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cleanup of docs, docs for survey

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This commit is contained in:
Lindsey Heagy
2016-02-07 13:04:13 -08:00
parent cb9a70bacc
commit 81c13b12e3
4 changed files with 91 additions and 34 deletions
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SimPEG/EM/FDEM/FDEM.py
+26 -24
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}\\\)
"""
@@ -204,7 +206,7 @@ class Problem_e(BaseFDEMProblem):
.. 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}
\\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}`.
@@ -223,7 +225,7 @@ class Problem_e(BaseFDEMProblem):
System matrix
.. math ::
\mathbf{A} = \mathbf{C}^T \mathbf{M_{\mu^{-1}}^f} \mathbf{C} + i \omega \mathbf{M^e_{\sigma}}
\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
@@ -265,7 +267,7 @@ class Problem_e(BaseFDEMProblem):
Right hand side for the system
.. math ::
\mathbf{RHS} = \mathbf{C}^T \mathbf{M_{\mu^{-1}}^f}\mathbf{s_m} -i\omega\mathbf{M_e}\mathbf{s_e}
\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
@@ -294,7 +296,7 @@ class Problem_e(BaseFDEMProblem):
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)
@@ -310,13 +312,13 @@ class Problem_b(BaseFDEMProblem):
.. 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 :math:`\mathbf{b}` using:
.. 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
@@ -336,7 +338,7 @@ class Problem_b(BaseFDEMProblem):
System matrix
.. math ::
\mathbf{A} = \mathbf{C} \mathbf{M^e_{\sigma}}^{-1} \mathbf{C}^T \mathbf{M_{\mu^{-1}}^f} + i \omega
\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
@@ -431,7 +433,7 @@ 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)
@@ -458,13 +460,13 @@ class Problem_j(BaseFDEMProblem):
.. 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
.. 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!!
@@ -484,7 +486,7 @@ class Problem_j(BaseFDEMProblem):
System matrix
.. math ::
\\mathbf{A} = \\mathbf{C} \\mathbf{M^e_{\\mu^{-1}}} \\mathbf{C}^T \\mathbf{M^f_{\\sigma^{-1}}} + i\\omega
\\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
@@ -511,7 +513,7 @@ class Problem_j(BaseFDEMProblem):
.. math ::
\\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}}}\mathbf{v} }{d \mathbf{m}}
\\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,)
@@ -543,6 +545,7 @@ class Problem_j(BaseFDEMProblem):
.. 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
@@ -573,7 +576,7 @@ class Problem_j(BaseFDEMProblem):
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:
@@ -604,7 +607,7 @@ class Problem_h(BaseFDEMProblem):
.. 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
"""
@@ -620,9 +623,8 @@ class Problem_h(BaseFDEMProblem):
"""
System matrix
.. math ::
\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
@@ -640,7 +642,7 @@ class Problem_h(BaseFDEMProblem):
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}}
\\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,)
@@ -664,7 +666,7 @@ class Problem_h(BaseFDEMProblem):
.. math ::
\mathbf{RHS} = \mathbf{M^e} \mathbf{s_m} + \mathbf{C}^T \mathbf{M_{\\rho}^f} \mathbf{s_e}
\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
@@ -701,7 +703,7 @@ 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
+5 -8
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@@ -186,8 +186,7 @@ class Fields_e(Fields):
:return: product of the secondary magnetic flux density derivative with respect to the inversion model with a vector
"""
S_mDeriv, _ = src.evalDeriv(self.prob, adjoint)
S_mDeriv = S_mDeriv(v)
S_mDeriv, _ = src.evalDeriv(self.prob, v, adjoint)
return 1./(1j * omega(src.freq)) * S_mDeriv
def _b(self, eSolution, srcList):
@@ -401,10 +400,9 @@ 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
@@ -616,7 +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)
@@ -821,8 +819,7 @@ class Fields_h(Fields):
:return: product of the secondary current density derivative with respect to the inversion model with a vector
"""
_,S_eDeriv = src.evalDeriv(self.prob, adjoint)
S_eDeriv = S_eDeriv(v)
_,S_eDeriv = src.evalDeriv(self.prob, v, adjoint)
return -S_eDeriv
def _j(self, hSolution, srcList):
SimPEG/EM/FDEM/SurveyFDEM.py
+42 -2
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@@ -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'],
@@ -61,6 +67,15 @@ class Rx(SimPEG.Survey.BaseRx):
return self.knownRxTypes[self.rxType][2]
def projectFields(self, src, mesh, u):
"""
Project fields to recievers to get data.
:param Source src: FDEM source
:param Mesh mesh: mesh used
:param Fields u: fields object
:rtype: numpy.ndarray
:return: fields projected to recievers
"""
P = self.getP(mesh)
u_part_complex = u[src, self.projField]
# get the real or imag component
@@ -69,6 +84,16 @@ class Rx(SimPEG.Survey.BaseRx):
return P*u_part
def projectFieldsDeriv(self, src, mesh, u, 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 u: 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 +120,13 @@ 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 +154,7 @@ 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 +162,22 @@ 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
:returns: 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
:returns: data
"""
data = SimPEG.Survey.Data(self)
for src in self.srcList:
for rx in src.rxList:
docs/em/api_FDEM.rst
+18
View File
@@ -144,6 +144,10 @@ H-J Formulation
API
===
FDEM Problem
------------
.. automodule:: SimPEG.EM.FDEM.FDEM
:show-inheritance:
:members:
@@ -157,3 +161,17 @@ FDEM Survey
:show-inheritance:
:members:
:undoc-members:
.. automodule:: SimPEG.EM.FDEM.SrcFDEM
:show-inheritance:
:members:
:undoc-members:
FDEM Fields
-----------
.. automodule:: SimPEG.EM.FDEM.FieldsFDEM
:show-inheritance:
:members:
:undoc-members: