeriv_u(src,vec)
# NOTE: Think b_p?Deriv_u should return a 2*nF size matrix
hx_px_u = lambda vec: Pbx*f._b_pxDeriv_u(src,vec)/mu_0
hy_px_u = lambda vec: Pby*f._b_pxDeriv_u(src,vec)/mu_0
hx_py_u = lambda vec: Pbx*f._b_pyDeriv_u(src,vec)/mu_0
hy_py_u = lambda vec: Pby*f._b_pyDeriv_u(src,vec)/mu_0
# Update the input vector
sDiag = lambda t: Utils.sdiag(mkvc(t,2))
# Define the components of the derivative
Hd = sDiag(1./(sDiag(hx_px)*hy_py - sDiag(hx_py)*hy_px))
Hd_uV = sDiag(hy_py)*hx_px_u(v) + sDiag(hx_px)*hy_py_u(v) - sDiag(hx_py)*hy_px_u(v) - sDiag(hy_px)*hx_py_u(v)
# Calculate components
if 'zxx' in self.rxType:
Zij = sDiag(Hd*( sDiag(ex_px)*hy_py - sDiag(ex_py)*hy_px ))
ZijN_uV = sDiag(hy_py)*ex_px_u(v) + sDiag(ex_px)*hy_py_u(v) - sDiag(ex_py)*hy_px_u(v) - sDiag(hy_px)*ex_py_u(v)
elif 'zxy' in self.rxType:
Zij = sDiag(Hd*(-sDiag(ex_px)*hx_py + sDiag(ex_py)*hx_px ))
ZijN_uV = -sDiag(hx_py)*ex_px_u(v) - sDiag(ex_px)*hx_py_u(v) + sDiag(ex_py)*hx_px_u(v) + sDiag(hx_px)*ex_py_u(v)
elif 'zyx' in self.rxType:
Zij = sDiag(Hd*( sDiag(ey_px)*hy_py - sDiag(ey_py)*hy_px ))
ZijN_uV = sDiag(hy_py)*ey_px_u(v) + sDiag(ey_px)*hy_py_u(v) - sDiag(ey_py)*hy_px_u(v) - sDiag(hy_px)*ey_py_u(v)
elif 'zyy' in self.rxType:
Zij = sDiag(Hd*(-sDiag(ey_px)*hx_py + sDiag(ey_py)*hx_px ))
ZijN_uV = -sDiag(hx_py)*ey_px_u(v) - sDiag(ey_px)*hx_py_u(v) + sDiag(ey_py)*hx_px_u(v) + sDiag(hx_px)*ey_py_u(v)
# Calculate the complex derivative
PDeriv_complex = Hd * (ZijN_uV - Zij * Hd_uV )
elif self.projType is 'T3D':
if self.locs.ndim == 3:
eFLocs = self.locs[:,:,0]
bFLocs = self.locs[:,:,1]
else:
eFLocs = self.locs
bFLocs = self.locs
# Get the projection
Pbx = mesh.getInterpolationMat(bFLocs,'Fx')
Pby = mesh.getInterpolationMat(bFLocs,'Fy')
Pbz = mesh.getInterpolationMat(bFLocs,'Fz')
# Get the fields at location
# px: x-polaration and py: y-polaration.
bx_px = Pbx*f[src,'b_px']
by_px = Pby*f[src,'b_px']
bz_px = Pbz*f[src,'b_px']
bx_py = Pbx*f[src,'b_py']
by_py = Pby*f[src,'b_py']
bz_py = Pbz*f[src,'b_py']
# Derivatives as lambda functions
# NOTE: Think b_p?Deriv_u should return a 2*nF size matrix
bx_px_u = lambda vec: Pbx*f._b_pxDeriv_u(src,vec)
by_px_u = lambda vec: Pby*f._b_pxDeriv_u(src,vec)
bz_px_u = lambda vec: Pbz*f._b_pxDeriv_u(src,vec)
bx_py_u = lambda vec: Pbx*f._b_pyDeriv_u(src,vec)
by_py_u = lambda vec: Pby*f._b_pyDeriv_u(src,vec)
bz_py_u = lambda vec: Pbz*f._b_pyDeriv_u(src,vec)
# Update the input vector
sDiag = lambda t: Utils.sdiag(mkvc(t,2))
# Define the components of the derivative
Hd = sDiag(1./(sDiag(bx_px)*by_py - sDiag(bx_py)*by_px))
Hd_uV = sDiag(by_py)*bx_px_u(v) + sDiag(bx_px)*by_py_u(v) - sDiag(bx_py)*by_px_u(v) - sDiag(by_px)*bx_py_u(v)
if 'tzx' in self.rxType:
Tij = sDiag(Hd*( - sDiag(by_px)*bz_py + sDiag(by_py)*bz_px ))
TijN_uV = -sDiag(by_px)*bz_py_u(v) - sDiag(bz_py)*by_px_u(v) + sDiag(by_py)*bz_px_u(v) + sDiag(bz_px)*by_py_u(v)
elif 'tzy' in self.rxType:
Tij = sDiag(Hd*( sDiag(bx_px)*bz_py - sDiag(bx_py)*bz_px ))
TijN_uV = sDiag(bz_py)*bx_px_u(v) + sDiag(bx_px)*bz_py_u(v) - sDiag(bx_py)*bz_px_u(v) - sDiag(bz_px)*bx_py_u(v)
# Calculate the complex derivative
PDeriv_complex = Hd * (TijN_uV - Tij * Hd_uV )
# Extract the real number for the real/imag components.
Pv = np.array(getattr(PDeriv_complex, real_or_imag))
elif adjoint:
# Note: The v vector is real and the return should be complex
if self.projType is 'Z1D':
Pex = mesh.getInterpolationMat(self.locs[:,-1],'Fx')
Pbx = mesh.getInterpolationMat(self.locs[:,-1],'Ex')
# ex = Pex*mkvc(f[src,'e_1d'],2)
# bx = Pbx*mkvc(f[src,'b_1d'],2)/mu_0
dP_deTv = -mkvc(Pex.T*Utils.sdiag(1./(Pbx*mkvc(f[src,'b_1d'],2)/mu_0)).T*v,2)
db_duv = Pbx.T/mu_0*Utils.sdiag(1./(Pbx*mkvc(f[src,'b_1d'],2)/mu_0))*(Utils.sdiag(1./(Pbx*mkvc(f[src,'b_1d'],2)/mu_0))).T*Utils.sdiag(Pex*mkvc(f[src,'e_1d'],2)).T*v
dP_dbTv = mkvc(f._bDeriv_u(src,db_duv,adjoint=True),2)
PDeriv_real = np.sum(np.hstack((dP_deTv,dP_dbTv)),1)
elif self.projType is 'Z2D':
raise NotImplementedError('Has not be implement for 2D impedance tensor')
elif self.projType is 'Z3D':
if self.locs.ndim == 3:
eFLocs = self.locs[:,:,0]
bFLocs = self.locs[:,:,1]
else:
eFLocs = self.locs
bFLocs = self.locs
# Get the projection
Pex = mesh.getInterpolationMat(eFLocs,'Ex')
Pey = mesh.getInterpolationMat(eFLocs,'Ey')
Pbx = mesh.getInterpolationMat(bFLocs,'Fx')
Pby = mesh.getInterpolationMat(bFLocs,'Fy')
# Get the fields at location
# px: x-polaration and py: y-polaration.
aex_px = mkvc(mkvc(f[src,'e_px'],2).T*Pex.T)
aey_px = mkvc(mkvc(f[src,'e_px'],2).T*Pey.T)
aex_py = mkvc(mkvc(f[src,'e_py'],2).T*Pex.T)
aey_py = mkvc(mkvc(f[src,'e_py'],2).T*Pey.T)
ahx_px = mkvc(mkvc(f[src,'b_px'],2).T/mu_0*Pbx.T)
ahy_px = mkvc(mkvc(f[src,'b_px'],2).T/mu_0*Pby.T)
ahx_py = mkvc(mkvc(f[src,'b_py'],2).T/mu_0*Pbx.T)
ahy_py = mkvc(mkvc(f[src,'b_py'],2).T/mu_0*Pby.T)
# Derivatives as lambda functions
aex_px_u = lambda vec: f._e_pxDeriv_u(src,Pex.T*vec,adjoint=True)
aey_px_u = lambda vec: f._e_pxDeriv_u(src,Pey.T*vec,adjoint=True)
aex_py_u = lambda vec: f._e_pyDeriv_u(src,Pex.T*vec,adjoint=True)
aey_py_u = lambda vec: f._e_pyDeriv_u(src,Pey.T*vec,adjoint=True)
ahx_px_u = lambda vec: f._b_pxDeriv_u(src,Pbx.T*vec,adjoint=True)/mu_0
ahy_px_u = lambda vec: f._b_pxDeriv_u(src,Pby.T*vec,adjoint=True)/mu_0
ahx_py_u = lambda vec: f._b_pyDeriv_u(src,Pbx.T*vec,adjoint=True)/mu_0
ahy_py_u = lambda vec: f._b_pyDeriv_u(src,Pby.T*vec,adjoint=True)/mu_0
# Update the input vector
# Define shortcuts
sDiag = lambda t: Utils.sdiag(mkvc(t,2))
sVec = lambda t: Utils.sp.csr_matrix(mkvc(t,2))
# Define the components of the derivative
aHd = sDiag(1./(sDiag(ahx_px)*ahy_py - sDiag(ahx_py)*ahy_px))
aHd_uV = lambda x: ahx_px_u(sDiag(ahy_py)*x) + ahx_px_u(sDiag(ahy_py)*x) - ahy_px_u(sDiag(ahx_py)*x) - ahx_py_u(sDiag(ahy_px)*x)
# Need to fix this to reflect the adjoint
if 'zxx' in self.rxType:
Zij = sDiag(aHd*( sDiag(ahy_py)*aex_px - sDiag(ahy_px)*aex_py))
ZijN_uV = lambda x: aex_px_u(sDiag(ahy_py)*x) + ahy_py_u(sDiag(aex_px)*x) - ahy_px_u(sDiag(aex_py)*x) - aex_py_u(sDiag(ahy_px)*x)
elif 'zxy' in self.rxType:
Zij = sDiag(aHd*(-sDiag(ahx_py)*aex_px + sDiag(ahx_px)*aex_py))
ZijN_uV = lambda x:-aex_px_u(sDiag(ahx_py)*x) - ahx_py_u(sDiag(aex_px)*x) + ahx_px_u(sDiag(aex_py)*x) + aex_py_u(sDiag(ahx_px)*x)
elif 'zyx' in self.rxType:
Zij = sDiag(aHd*( sDiag(ahy_py)*aey_px - sDiag(ahy_px)*aey_py))
ZijN_uV = lambda x: aey_px_u(sDiag(ahy_py)*x) + ahy_py_u(sDiag(aey_px)*x) - ahy_px_u(sDiag(aey_py)*x) - aey_py_u(sDiag(ahy_px)*x)
elif 'zyy' in self.rxType:
Zij = sDiag(aHd*(-sDiag(ahx_py)*aey_px + sDiag(ahx_px)*aey_py))
ZijN_uV = lambda x:-aey_px_u(sDiag(ahx_py)*x) - ahx_py_u(sDiag(aey_px)*x) + ahx_px_u(sDiag(aey_py)*x) + aey_py_u(sDiag(ahx_px)*x)
# Calculate the complex derivative
PDeriv_real = ZijN_uV(aHd*v) - aHd_uV(Zij.T*aHd*v)#
# NOTE: Need to reshape the output to go from 2*nU array to a (nU,2) matrix for each polarization
# PDeriv_real = np.hstack((mkvc(PDeriv_real[:len(PDeriv_real)/2],2),mkvc(PDeriv_real[len(PDeriv_real)/2::],2)))
PDeriv_real = PDeriv_real.reshape((2,mesh.nE)).T
elif self.projType is 'T3D':
if self.locs.ndim == 3:
bFLocs = self.locs[:,:,1]
else:
bFLocs = self.locs
# Get the projection
Pbx = mesh.getInterpolationMat(bFLocs,'Fx')
Pby = mesh.getInterpolationMat(bFLocs,'Fy')
Pbz = mesh.getInterpolationMat(bFLocs,'Fz')
# Get the fields at location
# px: x-polaration and py: y-polaration.
abx_px = mkvc(mkvc(f[src,'b_px'],2).T*Pbx.T)
aby_px = mkvc(mkvc(f[src,'b_px'],2).T*Pby.T)
abz_px = mkvc(mkvc(f[src,'b_px'],2).T*Pbz.T)
abx_py = mkvc(mkvc(f[src,'b_py'],2).T*Pbx.T)
aby_py = mkvc(mkvc(f[src,'b_py'],2).T*Pby.T)
abz_py = mkvc(mkvc(f[src,'b_py'],2).T*Pbz.T)
# Derivatives as lambda functions
abx_px_u = lambda vec: f._b_pxDeriv_u(src,Pbx.T*vec,adjoint=True)
aby_px_u = lambda vec: f._b_pxDeriv_u(src,Pby.T*vec,adjoint=True)
abz_px_u = lambda vec: f._b_pxDeriv_u(src,Pbz.T*vec,adjoint=True)
abx_py_u = lambda vec: f._b_pyDeriv_u(src,Pbx.T*vec,adjoint=True)
aby_py_u = lambda vec: f._b_pyDeriv_u(src,Pby.T*vec,adjoint=True)
abz_py_u = lambda vec: f._b_pyDeriv_u(src,Pbz.T*vec,adjoint=True)
# Update the input vector
# Define shortcuts
sDiag = lambda t: Utils.sdiag(mkvc(t,2))
sVec = lambda t: Utils.sp.csr_matrix(mkvc(t,2))
# Define the components of the derivative
aHd = sDiag(1./(sDiag(abx_px)*aby_py - sDiag(abx_py)*aby_px))
aHd_uV = lambda x: abx_px_u(sDiag(aby_py)*x) + abx_px_u(sDiag(aby_py)*x) - aby_px_u(sDiag(abx_py)*x) - abx_py_u(sDiag(aby_px)*x)
# Need to fix this to reflect the adjoint
if 'tzx' in self.rxType:
Tij = sDiag(aHd*( -sDiag(abz_py)*aby_px + sDiag(abz_px)*aby_py))
TijN_uV = lambda x: -abz_py_u(sDiag(aby_px)*x) - aby_px_u(sDiag(abz_py)*x) + aby_py_u(sDiag(abz_px)*x) + abz_px_u(sDiag(aby_py)*x)
elif 'tzy' in self.rxType:
Tij = sDiag(aHd*( sDiag(abz_py)*abx_px - sDiag(abz_px)*abx_py))
TijN_uV = lambda x: abx_px_u(sDiag(abz_py)*x) + abz_py_u(sDiag(abx_px)*x) - abx_py_u(sDiag(abz_px)*x) - abz_px_u(sDiag(abx_py)*x)
# Calculate the complex derivative
PDeriv_real = TijN_uV(aHd*v) - aHd_uV(Tij.T*aHd*v)#
# NOTE: Need to reshape the output to go from 2*nU array to a (nU,2) matrix for each polarization
# PDeriv_real = np.hstack((mkvc(PDeriv_real[:len(PDeriv_real)/2],2),mkvc(PDeriv_real[len(PDeriv_real)/2::],2)))
PDeriv_real = PDeriv_real.reshape((2,mesh.nE)).T
# Extract the data
if real_or_imag == 'imag':
Pv = 1j*PDeriv_real
elif real_or_imag == 'real':
Pv = PDeriv_real.astype(complex)
return Pv
#################
### Survey ###
#################
class Survey(SimPEGsurvey.BaseSurvey):
"""
Survey class for MT. Contains all the sources associated with the survey.
:param list srcList: List of sources associated with the survey
"""
srcPair = SrcMT.BaseMTSrc
def __init__(self, srcList, **kwargs):
# Sort these by frequency
self.srcList = srcList
SimPEGsurvey.BaseSurvey.__init__(self, **kwargs)
_freqDict = {}
for src in srcList:
if src.freq not in _freqDict:
_freqDict[src.freq] = []
_freqDict[src.freq] += [src]
self._freqDict = _freqDict
self._freqs = sorted([f for f in self._freqDict])
@property
def freqs(self):
"""Frequencies"""
return self._freqs
@property
def nFreq(self):
"""Number of frequencies"""
return len(self._freqDict)
# TODO: Rename to getSources
def getSrcByFreq(self, freq):
"""Returns the sources associated with a specific frequency."""
assert freq in self._freqDict, "The requested frequency is not in this survey."
return self._freqDict[freq]
def projectFields(self, u):
data = Data(self)
for src in self.srcList:
sys.stdout.flush()
for rx in src.rxList:
data[src, rx] = rx.projectFields(src, self.mesh, u)
return data
def projectFieldsDeriv(self, u):
raise Exception('Use Transmitters to project fields deriv.')
#################
### Data ###
#################
class Data(SimPEGsurvey.Data):
'''
Data class for MTdata. Stores the data vector indexed by the survey.
:param SimPEG survey object survey:
:param v vector of the data in order matching of the survey
'''
def __init__(self, survey, v=None):
# Pass the variables to the "parent" method
SimPEGsurvey.Data.__init__(self, survey, v)
# # Import data
# @classmethod
# def fromEDIFiles():
# pass
def toRecArray(self,returnType='RealImag'):
'''
Function that returns a numpy.recarray for a SimpegMT impedance data object.
