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 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)
def DerivProjfieldsTest(inputSetup, comp='All', freq=False):
survey, problem = NSEM.Utils.testUtils.setupSimpegNSEM_ePrimSec(
inputSetup, comp, freq)
print(
'Derivative test of data projection for eFormulation primary/secondary\n'
)
# problem.mapping = simpeg.Maps.ExpMap(problem.mesh)
# Initate things for the derivs Test
src = survey.srcList[0]
np.random.seed(1983)
u0x = np.random.randn(
survey.mesh.nE) + np.random.randn(survey.mesh.nE) * 1j
u0y = np.random.randn(
survey.mesh.nE) + np.random.randn(survey.mesh.nE) * 1j
u0 = np.vstack((simpeg.mkvc(u0x, 2), simpeg.mkvc(u0y, 2)))
f0 = problem.fieldsPair(survey.mesh, survey)
# u0 = np.hstack((simpeg.mkvc(u0_px,2),simpeg.mkvc(u0_py,2)))
f0[src, 'e_pxSolution'] = u0[:len(u0) / 2] # u0x
f0[src, 'e_pySolution'] = u0[len(u0) / 2::] # u0y
def fun(u):
f = problem.fieldsPair(survey.mesh, survey)
f[src, 'e_pxSolution'] = u[:len(u) / 2]
f[src, 'e_pySolution'] = u[len(u) / 2::]
return rx.eval(
src, survey.mesh,
f), lambda t: rx.evalDeriv(src, survey.mesh, f0, simpeg.mkvc(t, 2))
return simpeg.Tests.checkDerivative(fun, u0, num=3, plotIt=False, eps=FLR)
def resampleNSEMdataAtFreq(NSEMdata, freqs):
"""
Function to resample NSEMdata at set of frequencies
"""
# Make a rec array
NSEMrec = NSEMdata.toRecArray().data
# Find unique locations
uniLoc = np.unique(NSEMrec[['x','y','z']])
uniFreq = NSEMdata.survey.freqs
# Get the comps
dNames = NSEMrec.dtype
# Loop over all the locations and interpolate
for loc in uniLoc:
# Find the index of the station
ind = np.sqrt(np.sum((rec_to_ndarr(NSEMrec[['x','y','z']]) - rec_to_ndarr(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))*rec_to_ndarr(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(NSEMrec[ind]['freq'],NSEMrec[ind][comp],bounds_error=False)
tArrRec[comp] = simpeg.mkvc(int1d(freqs),2)
# Join together
try:
outRecArr = recFunc.stack_arrays((outRecArr,tArrRec))
except NameError:
outRecArr = tArrRec
# Make the NSEMdata and return
return Data.fromRecArray(outRecArr)
def run(plotIt=True, nFreq=1):
# 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 rx_orientation in ['xx', 'xy', 'yx', 'yy']:
rxList.append(NSEM.Rx.Point_impedance3D(simpeg.mkvc(loc, 2).T, rx_orientation, 'real'))
rxList.append(NSEM.Rx.Point_impedance3D(simpeg.mkvc(loc, 2).T, rx_orientation, 'imag'))
for rx_orientation in ['zx', 'zy']:
rxList.append(NSEM.Rx.Point_tipper3D(simpeg.mkvc(loc, 2).T, rx_orientation, 'real'))
rxList.append(NSEM.Rx.Point_tipper3D(simpeg.mkvc(loc, 2).T, rx_orientation, 'imag'))
# Source list
srcList = [
NSEM.Src.Planewave_xy_1Dprimary(rxList, freq)
for freq in np.logspace(3, -3, nFreq)
]
# Survey MT
survey = NSEM.Survey(srcList)
# Setup the problem object
problem = NSEM.Problem3D_ePrimSec(M, sigma=sig, sigmaPrimary=sigBG)
problem.pair(survey)
problem.Solver = Solver
# Calculate the data
fields = problem.fields()
dataVec = survey.eval(fields)
# Make the data
mtData = NSEM.Data(survey, dataVec)
# Add plots
if plotIt:
pass
def convert3Dto1Dobject(NSEMdata, rxType3D='yx'):
# Find the unique locations
# Need to find the locations
recDataTemp = NSEMdata.toRecArray().data.flatten()
