def bPrimary(self, prob):
eqLocs = prob._eqLocs
if eqLocs is 'FE':
gridX = prob.mesh.gridFx
gridY = prob.mesh.gridFy
gridZ = prob.mesh.gridFz
C = prob.mesh.edgeCurl
elif eqLocs is 'EF':
gridX = prob.mesh.gridEx
gridY = prob.mesh.gridEy
gridZ = prob.mesh.gridEz
C = prob.mesh.edgeCurl.T
srcfct = SrcUtils.MagneticDipoleFields
if prob.mesh._meshType is 'CYL':
if not prob.mesh.isSymmetric:
# TODO ?
raise NotImplementedError('Non-symmetric cyl mesh not implemented yet!')
bx = srcfct(self.loc, gridX, 'x', mu=self.mu, moment=self.moment)
bz = srcfct(self.loc, gridZ, 'z', mu=self.mu, moment=self.moment)
b = np.concatenate((bx,bz))
else:
bx = srcfct(self.loc, gridX, 'x', mu=self.mu, moment=self.moment)
by = srcfct(self.loc, gridY, 'y', mu=self.mu, moment=self.moment)
bz = srcfct(self.loc, gridZ, 'z', mu=self.mu, moment=self.moment)
b = np.concatenate((bx,by,bz))
return b
def _bfromVectorPotential(self, prob):
if prob._eqLocs is 'FE':
gridX = prob.mesh.gridEx
gridY = prob.mesh.gridEy
gridZ = prob.mesh.gridEz
C = prob.mesh.edgeCurl
elif prob._eqLocs is 'EF':
gridX = prob.mesh.gridFx
gridY = prob.mesh.gridFy
gridZ = prob.mesh.gridFz
C = prob.mesh.edgeCurl.T
if prob.mesh._meshType is 'CYL':
if not prob.mesh.isSymmetric:
raise NotImplementedError('Non-symmetric cyl mesh not '
'implemented yet!')
a = MagneticLoopVectorPotential(self.loc, gridY, 'y',
radius=self.radius, mu=self.mu)
else:
srcfct = MagneticLoopVectorPotential
ax = srcfct(self.loc, gridX, 'x', mu=self.mu, radius=self.radius)
ay = srcfct(self.loc, gridY, 'y', mu=self.mu, radius=self.radius)
az = srcfct(self.loc, gridZ, 'z', mu=self.mu, radius=self.radius)
a = np.concatenate((ax, ay, az))
return C*a
def tovec(self):
val = []
for src in self.survey.srcList:
for rx in src.rxList:
for t in rx.times:
val.append(self[src, rx, t])
return np.concatenate(val)
def tovec(self):
val = []
for src in self.survey.srcList:
for rx in src.rxList:
for t in rx.times:
val.append(self[src, rx, t])
return np.concatenate(val)
def bPrimary(self, prob):
eqLocs = prob._eqLocs
if eqLocs is 'FE':
gridX = prob.mesh.gridEx
gridY = prob.mesh.gridEy
gridZ = prob.mesh.gridEz
C = prob.mesh.edgeCurl
elif eqLocs is 'EF':
gridX = prob.mesh.gridFx
gridY = prob.mesh.gridFy
gridZ = prob.mesh.gridFz
C = prob.mesh.edgeCurl.T
if prob.mesh._meshType is 'CYL':
if not prob.mesh.isSymmetric:
# TODO ?
raise NotImplementedError('Non-symmetric cyl mesh not implemented yet!')
a = SrcUtils.MagneticDipoleVectorPotential(self.loc, gridY, 'y', moment=self.radius, mu=self.mu)
else:
srcfct = SrcUtils.MagneticDipoleVectorPotential
ax = srcfct(self.loc, gridX, 'x', self.radius, mu=self.mu)
ay = srcfct(self.loc, gridY, 'y', self.radius, mu=self.mu)
az = srcfct(self.loc, gridZ, 'z', self.radius, mu=self.mu)
a = np.concatenate((ax, ay, az))
return C*a
def _bfromVectorPotential(self, prob):
if prob._eqLocs is 'FE':
gridX = prob.mesh.gridEx
gridY = prob.mesh.gridEy
gridZ = prob.mesh.gridEz
C = prob.mesh.edgeCurl
elif prob._eqLocs is 'EF':
gridX = prob.mesh.gridFx
gridY = prob.mesh.gridFy
gridZ = prob.mesh.gridFz
C = prob.mesh.edgeCurl.T
if prob.mesh._meshType is 'CYL':
if not prob.mesh.isSymmetric:
raise NotImplementedError('Non-symmetric cyl mesh not '
'implemented yet!')
a = MagneticLoopVectorPotential(self.loc,
gridY,
'y',
radius=self.radius,
mu=self.mu)
else:
srcfct = MagneticLoopVectorPotential
ax = srcfct(self.loc, gridX, 'x', mu=self.mu, radius=self.radius)
ay = srcfct(self.loc, gridY, 'y', mu=self.mu, radius=self.radius)
az = srcfct(self.loc, gridZ, 'z', mu=self.mu, radius=self.radius)
a = np.concatenate((ax, ay, az))
return C * a
def __getitem__(self, key):
src, rx, t = self._ensureCorrectKey(key)
if rx is not None:
if rx not in self._dataDict[src]:
raise Exception('Data for receiver has not yet been set.')
return self._dataDict[src][rx][t]
return np.concatenate([self[src, rx, t] for rx in src.rxList])
def __getitem__(self, key):
src, rx, t = self._ensureCorrectKey(key)
if rx is not None:
if rx not in self._dataDict[src]:
raise Exception('Data for receiver has not yet been set.')
return self._dataDict[src][rx][t]
return np.concatenate([self[src,rx, t] for rx in src.rxList])
def gridCC(self):
"""
Cell-centered grid
"""
if getattr(self, '_gridCC', None) is None:
self._gridCC = np.concatenate([self.aveN2CC*self.gridN[:, i]
for i in range(self.dim)]).reshape(
(-1, self.dim), order='F')
return self._gridCC
def gridCC(self):
"""
Cell-centered grid
"""
if getattr(self, '_gridCC', None) is None:
self._gridCC = np.concatenate([
self.aveN2CC * self.gridN[:, i] for i in range(self.dim)
]).reshape((-1, self.dim), order='F')
return self._gridCC
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
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
"""
formulation = prob._formulation
if formulation is 'EB':
gridX = prob.mesh.gridFx
gridY = prob.mesh.gridFy
gridZ = prob.mesh.gridFz
C = prob.mesh.edgeCurl
elif formulation is 'HJ':
gridX = prob.mesh.gridEx
gridY = prob.mesh.gridEy
gridZ = prob.mesh.gridEz
C = prob.mesh.edgeCurl.T
srcfct = MagneticDipoleFields
if prob.mesh._meshType is 'CYL':
if not prob.mesh.isSymmetric:
# TODO ?
raise NotImplementedError(
'Non-symmetric cyl mesh not implemented yet!')
bx = srcfct(self.loc, gridX, 'x', mu=self.mu, moment=self.moment)
bz = srcfct(self.loc, gridZ, 'z', mu=self.mu, moment=self.moment)
b = np.concatenate((bx, bz))
else:
bx = srcfct(self.loc, gridX, 'x', mu=self.mu, moment=self.moment)
by = srcfct(self.loc, gridY, 'y', mu=self.mu, moment=self.moment)
bz = srcfct(self.loc, gridZ, 'z', mu=self.mu, moment=self.moment)
b = np.concatenate((bx, by, bz))
return b
def bPrimary(self, prob):
"""
The primary magnetic flux density from the analytic solution for magnetic fields from a dipole
:param BaseFDEMProblem prob: FDEM problem
:rtype: numpy.ndarray
:return: primary magnetic field
"""
formulation = prob._formulation
if formulation is 'EB':
gridX = prob.mesh.gridFx
gridY = prob.mesh.gridFy
gridZ = prob.mesh.gridFz
C = prob.mesh.edgeCurl
elif formulation is 'HJ':
gridX = prob.mesh.gridEx
gridY = prob.mesh.gridEy
gridZ = prob.mesh.gridEz
C = prob.mesh.edgeCurl.T
srcfct = MagneticDipoleFields
if prob.mesh._meshType is 'CYL':
if not prob.mesh.isSymmetric:
# TODO ?
raise NotImplementedError('Non-symmetric cyl mesh not implemented yet!')
bx = srcfct(self.loc, gridX, 'x', mu=self.mu, moment=self.moment)
bz = srcfct(self.loc, gridZ, 'z', mu=self.mu, moment=self.moment)
b = np.concatenate((bx,bz))
else:
bx = srcfct(self.loc, gridX, 'x', mu=self.mu, moment=self.moment)
by = srcfct(self.loc, gridY, 'y', mu=self.mu, moment=self.moment)
bz = srcfct(self.loc, gridZ, 'z', mu=self.mu, moment=self.moment)
b = np.concatenate((bx,by,bz))
return b
def bPrimary(self, prob):
"""
The primary magnetic flux density from the analytic solution for
magnetic fields from a dipole
:param BaseFDEMProblem prob: FDEM problem
:rtype: numpy.ndarray
:return: primary magnetic field
"""
formulation = prob._formulation
if formulation is "EB":
gridX = prob.mesh.gridFx
gridY = prob.mesh.gridFy
gridZ = prob.mesh.gridFz
elif formulation is "HJ":
gridX = prob.mesh.gridEx
gridY = prob.mesh.gridEy
gridZ = prob.mesh.gridEz
srcfct = MagneticDipoleFields
if prob.mesh._meshType is "CYL":
if not prob.mesh.isSymmetric:
# TODO ?
raise NotImplementedError("Non-symmetric cyl mesh not implemented yet!")
bx = srcfct(self.loc, gridX, "x", mu=self.mu, moment=self.moment)
bz = srcfct(self.loc, gridZ, "z", mu=self.mu, moment=self.moment)
b = np.concatenate((bx, bz))
else:
bx = srcfct(self.loc, gridX, "x", mu=self.mu, moment=self.moment)
by = srcfct(self.loc, gridY, "y", mu=self.mu, moment=self.moment)
bz = srcfct(self.loc, gridZ, "z", mu=self.mu, moment=self.moment)
b = np.concatenate((bx, by, bz))
return Utils.mkvc(b)
def appResNorm(sigmaHalf):
nFreq = 26
m1d = Mesh.TensorMesh([[(100,5,1.5),(100.,10),(100,5,1.5)]], x0=['C'])
sigma = np.zeros(m1d.nC) + sigmaHalf
sigma[m1d.gridCC[:]>200] = 1e-8
# Calculate the analytic fields
freqs = np.logspace(4,-4,nFreq)
Z = []
for freq in freqs:
Ed, Eu, Hd, Hu = NSEM.Utils.getEHfields(m1d,sigma,freq,np.array([200]))
Z.append((Ed + Eu)/(Hd + Hu))
Zarr = np.concatenate(Z)
app_r, app_p = NSEM.Utils.appResPhs(freqs,Zarr)
return np.linalg.norm(np.abs(app_r - np.ones(nFreq)/sigmaHalf)) / np.log10(sigmaHalf)
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
"""
formulation = prob._formulation
if formulation is 'EB':
gridX = prob.mesh.gridEx
gridY = prob.mesh.gridEy
gridZ = prob.mesh.gridEz
C = prob.mesh.edgeCurl
elif formulation is 'HJ':
gridX = prob.mesh.gridFx
gridY = prob.mesh.gridFy
gridZ = prob.mesh.gridFz
C = prob.mesh.edgeCurl.T
if prob.mesh._meshType is 'CYL':
if not prob.mesh.isSymmetric:
# TODO ?
raise NotImplementedError(
'Non-symmetric cyl mesh not implemented yet!')
a = MagneticDipoleVectorPotential(self.loc,
gridY,
'y',
moment=self.radius,
mu=self.mu)
else:
srcfct = MagneticDipoleVectorPotential
ax = srcfct(self.loc, gridX, 'x', self.radius, mu=self.mu)
ay = srcfct(self.loc, gridY, 'y', self.radius, mu=self.mu)
az = srcfct(self.loc, gridZ, 'z', self.radius, mu=self.mu)
a = np.concatenate((ax, ay, az))
return C * a
def bPrimary(self, prob):
"""
The primary magnetic flux density from a magnetic vector potential
:param BaseFDEMProblem prob: FDEM problem
:rtype: numpy.ndarray
:return: primary magnetic field
"""
formulation = prob._formulation
if formulation is 'EB':
gridX = prob.mesh.gridEx
gridY = prob.mesh.gridEy
gridZ = prob.mesh.gridEz
C = prob.mesh.edgeCurl
elif formulation is 'HJ':
gridX = prob.mesh.gridFx
gridY = prob.mesh.gridFy
gridZ = prob.mesh.gridFz
C = prob.mesh.edgeCurl.T
if prob.mesh._meshType is 'CYL':
if not prob.mesh.isSymmetric:
# TODO ?
raise NotImplementedError('Non-symmetric cyl mesh not '
'implemented yet!')
assert (np.linalg.norm(self.orientation - np.r_[0., 0., 1.]) <
1e-6), ('for cylindrical symmetry, the dipole must be '
'oriented in the Z direction')
a = self._srcFct(gridY, 'y')
else:
ax = self._srcFct(gridX, 'x')
ay = self._srcFct(gridY, 'y')
az = self._srcFct(gridZ, 'z')
a = np.concatenate((ax, ay, az))
return C * a
def bPrimary(self, prob):
"""
The primary magnetic flux density from a magnetic vector potential
:param BaseFDEMProblem prob: FDEM problem
:rtype: numpy.ndarray
:return: primary magnetic field
"""
formulation = prob._formulation
if formulation is "EB":
gridX = prob.mesh.gridEx
gridY = prob.mesh.gridEy
gridZ = prob.mesh.gridEz
C = prob.mesh.edgeCurl
elif formulation is "HJ":
gridX = prob.mesh.gridFx
gridY = prob.mesh.gridFy
gridZ = prob.mesh.gridFz
C = prob.mesh.edgeCurl.T
if prob.mesh._meshType is "CYL":
if not prob.mesh.isSymmetric:
# TODO ?
raise NotImplementedError("Non-symmetric cyl mesh not " "implemented yet!")
assert np.linalg.norm(self.orientation - np.r_[0.0, 0.0, 1.0]) < 1e-6, (
"for cylindrical symmetry, the dipole must be " "oriented in the Z direction"
)
a = self._srcFct(gridY, "y")
else:
ax = self._srcFct(gridX, "x")
ay = self._srcFct(gridY, "y")
az = self._srcFct(gridZ, "z")
a = np.concatenate((ax, ay, az))
return C * a
def bPrimary(self, prob):
"""
The primary magnetic flux density from a magnetic vector potential
:param BaseFDEMProblem prob: FDEM problem
:rtype: numpy.ndarray
:return: primary magnetic field
"""
formulation = prob._formulation
if formulation is 'EB':
gridX = prob.mesh.gridEx
gridY = prob.mesh.gridEy
gridZ = prob.mesh.gridEz
C = prob.mesh.edgeCurl
elif formulation is 'HJ':
gridX = prob.mesh.gridFx
gridY = prob.mesh.gridFy
gridZ = prob.mesh.gridFz
C = prob.mesh.edgeCurl.T
if prob.mesh._meshType is 'CYL':
if not prob.mesh.isSymmetric:
# TODO ?
raise NotImplementedError('Non-symmetric cyl mesh not implemented yet!')
a = MagneticDipoleVectorPotential(self.loc, gridY, 'y', mu=self.mu, moment=self.moment)
else:
srcfct = MagneticDipoleVectorPotential
ax = srcfct(self.loc, gridX, 'x', mu=self.mu, moment=self.moment)
ay = srcfct(self.loc, gridY, 'y', mu=self.mu, moment=self.moment)
az = srcfct(self.loc, gridZ, 'z', mu=self.mu, moment=self.moment)
a = np.concatenate((ax, ay, az))
return C*a
def getSource(self,freq):
"""
:param float freq: Frequency
:rtype: numpy.ndarray (nE, nTx)
:return: RHS
"""
Txs = self.survey.getTransmitters(freq)
rhs = range(len(Txs))
solType = self.solType
if solType == 'e' or solType == 'b':
gridEJx = self.mesh.gridEx
gridEJy = self.mesh.gridEy
gridEJz = self.mesh.gridEz
nEJ = self.mesh.nE
gridBHx = self.mesh.gridFx
gridBHy = self.mesh.gridFy
gridBHz = self.mesh.gridFz
nBH = self.mesh.nF
C = self.mesh.edgeCurl
mui = self.MfMui
elif solType == 'h' or solType == 'j':
gridEJx = self.mesh.gridFx
gridEJy = self.mesh.gridFy
gridEJz = self.mesh.gridFz
nEJ = self.mesh.nF
gridBHx = self.mesh.gridEx
gridBHy = self.mesh.gridEy
gridBHz = self.mesh.gridEz
nBH = self.mesh.nE
C = self.mesh.edgeCurl.T
mui = self.MeMuI
else:
NotImplementedError('Only E or F sources')
for i, tx in enumerate(Txs):
if self.mesh._meshType is 'CYL':
if self.mesh.isSymmetric:
if tx.txType == 'VMD':
SRC = Sources.MagneticDipoleVectorPotential(tx.loc, gridEJy, 'y')
elif tx.txType =='CircularLoop':
SRC = Sources.MagneticLoopVectorPotential(tx.loc, gridEJy, 'y', tx.radius)
else:
raise NotImplementedError('Only VMD and CircularLoop')
else:
raise NotImplementedError('Non-symmetric cyl mesh not implemented yet!')
elif self.mesh._meshType is 'TENSOR':
if tx.txType == 'VMD':
src = Sources.MagneticDipoleVectorPotential
SRCx = src(tx.loc, gridEJx, 'x')
SRCy = src(tx.loc, gridEJy, 'y')
SRCz = src(tx.loc, gridEJz, 'z')
elif tx.txType == 'VMD_B':
src = Sources.MagneticDipoleFields
SRCx = src(tx.loc, gridBHx, 'x')
SRCy = src(tx.loc, gridBHy, 'y')
SRCz = src(tx.loc, gridBHz, 'z')
elif tx.txType == 'CircularLoop':
src = Sources.MagneticLoopVectorPotential
SRCx = src(tx.loc, gridEJx, 'x', tx.radius)
SRCy = src(tx.loc, gridEJy, 'y', tx.radius)
SRCz = src(tx.loc, gridEJz, 'z', tx.radius)
else:
raise NotImplemented('%s txType is not implemented' % tx.txType)
SRC = np.concatenate((SRCx, SRCy, SRCz))
else:
raise Exception('Unknown mesh for VMD')
rhs[i] = SRC
# b-forumlation
if tx.txType == 'VMD_B':
b_0 = np.concatenate(rhs).reshape((nBH, len(Txs)), order='E')
else:
a = np.concatenate(rhs).reshape((nEJ, len(Txs)), order='F')
b_0 = C*a
if solType == 'b' or solType == 'h':
return b_0
elif solType == 'e' or solType == 'j':
return C.T*mui*b_0
def fget(self):
if self._gridCC is None:
self._gridCC = np.concatenate([self.aveN2CC*self.gridN[:,i] for i in range(self.dim)]).reshape((-1,self.dim), order='F')
return self._gridCC
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 = 26
freqs = np.logspace(2, -3, nFreq)
# Set mesh parameters
ct = 10
air = simpeg.Utils.meshTensor([(ct, 25, 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], 25, -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 = 1e-2
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.InjectActiveCells(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 = []
rxList.append(
NSEM.Rx.Point_impedance1D(simpeg.mkvc(np.array([-0.5]), 2).T, 'real'))
rxList.append(
NSEM.Rx.Point_impedance1D(simpeg.mkvc(np.array([-0.5]), 2).T, 'imag'))
# Source list
srcList = []
for freq in freqs:
srcList.append(NSEM.Src.Planewave_xy_1Dprimary(rxList, freq))
# Make the survey
survey = NSEM.Survey(srcList)
survey.mtrue = m_true
## Set the problem
problem = NSEM.Problem1D_ePrimSec(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 + 0.01 * abs(
survey.dtrue) * np.random.randn(*survey.dtrue.shape)
if plotIt:
fig = NSEM.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.ProjectedGNCG(maxIter=25)
opt.counter = C
opt.lower = np.log(1e-4)
opt.upper = np.log(5)
opt.LSshorten = 0.1
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[active]], m1d.x0)
reg = simpeg.Regularization.Tikhonov(regMesh)
reg.mrefInSmooth = True
reg.alpha_s = 1e-1
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.
beta.coolingFactor = 4.
betaest = simpeg.Directives.BetaEstimate_ByEig(beta0_ratio=100.)
betaest.beta0 = 1.
targmis = simpeg.Directives.TargetMisfit()
targmis.target = survey.nD
# Create an inversion object
inv = simpeg.Inversion.BaseInversion(
invProb, directiveList=[beta, betaest, targmis])
## Run the inversion
mopt = inv.run(m_0)
if plotIt:
fig = NSEM.Utils.dataUtils.plotMT1DModelData(problem, [mopt])
fig.suptitle('Target - smooth true')
fig.axes[0].set_ylim([-10000, 500])
plt.show()
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 = 26
freqs = np.logspace(2,-3,nFreq)
# Set mesh parameters
ct = 10
air = simpeg.Utils.meshTensor([(ct,25,1.4)])
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],25,-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 = 1e-2
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.InjectActiveCells(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 = []
rxList.append(NSEM.Rx.Point_impedance1D(simpeg.mkvc(np.array([-0.5]),2).T,'real'))
rxList.append(NSEM.Rx.Point_impedance1D(simpeg.mkvc(np.array([-0.5]),2).T,'imag'))
# Source list
srcList =[]
for freq in freqs:
srcList.append(NSEM.Src.Planewave_xy_1Dprimary(rxList,freq))
# Make the survey
survey = NSEM.Survey(srcList)
survey.mtrue = m_true
## Set the problem
problem = NSEM.Problem1D_ePrimSec(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 + 0.01*abs(survey.dtrue)*np.random.randn(*survey.dtrue.shape)
if plotIt:
fig = NSEM.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.ProjectedGNCG(maxIter = 25)
opt.counter = C
opt.lower = np.log(1e-4)
opt.upper = np.log(5)
opt.LSshorten = 0.1
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[active]],m1d.x0)
reg = simpeg.Regularization.Tikhonov(regMesh)
reg.mrefInSmooth = True
reg.alpha_s = 1e-1
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.
beta.coolingFactor = 4.
betaest = simpeg.Directives.BetaEstimate_ByEig(beta0_ratio=100.)
betaest.beta0 = 1.
targmis = simpeg.Directives.TargetMisfit()
targmis.target = survey.nD
# Create an inversion object
inv = simpeg.Inversion.BaseInversion(invProb, directiveList=[beta,betaest,targmis])
## Run the inversion
mopt = inv.run(m_0)
if plotIt:
fig = NSEM.Utils.dataUtils.plotMT1DModelData(problem,[mopt])
fig.suptitle('Target - smooth true')
fig.axes[0].set_ylim([-10000,500])
plt.show()
def MagneticLoopVectorPotential(srcLoc, obsLoc, component, radius, orientation='Z', mu=mu_0):
"""
Calculate the vector potential of horizontal circular loop
at given locations
:param numpy.ndarray srcLoc: Location of the source(s) (x, y, z)
:param numpy.ndarray,SimPEG.Mesh obsLoc: Where the potentials will be calculated (x, y, z) or a SimPEG Mesh
:param str,list component: The component to calculate - 'x', 'y', or 'z' if an array, or grid type if mesh, can be a list
:param numpy.ndarray I: Input current of the loop
:param numpy.ndarray radius: radius of the loop
:rtype: numpy.ndarray
:return: The vector potential each dipole at each observation location
"""
if isinstance(orientation, str):
if orientation.upper() != 'Z':
raise NotImplementedError('Only Z oriented loops implemented')
elif not np.allclose(orientation, np.r_[0., 0., 1.]):
raise NotImplementedError('Only Z oriented loops implemented')
if type(component) in [list, tuple]:
out = list(range(len(component)))
for i, comp in enumerate(component):
out[i] = MagneticLoopVectorPotential(srcLoc, obsLoc, comp, radius,
orientation, mu)
return np.concatenate(out)
if isinstance(obsLoc, Mesh.BaseMesh):
mesh = obsLoc
assert component in ['Ex','Ey','Ez','Fx','Fy','Fz'], "Components must be in: ['Ex','Ey','Ez','Fx','Fy','Fz']"
return MagneticLoopVectorPotential(srcLoc, getattr(mesh,'grid'+component), component[1], radius, mu)
srcLoc = np.atleast_2d(srcLoc)
obsLoc = np.atleast_2d(obsLoc)
n = obsLoc.shape[0]
nSrc = srcLoc.shape[0]
if component=='z':
A = np.zeros((n, nSrc))
if nSrc ==1:
return A.flatten()
return A
else:
A = np.zeros((n, nSrc))
for i in range (nSrc):
x = obsLoc[:, 0] - srcLoc[i, 0]
y = obsLoc[:, 1] - srcLoc[i, 1]
z = obsLoc[:, 2] - srcLoc[i, 2]
r = np.sqrt(x**2 + y**2)
m = (4 * radius * r) / ((radius + r)**2 + z**2)
m[m > 1.] = 1.