:param str returnType: Switches between returning a rec array where the impedance is split to real and imaginary ('RealImag') or is a complex ('Complex')
'''
# Define the record fields
dtRI = [('freq',float),('x',float),('y',float),('z',float),('zxxr',float),('zxxi',float),('zxyr',float),('zxyi',float),
('zyxr',float),('zyxi',float),('zyyr',float),('zyyi',float),('tzxr',float),('tzxi',float),('tzyr',float),('tzyi',float)]
dtCP = [('freq',float),('x',float),('y',float),('z',float),('zxx',complex),('zxy',complex),('zyx',complex),('zyy',complex),('tzx',complex),('tzy',complex)]
impList = ['zxxr','zxxi','zxyr','zxyi','zyxr','zyxi','zyyr','zyyi']
for src in self.survey.srcList:
# Temp array for all the receivers of the source.
# Note: needs to be written more generally, using diffterent rxTypes and not all the data at the locaitons
# Assume the same locs for all RX
locs = src.rxList[0].locs
if locs.shape[1] == 1:
locs = np.hstack((np.array([[0.0,0.0]]),locs))
elif locs.shape[1] == 2:
locs = np.hstack((np.array([[0.0]]),locs))
tArrRec = np.concatenate((src.freq*np.ones((locs.shape[0],1)),locs,np.nan*np.ones((locs.shape[0],12))),axis=1).view(dtRI)
# np.array([(src.freq,rx.locs[0,0],rx.locs[0,1],rx.locs[0,2],np.nan ,np.nan ,np.nan ,np.nan ,np.nan ,np.nan ,np.nan ,np.nan ) for rx in src.rxList],dtype=dtRI)
# Get the type and the value for the DataMT object as a list
typeList = [[rx.rxType.replace('z1d','zyx'),self[src,rx]] for rx in src.rxList]
# Insert the values to the temp array
for nr,(key,val) in enumerate(typeList):
tArrRec[key] = mkvc(val,2)
# Masked array
mArrRec = np.ma.MaskedArray(rec2ndarr(tArrRec),mask=np.isnan(rec2ndarr(tArrRec))).view(dtype=tArrRec.dtype)
# Unique freq and loc of the masked array
uniFLmarr = np.unique(mArrRec[['freq','x','y','z']]).copy()
try:
outTemp = recFunc.stack_arrays((outTemp,mArrRec))
#outTemp = np.concatenate((outTemp,dataBlock),axis=0)
except NameError as e:
outTemp = mArrRec
if 'RealImag' in returnType:
outArr = outTemp
elif 'Complex' in returnType:
# Add the real and imaginary to a complex number
outArr = np.empty(outTemp.shape,dtype=dtCP)
for comp in ['freq','x','y','z']:
outArr[comp] = outTemp[comp].copy()
for comp in ['zxx','zxy','zyx','zyy','tzx','tzy']:
outArr[comp] = outTemp[comp+'r'].copy() + 1j*outTemp[comp+'i'].copy()
else:
raise NotImplementedError('{:s} is not implemented, as to be RealImag or Complex.')
# Return
return outArr
@classmethod
def fromRecArray(cls, recArray, srcType='primary'):
"""
Class method that reads in a numpy record array to MTdata object.
Only imports the impedance data.
"""
if srcType=='primary':
src = SrcMT.polxy_1Dprimary
elif srcType=='total':
src = SrcMT.polxy_1DhomotD
else:
raise NotImplementedError('{:s} is not a valid source type for MTdata')
# Find all the frequencies in recArray
uniFreq = np.unique(recArray['freq'])
srcList = []
dataList = []
for freq in uniFreq:
# Initiate rxList
rxList = []
# Find that data for freq
dFreq = recArray[recArray['freq'] == freq].copy()
# Find the impedance rxTypes in the recArray.
rxTypes = [ comp for comp in recArray.dtype.names if (len(comp)==4 or len(comp)==3) and 'z' in comp]
for rxType in rxTypes:
# Find index of not nan values in rxType
notNaNind = ~np.isnan(dFreq[rxType])
if np.any(notNaNind): # Make sure that there is any data to add.
locs = rec2ndarr(dFreq[['x','y','z']][notNaNind].copy())
if dFreq[rxType].dtype.name in 'complex128':
rxList.append(Rx(locs,rxType+'r'))
dataList.append(dFreq[rxType][notNaNind].real.copy())
rxList.append(Rx(locs,rxType+'i'))
dataList.append(dFreq[rxType][notNaNind].imag.copy())
else:
rxList.append(Rx(locs,rxType))
dataList.append(dFreq[rxType][notNaNind].copy())
srcList.append(src(rxList,freq))
# Make a survey
survey = Survey(srcList)
dataVec = np.hstack(dataList)
return cls(survey,dataVec)
SimPEG/MT/Utils/MT1Danalytic.py
+108
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@@ -0,0 +1,108 @@
# Analytic solution of EM fields due to a plane wave
import numpy as np, SimPEG as simpeg
from scipy.constants import mu_0, epsilon_0 as eps_0
def getEHfields(m1d,sigma,freq,zd,scaleUD=True):
'''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 bollean, scaleUD: scales the output to be 1 at the top, increases numeracal stability.
Assumes a halfspace with the same conductive as the last cell below.
'''
# Note add an error check for the mesh and sigma are the same size.
# Constants: Assume constant
mu = mu_0*np.ones((m1d.nC+1))
eps = eps_0*np.ones((m1d.nC+1))
# Angular freq
w = 2*np.pi*freq
# Add the halfspace value to the property
sig = np.concatenate((np.array([sigma[0]]),sigma))
# Calculate the wave number
k = np.sqrt(eps*mu*w**2-1j*mu*sig*w)
# Initiate the propagation matrix, in the order down up.
UDp = np.zeros((2,m1d.nC+1),dtype=complex)
UDp[1,0] = 1. # Set the wave amplitude as 1 into the half-space at the bottom of the mesh
# Loop over all the layers, starting at the bottom layer
for lnr, h in enumerate(m1d.hx): # lnr-number of layer, h-thickness of the layer
# 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
# Build the propagation matrix
# 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]])
# 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)]])
# The down and up component in current layer.
UDp[:,lnr+1] = elamh.dot(Pjinv.dot(Pj1)).dot(UDp[:,lnr])
if scaleUD:
UDp[:,lnr+1::-1] = UDp[:,lnr+1::-1]/UDp[1,lnr+1]
# Calculate the fields
Ed = np.empty((zd.size,),dtype=complex)
Eu = np.empty((zd.size,),dtype=complex)
Hd = np.empty((zd.size,),dtype=complex)
Hu = np.empty((zd.size,),dtype=complex)
# Loop over the layers and calculate the fields
# In the halfspace below the mesh
dup = m1d.vectorNx[0]
dind = dup >= zd
Ed[dind] = UDp[1,0]*np.exp(-1j*k[0]*(dup-zd[dind]))
Eu[dind] = UDp[0,0]*np.exp(1j*k[0]*(dup-zd[dind]))
Hd[dind] = (k[0]/(w*mu[0]))*UDp[1,0]*np.exp(-1j*k[0]*(dup-zd[dind]))
Hu[dind] = -(k[0]/(w*mu[0]))*UDp[0,0]*np.exp(1j*k[0]*(dup-zd[dind]))
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.
: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.
"""
# 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] = (mu_0*om)/np.sqrt(mu_0*eps_0*(om)**2 - 1j*mu_0*sigma[0]*om)
for nr,hi in enumerate(h):
# Calculate the wave number
# print nr,sigma[nr]
k = np.sqrt(mu_0*eps_0*om**2 - 1j*mu_0*sigma[nr]*om)
Z = (mu_0*om)/k
Zall[nr+1] = Z *((Zall[nr] + Z*np.tanh(1j*k*hi))/(Z + Zall[nr]*np.tanh(1j*k*hi)))
#pdb.set_trace()
Z1d[nrFr] = Zall[-1]
return Z1d
SimPEG/MT/Utils/MT1Dsolutions.py
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import numpy as np, SimPEG as simpeg
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]]
# Set the boundary conditions
Ed, Eu, Hd, Hu = getEHfields(m1d,sigma,freq,m1d.vectorNx)
Etot = (Ed + Eu)
if sourceAmp is not None:
Etot = ((Etot/Etot[-1])*sourceAmp) # Scale the fields to be equal to sourceAmp at the top
## Note: The analytic solution is derived with e^iwt
bc = np.r_[Etot[0],Etot[-1]]
# 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
SimPEG/MT/Utils/__init__.py
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from MT1Dsolutions import * # Add the names of the functions
from MT1Danalytic import *
from dataUtils import *
from ediFilesUtils import *
SimPEG/MT/Utils/dataUtils.py
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# Utils used for the data,
import numpy as np, matplotlib.pyplot as plt, sys
import SimPEG as simpeg
import numpy.lib.recfunctions as recFunc
from scipy.constants import mu_0
from scipy import interpolate as sciint
def getAppRes(MTdata):
# Make impedance
zList = []
for src in MTdata.survey.srcList:
zc = [src.freq]
for rx in src.rxList:
if 'i' in rx.rxType:
m=1j
else:
m = 1
zc.append(m*MTdata[src,rx])
zList.append(zc)
return [appResPhs(zList[i][0],np.sum(zList[i][1:3])) for i in np.arange(len(zList))]
def rotateData(MTdata,rotAngle):
'''
Function that rotates clockwist by rotAngle (- negative for a counter-clockwise rotation)
'''
recData = MTdata.toRecArray('Complex')
impData = rec2ndarr(recData[['zxx','zxy','zyx','zyy']],complex)
# Make the rotation matrix
# c,s,zxx,zxy,zyx,zyy = sympy.symbols('c,s,zxx,zxy,zyx,zyy')
# rotM = sympy.Matrix([[c,-s],[s, c]])
# zM = sympy.Matrix([[zxx,zxy],[zyx,zyy]])
# rotM*zM*rotM.T
# [c*(c*zxx - s*zyx) - s*(c*zxy - s*zyy), c*(c*zxy - s*zyy) + s*(c*zxx - s*zyx)],
# [c*(c*zyx + s*zxx) - s*(c*zyy + s*zxy), c*(c*zyy + s*zxy) + s*(c*zyx + s*zxx)]])
s = np.sin(-np.deg2rad(rotAngle))
c = np.cos(-np.deg2rad(rotAngle))
rotMat = np.array([[c,-s],[s,c]])
rotData = (rotMat.dot(impData.reshape(-1,2,2).dot(rotMat.T))).transpose(1,0,2).reshape(-1,4)
outRec = recData.copy()
for nr,comp in enumerate(['zxx','zxy','zyx','zyy']):
outRec[comp] = rotData[:,nr]
from SimPEG import MT
return MT.Data.fromRecArray(outRec)
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
def skindepth(rho,freq):
''' Function to calculate the skindepth of EM waves'''
return np.sqrt( (rho*((1/(freq * mu_0 * np.pi )))))
def rec2ndarr(x,dt=float):
return x.view((dt, len(x.dtype.names)))
def makeAnalyticSolution(mesh,model,elev,freqs):
from SimPEG import MT
data1D = []
for freq in freqs:
anaEd, anaEu, anaHd, anaHu = MT.Utils.MT1Danalytic.getEHfields(mesh,model,freq,elev)
anaE = anaEd+anaEu
anaH = anaHd+anaHu
anaZ = anaE/anaH
# Add to the list
data1D.append((freq,0,0,elev,anaZ[0]))
dataRec = np.array(data1D,dtype=[('freq',float),('x',float),('y',float),('z',float),('zyx',complex)])
return dataRec
def plotMT1DModelData(problem,models,symList=None):
from SimPEG import MT
# Setup the figure
fontSize = 15
fig = plt.figure(figsize=[9,7])
axM = fig.add_axes([0.075,.1,.25,.875])
axM.set_xlabel('Resistivity [Ohm*m]',fontsize=fontSize)
axM.set_xlim(1e-1,1e5)
axM.set_ylim(-10000,5000)
axM.set_ylabel('Depth [km]',fontsize=fontSize)
axR = fig.add_axes([0.42,.575,.5,.4])
axR.set_xscale('log')
axR.set_yscale('log')
axR.invert_xaxis()
# axR.set_xlabel('Frequency [Hz]')
axR.set_ylabel('Apparent resistivity [Ohm m]',fontsize=fontSize)
axP = fig.add_axes([0.42,.1,.5,.4])
axP.set_xscale('log')
axP.invert_xaxis()
axP.set_ylim(0,90)
axP.set_xlabel('Frequency [Hz]',fontsize=fontSize)
axP.set_ylabel('Apparent phase [deg]',fontsize=fontSize)
# if not symList:
# symList = ['x']*len(models)
import plotDataTypes as pDt
# Loop through the models.
modelList = [problem.survey.mtrue]
modelList.extend(models)
if False:
modelList = [problem.mapping.sigmaMap*mod for mod in modelList]
for nr, model in enumerate(modelList):
# Calculate the data
if nr==0:
data1D = problem.dataPair(problem.survey,problem.survey.dobs).toRecArray('Complex')
else:
data1D = problem.dataPair(problem.survey,problem.survey.dpred(model)).toRecArray('Complex')
# Plot the data and the model
colRat = nr/((len(modelList)-1.999)*1.)
if colRat > 1.:
col = 'k'
else:
col = plt.cm.seismic(1-colRat)
# The model - make the pts to plot
meshPts = np.concatenate((problem.mesh.gridN[0:1],np.kron(problem.mesh.gridN[1::],np.ones(2))[:-1]))
modelPts = np.kron(1./(problem.mapping.sigmaMap*model),np.ones(2,))
axM.semilogx(modelPts,meshPts,color=col)
## Data
# Appres
pDt.plotIsoStaImpedance(axR,np.array([0,0]),data1D,'zyx','res',pColor=col)
# Appphs
pDt.plotIsoStaImpedance(axP,np.array([0,0]),data1D,'zyx','phs',pColor=col)
try:
allData = np.concatenate((allData,simpeg.mkvc(data1D['zyx'],2)),1)
except:
allData = simpeg.mkvc(data1D['zyx'],2)
freq = simpeg.mkvc(data1D['freq'],2)
res, phs = appResPhs(freq,allData)
stdCol = 'gray'
axRtw = axR.twinx()
axRtw.set_ylabel('Std of log10',color=stdCol)
[(t.set_color(stdCol), t.set_rotation(-45)) for t in axRtw.get_yticklabels()]
axPtw = axP.twinx()
axPtw.set_ylabel('Std ',color=stdCol)
[t.set_color(stdCol) for t in axPtw.get_yticklabels()]
axRtw.plot(freq, np.std(np.log10(res),1),'--',color=stdCol)
axPtw.plot(freq, np.std(phs,1),'--',color=stdCol)
# Fix labels and ticks
yMtick = [l/1000 for l in axM.get_yticks().tolist()]
axM.set_yticklabels(yMtick)
[ l.set_rotation(90) for l in axM.get_yticklabels()]
[ l.set_rotation(90) for l in axR.get_yticklabels()]
[(t.set_color(stdCol), t.set_rotation(-45)) for t in axRtw.get_yticklabels()]
[t.set_color(stdCol) for t in axPtw.get_yticklabels()]
for ax in [axM,axR,axP]:
ax.xaxis.set_tick_params(labelsize=fontSize)
ax.yaxis.set_tick_params(labelsize=fontSize)
return fig
def printTime():
import time
print time.strftime("%a, %d %b %Y %H:%M:%S +0000", time.localtime())
def convert3Dto1Dobject(MTdata,rxType3D='zyx'):
from SimPEG import MT
# Find the unique locations
# Need to find the locations
recDataTemp = MTdata.toRecArray()
# Check if survey.std has been assigned.
## NEED TO: write this...
# Calculte and add the DET of the tensor to the recArray
if 'det' in rxType3D:
Zon = (recDataTemp['zxxr']+1j*recDataTemp['zxxi'])*(recDataTemp['zyyr']+1j*recDataTemp['zyyi'])
Zoff = (recDataTemp['zxyr']+1j*recDataTemp['zxyi'])*(recDataTemp['zyxr']+1j*recDataTemp['zyxi'])
det = np.sqrt(Zon.data - Zoff.data)
recData = recFunc.append_fields(recDataTemp,['zdetr','zdeti'],[det.real,det.imag] )
else:
recData = recDataTemp
uniLocs = rec2ndarr(np.unique(recData[['x','y','z']])).data
mtData1DList = []
if 'zxy' in rxType3D:
corr = -1 # Shift the data to comply with the quadtrature of the 1d problem
else:
corr = 1
for loc in uniLocs:
# Make the receiver list
rx1DList = []
for rxType in ['z1dr','z1di']:
rx1DList.append(MT.Rx(simpeg.mkvc(loc,2).T,rxType))
# Source list
locrecData = recData[np.sqrt(np.sum( (rec2ndarr(recData[['x','y','z']]).data - loc )**2,axis=1)) < 1e-5]
dat1DList = []
src1DList = []
for freq in locrecData['freq']:
src1DList.append(MT.SrcMT.src_polxy_1Dprimary(rx1DList,freq))
for comp in ['r','i']:
dat1DList.append( corr * locrecData[rxType3D+comp][locrecData['freq']== freq].data )
# Make the survey
sur1D = MT.Survey(src1DList)
# Make the data
dataVec = np.hstack(dat1DList)
dat1D = MT.Data(sur1D,dataVec)
sur1D.dobs = dataVec
# Need to take MTdata.survey.std and split it as well.
std=0.05
sur1D.std = np.abs(sur1D.dobs*std) #+ 0.01*np.linalg.norm(sur1D.dobs)
mtData1DList.append(dat1D)
# Return the the list of data.
return mtData1DList
def resampleMTdataAtFreq(MTdata,freqs):
"""
Function to resample MTdata at set of frequencies
"""
from SimPEG import MT
# Make a rec array
MTrec = MTdata.toRecArray().data
# Find unique locations
uniLoc = np.unique(MTrec[['x','y','z']])
uniFreq = MTdata.survey.freqs
# Get the comps
dNames = MTrec.dtype
# Loop over all the locations and interpolate
for loc in uniLoc:
# Find the index of the station
ind = np.sqrt(np.sum((rec2ndarr(MTrec[['x','y','z']]) - rec2ndarr(loc))**2,axis=1)) < 1. # Find dist of 1 m accuracy
# Make a temporary recArray and interpolate all the components
tArrRec = np.concatenate((simpeg.mkvc(freqs,2),np.ones((len(freqs),1))*rec2ndarr(loc),np.nan*np.ones((len(freqs),12))),axis=1).view(dNames)
for comp in ['zxxr','zxxi','zxyr','zxyi','zyxr','zyxi','zyyr','zyyi','tzxr','tzxi','tzyr','tzyi']:
int1d = sciint.interp1d(MTrec[ind]['freq'],MTrec[ind][comp],bounds_error=False)
tArrRec[comp] = simpeg.mkvc(int1d(freqs),2)
# Join together
try:
outRecArr = recFunc.stack_arrays((outRecArr,tArrRec))
except NameError as e:
outRecArr = tArrRec
# Make the MTdata and return
return MT.Data.fromRecArray(outRecArr)
SimPEG/MT/Utils/ediFilesUtils.py
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# Functions to import and export MT EDI files.
from SimPEG import mkvc
from scipy.constants import mu_0
from numpy.lib import recfunctions as recFunc
from SimPEG.MT.Utils.dataUtils import rec2ndarr
# Import modules
import numpy as np
import os, sys, re
try:
import osr
except ImportError as e:
print 'Could not import osr, missing the gdal package'
pass
class EDIimporter:
"""
A class to import EDIfiles.
"""
_impUnitEDI2SI = 4*np.pi*1e-4 # Convert Z[mV/km/nT] (as in EDI)to Z[V/A] SI unit
_impUnitSI2EDI = 1./_impUnitEDI2SI # ConvertZ[V/A] SI unit to Z[mV/km/nT] (as in EDI)
# Properties
filesList = None
comps = None
# Hidden properties
_outEPSG = None
_2out = None
def __init__(self, EDIfilesList, compList=None, outEPSG=None):
# Set the fileList
self.filesList = EDIfilesList
# Set the components to import
if compList is None:
self.comps = ['ZXXR','ZXYR','ZYXR','ZYYR','ZXXI','ZXYI','ZYXI','ZYYI','ZXX.VAR','ZXY.VAR','ZYX.VAR','ZYY.VAR']
else:
self.comps = compList
if outEPSG is not None:
self._outEPSG = outEPSG
def __call__(self,comps=None):
if comps is None:
return self._data
return self._data[comps]
def importFiles(self):
"""
Function to import EDI files into a object.
"""
# Constants that are needed for convertion of units
# Temp lists
tmpStaList = []
tmpCompList = ['freq','x','y','z']
tmpCompList.extend(self.comps)
# Make the outarray
dtRI = [(compS.lower().replace('.',''),float) for compS in tmpCompList]
# Loop through all the files
for nrEDI, EDIfile in enumerate(self.filesList):
# Read the file into a list of the lines
with open(EDIfile,'r') as fid:
EDIlines = fid.readlines()
# Find the location
latD, longD, elevM = _findLatLong(EDIlines)
# Transfrom coordinates
transCoord = self._transfromPoints(longD,latD)
# Extract the name of the file (station)
EDIname = EDIfile.split(os.sep)[-1].split('.')[0]
# Arrange the data
staList = [EDIname, EDIfile, transCoord[0], transCoord[1], elevM[0]]
# Add to the station list
tmpStaList.extend(staList)
# Read the frequency data
freq = _findEDIcomp('>FREQ',EDIlines)
# Make the temporary rec array.
tArrRec = ( np.nan*np.ones( (len(freq),len(dtRI)) ) ).view(dtRI) #np.concatenate((freq*np.ones((locs.shape[0],1)),locs,np.nan*np.ones((locs.shape[0],8))),axis=1).view(dtRI)
# Add data to the array
tArrRec['freq'] = mkvc(freq,2)
tArrRec['x'] = mkvc(np.ones((len(freq),1))*transCoord[0],2)
tArrRec['y'] = mkvc(np.ones((len(freq),1))*transCoord[1],2)
tArrRec['z'] = mkvc(np.ones((len(freq),1))*elevM[0],2)
for comp in self.comps:
# Deal with converting units of the impedance tensor
if 'Z' in comp:
unitConvert = self._impUnitEDI2SI
else:
unitConvert = 1
# Rotate the data since EDI x is *north, y *east but Simpeg uses x *east, y *north (* means internal reference frame)
key = [comp.lower().replace('.','').replace(s,t) for s,t in [['xx','yy'],['xy','yx'],['yx','xy'],['yy','xx']] if s in comp.lower()][0]
tArrRec[key] = mkvc(unitConvert*_findEDIcomp('>'+comp,EDIlines),2)
# Make a masked array
mArrRec = np.ma.MaskedArray(rec2ndarr(tArrRec),mask=np.isnan(rec2ndarr(tArrRec))).view(dtype=tArrRec.dtype)
try:
outTemp = recFunc.stack_arrays((outTemp,mArrRec))
except NameError as e:
outTemp = mArrRec
# Assign the data
self._data = outTemp
# % Assign the data to the obj
# nOutData=length(obj.data);
# obj.data(nOutData+1:nOutData+length(TEMP.data),:) = TEMP.data;
def _transfromPoints(self,longD,latD):
# Coordinates convertor
if self._2out is None:
src = osr.SpatialReference()
src.ImportFromEPSG(4326)
out = osr.SpatialReference()
if self._outEPSG is None:
# Find the UTM EPSG number
Nnr = 700 if latD < 0.0 else 600
utmZ = int(1+(longD+180.0)/6.0)
self._outEPSG = 32000 + Nnr + utmZ
out.ImportFromEPSG(self._outEPSG)
self._2out = osr.CoordinateTransformation(src,out)
# Return the transfrom
return self._2out.TransformPoint(longD,latD)
# Hidden functions
def _findLatLong(fileLines):
latDMS = np.array(fileLines[_findLine('LAT=',fileLines)[0]].split('=')[1].split()[0].split(':'),float)
longDMS = np.array(fileLines[_findLine('LONG=',fileLines)[0]].split('=')[1].split()[0].split(':'),float)
elevM = np.array([fileLines[_findLine('ELEV=',fileLines)[0]].split('=')[1].split()[0]],float)
# Convert to D.ddddd values
latS = np.sign(latDMS[0])
longS = np.sign(longDMS[0])
latD = latDMS[0] + latS*latDMS[1]/60 + latS*latDMS[2]/3600
longD = longDMS[0] + longS*longDMS[1]/60 + longS*longDMS[2]/3600
return latD, longD, elevM
def _findLine(comp,fileLines):
""" Find a line number in the file"""
# Line counter
c = 0
# List of indices for found lines
found = []
# Loop through all the lines
for line in fileLines:
if comp in line:
# Append if found
found.append(c)
# Increse the counter
c += 1
# Return the found indices
return found
def _findEDIcomp(comp,fileLines,dt=float):
"""
Extract the data vector.
Returns a list of the data.
"""
# Find the data
headLine, indHead = [(st,nr) for nr,st in enumerate(fileLines) if re.search(comp,st)][0]
# Extract the data
nrVec = int(headLine.split()[-1])
c = 0
dataList = []
while c < nrVec:
indHead += 1
dataList.extend(fileLines[indHead].split())
c = len(dataList)
return np.array(dataList,dt)
SimPEG/MT/Utils/plotDataTypes.py
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from matplotlib import pyplot as plt, colors, numpy as np
def rec2nd(structArray):
""" Converts a structured/record array to ndarray to do operations on."""
return structArray.view((np.float,len(structArray.dtype.names)))
def plotIsoFreqNSimpedance(ax,freq,array,flag,par='abs',colorbar=True,colorNorm='SymLog',cLevel=True,contour=True):
indUniFreq = np.where(freq==array['freq'])
x, y = array['x'][indUniFreq],array['y'][indUniFreq]
if par == 'abs':
zPlot = np.abs(array[flag][indUniFreq])
cmap = plt.get_cmap('OrRd_r')#seismic')
level = np.logspace(0,-5,31)
clevel = np.logspace(0,-4,5)
plotNorm = colors.LogNorm()
elif par == 'real':
zPlot = np.real(array[flag][indUniFreq])
cmap = plt.get_cmap('RdYlBu')
if cLevel:
level = np.concatenate((-np.logspace(0,-10,31),np.logspace(-10,0,31)))
clevel = np.concatenate((-np.logspace(0,-8,5),np.logspace(-8,0,5)))
else:
level = np.linspace(zPlot.min(),zPlot.max(),100)
clevel = np.linspace(zPlot.min(),zPlot.max(),10)
if colorNorm=='SymLog':
plotNorm = colors.SymLogNorm(1e-10,linscale=2)
else:
plotNorm = colors.Normalize()
elif par == 'imag':
zPlot = np.imag(array[flag][indUniFreq])
cmap = plt.get_cmap('RdYlBu')
level = np.concatenate((-np.logspace(0,-10,31),np.logspace(-10,0,31)))
clevel = np.concatenate((-np.logspace(0,-8,5),np.logspace(-8,0,5)))
plotNorm = colors.SymLogNorm(1e-10,linscale=2)
if cLevel:
level = np.concatenate((-np.logspace(0,-10,31),np.logspace(-10,0,31)))
clevel = np.concatenate((-np.logspace(0,-8,5),np.logspace(-8,0,5)))
else:
level = np.linspace(zPlot.min(),zPlot.max(),100)
clevel = np.linspace(zPlot.min(),zPlot.max(),10)
if colorNorm=='SymLog':
plotNorm = colors.SymLogNorm(1e-10,linscale=2)
elif colorNorm=='Lin':
plotNorm = colors.Normalize()
if contour:
cs = ax.tricontourf(x,y,zPlot,levels=level,cmap=cmap,norm=plotNorm)#,extend='both')
else:
uniX,uniY = np.unique(x),np.unique(y)
X,Y = np.meshgrid(np.append(uniX-25,uniX[-1]+25),np.append(uniY-25,uniY[-1]+25))
cs = ax.pcolor(X,Y,np.reshape(zPlot,(len(uniY),len(uniX))),cmap=cmap,norm=plotNorm)
if colorbar:
plt.colorbar(cs,cax=ax.cax,ticks=clevel,format='%1.2e')
ax.set_title(flag+' '+par,fontsize=8)
return cs
def plotIsoFreqNSDiff(ax,freq,arrayList,flag,par='abs',colorbar=True,cLevel=True,mask=None,contourLine=True,useLog=False):
indUniFreq0 = np.where(freq==arrayList[0]['freq'])
indUniFreq1 = np.where(freq==arrayList[1]['freq'])
seicmap = plt.get_cmap('RdYlBu')#seismic')
x, y = arrayList[0]['x'][indUniFreq0],arrayList[0]['y'][indUniFreq0]
if par == 'abs':
if useLog:
zPlot = (np.log10(np.abs(arrayList[0][flag][indUniFreq0])) - np.log10(np.abs(arrayList[1][flag][indUniFreq1])))/np.log10(np.abs(arrayList[1][flag][indUniFreq1]))
else:
zPlot = (np.abs(arrayList[0][flag][indUniFreq0]) - np.abs(arrayList[1][flag][indUniFreq1]))/np.abs(arrayList[1][flag][indUniFreq1])
if mask:
maskInd = np.logical_or(np.abs(arrayList[0][flag][indUniFreq0])< 1e-3,np.abs(arrayList[1][flag][indUniFreq1]) < 1e-3)
zPlot = np.ma.array(zPlot)
zPlot[maskInd] = mask
if cLevel:
level = np.arange(-200,201,10)
clevel = np.arange(-200,201,25)
else:
level = np.linspace(zPlot.min(),zPlot.max(),100)
clevel = np.linspace(zPlot.min(),zPlot.max(),10)
elif par == 'real':
if useLog:
zPlot = (np.log10(np.real(arrayList[0][flag][indUniFreq0])) -np.log10(np.real(arrayList[1][flag][indUniFreq1])))/np.log10(np.abs((np.real(arrayList[1][flag][indUniFreq1]))))
else:
zPlot = (np.real(arrayList[0][flag][indUniFreq0]) -np.real(arrayList[1][flag][indUniFreq1]))/np.abs((np.real(arrayList[1][flag][indUniFreq1])))
if mask:
maskInd = np.logical_or(np.abs(np.real(arrayList[0][flag][indUniFreq0])) < 1e-3,np.abs(np.real(arrayList[1][flag][indUniFreq1])) < 1e-3)
zPlot = np.ma.array(zPlot)
zPlot[maskInd] = mask
if cLevel:
level = np.arange(-200,201,10)
clevel = np.arange(-200,201,25)
else:
level = np.linspace(zPlot.min(),zPlot.max(),100)
clevel = np.linspace(zPlot.min(),zPlot.max(),10)
elif par == 'imag':
if useLog:
zPlot = (np.log10(np.imag(arrayList[0][flag][indUniFreq0])) -np.log10(np.imag(arrayList[1][flag][indUniFreq1])))/np.log10(np.abs((np.imag(arrayList[1][flag][indUniFreq1]))))
else:
zPlot = (np.imag(arrayList[0][flag][indUniFreq0]) -np.imag(arrayList[1][flag][indUniFreq1]))/np.abs((np.imag(arrayList[1][flag][indUniFreq1])))
if mask:
maskInd = np.logical_or(np.abs(np.imag(arrayList[0][flag][indUniFreq0])) < 1e-3,np.abs(np.imag(arrayList[1][flag][indUniFreq1])) < 1e-3)
zPlot = np.ma.array(zPlot)
zPlot[maskInd] = mask
if cLevel:
level = np.arange(-200,201,10)
clevel = np.arange(-200,201,25)
else:
level = np.linspace(zPlot.min(),zPlot.max(),100)
clevel = np.linspace(zPlot.min(),zPlot.max(),10)
cs = ax.tricontourf(x,y,zPlot*100,levels=level*100,cmap=seicmap,extend='both') #,norm=colors.SymLogNorm(1e-2,linscale=2))
if contourLine:
csl = ax.tricontour(x,y,zPlot*100,levels=clevel*100,colors='k')
plt.clabel(csl, fontsize=7, inline=1,fmt='%1.1e',inline_spacing=10)
if colorbar:
cb = plt.colorbar(cs,cax=ax.cax,ticks=clevel*100,format='%1.1e')
for t in cb.ax.get_yticklabels():
t.set_rotation(60)
t.set_fontsize(8)
ax.set_title(flag+' '+par,fontsize=8)
def plotIsoFreqNStipper(ax,freq,array,flag,par='abs',colorbar=True,colorNorm='SymLog',cLevel=True,contour=True):
indUniFreq = np.where(freq==array['freq'])
x, y = array['x'][indUniFreq],array['y'][indUniFreq]
if par == 'abs':
cmap = plt.get_cmap('OrRd_r')#seismic')
zPlot = np.abs(array[flag][indUniFreq])
if cLevel:
level = np.logspace(-4,0,33)
clevel = np.logspace(-4,0,5)
else:
level = np.linspace(zPlot.min(),zPlot.max(),100)
clevel = np.linspace(zPlot.min(),zPlot.max(),10)
if colorNorm=='SymLog':
plotNorm = colors.LogNorm()
else:
plotNorm = colors.Normalize()
elif par == 'real':
cmap = plt.get_cmap('RdYlBu')
zPlot = np.real(array[flag][indUniFreq])
if cLevel:
level = np.concatenate((-np.logspace(0,-4,33),np.logspace(-4,0,33)))
clevel = np.concatenate((-np.logspace(0,-4,5),np.logspace(-4,0,5)))
else:
level = np.linspace(zPlot.min(),zPlot.max(),100)
clevel = np.linspace(zPlot.min(),zPlot.max(),10)
if colorNorm=='SymLog':
plotNorm = colors.SymLogNorm(1e-4,linscale=2)
else:
plotNorm = colors.Normalize()
elif par == 'imag':
cmap = plt.get_cmap('RdYlBu')
zPlot = np.imag(array[flag][indUniFreq])
if cLevel:
level = np.concatenate((-np.logspace(0,-4,33),np.logspace(-4,0,33)))
clevel = np.concatenate((-np.logspace(0,-4,5),np.logspace(-4,0,5)))
else:
level = np.linspace(zPlot.min(),zPlot.max(),100)
clevel = np.linspace(zPlot.min(),zPlot.max(),10)
if colorNorm=='SymLog':
plotNorm = colors.SymLogNorm(1e-4,linscale=2)
else:
plotNorm = colors.Normalize()
if contour:
cs = ax.tricontourf(x,y,zPlot,levels=level,cmap=cmap,norm=plotNorm)#,extend='both')
else:
uniX,uniY = np.unique(x),np.unique(y)
X,Y = np.meshgrid(np.append(uniX-25,uniX[-1]+25),np.append(uniY-25,uniY[-1]+25))
cs = ax.pcolor(X,Y,np.reshape(zPlot,(len(uniY),len(uniX))),levels=level,cmap=cmap,norm=plotNorm,edgecolors='k', linewidths=0.5)
if colorbar:
plt.colorbar(cs,cax=ax.cax,ticks=clevel,format='%1.2e')
ax.set_title(flag+' '+par,fontsize=8)
def plotIsoStaImpedance(ax,loc,array,flag,par='abs',pSym='s',pColor=None):
appResFact = 1/(8*np.pi**2*10**(-7))
treshold = 1.0 # 1 meter
indUniSta = np.sqrt(np.sum((rec2nd(array[['x','y']])-loc)**2,axis=1)) < treshold
freq = array['freq'][indUniSta]
if par == 'abs':
zPlot = np.abs(array[flag][indUniSta])
elif par == 'real':
zPlot = np.real(array[flag][indUniSta])
elif par == 'imag':
zPlot = np.imag(array[flag][indUniSta])
elif par == 'res':
zPlot = (appResFact/freq)*np.abs(array[flag][indUniSta])**2
elif par == 'phs':
zPlot = np.arctan2(array[flag][indUniSta].imag,array[flag][indUniSta].real)*(180/np.pi)
if not pColor:
if 'xx' in flag:
lab = 'XX'
pColor = 'g'
elif 'xy' in flag:
lab = 'XY'
pColor = 'r'
elif 'yx' in flag:
lab = 'YX'
pColor = 'b'
elif 'yy' in flag:
lab = 'YY'
pColor = 'y'
ax.plot(freq,zPlot,color=pColor,marker=pSym,label=flag)
def plotPsudoSectNSimpedance(ax,sectDict,array,flag,par='abs',colorbar=True,colorNorm='None',cLevel=None,contour=True):
indSect = np.where(sectDict.values()[0]==array[sectDict.keys()[0]])
# Define the plot axes
if 'x' in sectDict.keys()[0]:
x = array['y'][indSect]
else:
x = array['x'][indSect]
y = array['freq'][indSect]
if par == 'abs':
zPlot = np.abs(array[flag][indSect])
cmap = plt.get_cmap('OrRd_r')#seismic')
if cLevel:
level = np.logspace(0,-5,31,endpoint=True)
clevel = np.logspace(0,-4,5,endpoint=True)
else:
level = np.linspace(zPlot.min(),zPlot.max(),100,endpoint=True)
clevel = np.linspace(zPlot.min(),zPlot.max(),10,endpoint=True)
elif par == 'ares':
zPlot = np.abs(array[flag][indSect])**2/(8*np.pi**2*10**(-7)*array['freq'][indSect])
cmap = plt.get_cmap('RdYlBu')#seismic)
if cLevel:
zMax = np.log10(cLevel[1])
zMin = np.log10(cLevel[0])
else:
zMax = (np.ceil(np.log10(np.abs(zPlot).max())))
zMin = (np.floor(np.log10(np.abs(zPlot).min())))
level = np.logspace(zMin,zMax,(zMax-zMin)*8+1,endpoint=True)
clevel = np.logspace(zMin,zMax,(zMax-zMin)*2+1,endpoint=True)
plotNorm = colors.LogNorm()
elif par == 'aphs':
zPlot = np.arctan2(array[flag][indSect].imag,array[flag][indSect].real)*(180/np.pi)
cmap = plt.get_cmap('RdYlBu')#seismic)
if cLevel:
zMax = cLevel[1]
zMin = cLevel[0]
else:
zMax = (np.ceil(zPlot).max())
zMin = (np.floor(zPlot).min())
level = np.arange(zMin,zMax+.1,1)
clevel = np.arange(zMin,zMax+.1,10)
plotNorm = colors.Normalize()
elif par == 'real':
zPlot = np.real(array[flag][indSect])
cmap = plt.get_cmap('Spectral') #('RdYlBu')
if cLevel:
zMax = np.log10(cLevel[1])
zMin = np.log10(cLevel[0])
else:
zMax = (np.ceil(np.log10(np.abs(zPlot).max())))
zMin = (np.floor(np.log10(np.abs(zPlot).min())))
level = np.concatenate((-np.logspace(zMax,zMin-.125,(zMax-zMin)*8+1,endpoint=True),np.logspace(zMin-.125,zMax,(zMax-zMin)*8+1,endpoint=True)))
clevel = np.concatenate((-np.logspace(zMax,zMin,(zMax-zMin)*1+1,endpoint=True),np.logspace(zMin,zMax,(zMax-zMin)*1+1,endpoint=True)))
plotNorm = colors.SymLogNorm(np.abs(level).min(),linscale=0.1)
elif par == 'imag':
zPlot = np.imag(array[flag][indSect])
cmap = plt.get_cmap('Spectral') #('RdYlBu')
if cLevel:
zMax = np.log10(cLevel[1])
zMin = np.log10(cLevel[0])
else:
zMax = (np.ceil(np.log10(np.abs(zPlot).max())))
zMin = (np.floor(np.log10(np.abs(zPlot).min())))
level = np.concatenate((-np.logspace(zMax,zMin-.125,(zMax-zMin)*8+1,endpoint=True),np.logspace(zMin-.125,zMax,(zMax-zMin)*8+1,endpoint=True)))
clevel = np.concatenate((-np.logspace(zMax,zMin,(zMax-zMin)*1+1,endpoint=True),np.logspace(zMin,zMax,(zMax-zMin)*1+1,endpoint=True)))
plotNorm = colors.SymLogNorm(np.abs(level).min(),linscale=0.1)
if colorNorm=='SymLog':
plotNorm = colors.SymLogNorm(np.abs(level).min(),linscale=0.1)
elif colorNorm=='Lin':
plotNorm = colors.Normalize()
elif colorNorm=='Log':
plotNorm = colors.LogNorm()
if contour:
cs = ax.tricontourf(x,y,zPlot,levels=level,cmap=cmap,norm=plotNorm)#,extend='both')
else:
uniX,uniY = np.unique(x),np.unique(y)
X,Y = np.meshgrid(np.append(uniX-25,uniX[-1]+25),np.append(uniY-25,uniY[-1]+25))
cs = ax.pcolor(X,Y,np.reshape(zPlot,(len(uniY),len(uniX))),cmap=cmap,norm=plotNorm)
if colorbar:
csB = plt.colorbar(cs,cax=ax.cax,ticks=clevel,format='%1.2e')
# csB.on_mappable_changed(cs)
ax.set_title(flag+' '+par,fontsize=8)
return cs, csB
return cs,None
def plotPsudoSectNSDiff(ax,sectDict,arrayList,flag,par='abs',colorbar=True,colorNorm='SymLog',cLevel=None,contour=True,mask=None,useLog=False):
def sortInArr(arr):
return np.sort(arr,order=['freq','x','y','z'])
# Find the index for the slice
indSect0 = np.where(sectDict.values()[0]==arrayList[0][sectDict.keys()[0]])
indSect1 = np.where(sectDict.values()[0]==arrayList[1][sectDict.keys()[0]])
# Extract and sort the mats
arr0 = sortInArr(arrayList[0][indSect0])
arr1 = sortInArr(arrayList[1][indSect1])
# Define the plot axes
if 'x' in sectDict.keys()[0]:
x0 = arr0['y']
x1 = arr1['y']
else:
x0 = arr0['x']
x1 = arr1['x']
y0 = arr0['freq']
y1 = arr1['freq']
if par == 'abs':
if useLog:
zPlot = (np.log10(np.abs(arr0[flag])) - np.log10(np.abs(arr1[flag])))/np.log10(np.abs(arr1[flag]))
else:
zPlot = (np.abs(arr0[flag]) - np.abs(arr1[flag]))/np.abs(arr1[flag])
if mask:
maskInd = np.logical_or(np.abs(arr0[flag])< 1e-3,np.abs(arr1[flag]) < 1e-3)
zPlot = np.ma.array(zPlot)
zPlot[maskInd] = mask
cmap = plt.get_cmap('RdYlBu')#seismic)
elif par == 'ares':
arF = 1/(8*np.pi**2*10**(-7))
if useLog:
zPlot = (np.log10((arF/arr0['freq'])*np.abs(arr0[flag])**2) - np.log10((arF/arr1['freq'])*np.abs(arr1[flag])**2))/np.log10((arF/arr1['freq'])*np.abs(arr1[flag])**2)
else:
zPlot = ((arF/arr0['freq'])*np.abs(arr0[flag])**2 - (arF/arr1['freq'])*np.abs(arr1[flag])**2)/((arF/arr1['freq'])*np.abs(arr1[flag])**2)
if mask:
maskInd = np.logical_or(np.abs(arr0[flag])< 1e-3,np.abs(arr1[flag]) < 1e-3)
zPlot = np.ma.array(zPlot)
zPlot[maskInd] = mask
cmap = plt.get_cmap('Spectral')#seismic)
elif par == 'aphs':
if useLog:
zPlot = (np.log10(np.arctan2(arr0[flag].imag,arr0[flag].real)*(180/np.pi)) - np.log10(np.arctan2(arr1[flag].imag,arr1[flag].real)*(180/np.pi)) )/np.log10(np.arctan2(arr1[flag].imag,arr1[flag].real)*(180/np.pi))
else:
zPlot = ( np.arctan2(arr0[flag].imag,arr0[flag].real)*(180/np.pi) - np.arctan2(arr1[flag].imag,arr1[flag].real)*(180/np.pi) )/(np.arctan2(arr1[flag].imag,arr1[flag].real)*(180/np.pi))
if mask:
maskInd = np.logical_or(np.abs(arr0[flag])< 1e-3,np.abs(arr1[flag]) < 1e-3)
zPlot = np.ma.array(zPlot)
zPlot[maskInd] = mask
cmap = plt.get_cmap('Spectral')#seismic)
elif par == 'real':
if useLog:
zPlot = (np.log10(arr0[flag].real) - np.log10(arr1[flag].real))/np.log10(arr1[flag].real)
else:
zPlot = (arr0[flag].real - arr1[flag].real)/arr1[flag].real
if mask:
maskInd = np.logical_or(arr0[flag].real< 1e-3,arr1[flag].real < 1e-3)
zPlot = np.ma.array(zPlot)
zPlot[maskInd] = mask
cmap = plt.get_cmap('Spectral') #('Spectral')
elif par == 'imag':
if useLog:
zPlot = (np.log10(arr0[flag].imag) - np.log10(arr1[flag].imag))/np.log10(arr1[flag].imag)
else:
zPlot = (arr0[flag].imag - arr1[flag].imag)/arr1[flag].imag
if mask:
maskInd = np.logical_or(arr0[flag].imag< 1e-3,arr1[flag].imag < 1e-3)
zPlot = np.ma.array(zPlot)
zPlot[maskInd] = mask
cmap = plt.get_cmap('Spectral') #('RdYlBu')
if cLevel:
zMax = np.log10(cLevel[1])
zMin = np.log10(cLevel[0])
else:
zMax = (np.ceil(np.log10(np.abs(zPlot).max())))
zMin = (np.floor(np.log10(np.abs(zPlot).min())))
if colorNorm=='SymLog':
level = np.concatenate((-np.logspace(zMax,zMin-.125,(zMax-zMin)*8+1,endpoint=True),np.logspace(zMin-.125,zMax,(zMax-zMin)*8+1,endpoint=True)))
clevel = np.concatenate((-np.logspace(zMax,zMin,(zMax-zMin)*1+1,endpoint=True),np.logspace(zMin,zMax,(zMax-zMin)*1+1,endpoint=True)))
plotNorm = colors.SymLogNorm(np.abs(level).min(),linscale=0.1)
elif colorNorm=='Lin':
if cLevel:
level = np.arange(cLevel[0],cLevel[1]+.1,(cLevel[1] - cLevel[0])/50.)
clevel = np.arange(cLevel[0],cLevel[1]+.1,(cLevel[1] - cLevel[0])/10.)
else:
level = np.arange(zPlot.min(),zPlot.max(),(zPlot.max() - zPlot.min())/50.)
clevel = np.arange(zPlot.min(),zPlot.max(),(zPlot.max() - zPlot.min())/10.)
plotNorm = colors.Normalize()
elif colorNorm=='Log':
level = np.logspace(zMin-.125,zMax,(zMax-zMin)*8+1,endpoint=True)
clevel = np.logspace(zMin,zMax,(zMax-zMin)*2+1,endpoint=True)
plotNorm = colors.LogNorm()
if contour:
cs = ax.tricontourf(x0,y0,zPlot*100,levels=level*100,cmap=cmap,norm=plotNorm,extend='both')#,extend='both')
else:
uniX,uniY = np.unique(x0),np.unique(y0)
X,Y = np.meshgrid(np.append(uniX-25,uniX[-1]+25),np.append(uniY-25,uniY[-1]+25))
cs = ax.pcolor(X,Y,np.reshape(zPlot,(len(uniY),len(uniX))),cmap=cmap,norm=plotNorm)
if colorbar:
csB = plt.colorbar(cs,cax=ax.cax,ticks=clevel*100,format='%1.2e')
# csB.on_mappable_changed(cs)
ax.set_title(flag+' '+par + ' diff',fontsize=8)
return cs, csB
return cs,None
SimPEG/MT/Utils/sourceUtils.py
+178
View File
@@ -0,0 +1,178 @@
import SimPEG as simpeg, numpy as np
def homo1DModelSource(mesh,freq,sigma_1d):
'''
Function that calculates and return background fields
:param Simpeg mesh object mesh: Holds information on the discretization
:param float freq: The frequency to solve at
:param np.array sigma_1d: Background model of conductivity to base the calculations on, 1d model.
:rtype: numpy.ndarray (mesh.nE,2)
:return: eBG_bp, E fields for the background model at both polarizations.
'''
# import
from SimPEG.MT.Utils import get1DEfields
# Get a 1d solution for a halfspace background
if mesh.dim == 1:
mesh1d = mesh
elif mesh.dim == 2:
mesh1d = simpeg.Mesh.TensorMesh([mesh.hy],np.array([mesh.x0[1]]))
elif mesh.dim == 3:
mesh1d = simpeg.Mesh.TensorMesh([mesh.hz],np.array([mesh.x0[2]]))
# # Note: Everything is using e^iwt
e0_1d = get1DEfields(mesh1d,sigma_1d,freq)
if mesh.dim == 1:
eBG_px = simpeg.mkvc(e0_1d,2)
eBG_py = -simpeg.mkvc(e0_1d,2) # added a minus to make the results in the correct quadrents.
elif mesh.dim == 2:
ex_px = np.zeros(mesh.vnEx,dtype=complex)
ey_px = np.zeros((mesh.nEy,1),dtype=complex)
for i in np.arange(mesh.vnEx[0]):
ex_px[i,:] = -e0_1d
eBG_px = np.vstack((simpeg.Utils.mkvc(ex_px,2),ey_px))
# Setup y (north) polarization (_py)
ex_py = np.zeros((mesh.nEx,1), dtype='complex128')
ey_py = np.zeros(mesh.vnEy, dtype='complex128')
# Assign the source to ey_py
for i in np.arange(mesh.vnEy[0]):
ey_py[i,:] = e0_1d
# ey_py[1:-1,1:-1,1:-1] = 0
eBG_py = np.vstack((ex_py,simpeg.Utils.mkvc(ey_py,2),ez_py))
elif mesh.dim == 3:
# Setup x (east) polarization (_x)
ex_px = np.zeros(mesh.vnEx,dtype=complex)
ey_px = np.zeros((mesh.nEy,1),dtype=complex)
ez_px = np.zeros((mesh.nEz,1),dtype=complex)
# Assign the source to ex_x
for i in np.arange(mesh.vnEx[0]):
for j in np.arange(mesh.vnEx[1]):
ex_px[i,j,:] = -e0_1d
eBG_px = np.vstack((simpeg.Utils.mkvc(ex_px,2),ey_px,ez_px))
# Setup y (north) polarization (_py)
ex_py = np.zeros((mesh.nEx,1), dtype='complex128')
ey_py = np.zeros(mesh.vnEy, dtype='complex128')
ez_py = np.zeros((mesh.nEz,1), dtype='complex128')
# Assign the source to ey_py
for i in np.arange(mesh.vnEy[0]):
for j in np.arange(mesh.vnEy[1]):
ey_py[i,j,:] = e0_1d
# ey_py[1:-1,1:-1,1:-1] = 0
eBG_py = np.vstack((ex_py,simpeg.Utils.mkvc(ey_py,2),ez_py))
# Return the electric fields
eBG_bp = np.hstack((eBG_px,eBG_py))
return eBG_bp
def analytic1DModelSource(mesh,freq,sigma_1d):
'''
Function that calculates and return background fields
:param Simpeg mesh object mesh: Holds information on the discretization
:param float freq: The frequency to solve at
:param np.array sigma_1d: Background model of conductivity to base the calculations on, 1d model.
:rtype: numpy.ndarray (mesh.nE,2)
:return: eBG_bp, E fields for the background model at both polarizations.
'''
# import
from SimPEG.MT.Utils import getEHfields
# Get a 1d solution for a halfspace background
if mesh.dim == 1:
mesh1d = mesh
elif mesh.dim == 2:
mesh1d = simpeg.Mesh.TensorMesh([mesh.hy],np.array([mesh.x0[1]]))
elif mesh.dim == 3:
mesh1d = simpeg.Mesh.TensorMesh([mesh.hz],np.array([mesh.x0[2]]))
# # Note: Everything is using e^iwt
Eu, Ed, _, _ = getEHfields(mesh1d,sigma_1d,freq,mesh.vectorNz)
# Make the fields into a dictionary of location and the fields
e0_1d = Eu+Ed
E1dFieldDict = dict(zip(mesh.vectorNz,e0_1d))
if mesh.dim == 1:
eBG_px = simpeg.mkvc(e0_1d,2)
eBG_py = -simpeg.mkvc(e0_1d,2) # added a minus to make the results in the correct quadrents.
elif mesh.dim == 2:
ex_px = np.zeros(mesh.vnEx,dtype=complex)
ey_px = np.zeros((mesh.nEy,1),dtype=complex)
for i in np.arange(mesh.vnEx[0]):
ex_px[i,:] = -e0_1d
eBG_px = np.vstack((simpeg.Utils.mkvc(ex_px,2),ey_px))
# Setup y (north) polarization (_py)
ex_py = np.zeros((mesh.nEx,1), dtype='complex128')
ey_py = np.zeros(mesh.vnEy, dtype='complex128')
# Assign the source to ey_py
for i in np.arange(mesh.vnEy[0]):
ey_py[i,:] = e0_1d
# ey_py[1:-1,1:-1,1:-1] = 0
eBG_py = np.vstack((ex_py,simpeg.Utils.mkvc(ey_py,2),ez_py))
elif mesh.dim == 3:
# Setup x (east) polarization (_x)
ex_px = -np.array([E1dFieldDict[i] for i in mesh.gridEx[:,2]]).reshape(-1,1)
ey_px = np.zeros((mesh.nEy,1),dtype=complex)
ez_px = np.zeros((mesh.nEz,1),dtype=complex)
# Construct the full fields
eBG_px = np.vstack((ex_px,ey_px,ez_px))
# Setup y (north) polarization (_py)
ex_py = np.zeros((mesh.nEx,1), dtype='complex128')
ey_py = np.array([E1dFieldDict[i] for i in mesh.gridEy[:,2]]).reshape(-1,1)
ez_py = np.zeros((mesh.nEz,1), dtype='complex128')
# Construct the full fields
eBG_py = np.vstack((ex_py,simpeg.Utils.mkvc(ey_py,2),ez_py))
# Return the electric fields
eBG_bp = np.hstack((eBG_px,eBG_py))
return eBG_bp
# def homo3DModelSource(mesh,model,freq):
# '''
# Function that estimates 1D analytic background fields from a 3D model.
# :param Simpeg mesh object mesh: Holds information on the discretization
# :param float freq: The frequency to solve at
# :param np.array sigma_1d: Background model of conductivity to base the calculations on, 1d model.
# :rtype: numpy.ndarray (mesh.nE,2)
# :return: eBG_bp, E fields for the background model at both polarizations.
# '''
# if mesh.dim < 3:
# raise IOError('Input mesh has to have 3 dimensions.')
# # Get the locations
# a = mesh.gridCC[:,0:2].copy()
# unixy = np.unique(a.view(a.dtype.descr * a.shape[1])).view(float).reshape(-1,2)
# uniz = np.unique(mesh.gridCC[:,2])
# # # Note: Everything is using e^iwt
# # Need to loop thourgh the xy locations, assess the model and calculate the fields at the phusdo cell centers.
# # Then interpolate the cc fields to the edges.
# e0_1d = get1DEfields(mesh1d,sigma_1d,freq)
# elif mesh.dim == 3:
# # Setup x (east) polarization (_x)
# ex_px = np.zeros(mesh.vnEx,dtype=complex)
# ey_px = np.zeros((mesh.nEy,1),dtype=complex)
# ez_px = np.zeros((mesh.nEz,1),dtype=complex)
# # Assign the source to ex_x
# for i in np.arange(mesh.vnEx[0]):
# for j in np.arange(mesh.vnEx[1]):
# ex_px[i,j,:] = -e0_1d
# eBG_px = np.vstack((simpeg.Utils.mkvc(ex_px,2),ey_px,ez_px))
# # Setup y (north) polarization (_py)
# ex_py = np.zeros((mesh.nEx,1), dtype='complex128')
# ey_py = np.zeros(mesh.vnEy, dtype='complex128')
# ez_py = np.zeros((mesh.nEz,1), dtype='complex128')
# # Assign the source to ey_py
# for i in np.arange(mesh.vnEy[0]):
# for j in np.arange(mesh.vnEy[1]):
# ey_py[i,j,:] = e0_1d
# # ey_py[1:-1,1:-1,1:-1] = 0
# eBG_py = np.vstack((ex_py,simpeg.Utils.mkvc(ey_py,2),ez_py))
# # Return the electric fields
# eBG_bp = np.hstack((eBG_px,eBG_py))
# return eBG_bp
SimPEG/MT/Utils/srcUtils.py
+46
View File
@@ -0,0 +1,46 @@
import SimPEG as simpeg, numpy as np
def homo1DModelSource(mesh,freq,m_back):
'''
Function that calculates and return background fields for a 3D mesh and model.
The calculuations use 1D field solution for a vertical slice throught model (south-western most column),
which is assigned at the fields everywhere for the respective polarizations.2
:param Simpeg mesh object mesh: Holds information on the discretization
:param float freq: The frequency to solve at
:param np.array m_back: Background model of conductivity to base the calculations on.
:rtype: numpy.ndarray (mesh.nE,2)
:return: eBG_bp, E fields for the background model at both polarizations.
'''
# import
from SimPEG.MT.Utils import get1DEfields
# Get a 1d solution for a halfspace background
mesh1d = simpeg.Mesh.TensorMesh([mesh.hz],np.array([mesh.x0[2]]))
# Note: Everything is using e^iwt
e0_1d = get1DEfields(mesh1d,mesh.r(m_back,'CC','CC','M')[0,0,:],freq)
# Setup x (east) polarization (_x)
ex_px = np.zeros(mesh.vnEx,dtype=complex)
ey_px = np.zeros((mesh.nEy,1),dtype=complex)
ez_px = np.zeros((mesh.nEz,1),dtype=complex)
# Assign the source to ex_x
for i in np.arange(mesh.vnEx[0]):
for j in np.arange(mesh.vnEx[1]):
ex_px[i,j,:] = -e0_1d
eBG_px = np.vstack((simpeg.Utils.mkvc(ex_px,2),ey_px,ez_px))
# Setup y (north) polarization (_py)
ex_py = np.zeros((mesh.nEx,1), dtype='complex128')
ey_py = np.zeros(mesh.vnEy, dtype='complex128')
ez_py = np.zeros((mesh.nEz,1), dtype='complex128')
# Assign the source to ey_py
for i in np.arange(mesh.vnEy[0]):
for j in np.arange(mesh.vnEy[1]):
ey_py[i,j,:] = e0_1d
# ey_py[1:-1,1:-1,1:-1] = 0
eBG_py = np.vstack((ex_py,simpeg.Utils.mkvc(ey_py,2),ez_py))
# Return the electric fields
eBG_bp = np.hstack((eBG_px,eBG_py))
return eBG_bp
SimPEG/MT/__init__.py
+5
View File
@@ -0,0 +1,5 @@
import Utils
from SurveyMT import Rx, Survey, Data
from FieldsMT import Fields1D_e, Fields3D_e
import Problem1D, Problem2D, Problem3D
import SrcMT
SimPEG/Mesh/DiffOperators.py
+1 -53
View File
@@ -565,58 +565,7 @@ class DiffOperators(object):
return Pbc, Pin, Pout
def unitCellGradx():
doc = """Cell centered Gradient in the x dimension used for
regularization. The gradient operator is square (nC-by-nC)"""
def fget(self):
if self.dim < 3: return None
if getattr(self, '_unitCellGradx', None) is None:
n = self.vnC
gx = ddx(n[0]-1)
gx_square = sp.vstack((gx,gx[-1,:]*-1), format="csr")
self._unitCellGradx = kron3(speye(n[2]), speye(n[1]), gx_square)
return self._unitCellGradx
return locals()
unitCellGradx = property(**unitCellGradx())
def unitCellGrady():
doc = """Cell centered Gradient in they dimension used for
regularization. The gradient operator is square (nC-by-nC)"""
def fget(self):
if self.dim < 3: return None
if getattr(self, '_unitCellGrady', None) is None:
n = self.vnC
gy = ddx(n[1]-1)
gy_square = sp.vstack((gy,gy[-1,:]*-1), format="csr")
self._unitCellGrady = kron3(speye(n[2]), gy_square, speye(n[0]))
return self._unitCellGrady
return locals()
unitCellGrady = property(**unitCellGrady())
def unitCellGradz():
doc = """Cell centered Gradient in they dimension used for
regularization. The gradient operator is square (nC-by-nC)"""
def fget(self):
if self.dim < 3: return None
if getattr(self, '_unitCellGradz', None) is None:
n = self.vnC
gz = ddx(n[2]-1)
gz_square = sp.vstack((gz,gz[-1,:]*-1), format="csr")
self._unitCellGradz = kron3( gz_square , speye(n[1]), speye(n[0]))
return self._unitCellGradz
return locals()
unitCellGradz = property(**unitCellGradz())
# --------------- Averaging ---------------------
@property
@@ -797,4 +746,3 @@ class DiffOperators(object):
kron3(av(n[2]), speye(n[1]+1), av(n[0])),
kron3(speye(n[2]+1), av(n[1]), av(n[0]))), format="csr")
return self._aveN2F
SimPEG/Optimization.py
-15
View File
@@ -990,19 +990,4 @@ class ProjectedGNCG(BFGS, Minimize, Remember):
cgFlag = 1
# End CG Iterations
# Take a gradient step on the active cells if exist
if temp != self.xc.size:
rhs_a = (Active) * -self.g
dm_i = max( abs( delx ) )
dm_a = max( abs(rhs_a) )
delx = delx + rhs_a * dm_i / dm_a /10.
# Only keep gradients going in the right direction on the active set
indx = ((self.xc<=self.lower) & (delx < 0)) | ((self.xc>=self.upper) & (delx > 0))
delx[indx] = 0.
return delx
SimPEG/Regularization.py
-209
View File
@@ -281,212 +281,3 @@ class Tikhonov(BaseRegularization):
r = self.W * ( self.mapping * (m - self.mref) )
out = mD.T * ( self.W.T * r )
return out
class Simple(BaseRegularization):
"""
Only for tensor mesh
"""
smoothModel = True #: SMOOTH and SMOOTH_MOD_DIF options
alpha_s = Utils.dependentProperty('_alpha_s', 1.0, ['_W', '_Ws'], "Smallness weight")
alpha_x = Utils.dependentProperty('_alpha_x', 1.0, ['_W', '_Wx'], "Weight for the first derivative in the x direction")
alpha_y = Utils.dependentProperty('_alpha_y', 1.0, ['_W', '_Wy'], "Weight for the first derivative in the y direction")
alpha_z = Utils.dependentProperty('_alpha_z', 1.0, ['_W', '_Wz'], "Weight for the first derivative in the z direction")
def __init__(self, mesh, mapping=None, **kwargs):
BaseRegularization.__init__(self, mesh, mapping=mapping, **kwargs)
@property
def Ws(self):
"""Regularization matrix Ws"""
if getattr(self,'_Ws', None) is None:
self._Ws = Utils.sdiag((self.mesh.vol*self.alpha_s)**0.5)
return self._Ws
@property
def Wx(self):
"""Regularization matrix Wx"""
if getattr(self, '_Wx', None) is None:
self._Wx = Utils.sdiag((self.mesh.vol*self.alpha_x)**0.5)*self.mesh.unitCellGradx
return self._Wx
@property
def Wy(self):
"""Regularization matrix Wy"""
if getattr(self, '_Wy', None) is None:
self._Wy = Utils.sdiag((self.mesh.vol*self.alpha_y)**0.5)*self.mesh.unitCellGrady
return self._Wy
@property
def Wz(self):
"""Regularization matrix Wz"""
if getattr(self, '_Wz', None) is None:
self._Wz = Utils.sdiag((self.mesh.vol*self.alpha_z)**0.5)*self.mesh.unitCellGradz
return self._Wz
@property
def Wsmooth(self):
"""Full smoothness regularization matrix W"""
if getattr(self, '_Wsmooth', None) is None:
wlist = (self.Wx,)
if self.mesh.dim > 1:
wlist += (self.Wy,)
if self.mesh.dim > 2:
wlist += (self.Wz,)
self._Wsmooth = sp.vstack(wlist)
return self._Wsmooth
@property
def W(self):
"""Full regularization matrix W"""
if getattr(self, '_W', None) is None:
wlist = (self.Ws, self.Wsmooth)
self._W = sp.vstack(wlist)
return self._W
@Utils.timeIt
def eval(self, m):
if self.smoothModel == True:
r1 = self.Wsmooth * ( self.mapping * (m) )
r2 = self.Ws * ( self.mapping * (m - self.mref) )
return 0.5*(r1.dot(r1)+r2.dot(r2))
elif self.smoothModel == False:
r = self.W * ( self.mapping * (m - self.mref) )
return 0.5*r.dot(r)
@Utils.timeIt
def evalDeriv(self, m):
"""
The regularization is:
.. math::
R(m) = \\frac{1}{2}\mathbf{(m-m_\\text{ref})^\\top W^\\top W(m-m_\\text{ref})}
So the derivative is straight forward:
.. math::
R(m) = \mathbf{W^\\top W (m-m_\\text{ref})}
"""
if self.smoothModel == True:
mD1 = self.mapping.deriv(m)
mD2 = self.mapping.deriv(m - self.mref)
r1 = self.Wsmooth * ( self.mapping * (m))
r2 = self.Ws * ( self.mapping * (m - self.mref) )
out1 = mD1.T * ( self.Wsmooth.T * r1 )
out2 = mD2.T * ( self.Ws.T * r2 )
out = out1+out2
elif self.smoothModel == False:
mD = self.mapping.deriv(m - self.mref)
r = self.W * ( self.mapping * (m - self.mref) )
out = mD.T * ( self.W.T * r )
return out
class SparseRegularization(Simple):
eps = 1e-1
m = None
gamma = 1.
p = 0.
qx = 2.
qy = 2.
qz = 2.
def __init__(self, mesh, mapping=None, **kwargs):
Simple.__init__(self, mesh, mapping=mapping, **kwargs)
@property
def Wsmooth(self):
"""Full smoothness regularization matrix W"""
if getattr(self, '_Wsmooth', None) is None:
wlist = (self.Wx, self.Wxx)
if self.mesh.dim > 1:
wlist += (self.Wy, self.Wyy)
if self.mesh.dim > 2:
wlist += (self.Wz, self.Wzz)
self._Wsmooth = sp.vstack(wlist)
return self._Wsmooth
@property
def W(self):
"""Full regularization matrix W"""
if getattr(self, '_W', None) is None:
wlist = (self.Ws, self.Wsmooth)
self._W = sp.vstack(wlist)
return self._W
@property
def Ws(self):
"""Regularization matrix Ws"""
if getattr(self, 'm', None) is None:
self.Rs = Utils.speye(self.mesh.nC)
else:
f_m = self.m
self.rs = self.R(f_m , self.p, self.eps)
#print "Min rs: " + str(np.max(self.rs)) + "Max rs: " + str(np.min(self.rs))
self.Rs = Utils.sdiag( self.rs )
self._Ws = Utils.sdiag((self.mesh.vol*self.alpha_s*self.gamma)**0.5)*self.Rs
return self._Ws
@property
def Wx(self):
"""Regularization matrix Wx"""
if getattr(self, 'm', None) is None:
self.Rx = Utils.speye(self.mesh.unitCellGradx.shape[0])
else:
f_m = self.mesh.unitCellGradx * self.m
self.rx = self.R( f_m , self.qx, self.eps)
self.Rx = Utils.sdiag( self.rx )
if getattr(self, '_Wx', None) is None:
self._Wx = Utils.sdiag((self.mesh.vol*self.alpha_x*self.gamma)**0.5)*self.Rx*self.mesh.unitCellGradx
return self._Wx
@property
def Wy(self):
"""Regularization matrix Wy"""
if getattr(self, 'm', None) is None:
self.Ry = Utils.speye(self.mesh.unitCellGrady.shape[0])
else:
f_m = self.mesh.unitCellGrady * self.m
self.ry = self.R( f_m , self.qy, self.eps)
self.Ry = Utils.sdiag( self.ry )
if getattr(self, '_Wy', None) is None:
self._Wy = Utils.sdiag((self.mesh.vol*self.alpha_y*self.gamma)**0.5)*self.Ry*self.mesh.unitCellGrady
return self._Wy
@property
def Wz(self):
"""Regularization matrix Wz"""
if getattr(self, 'm', None) is None:
self.Rz = Utils.speye(self.mesh.unitCellGradz.shape[0])
else:
f_m = self.mesh.unitCellGradz * self.m
self.rz = self.R( f_m , self.qz, self.eps)
self.Rz = Utils.sdiag( self.rz )
if getattr(self, '_Wz', None) is None:
self._Wz = Utils.sdiag((self.mesh.vol*self.alpha_z*self.gamma)**0.5)*self.Rz*self.mesh.unitCellGradz
return self._Wz
def R(self, f_m , p, dec):
eta = (self.eps**(1-p/2.))**0.5
r = eta / (f_m**2.+self.eps**2.)**((1-p/2.)/2.)
return r
SimPEG/Utils/matutils.py
+1 -2
View File
@@ -2,7 +2,6 @@ import numpy as np
import scipy.sparse as sp
from codeutils import isScalar
def mkvc(x, numDims=1):
"""Creates a vector with the number of dimension specified
@@ -41,7 +40,7 @@ def mkvc(x, numDims=1):
def sdiag(h):
"""Sparse diagonal matrix"""
if isinstance(h, Zero):
return h
return Zero()
return sp.spdiags(mkvc(h), 0, h.size, h.size, format="csr")
docs/em/api_FDEM.rst
+62 -42
View File
@@ -19,14 +19,14 @@ Electromagnetic phenomena are governed by Maxwell's equations. They describe the
Fourier Transform Convention
----------------------------
In order to examine Maxwell's equations in the frequency domain, we must first define our choice of harmonic time-dependence by choosing a Fourier transform convention. We use the \\(e^{i \\omega t} \\) convention, so we define our Fourier Transform pair as
In order to examine Maxwell's equations in the frequency domain, we must first define our choice of harmonic time-dependence by choosing a Fourier transform convention. We use the :math:`e^{i \omega t}` convention, so we define our Fourier Transform pair as
.. math ::
F(\omega) = \int_{-\infty}^{\infty} f(t) e^{- i \omega t} dt \\
F(\omega) = \int_{-\infty}^{\infty} f(t) e^{- i \omega t} dt \\
f(t) = \frac{1}{2\pi}\int_{-\infty}^{\infty} F(\omega) e^{i \omega t} d \omega
f(t) = \frac{1}{2\pi}\int_{-\infty}^{\infty} F(\omega) e^{i \omega t} d \omega
where \\(\\omega\\) is angular frequency, \\(t\\) is time, \\(F(\\omega)\\) is the function defined in the frequency domain and \\(f(t)\\) is the function defined in the time domain.
where :math:`\omega` is angular frequency, :math:`t` is time, :math:`F(\omega)` is the function defined in the frequency domain and :math:`f(t)` is the function defined in the time domain.
Maxwell's Equations
@@ -34,44 +34,46 @@ Maxwell's Equations
In the frequency domain, Maxwell's equations are given by
.. math ::
\curl \vec{E} = - i \omega \vec{B} \\
\curl \vec{E} + i \omega \vec{B} = \vec{S_m}\\
\curl \vec{H} = \vec{J} + i \omega \vec{D} + \vec{S} \\
\curl \vec{H} - \vec{J} - i \omega \vec{D} = \vec{S_e} \\
\div \vec{B} = 0 \\
\div \vec{B} = 0 \\
\div \vec{D} = \rho_f
\div \vec{D} = \rho_f
where:
- \\(\\vec{E}\\) : electric field (\\(V/m\\))
- \\(\\vec{H}\\) : magnetic field (\\(A/m\\))
- \\(\\vec{B}\\) : magnetic flux density (\\(Wb/m^2\\))
- \\(\\vec{D}\\) : electric displacement / electric flux density (\\(C/m^2\\))
- \\(\\vec{J}\\) : electric current density (\\(A/m^2\\))
- \\(\\rho_f\\) : free charge density
- :math:`\vec{E}` : electric field (:math:`V/m` )
- :math:`\vec{H}` : magnetic field (:math:`A/m` )
- :math:`\vec{B}` : magnetic flux density (:math:`Wb/m^2` )
- :math:`\vec{D}` : electric displacement / electric flux density (:math:`C/m^2` )
- :math:`\vec{J}` : electric current density (:math:`A/m^2` )
- :math:`\vec{S_m}` : magnetic source term (:math:`V/m^2` )
- :math:`\vec{S_e}` : electric source term (:math:`A/m^2` )
- :math:`\rho_f` : free charge density (:math:`\Omega m` )
The source term is \\(\\vec{S}\\)
Constitutive Relations
----------------------
The fields and fluxes are related through the constitutive relations. At each frequency, they are given by
.. math ::
\vec{J} = \sigma \vec{E} \\
\vec{J} = \sigma \vec{E} \\
\vec{B} = \mu \vec{H} \\
\vec{B} = \mu \vec{H} \\
\vec{D} = \varepsilon \vec{E}
\vec{D} = \varepsilon \vec{E}
where:
- \\(\\sigma\\) : electrical conductivity \\(S/m\\)
- \\(\\mu\\) : magnetic permeability \\(H/m\\)
- \\(\\varepsilon\\) : dielectric permittivity \\(F/m\\)
- :math:`\sigma` : electrical conductivity (:math:`S/m`)
- :math:`\mu` : magnetic permeability (:math:`H/m`)
- :math:`\varepsilon` : dielectric permittivity (:math:`F/m`)
\\(\\sigma\\), \\(\\mu\\), \\(\\varepsilon\\) are physical properties which depend on the material. \\(\\sigma\\) describes how easily electric current passes through a material, \\(\\mu\\) describes how easily a material is magnetized, and \\(\\varepsilon\\) describes how easily a material is electrically polarized. In most geophysical applications of EM, \\(\\sigma\\) is the the primary physical property of interest, and \\(\\mu\\), \\(\\varepsilon\\) are assumed to have their free-space values \\(\\mu_0 = 4\\pi \\times 10^{-7} H/m \\), \\(\\varepsilon_0 = 8.85 \\times 10^{-12} F/m\\)
:math:`\sigma`, :math:`\mu`, :math:`\varepsilon` are physical properties which depend on the material. :math:`\sigma` describes how easily electric current passes through a material, :math:`\mu` describes how easily a material is magnetized, and :math:`\varepsilon` describes how easily a material is electrically polarized. In most geophysical applications of EM, :math:`\sigma` is the the primary physical property of interest, and :math:`\mu`, :math:`\varepsilon` are assumed to have their free-space values :math:`\mu_0 = 4\pi \times 10^{-7} H/m` , :math:`\varepsilon_0 = 8.85 \times 10^{-12} F/m`
Quasi-static Approximation
@@ -80,8 +82,8 @@ Quasi-static Approximation
For the frequency range typical of most geophysical surveys, the contribution of the electric displacement is negligible compared to the electric current density. In this case, we use the Quasi-static approximation and assume that this term can be neglected, giving
.. math ::
\nabla \times \vec{E} = -i \omega \vec{B} \\
\nabla \times \vec{H} = \vec{J} + \vec{S}
\nabla \times \vec{E} + i \omega \vec{B} = \vec{S_m} \\
\nabla \times \vec{H} - \vec{J} = \vec{S_e}
Implementation in SimPEG.EM
@@ -90,14 +92,14 @@ Implementation in SimPEG.EM
We consider two formulations in SimPEG.EM, both first-order and both in terms of one field and one flux. We allow for the definition of magnetic and electric sources (see for example: Ward and Hohmann, starting on page 144). The E-B formulation is in terms of the electric field and the magnetic flux:
.. math ::
\nabla \times \vec{E} + i \omega \vec{B} = \vec{S}_m \\
\nabla \times \mu^{-1} \vec{B} - \sigma \vec{E} = \vec{S}_e
\nabla \times \vec{E} + i \omega \vec{B} = \vec{S}_m \\
\nabla \times \mu^{-1} \vec{B} - \sigma \vec{E} = \vec{S}_e
The H-J formulation is in terms of the current density and the magnetic field:
.. math ::
\nabla \times \sigma^{-1} \vec{J} + i \omega \mu \vec{H} = \vec{S}_m \\
\nabla \times \vec{H} - \vec{J} = \vec{S}_e
\nabla \times \sigma^{-1} \vec{J} + i \omega \mu \vec{H} = \vec{S}_m \\
\nabla \times \vec{H} - \vec{J} = \vec{S}_e
Discretizing
@@ -106,34 +108,34 @@ For both formulations, we use a finite volume discretization
and discretize fields on cell edges, fluxes on cell faces and
physical properties in cell centers. This is particularly
important when using symmetry to reduce the dimensionality of a problem
(for instance on a 2D CylMesh, there are \\(r\\), \\(z\\) faces and \\(\\theta\\) edges)
(for instance on a 2D CylMesh, there are :math:`r`, :math:`z` faces and :math:`\theta` edges)
.. figure:: ../images/finitevolrealestate.png
:align: center
:scale: 60 %
:align: center
:scale: 60 %
For the two formulations, the discretization of the physical properties, fields and fluxes are summarized below.
