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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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SimPEG/Directives.py
+41 -45
View File
@@ -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")