# m might be slightly larger than 1 due to rounding errors
# but ellipke requires 0 <= m <= 1
K = ellipk(m)
E = ellipe(m)
ind = (r > 0) & (m < 1)
# % 1/r singular at r = 0 and K(m) singular at m = 1
Aphi = np.zeros(n)
# % Common factor is (mu * I) / pi with I = 1 and mu = 4e-7 * pi.
Aphi[ind] = ((mu / (np.pi * np.sqrt(m[ind])) *
np.sqrt(radius / r[ind]) *((1. - m[ind] / 2.) *
K[ind] - E[ind])))
if component == 'x':
A[ind, i] = Aphi[ind] * (-y[ind] / r[ind] )
elif component == 'y':
A[ind, i] = Aphi[ind] * ( x[ind] / r[ind] )
else:
raise ValueError('Invalid component')
if nSrc == 1:
return A.flatten()
return A
def MagneticDipoleVectorPotential(srcLoc, obsLoc, component, moment=1.,
orientation=np.r_[0., 0., 1.],
mu=mu_0):
"""
Calculate the vector potential of a set of magnetic dipoles
at given locations 'ref. <http://en.wikipedia.org/wiki/Dipole#Magnetic_vector_potential>'
:param numpy.ndarray srcLoc: Location of the source(s) (x, y, z)
:param numpy.ndarray,SimPEG.Mesh obsLoc: Where the potentials will be
calculated (x, y, z) or a
SimPEG Mesh
:param str,list component: The component to calculate - 'x', 'y', or
'z' if an array, or grid type if mesh, can
be a list
:param numpy.ndarray orientation: The vector dipole moment
:rtype: numpy.ndarray
:return: The vector potential each dipole at each observation location
"""
# TODO: break this out!
if isinstance(orientation, str):
orientation = orientationDict[orientation]
assert np.linalg.norm(np.array(orientation), 2) == 1., ("orientation must "
"be a unit vector")
if type(component) in [list, tuple]:
out = list(range(len(component)))
for i, comp in enumerate(component):
out[i] = MagneticDipoleVectorPotential(srcLoc, obsLoc, comp,
orientation=orientation,
mu=mu)
return np.concatenate(out)
if isinstance(obsLoc, Mesh.BaseMesh):
mesh = obsLoc
assert component in ['Ex', 'Ey', 'Ez', 'Fx', 'Fy', 'Fz'], ("Components"
"must be in: ['Ex','Ey','Ez','Fx','Fy','Fz']")
return MagneticDipoleVectorPotential(srcLoc, getattr(mesh, 'grid' +
component),
component[1],
orientation=orientation)
if component == 'x':
dimInd = 0
elif component == 'y':
dimInd = 1
elif component == 'z':
dimInd = 2
else:
raise ValueError('Invalid component')
srcLoc = np.atleast_2d(srcLoc)
obsLoc = np.atleast_2d(obsLoc)
orientation = np.atleast_2d(orientation)
nObs = obsLoc.shape[0]
nSrc = srcLoc.shape[0]
m = moment*np.array(orientation).repeat(nObs, axis=0)
A = np.empty((nObs, nSrc))
for i in range(nSrc):
dR = obsLoc - srcLoc[i, np.newaxis].repeat(nObs, axis=0)
mCr = np.cross(m, dR)
r = np.sqrt((dR**2).sum(axis=1))
A[:, i] = +(mu/(4*np.pi)) * mCr[:, dimInd]/(r**3)
if nSrc == 1:
return A.flatten()
return A
def fget(self):
if self._gridCC is None:
self._gridCC = np.concatenate([self.aveN2CC*self.gridN[:,i] for i in range(self.dim)]).reshape((-1,self.dim), order='F')
return self._gridCC
def MagneticDipoleVectorPotential(srcLoc, obsLoc, component, moment=1.,
orientation=np.r_[0., 0., 1.],
mu=mu_0):
"""
Calculate the vector potential of a set of magnetic dipoles
at given locations 'ref. <http://en.wikipedia.org/wiki/Dipole#Magnetic_vector_potential>'
:param numpy.ndarray srcLoc: Location of the source(s) (x, y, z)
:param numpy.ndarray,SimPEG.Mesh obsLoc: Where the potentials will be
calculated (x, y, z) or a
SimPEG Mesh
:param str,list component: The component to calculate - 'x', 'y', or
'z' if an array, or grid type if mesh, can
be a list
:param numpy.ndarray orientation: The vector dipole moment
:rtype: numpy.ndarray
:return: The vector potential each dipole at each observation location
"""
# TODO: break this out!
if isinstance(orientation, str):
orientation = orientationDict[orientation]
assert np.linalg.norm(np.array(orientation), 2) == 1., ("orientation must "
"be a unit vector")
if type(component) in [list, tuple]:
out = range(len(component))
for i, comp in enumerate(component):
out[i] = MagneticDipoleVectorPotential(srcLoc, obsLoc, comp,
orientation=orientation,
mu=mu)
return np.concatenate(out)
if isinstance(obsLoc, Mesh.BaseMesh):
mesh = obsLoc
assert component in ['Ex', 'Ey', 'Ez', 'Fx', 'Fy', 'Fz'], ("Components"
"must be in: ['Ex','Ey','Ez','Fx','Fy','Fz']")
return MagneticDipoleVectorPotential(srcLoc, getattr(mesh, 'grid' +
component),
component[1],
orientation=orientation)
if component == 'x':
dimInd = 0
elif component == 'y':
dimInd = 1
elif component == 'z':
dimInd = 2
else:
raise ValueError('Invalid component')
srcLoc = np.atleast_2d(srcLoc)
obsLoc = np.atleast_2d(obsLoc)
orientation = np.atleast_2d(orientation)
nObs = obsLoc.shape[0]
nSrc = srcLoc.shape[0]
m = moment*np.array(orientation).repeat(nObs, axis=0)
A = np.empty((nObs, nSrc))
for i in range(nSrc):
dR = obsLoc - srcLoc[i, np.newaxis].repeat(nObs, axis=0)
mCr = np.cross(m, dR)
r = np.sqrt((dR**2).sum(axis=1))
A[:, i] = +(mu/(4*np.pi)) * mCr[:, dimInd]/(r**3)
if nSrc == 1:
return A.flatten()
return A
def MagneticLoopVectorPotential(srcLoc, obsLoc, component, radius, orientation='Z', mu=mu_0):
"""
Calculate the vector potential of horizontal circular loop
at given locations
:param numpy.ndarray srcLoc: Location of the source(s) (x, y, z)
:param numpy.ndarray,SimPEG.Mesh obsLoc: Where the potentials will be calculated (x, y, z) or a SimPEG Mesh
:param str,list component: The component to calculate - 'x', 'y', or 'z' if an array, or grid type if mesh, can be a list
:param numpy.ndarray I: Input current of the loop
:param numpy.ndarray radius: radius of the loop
:rtype: numpy.ndarray
:return: The vector potential each dipole at each observation location
"""
if isinstance(orientation, str):
if orientation.upper() != 'Z':
raise NotImplementedError, 'Only Z oriented loops implemented'
elif not np.allclose(orientation, np.r_[0., 0., 1.]):
raise NotImplementedError, 'Only Z oriented loops implemented'
if type(component) in [list, tuple]:
out = range(len(component))
for i, comp in enumerate(component):
out[i] = MagneticLoopVectorPotential(srcLoc, obsLoc, comp, radius,
orientation, mu)
return np.concatenate(out)
if isinstance(obsLoc, Mesh.BaseMesh):
mesh = obsLoc
assert component in ['Ex','Ey','Ez','Fx','Fy','Fz'], "Components must be in: ['Ex','Ey','Ez','Fx','Fy','Fz']"
return MagneticLoopVectorPotential(srcLoc, getattr(mesh,'grid'+component), component[1], radius, mu)
srcLoc = np.atleast_2d(srcLoc)
obsLoc = np.atleast_2d(obsLoc)
n = obsLoc.shape[0]
nSrc = srcLoc.shape[0]
if component=='z':
A = np.zeros((n, nSrc))
if nSrc ==1:
return A.flatten()
return A
else:
A = np.zeros((n, nSrc))
for i in range (nSrc):
x = obsLoc[:, 0] - srcLoc[i, 0]
y = obsLoc[:, 1] - srcLoc[i, 1]
z = obsLoc[:, 2] - srcLoc[i, 2]
r = np.sqrt(x**2 + y**2)
m = (4 * radius * r) / ((radius + r)**2 + z**2)
m[m > 1.] = 1.
# m might be slightly larger than 1 due to rounding errors
# but ellipke requires 0 <= m <= 1
K = ellipk(m)
E = ellipe(m)
ind = (r > 0) & (m < 1)
# % 1/r singular at r = 0 and K(m) singular at m = 1
Aphi = np.zeros(n)
# % Common factor is (mu * I) / pi with I = 1 and mu = 4e-7 * pi.
Aphi[ind] = ((mu / (np.pi * np.sqrt(m[ind])) *
np.sqrt(radius / r[ind]) *((1. - m[ind] / 2.) *
K[ind] - E[ind])))
if component == 'x':
A[ind, i] = Aphi[ind] * (-y[ind] / r[ind] )
elif component == 'y':
A[ind, i] = Aphi[ind] * ( x[ind] / r[ind] )
else:
raise ValueError('Invalid component')
if nSrc == 1:
return A.flatten()
return A