.. figure:: ../images/ebjhdiscretizations.png
:align: center
:scale: 60 %
:align: center
:scale: 60 %
Note that resistivity is the inverse of conductivity, \\(\\rho = \\sigma^{-1}\\).
Note that resistivity is the inverse of conductivity, :math:`\rho = \sigma^{-1}`.
E-B Formulation:
****************
E-B Formulation
---------------
.. math ::
\mathbf{C} \mathbf{e} + i \omega \mathbf{b} = \mathbf{s_m} \\
\mathbf{C^T} \mathbf{M^f_{\mu^{-1}}} \mathbf{b} - \mathbf{M^e_\sigma} \mathbf{e} = \mathbf{M^e} \mathbf{s_e}
\mathbf{C} \mathbf{e} + i \omega \mathbf{b} = \mathbf{s_m} \\
\mathbf{C^T} \mathbf{M^f_{\mu^{-1}}} \mathbf{b} - \mathbf{M^e_\sigma} \mathbf{e} = \mathbf{M^e} \mathbf{s_e}
H-J Formulation:
****************
H-J Formulation
---------------
.. math ::
\mathbf{C^T} \mathbf{M^f_\rho} \mathbf{j} + i \omega \mathbf{M^e_\mu} \mathbf{h} = \mathbf{M^e} \mathbf{s_m} \\
\mathbf{C} \mathbf{h} - \mathbf{j} = \mathbf{s_e}
\mathbf{C^T} \mathbf{M^f_\rho} \mathbf{j} + i \omega \mathbf{M^e_\mu} \mathbf{h} = \mathbf{M^e} \mathbf{s_m} \\
\mathbf{C} \mathbf{h} - \mathbf{j} = \mathbf{s_e}
.. Forward Problem
@@ -144,6 +146,10 @@ H-J Formulation:
API
===
FDEM Problem
------------
.. automodule:: SimPEG.EM.FDEM.FDEM
:show-inheritance:
:members:
@@ -157,3 +163,17 @@ FDEM Survey
:show-inheritance:
:members:
:undoc-members:
.. automodule:: SimPEG.EM.FDEM.SrcFDEM
:show-inheritance:
:members:
:undoc-members:
FDEM Fields
-----------
.. automodule:: SimPEG.EM.FDEM.FieldsFDEM
:show-inheritance:
:members:
:undoc-members:
docs/em/api_TDEM.rst
+299
View File
@@ -48,6 +48,305 @@
\newcommand{\I}{\vec{I}}
Time Domain Electromagnetics
****************************
.. _api_TDEM_derivation:
Time-Domain EM Derivation
=========================
The following shows the derivation for the TDEM problem. We use the b-formulation below.
(More to come soon..!)
Sensitivity Calculation
-----------------------
.. math::
\begin{align}
\dcurl \e^{(t+1)} + \frac{\b^{(t+1)} - \b^{(t)}}{\delta t} = 0 \\
\dcurl^\top \MfMui \b^{(t+1)} - \MeSig \e^{(t+1)} = \Me \j_s^{(t+1)}
\end{align}
Using Gauss-Newton to solve the inverse problem requires the ability to calculate the product of the
Jacobian and a vector, as well as the transpose of the Jacobian times a vector.
The above system can be rewritten as:
.. math::
\begin{align}
\mathbf{A} \u^{(t+1)} + \mathbf{B} \u^{(t)}= \s^{(t+1)}
\end{align}
where
.. math::
\begin{align}
\mathbf{A} =
\left[
\begin{array}{cc}
\frac{1}{\delta t} \MfMui & \MfMui\dcurl \\
\dcurl^\top \MfMui & -\MeSig
\end{array}
\right] \\
\mathbf{B} =
\left[
\begin{array}{cc}
-\frac{1}{\delta t} \MfMui & 0 \\
0 & 0
\end{array}
\right] \\
\u^{(k)} = \left[
\begin{array}{c}
\b^{(k)}\\
\e^{(k)}
\end{array}
\right] \\
\s^{(k)} = \left[
\begin{array}{c}
0\\
\Me \j^{(k)}_s
\end{array}
\right]
\end{align}
.. note::
Here we have multiplied through by \\(\\MfMui\\) to make A and B symmetric!
The entire time dependent system can be written in a single matrix expression
.. math::
\begin{align}
\hat{\mathbf{A}} \hat{u} = \hat{s}
\end{align}
where
.. math::
\begin{align}
\mathbf{\hat{A}} = \left[
\begin{array}{cccc}
A & 0 & & \\
B & A & & \\
& \ddots & \ddots & \\
& & B & A
\end{array}
\right] \\
\hat{u} = \left[
\begin{array}{c}
\u^{(1)} \\
\u^{(2)} \\
\vdots \\
\u^{(N)}
\end{array} \right]\\
\hat{s} = \left[
\begin{array}{c}
\s^{(1)} - \mathbf{B} \u^{(0)} \\
\s^{(2)} \\
\vdots \\
\s^{(N)}
\end{array}
\right]
\end{align}
For the fields \\(\\u\\), the measured data is given by
.. math::
\begin{align}
\vec{d} = \mathbf{Q} \u
\end{align}
The sensitivity matrix **J** is then defined as
.. math::
\begin{align}
\mathbf{J} = \mathbf{Q} \frac{\partial \u}{\partial \sigma}
\end{align}
Defining the function \\(\\c(m,\\u)\\) to be
.. math::
\begin{align}
\vec{c}(m,\u) = \hat{\mathbf{A}} \vec{u} - \vec{q} = \vec{0}
\end{align}
then
.. math::
\begin{align}
\frac{\partial \vec{c}}{\partial m} \partial m
+ \frac{\partial \vec{c}}{\partial \u} \partial \vec{u} = 0
\end{align}
or
.. math::
\begin{align}
\frac{\partial \vec{u}}{\partial m} = -\left(\frac{\partial \vec{c}}{\partial \u} \right)^{-1} \frac{\partial \vec{c}}{\partial m}
\end{align}
Differentiating, we find that
.. math::
\begin{align}
\frac{\partial \vec{c}}{\partial \hat{u}} = \hat{\mathbf{A}}
\end{align}
and
.. math::
\begin{align}
\frac{\partial \vec{c}}{\partial \sigma} = \mathbf{G}_\sigma =
\left[
\begin{array}{c}
g_\sigma^{(1)}\\
g_\sigma^{(2)}\\
\vdots \\
g_\sigma^{(N)}
\end{array}
\right]
\end{align}
with
.. math::
\begin{align}
g_\sigma^{(n)} =
\left[
\begin{array}{c}
\mathbf{0} \\
- \diag{\e^{(n)}} \Ace \diag{\vec{V}}
\end{array}
\right]
\end{align}
Implementing **J** times a vector
---------------------------------
Multiplying **J** onto a vector can be broken into three steps
* Compute \\(\\vec{p} = \\mathbf{G}m\\)
* Solve \\(\\hat{\\mathbf{A}} \\vec{y} = \\vec{p}\\)
* Compute \\(\\vec{w} = -\\mathbf{Q} \\vec{y}\\)
.. math::
\begin{align}
\vec{p}^{(n)} = \left[
\begin{array}{c}
\vec{p}_b^{(n)} \\
\vec{p}_e^{(n)}
\end{array}
\right] \\
\vec{p}_b^{(n)} = 0 \\
\vec{p}_e^{(n)} = - \diag{\e^{(n)}} \Ace \diag{V} m
\end{align}
For all time steps:
.. math::
\begin{align}
\frac{1}{\delta t} \MfMui\vec{y}_{b}^{(t+1)} + \MfMui\dcurl \vec{y}_{e}^{(t+1)}
- \frac{1}{\delta t} \MfMui \vec{y}_{b}^{(t)}
= \vec{p}_b^{(t+1)} \\
\dcurl^\top \MfMui \vec{y}_b^{(t+1)} - \MeSig \vec{y}_e^{(t+1)} = \vec{p}_e^{(t+1)}
\end{align}
and
.. math::
\begin{align}
\left( \MfMui \dcurl \MeSig^{-1} \dcurl^\top \MfMui + \frac{1}{\delta t} \MfMui \right) \vec{y}_{b}^{(t+1)} =
\frac{1}{\delta t} \MfMui \vec{y}_b^{(t)}
+ \MfMui \dcurl \MeSig^{-1} \vec{p}_e^{(t+1)} + \vec{p}_b^{(t+1)} \\
\vec{y}_e^{(t+1)} = \MeSig^{-1} \dcurl^\top \MfMui \vec{y}_b^{(t+1)} - \MeSig^{-1} \vec{p}_e^{(t+1)}
\end{align}
.. note::
For the first time step, \\\(t=0\\\), the term: \\\(\\frac{1}{\\delta t} \\MfMui \\vec{y}_b^{(0)}\\\) is zero.
Implementing **J** transpose times a vector
-------------------------------------------
Multiplying \\(\\mathbf{J}^\\top\\) onto a vector can be broken into three steps
* Compute \\(\\vec{p} = \\mathbf{Q}^\\top \\vec{v}\\)
* Solve \\(\\hat{\\mathbf{A}}^\\top \\vec{y} = \\vec{p}\\)
* Compute \\(\\vec{w} = -\\mathbf{G}^\\top y\\)
.. math::
\mathbf{\hat{A}}^\top = \left[
\begin{array}{cccc}
A & B & & \\
& \ddots & \ddots & \\
& & A & B \\
& & 0 & A
\end{array}
\right]
For the all time-steps (going backwards in time):
.. math::
A \vec{y}^{(t)} + B \vec{y}^{(t+1)} = \vec{p}^{(t)}
.. math::
\begin{align}
\frac{1}{\delta t} \MfMui\vec{y}_{b}^{(t)} + \MfMui\dcurl \vec{y}_{e}^{(t)}
- \frac{1}{\delta t} \MfMui \vec{y}_{b}^{(t+1)}
= \vec{p}_b^{(t)} \\
\dcurl^\top \MfMui \vec{y}_b^{(t)} - \MeSig \vec{y}_e^{(t)} = \vec{p}_e^{(t)}
\end{align}
and
.. math::
\begin{align}
\left( \MfMui \dcurl \MeSig^{-1} \dcurl^\top \MfMui + \frac{1}{\delta t} \MfMui \right) \vec{y}_{b}^{(t)} =
\frac{1}{\delta t} \MfMui \vec{y}_b^{(t+1)}
+ \MfMui \dcurl \MeSig^{-1} \vec{p}_e^{(t)} + \vec{p}_b^{(t)} \\
\vec{y}_e^{(t)} = \MeSig^{-1} \dcurl^\top \MfMui \vec{y}_b^{(t)} - \MeSig^{-1} \vec{p}_e^{(t)}
\end{align}
.. note::
For the last time step, \\\(t=N\\\), the term: \\\(\\frac{1}{\\delta t} \\MfMui \\vec{y}_b^{(N+1)}\\\) is zero.
TDEM - B formulation
====================
docs/em/api_TDEM_derivation.rst
-341
View File
@@ -1,341 +0,0 @@
.. _api_TDEM_derivation:
.. math::
\renewcommand{\div}{\nabla\cdot\,}
\newcommand{\grad}{\vec \nabla}
\newcommand{\curl}{{\vec \nabla}\times\,}
\newcommand {\J}{{\vec J}}
\renewcommand{\H}{{\vec H}}
\newcommand {\E}{{\vec E}}
\newcommand{\dcurl}{{\mathbf C}}
\newcommand{\dgrad}{{\mathbf G}}
\newcommand{\Acf}{{\mathbf A_c^f}}
\newcommand{\Ace}{{\mathbf A_c^e}}
\renewcommand{\S}{{\mathbf \Sigma}}
\newcommand{\St}{{\mathbf \Sigma_\tau}}
\newcommand{\T}{{\mathbf T}}
\newcommand{\Tt}{{\mathbf T_\tau}}
\newcommand{\diag}[1]{\,{\sf diag}\left( #1 \right)}
\newcommand{\M}{{\mathbf M}}
\newcommand{\MfMui}{{\M^f_{\mu^{-1}}}}
\newcommand{\MeSig}{{\M^e_\sigma}}
\newcommand{\MeSigInf}{{\M^e_{\sigma_\infty}}}
\newcommand{\MeSigO}{{\M^e_{\sigma_0}}}
\newcommand{\Me}{{\M^e}}
\newcommand{\Mes}[1]{{\M^e_{#1}}}
\newcommand{\Mee}{{\M^e_e}}
\newcommand{\Mej}{{\M^e_j}}
\newcommand{\BigO}[1]{\mathcal{O}\bigl(#1\bigr)}
\newcommand{\bE}{\mathbf{E}}
\newcommand{\bH}{\mathbf{H}}
\newcommand{\B}{\vec{B}}
\newcommand{\D}{\vec{D}}
\renewcommand{\H}{\vec{H}}
\newcommand{\s}{\vec{s}}
\newcommand{\bfJ}{\bf{J}}
\newcommand{\vecm}{\vec m}
\renewcommand{\Re}{\mathsf{Re}}
\renewcommand{\Im}{\mathsf{Im}}
\renewcommand {\j} { {\vec j} }
\newcommand {\h} { {\vec h} }
\renewcommand {\b} { {\vec b} }
\newcommand {\e} { {\vec e} }
\newcommand {\c} { {\vec c} }
\renewcommand {\d} { {\vec d} }
\renewcommand {\u} { {\vec u} }
\newcommand{\I}{\vec{I}}
Time-Domain EM Derivation
*************************
The following shows the derivation for the TDEM problem. We use the b-formulation below.
(More to come soon..!)
Sensitivity Calculation
=======================
.. math::
\begin{align}
\dcurl \e^{(t+1)} + \frac{\b^{(t+1)} - \b^{(t)}}{\delta t} = 0 \\
\dcurl^\top \MfMui \b^{(t+1)} - \MeSig \e^{(t+1)} = \Me \j_s^{(t+1)}
\end{align}
Using Gauss-Newton to solve the inverse problem requires the ability to calculate the product of the
Jacobian and a vector, as well as the transpose of the Jacobian times a vector.
The above system can be rewritten as:
.. math::
\begin{align}
\mathbf{A} \u^{(t+1)} + \mathbf{B} \u^{(t)}= \s^{(t+1)}
\end{align}
where
.. math::
\begin{align}
\mathbf{A} =
\left[
\begin{array}{cc}
\frac{1}{\delta t} \MfMui & \MfMui\dcurl \\
\dcurl^\top \MfMui & -\MeSig
\end{array}
\right] \\
\mathbf{B} =
\left[
\begin{array}{cc}
-\frac{1}{\delta t} \MfMui & 0 \\
0 & 0
\end{array}
\right] \\
\u^{(k)} = \left[
\begin{array}{c}
\b^{(k)}\\
\e^{(k)}
\end{array}
\right] \\
\s^{(k)} = \left[
\begin{array}{c}
0\\
\Me \j^{(k)}_s
\end{array}
\right]
\end{align}
.. note::
Here we have multiplied through by \\(\\MfMui\\) to make A and B symmetric!
The entire time dependent system can be written in a single matrix expression
.. math::
\begin{align}
\hat{\mathbf{A}} \hat{u} = \hat{s}
\end{align}
where
.. math::
\begin{align}
\mathbf{\hat{A}} = \left[
\begin{array}{cccc}
A & 0 & & \\
B & A & & \\
& \ddots & \ddots & \\
& & B & A
\end{array}
\right] \\
\hat{u} = \left[
\begin{array}{c}
\u^{(1)} \\
\u^{(2)} \\
\vdots \\
\u^{(N)}
\end{array} \right]\\
\hat{s} = \left[
\begin{array}{c}
\s^{(1)} - \mathbf{B} \u^{(0)} \\
\s^{(2)} \\
\vdots \\
\s^{(N)}
\end{array}
\right]
\end{align}
For the fields \\(\\u\\), the measured data is given by
.. math::
\begin{align}
\vec{d} = \mathbf{Q} \u
\end{align}
The sensitivity matrix **J** is then defined as
.. math::
\begin{align}
\mathbf{J} = \mathbf{Q} \frac{\partial \u}{\partial \sigma}
\end{align}
Defining the function \\(\\c(m,\\u)\\) to be
.. math::
\begin{align}
\vec{c}(m,\u) = \hat{\mathbf{A}} \vec{u} - \vec{q} = \vec{0}
\end{align}
then
.. math::
\begin{align}
\frac{\partial \vec{c}}{\partial m} \partial m
+ \frac{\partial \vec{c}}{\partial \u} \partial \vec{u} = 0
\end{align}
or
.. math::
\begin{align}
\frac{\partial \vec{u}}{\partial m} = -\left(\frac{\partial \vec{c}}{\partial \u} \right)^{-1} \frac{\partial \vec{c}}{\partial m}
\end{align}
Differentiating, we find that
.. math::
\begin{align}
\frac{\partial \vec{c}}{\partial \hat{u}} = \hat{\mathbf{A}}
\end{align}
and
.. math::
\begin{align}
\frac{\partial \vec{c}}{\partial \sigma} = \mathbf{G}_\sigma =
\left[
\begin{array}{c}
g_\sigma^{(1)}\\
g_\sigma^{(2)}\\
\vdots \\
g_\sigma^{(N)}
\end{array}
\right]
\end{align}
with
.. math::
\begin{align}
g_\sigma^{(n)} =
\left[
\begin{array}{c}
\mathbf{0} \\
- \diag{\e^{(n)}} \Ace \diag{\vec{V}}
\end{array}
\right]
\end{align}
Implementing **J** times a vector
=================================
Multiplying **J** onto a vector can be broken into three steps
* Compute \\(\\vec{p} = \\mathbf{G}m\\)
* Solve \\(\\hat{\\mathbf{A}} \\vec{y} = \\vec{p}\\)
* Compute \\(\\vec{w} = -\\mathbf{Q} \\vec{y}\\)
.. math::
\begin{align}
\vec{p}^{(n)} = \left[
\begin{array}{c}
\vec{p}_b^{(n)} \\
\vec{p}_e^{(n)}
\end{array}
\right] \\
\vec{p}_b^{(n)} = 0 \\
\vec{p}_e^{(n)} = - \diag{\e^{(n)}} \Ace \diag{V} m
\end{align}
For all time steps:
.. math::
\begin{align}
\frac{1}{\delta t} \MfMui\vec{y}_{b}^{(t+1)} + \MfMui\dcurl \vec{y}_{e}^{(t+1)}
- \frac{1}{\delta t} \MfMui \vec{y}_{b}^{(t)}
= \vec{p}_b^{(t+1)} \\
\dcurl^\top \MfMui \vec{y}_b^{(t+1)} - \MeSig \vec{y}_e^{(t+1)} = \vec{p}_e^{(t+1)}
\end{align}
and
.. math::
\begin{align}
\left( \MfMui \dcurl \MeSig^{-1} \dcurl^\top \MfMui + \frac{1}{\delta t} \MfMui \right) \vec{y}_{b}^{(t+1)} =
\frac{1}{\delta t} \MfMui \vec{y}_b^{(t)}
+ \MfMui \dcurl \MeSig^{-1} \vec{p}_e^{(t+1)} + \vec{p}_b^{(t+1)} \\
\vec{y}_e^{(t+1)} = \MeSig^{-1} \dcurl^\top \MfMui \vec{y}_b^{(t+1)} - \MeSig^{-1} \vec{p}_e^{(t+1)}
\end{align}
.. note::
For the first time step, \\\(t=0\\\), the term: \\\(\\frac{1}{\\delta t} \\MfMui \\vec{y}_b^{(0)}\\\) is zero.
Implementing **J** transpose times a vector
===========================================
Multiplying \\(\\mathbf{J}^\\top\\) onto a vector can be broken into three steps
* Compute \\(\\vec{p} = \\mathbf{Q}^\\top \\vec{v}\\)
* Solve \\(\\hat{\\mathbf{A}}^\\top \\vec{y} = \\vec{p}\\)
* Compute \\(\\vec{w} = -\\mathbf{G}^\\top y\\)
.. math::
\mathbf{\hat{A}}^\top = \left[
\begin{array}{cccc}
A & B & & \\
& \ddots & \ddots & \\
& & A & B \\
& & 0 & A
\end{array}
\right]
For the all time-steps (going backwards in time):
.. math::
A \vec{y}^{(t)} + B \vec{y}^{(t+1)} = \vec{p}^{(t)}
.. math::
\begin{align}
\frac{1}{\delta t} \MfMui\vec{y}_{b}^{(t)} + \MfMui\dcurl \vec{y}_{e}^{(t)}
- \frac{1}{\delta t} \MfMui \vec{y}_{b}^{(t+1)}
= \vec{p}_b^{(t)} \\
\dcurl^\top \MfMui \vec{y}_b^{(t)} - \MeSig \vec{y}_e^{(t)} = \vec{p}_e^{(t)}
\end{align}
and
.. math::
\begin{align}
\left( \MfMui \dcurl \MeSig^{-1} \dcurl^\top \MfMui + \frac{1}{\delta t} \MfMui \right) \vec{y}_{b}^{(t)} =
\frac{1}{\delta t} \MfMui \vec{y}_b^{(t+1)}
+ \MfMui \dcurl \MeSig^{-1} \vec{p}_e^{(t)} + \vec{p}_b^{(t)} \\
\vec{y}_e^{(t)} = \MeSig^{-1} \dcurl^\top \MfMui \vec{y}_b^{(t)} - \MeSig^{-1} \vec{p}_e^{(t)}
\end{align}
.. note::
For the last time step, \\\(t=N\\\), the term: \\\(\\frac{1}{\\delta t} \\MfMui \\vec{y}_b^{(N+1)}\\\) is zero.
docs/em/api_Utils.rst
+10 -9
View File
@@ -4,6 +4,16 @@ simpegEM Utilities
SimPEG for EM provides a few EM specific utility codes,
sources, and analytic functions.
Utilities for Electromagnetics
==============================
.. automodule:: SimPEG.EM.Utils
:show-inheritance:
:members:
:undoc-members:
:inherited-members:
Analytic Functions - Time
=========================
@@ -22,12 +32,3 @@ Analytic Functions - Frequency
:members:
:undoc-members:
:inherited-members:
Sources
=======
.. autoclass:: SimPEG.EM.FDEM.SrcFDEM.MagDipole
:show-inheritance:
:members:
:undoc-members:
docs/em/index.rst
+9 -27
View File
@@ -3,42 +3,24 @@ Electromagnetics
================
`SimPEG.EM` uses SimPEG as the framework for the forward and inverse
electromagnetics geophysical problems.
electromagnetics geophysical problems.
Time Domian Electromagnetics
----------------------------
.. toctree::
:maxdepth: 2
api_TDEM_derivation
To solve for predicted data, we follow the framework shown below. The model is
what we invert for. This is mapped to a physical property on the simulation
mesh. A source which is used to excite the system is specified. Having a model
and a source, we can solve Maxwell's equations for fields. We sample these
fields with recievers to give us predicted data.
Code for Time Domian Electromagnetics
-------------------------------------
.. image:: ../images/simpegEM_noMath.png
:scale: 50%
.. toctree::
:maxdepth: 2
api_TDEM
Frequency Domian Electromagnetics
---------------------------------
.. toctree::
:maxdepth: 2
api_FDEM
Utility Codes
-------------
.. toctree::
:maxdepth: 2
api_TDEM
api_Utils
docs/examples/MT_1D_ForwardAndInversion.rst
+27
View File
@@ -0,0 +1,27 @@
.. _examples_MT_1D_ForwardAndInversion:
.. --------------------------------- ..
.. ..
.. THIS FILE IS AUTO GENEREATED ..
.. ..
.. SimPEG/Examples/__init__.py ..
.. ..
.. --------------------------------- ..
MT: 1D: Inversion
=======================
Forward model 1D MT data.
Setup and run a MT 1D inversion.
.. plot::
from SimPEG import Examples
Examples.MT_1D_ForwardAndInversion.run()
.. literalinclude:: ../../SimPEG/Examples/MT_1D_ForwardAndInversion.py
:language: python
:linenos:
docs/examples/MT_3D_Foward.rst
+26
View File
@@ -0,0 +1,26 @@
.. _examples_MT_3D_Foward:
.. --------------------------------- ..
.. ..
.. THIS FILE IS AUTO GENEREATED ..
.. ..
.. SimPEG/Examples/__init__.py ..
.. ..
.. --------------------------------- ..
MT: 3D: Forward
=======================
Forward model 3D MT data.
.. plot::
from SimPEG import Examples
Examples.MT_3D_Foward.run()
.. literalinclude:: ../../SimPEG/Examples/MT_3D_Foward.py
:language: python
:linenos:
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docs/index.rst
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@@ -49,9 +49,7 @@ Examples
.. toctree::
:maxdepth: 2
api_Examples
Packages
********
@@ -60,9 +58,9 @@ Packages
:maxdepth: 3
em/index
mt/index
flow/index
Finite Volume
*************
docs/mt/index.rst
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Magnetotellurics
****************
SimPEG (Simulation and Parameter Estimation in Geophysics) is a python
package for simulation and gradient based parameter estimation in the
context of geoscience applications.
simpegMT uses SimPEG as the framework for the forward and inverse
magnetotellurics geophysical problems.
Problem
=======
.. autoclass:: SimPEG.MT.BaseMT.BaseMTProblem
:show-inheritance:
:members:
:undoc-members:
tests/examples/test_examples.py
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@@ -1,8 +1,28 @@
import unittest
import sys
import os
from SimPEG import Examples
import numpy as np
class compareInitFiles(unittest.TestCase):
def test_compareInitFiles(self):
print 'Checking that __init__.py up-to-date in SimPEG/Examples'
fName = os.path.abspath(__file__)
ExamplesDir = os.path.sep.join(fName.split(os.path.sep)[:-3] + ['SimPEG', 'Examples'])
files = os.listdir(ExamplesDir)
pyfiles = []
[pyfiles.append(py.rstrip('.py')) for py in files if py.endswith('.py') and py != '__init__.py']
setdiff = set(pyfiles) - set(Examples.__examples__)
print ' Any missing files? ', setdiff
didpass = (setdiff == set())
self.assertTrue(didpass, "Examples not up to date, run 'python __init__.py' from SimPEG/Examples to update")
def get(test):
def test_func(self):
print '\nTesting %s.run(plotIt=False)\n'%test
@@ -10,11 +30,11 @@ def get(test):
self.assertTrue(True)
return test_func
attrs = dict()
for test in Examples.__examples__:
attrs['test_'+test] = get(test)
TestExamples = type('TestExamples', (unittest.TestCase,), attrs)
if __name__ == '__main__':
unittest.main()
tests/mt/__init__.py
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import os
import glob
import unittest
if __name__ == '__main__':
test_file_strings = glob.glob('test_*.py')
module_strings = [str[0:len(str)-3] for str in test_file_strings]
suites = [unittest.defaultTestLoader.loadTestsFromName(str) for str
in module_strings]
testSuite = unittest.TestSuite(suites)
unittest.TextTestRunner(verbosity=2).run(testSuite)
tests/mt/test_ApparentResistivityAnalytic.py
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import unittest
from SimPEG import *
from SimPEG import MT
TOL = 1e-6
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
def appResNorm(sigmaHalf):
nFreq = 26
m1d = Mesh.TensorMesh([[(100,5,1.5),(100.,10),(100,5,1.5)]], x0=['C'])
sigma = np.zeros(m1d.nC) + sigmaHalf
sigma[m1d.gridCC[:]>200] = 1e-8
# Calculate the analytic fields
freqs = np.logspace(4,-4,nFreq)
Z = []
for freq in freqs:
Ed, Eu, Hd, Hu = MT.Utils.getEHfields(m1d,sigma,freq,np.array([200]))
Z.append((Ed + Eu)/(Hd + Hu))
Zarr = np.concatenate(Z)
app_r, app_p = appResPhs(freqs,Zarr)
return np.linalg.norm(np.abs(app_r - np.ones(nFreq)/sigmaHalf)) / np.log10(sigmaHalf)
class TestAnalytics(unittest.TestCase):
def setUp(self):
pass
def test_appRes2en1(self):self.assertLess(appResNorm(2e-1), TOL)
def test_appRes2en2(self):self.assertLess(appResNorm(2e-2), TOL)
def test_appRes2en3(self):self.assertLess(appResNorm(2e-3), TOL)
def test_appRes2en4(self):self.assertLess(appResNorm(2e-4), TOL)
def test_appRes2en5(self):self.assertLess(appResNorm(2e-5), TOL)
def test_appRes2en6(self):self.assertLess(appResNorm(2e-6), TOL)
if __name__ == '__main__':
unittest.main()
tests/mt/test_Problem1D_againstAnalyticHalfspace.py
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import unittest
import SimPEG as simpeg
from SimPEG import MT
from SimPEG.Utils import meshTensor
import numpy as np
# Define the tolerances
TOLr = 5e-2
TOLp = 5e-2
def setupSurvey(sigmaHalf,tD=True):
# Frequency
nFreq = 33
freqs = np.logspace(3,-3,nFreq)
# Make the mesh
ct = 5
air = meshTensor([(ct,25,1.3)])
# coreT0 = meshTensor([(ct,15,1.2)])
# coreT1 = np.kron(meshTensor([(coreT0[-1],15,1.3)]),np.ones((7,)))
core = np.concatenate( ( np.kron(meshTensor([(ct,15,-1.2)]),np.ones((10,))) , meshTensor([(ct,20)]) ) )
bot = meshTensor([(core[0],10,-1.3)])
x0 = -np.array([np.sum(np.concatenate((core,bot)))])
m1d = simpeg.Mesh.TensorMesh([np.concatenate((bot,core,air))], x0=x0)
# Make the model
sigma = np.zeros(m1d.nC) + sigmaHalf
sigma[m1d.gridCC > 0 ] = 1e-8
rxList = []
for rxType in ['z1dr','z1di']:
rxList.append(MT.Rx(simpeg.mkvc(np.array([0.0]),2).T,rxType))
# Source list
srcList =[]
if tD:
for freq in freqs:
srcList.append(MT.SrcMT.polxy_1DhomotD(rxList,freq))
else:
for freq in freqs:
srcList.append(MT.SrcMT.polxy_1Dprimary(rxList,freq))
survey = MT.Survey(srcList)
return survey, sigma, m1d
def getAppResPhs(MTdata):
# Make impedance
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
zList = []
for src in MTdata.survey.srcList:
zc = [src.freq]
for rx in src.rxList:
if 'i' in rx.rxType:
m=1j
else:
m = 1
zc.append(m*MTdata[src,rx])
zList.append(zc)
return [appResPhs(zList[i][0],np.sum(zList[i][1:3])) for i in np.arange(len(zList))]
def appRes_TotalFieldNorm(sigmaHalf):
# Make the survey
survey, sigma, mesh = setupSurvey(sigmaHalf)
problem = MT.Problem1D.eForm_TotalField(mesh)
problem.pair(survey)
# Get the fields
fields = problem.fields(sigma)
# Project the data
data = survey.projectFields(fields)
# Calculate the app res and phs
app_r = np.array(getAppResPhs(data))[:,0]
return np.linalg.norm(np.abs(app_r - np.ones(survey.nFreq)/sigmaHalf)*sigmaHalf)
def appPhs_TotalFieldNorm(sigmaHalf):
# Make the survey
survey, sigma, mesh = setupSurvey(sigmaHalf)
problem = MT.Problem1D.eForm_TotalField(mesh)
problem.pair(survey)
# Get the fields
fields = problem.fields(sigma)
# Project the data
data = survey.projectFields(fields)
# Calculate the app phs
app_p = np.array(getAppResPhs(data))[:,1]
return np.linalg.norm(np.abs(app_p - np.ones(survey.nFreq)*45)/ 45)
def appRes_psFieldNorm(sigmaHalf):
# Make the survey
survey, sigma, mesh = setupSurvey(sigmaHalf,False)
problem = MT.Problem1D.eForm_psField(mesh, sigmaPrimary = sigma)
problem.pair(survey)
# Get the fields
fields = problem.fields(sigma)
# Project the data
data = survey.projectFields(fields)
# Calculate the app res and phs
app_r = np.array(getAppResPhs(data))[:,0]
return np.linalg.norm(np.abs(app_r - np.ones(survey.nFreq)/sigmaHalf)*sigmaHalf)
def appPhs_psFieldNorm(sigmaHalf):
# Make the survey
survey, sigma, mesh = setupSurvey(sigmaHalf,False)
problem = MT.Problem1D.eForm_psField(mesh, sigmaPrimary = sigma)
problem.pair(survey)
# Get the fields
fields = problem.fields(sigma)
# Project the data
data = survey.projectFields(fields)
# Calculate the app phs
app_p = np.array(getAppResPhs(data))[:,1]
return np.linalg.norm(np.abs(app_p - np.ones(survey.nFreq)*45)/ 45)
class TestAnalytics(unittest.TestCase):
def setUp(self):
pass
# Total Fields
# def test_appRes2en1(self):self.assertLess(appRes_TotalFieldNorm(2e-1), TOLr)
# def test_appPhs2en1(self):self.assertLess(appPhs_TotalFieldNorm(2e-1), TOLp)
# def test_appRes2en2(self):self.assertLess(appRes_TotalFieldNorm(2e-2), TOLr)
# def test_appPhs2en2(self):self.assertLess(appPhs_TotalFieldNorm(2e-2), TOLp)
# def test_appRes2en3(self):self.assertLess(appRes_TotalFieldNorm(2e-3), TOLr)
# def test_appPhs2en3(self):self.assertLess(appPhs_TotalFieldNorm(2e-3), TOLp)
# def test_appRes2en4(self):self.assertLess(appRes_TotalFieldNorm(2e-4), TOLr)
# def test_appPhs2en4(self):self.assertLess(appPhs_TotalFieldNorm(2e-4), TOLp)
# def test_appRes2en5(self):self.assertLess(appRes_TotalFieldNorm(2e-5), TOLr)
# def test_appPhs2en5(self):self.assertLess(appPhs_TotalFieldNorm(2e-5), TOLp)
# def test_appRes2en6(self):self.assertLess(appRes_TotalFieldNorm(2e-6), TOLr)
# def test_appPhs2en6(self):self.assertLess(appPhs_TotalFieldNorm(2e-6), TOLp)
# Primary/secondary
def test_appRes2en2_ps(self):self.assertLess(appRes_psFieldNorm(2e-2), TOLr)
def test_appPhs2en2_ps(self):self.assertLess(appPhs_psFieldNorm(2e-2), TOLp)
if __name__ == '__main__':
unittest.main()
tests/mt/test_Problem1D_totalDvsPSvsAnalytic.py
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import unittest
import SimPEG as simpeg
from SimPEG import MT
from SimPEG.Utils import meshTensor
import numpy as np
# Define the tolerances
TOLr = 5e-2
TOLp = 5e-2
def setupSurvey(sigmaHalf,tD=True):
# Frequency
nFreq = 33
freqs = np.logspace(3,-3,nFreq)
# Make the mesh
ct = 5
air = meshTensor([(ct,25,1.3)])
# coreT0 = meshTensor([(ct,15,1.2)])
# coreT1 = np.kron(meshTensor([(coreT0[-1],15,1.3)]),np.ones((7,)))
core = np.concatenate( ( np.kron(meshTensor([(ct,15,-1.2)]),np.ones((10,))) , meshTensor([(ct,20)]) ) )
bot = meshTensor([(core[0],15,-1.3)])
x0 = -np.array([np.sum(np.concatenate((core,bot)))])
m1d = simpeg.Mesh.TensorMesh([np.concatenate((bot,core,air))], x0=x0)
# Make the model
sigma = np.zeros(m1d.nC) + sigmaHalf
sigma[m1d.gridCC > 0 ] = 1e-8
sigmaBack = sigma.copy()
# Add structure
shallow = (m1d.gridCC < -200) * (m1d.gridCC > -600)
deep = (m1d.gridCC < -3000) * (m1d.gridCC > -5000)
sigma[shallow] = 1
sigma[deep] = 0.1
rxList = []
for rxType in ['z1dr','z1di']:
rxList.append(MT.Rx(simpeg.mkvc(np.array([0.0]),2).T,rxType))
# Source list
srcList =[]
if tD:
for freq in freqs:
srcList.append(MT.SrcMT.polxy_1DhomotD(rxList,freq))
else:
for freq in freqs:
srcList.append(MT.SrcMT.polxy_1Dprimary(rxList,freq))
survey = MT.Survey(srcList)
return survey, sigma, m1d
def getAppResPhs(MTdata):
# Make impedance
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
zList = []
for src in MTdata.survey.srcList:
zc = [src.freq]
for rx in src.rxList:
if 'i' in rx.rxType:
m=1j
else:
m = 1
zc.append(m*MTdata[src,rx])
zList.append(zc)
return [appResPhs(zList[i][0],np.sum(zList[i][1:3])) for i in np.arange(len(zList))]
def calculateAnalyticSolution(srcList,mesh,model):
surveyAna = MT.Survey(srcList)
data1D = MT.Data(surveyAna)
for src in surveyAna.srcList:
elev = src.rxList[0].locs[0]
anaEd, anaEu, anaHd, anaHu = MT.Utils.MT1Danalytic.getEHfields(mesh,model,src.freq,elev)
anaE = anaEd+anaEu
anaH = anaHd+anaHu
# Scale the solution
# anaE = (anaEtemp/anaEtemp[-1])#.conj()
# anaH = (anaHtemp/anaEtemp[-1])#.conj()
anaZ = anaE/anaH
for rx in src.rxList:
data1D[src,rx] = getattr(anaZ, rx.projComp)
return data1D
def dataMis_AnalyticTotalDomain(sigmaHalf):
# Make the survey
# Total domain solution
surveyTD, sigma, mesh = setupSurvey(sigmaHalf)
problemTD = MT.Problem1D.eForm_TotalField(mesh)
problemTD.pair(surveyTD)
# Analytic data
dataAnaObj = calculateAnalyticSolution(surveyTD.srcList,mesh,sigma)
# dataTDObj = MT.DataMT.DataMT(surveyTD, surveyTD.dpred(sigma))
dataTD = surveyTD.dpred(sigma)
dataAna = simpeg.mkvc(dataAnaObj)
return np.all((dataTD - dataAna)/dataAna < 2.)
# surveyTD.dtrue = -simpeg.mkvc(dataAna,2)
# surveyTD.dobs = -simpeg.mkvc(dataAna,2)
# surveyTD.Wd = np.ones(surveyTD.dtrue.shape) #/(np.abs(surveyTD.dtrue)*0.01)
# # Setup the data misfit
# dmis = simpeg.DataMisfit.l2_DataMisfit(surveyTD)
# dmis.Wd = surveyTD.Wd
# return dmis.eval(sigma)
def dataMis_AnalyticPrimarySecondary(sigmaHalf):
# Make the survey
# Primary secondary
surveyPS, sigmaPS, mesh = setupSurvey(sigmaHalf,tD=False)
problemPS = MT.Problem1D.eForm_psField(mesh)
problemPS.sigmaPrimary = sigmaPS
problemPS.pair(surveyPS)
# Analytic data
dataAnaObj = calculateAnalyticSolution(surveyPS.srcList,mesh,sigmaPS)
dataPS = surveyPS.dpred(sigmaPS)
dataAna = simpeg.mkvc(dataAnaObj)
return np.all((dataPS - dataAna)/dataAna < 2.)
class TestNumericVsAnalytics(unittest.TestCase):
def setUp(self):
pass
# Total Fields
# def test_appRes2en2(self):self.assertTrue(dataMis_AnalyticTotalDomain(2e-2))
# Primary/secondary
def test_appRes2en2_ps(self):self.assertTrue(dataMis_AnalyticPrimarySecondary(2e-2))
if __name__ == '__main__':
unittest.main()
tests/mt/test_Problem3D_againstAnalytic.py
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# Test functions
from glob import glob
import numpy as np, sys, os, time, scipy, subprocess
import SimPEG as simpeg
import unittest
from SimPEG import MT
from SimPEG.Utils import meshTensor
from scipy.constants import mu_0
TOLr = 5e-2
TOL = 1e-4
FLR = 1e-20 # "zero", so if residual below this --> pass regardless of order
CONDUCTIVITY = 1e1
MU = mu_0
freq = [1e-1, 2e-1]
addrandoms = True
def getInputs():
"""
Function that returns Mesh, freqs, rx_loc, elev.
"""
# Make a mesh
# 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])
# M = simpeg.Mesh.TensorMesh([[(1000,6,-1.5),(1000.,6),(1000,6,1.5)],[(1000,6,-1.5),(1000.,2),(1000,6,1.5)],[(1000,6,-1.3),(1000.,6),(1000,6,1.3)]], x0=['C','C','C'])# Setup the model
M = simpeg.Mesh.TensorMesh([[(1000,6,-1.5),(1000.,4),(1000,6,1.5)],[(1000,6,-1.5),(1000.,4),(1000,6,1.5)],[(500,8,-1.3),(500.,8),(500,8,1.3)]], x0=['C','C','C'])# Setup the model
# Set the frequencies
freqs = np.logspace(1,-3,5)
elev = 0
## Setup the the survey object
# Receiver locations
rx_x, rx_y = np.meshgrid(np.arange(-1000,1001,500),np.arange(-1000,1001,500))
rx_loc = np.hstack((simpeg.Utils.mkvc(rx_x,2),simpeg.Utils.mkvc(rx_y,2),elev+np.zeros((np.prod(rx_x.shape),1))))
return M, freqs, rx_loc, elev
def random(conds):
''' Returns a halfspace model based on the inputs'''
M, freqs, rx_loc, elev = getInputs()
# Backround
sigBG = np.ones(M.nC)*conds
# Add randomness to the model (10% of the value).
sig = np.exp( np.log(sigBG) + np.random.randn(M.nC)*(conds)*1e-1 )
return (M, freqs, sig, sigBG, rx_loc)
def halfSpace(conds):
''' Returns a halfspace model based on the inputs'''
M, freqs, rx_loc, elev = getInputs()
# Model
ccM = M.gridCC
# conds = [1e-2]
groundInd = ccM[:,2] < elev
sig = np.zeros(M.nC) + 1e-8
sig[groundInd] = conds
# Set the background, not the same as the model
sigBG = np.zeros(M.nC) + 1e-8
sigBG[groundInd] = conds
return (M, freqs, sig, sigBG, rx_loc)
def blockInhalfSpace(conds):
''' Returns a halfspace model based on the inputs'''
M, freqs, rx_loc, elev = getInputs()
# Model
ccM = M.gridCC
# conds = [1e-2]
groundInd = ccM[:,2] < elev
sig = simpeg.Utils.ModelBuilder.defineBlock(M.gridCC,np.array([-1000,-1000,-1500]),np.array([1000,1000,-1000]),conds)
sig[~groundInd] = 1e-8
# Set the background, not the same as the model
sigBG = np.zeros(M.nC) + 1e-8
sigBG[groundInd] = conds[1]
return (M, freqs, sig, sigBG, rx_loc)
def twoLayer(conds):
''' Returns a 2 layer model based on the conductivity values given'''
M, freqs, rx_loc, elev = getInputs()
# Model
ccM = M.gridCC
groundInd = ccM[:,2] < elev
botInd = ccM[:,2] < -3000
sig = np.zeros(M.nC) + 1e-8
sig[groundInd] = conds[1]
sig[botInd] = conds[0]
# Set the background, not the same as the model
sigBG = np.zeros(M.nC) + 1e-8
sigBG[groundInd] = conds[1]
return (M, freqs, sig, sigBG, rx_loc)
def setupSimpegMTfwd_eForm_ps(inputSetup,comp='Imp',singleFreq=False,expMap=True):
M,freqs,sig,sigBG,rx_loc = inputSetup
# Make a receiver list
rxList = []
if comp == 'All':
for rxType in ['zxxr','zxxi','zxyr','zxyi','zyxr','zyxi','zyyr','zyyi','tzxr','tzxi','tzyr','tzyi']:
rxList.append(MT.Rx(rx_loc,rxType))
elif comp == 'Imp':
for rxType in ['zxxr','zxxi','zxyr','zxyi','zyxr','zyxi','zyyr','zyyi']:
rxList.append(MT.Rx(rx_loc,rxType))
elif comp == 'Tip':
for rxType in ['tzxr','tzxi','tzyr','tzyi']:
rxList.append(MT.Rx(rx_loc,rxType))
else:
rxList.append(MT.Rx(rx_loc,comp))
# Source list
srcList =[]
if singleFreq:
srcList.append(MT.SrcMT.polxy_1Dprimary(rxList,singleFreq))
else:
for freq in freqs:
srcList.append(MT.SrcMT.polxy_1Dprimary(rxList,freq))
# Survey MT
survey = MT.Survey(srcList)
## Setup the problem object
sigma1d = M.r(sigBG,'CC','CC','M')[0,0,:]
if expMap:
problem = MT.Problem3D.eForm_ps(M,sigmaPrimary= np.log(sigma1d) )
problem.mapping = simpeg.Maps.ExpMap(problem.mesh)
problem.curModel = np.log(sig)
else:
problem = MT.Problem3D.eForm_ps(M,sigmaPrimary= sigma1d)
problem.curModel = sig
problem.pair(survey)
problem.verbose = False
try:
from pymatsolver import MumpsSolver
problem.Solver = MumpsSolver
except:
pass
return (survey, problem)
def getAppResPhs(MTdata):
# Make impedance
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
recData = MTdata.toRecArray('Complex')
return appResPhs(recData['freq'],recData['zxy']), appResPhs(recData['freq'],recData['zyx'])
def JvecAdjointTest(inputSetup,comp='All',freq=False):
(M, freqs, sig, sigBG, rx_loc) = inputSetup
survey, problem = setupSimpegMTfwd_eForm_ps(inputSetup,comp='All',singleFreq=freq)
print 'Adjoint test of eForm primary/secondary for {:s} comp at {:s}\n'.format(comp,str(survey.freqs))
m = sig
u = problem.fields(m)
v = np.random.rand(survey.nD,)
# print problem.PropMap.PropModel.nP
w = np.random.rand(problem.mesh.nC,)
vJw = v.ravel().dot(problem.Jvec(m, w, u))
wJtv = w.ravel().dot(problem.Jtvec(m, v, u))
tol = np.max([TOL*(10**int(np.log10(np.abs(vJw)))),FLR])
print ' vJw wJtv vJw - wJtv tol abs(vJw - wJtv) < tol'
print vJw, wJtv, vJw - wJtv, tol, np.abs(vJw - wJtv) < tol
return np.abs(vJw - wJtv) < tol
# Test the Jvec derivative
def DerivJvecTest(inputSetup,comp='All',freq=False,expMap=True):
(M, freqs, sig, sigBG, rx_loc) = inputSetup
survey, problem = setupSimpegMTfwd_eForm_ps(inputSetup,comp=comp,singleFreq=freq,expMap=expMap)
print 'Derivative test of Jvec for eForm primary/secondary for {:s} comp at {:s}\n'.format(comp,survey.freqs)
# problem.mapping = simpeg.Maps.ExpMap(problem.mesh)
# problem.sigmaPrimary = np.log(sigBG)
x0 = np.log(sigBG)
# cond = sig[0]
# x0 = np.log(np.ones(problem.mesh.nC)*cond)
# problem.sigmaPrimary = x0
# if True:
# x0 = x0 + np.random.randn(problem.mesh.nC)*cond*1e-1
survey = problem.survey
def fun(x):
return survey.dpred(x), lambda x: problem.Jvec(x0, x)
return simpeg.Tests.checkDerivative(fun, x0, num=3, plotIt=False, eps=FLR)
def DerivProjfieldsTest(inputSetup,comp='All',freq=False):
survey, problem = setupSimpegMTfwd_eForm_ps(inputSetup,comp,freq)
print 'Derivative test of data projection for eFormulation primary/secondary\n\n'
# problem.mapping = simpeg.Maps.ExpMap(problem.mesh)
# Initate things for the derivs Test
src = survey.srcList[0]
rx = src.rxList[0]
u0x = np.random.randn(survey.mesh.nE)+np.random.randn(survey.mesh.nE)*1j
u0y = np.random.randn(survey.mesh.nE)+np.random.randn(survey.mesh.nE)*1j
u0 = np.vstack((simpeg.mkvc(u0x,2),simpeg.mkvc(u0y,2)))
f0 = problem.fieldsPair(survey.mesh,survey)
# u0 = np.hstack((simpeg.mkvc(u0_px,2),simpeg.mkvc(u0_py,2)))
f0[src,'e_pxSolution'] = u0[:len(u0)/2]#u0x
f0[src,'e_pySolution'] = u0[len(u0)/2::]#u0y
def fun(u):
f = problem.fieldsPair(survey.mesh,survey)
f[src,'e_pxSolution'] = u[:len(u)/2]
f[src,'e_pySolution'] = u[len(u)/2::]
return rx.projectFields(src,survey.mesh,f), lambda t: rx.projectFieldsDeriv(src,survey.mesh,f0,simpeg.mkvc(t,2))
return simpeg.Tests.checkDerivative(fun, u0, num=3, plotIt=False, eps=FLR)
def appResPhsHalfspace_eFrom_ps_Norm(sigmaHalf,appR=True,expMap=False):
if appR:
label = 'resistivity'
else:
label = 'phase'
# Make the survey and the problem
survey, problem = setupSimpegMTfwd_eForm_ps(halfSpace(sigmaHalf),expMap=expMap)
print 'Apperent {:s} test of eFormulation primary/secondary at {:g}\n\n'.format(label,sigmaHalf)
data = problem.dataPair(survey,survey.dpred(problem.curModel))
# Calculate the app phs
app_rpxy, app_rpyx = np.array(getAppResPhs(data))
if appR:
return np.all(np.abs(app_rpxy[0,:] - 1./sigmaHalf) * sigmaHalf < .4)
else:
return np.all(np.abs(app_rpxy[1,:] + 135) / 135 < .4)
class TestAnalytics(unittest.TestCase):
def setUp(self):
pass
# # Test apparent resistivity and phase
def test_appRes1en2(self):self.assertTrue(appResPhsHalfspace_eFrom_ps_Norm(1e-2))
def test_appPhs1en2(self):self.assertTrue(appResPhsHalfspace_eFrom_ps_Norm(1e-2,False))
def test_appRes1en3(self):self.assertTrue(appResPhsHalfspace_eFrom_ps_Norm(1e-3))
def test_appPhs1en3(self):self.assertTrue(appResPhsHalfspace_eFrom_ps_Norm(1e-3,False))
# Do a derivative test
def test_derivProj1(self):self.assertTrue(DerivProjfieldsTest(halfSpace(1e-2)))
# Do a derivative test of Jvec
# def test_derivJvec_zxxr(self):self.assertTrue(DerivJvecTest(random(1e-2),'zxxr',.1))
# def test_derivJvec_zxxi(self):self.assertTrue(DerivJvecTest(random(1e-2),'zxxi',.1))
# def test_derivJvec_zxyr(self):self.assertTrue(DerivJvecTest(random(1e-2),'zxyr',.1))
# def test_derivJvec_zxyi(self):self.assertTrue(DerivJvecTest(random(1e-2),'zxyi',.1))
# def test_derivJvec_zyxr(self):self.assertTrue(DerivJvecTest(random(1e-2),'zyxr',.1))
# def test_derivJvec_zyxi(self):self.assertTrue(DerivJvecTest(random(1e-2),'zyxi',.1))
# def test_derivJvec_zyyr(self):self.assertTrue(DerivJvecTest(random(1e-2),'zyyr',.1))
# def test_derivJvec_zyyi(self):self.assertTrue(DerivJvecTest(random(1e-2),'zyyi',.1))
def test_derivJvec_All(self):self.assertTrue(DerivJvecTest(random(1e-2),'All',.1))
# Test the adjoint of Jvec and Jtvec
# def test_JvecAdjoint_zxxr(self):self.assertTrue(JvecAdjointTest(random(1e-2),'zxxr',.1))
# def test_JvecAdjoint_zxxi(self):self.assertTrue(JvecAdjointTest(random(1e-2),'zxxi',.1))
# def test_JvecAdjoint_zxyr(self):self.assertTrue(JvecAdjointTest(random(1e-2),'zxyr',.1))
# def test_JvecAdjoint_zxyi(self):self.assertTrue(JvecAdjointTest(random(1e-2),'zxyi',.1))
# def test_JvecAdjoint_zyxr(self):self.assertTrue(JvecAdjointTest(random(1e-2),'zyxr',.1))
# def test_JvecAdjoint_zyxi(self):self.assertTrue(JvecAdjointTest(random(1e-2),'zyxi',.1))
# def test_JvecAdjoint_zyyr(self):self.assertTrue(JvecAdjointTest(random(1e-2),'zyyr',.1))
# def test_JvecAdjoint_zyyi(self):self.assertTrue(JvecAdjointTest(random(1e-2),'zyyi',.1))
def test_JvecAdjoint_All(self):self.assertTrue(JvecAdjointTest(random(1e-2),'All',.1))
if __name__ == '__main__':
unittest.main()