# 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 - Zoff)
recData = recFunc.append_fields(recDataTemp, ['zdetr', 'zdeti'],
[det.real, det.imag])
else:
recData = recDataTemp
uniLocs = rec_to_ndarr(np.unique(recData[['x', 'y', 'z']]))
mtData1DList = []
if 'xy' 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 = []
rx1DList.append(Point_impedance1D(simpeg.mkvc(loc, 2).T, 'real'))
rx1DList.append(Point_impedance1D(simpeg.mkvc(loc, 2).T, 'imag'))
# Source list
locrecData = recData[np.sqrt(
np.sum((rec_to_ndarr(recData[['x', 'y', 'z']]) -
loc)**2, axis=1)) < 1e-5]
dat1DList = []
src1DList = []
for freq in locrecData['freq']:
src1DList.append(Planewave_xy_1Dprimary(rx1DList, freq))
for comp in ['r', 'i']:
dat1DList.append(
corr *
locrecData[rxType3D + comp][locrecData['freq'] == freq])
# Make the survey
sur1D = Survey(src1DList)
# Make the data
dataVec = np.hstack(dat1DList)
dat1D = Data(sur1D, dataVec)
sur1D.dobs = dataVec
# Need to take NSEMdata.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 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 rx_orientation in ['xx','xy','yx','yy']:
rxList.append(NSEM.Rx.Point_impedance3D(simpeg.mkvc(loc,2).T,rx_orientation, 'real'))
rxList.append(NSEM.Rx.Point_impedance3D(simpeg.mkvc(loc,2).T,rx_orientation, 'imag'))
for rx_orientation in ['zx','zy']:
rxList.append(NSEM.Rx.Point_tipper3D(simpeg.mkvc(loc,2).T,rx_orientation, 'real'))
rxList.append(NSEM.Rx.Point_tipper3D(simpeg.mkvc(loc,2).T,rx_orientation, 'imag'))
# Source list
srcList =[]
for freq in np.logspace(3,-3,nFreq):
srcList.append(NSEM.Src.Planewave_xy_1Dprimary(rxList,freq))
# Survey MT
survey = NSEM.Survey(srcList)
## Setup the problem object
problem = NSEM.Problem3D_ePrimSec(M, sigmaPrimary=sigBG)
problem.pair(survey)
problem.Solver = Solver
# Calculate the data
fields = problem.fields(sig)
dataVec = survey.eval(fields)
# Make the data
mtData = NSEM.Data(survey,dataVec)
# Add plots
if plotIt:
pass
def convert3Dto1Dobject(NSEMdata, rxType3D='yx'):
# Find the unique locations
# Need to find the locations
recDataTemp = NSEMdata.toRecArray().data.flatten()
# 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 - Zoff)
recData = recFunc.append_fields(recDataTemp,['zdetr','zdeti'],[det.real,det.imag] )
else:
recData = recDataTemp
uniLocs = rec_to_ndarr(np.unique(recData[['x','y','z']]))
mtData1DList = []
if 'xy' 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 = []
rx1DList.append(Point_impedance1D(simpeg.mkvc(loc,2).T,'real'))
rx1DList.append(Point_impedance1D(simpeg.mkvc(loc,2).T,'imag'))
# Source list
locrecData = recData[np.sqrt(np.sum( (rec_to_ndarr(recData[['x','y','z']]) - loc )**2,axis=1)) < 1e-5]
dat1DList = []
src1DList = []
for freq in locrecData['freq']:
src1DList.append(Planewave_xy_1Dprimary(rx1DList,freq))
for comp in ['r','i']:
dat1DList.append( corr * locrecData[rxType3D+comp][locrecData['freq']== freq] )
# Make the survey
sur1D = Survey(src1DList)
# Make the data
dataVec = np.hstack(dat1DList)
dat1D = Data(sur1D,dataVec)
sur1D.dobs = dataVec
# Need to take NSEMdata.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 setupSurvey(sigmaHalf,tD=True):
# Frequency
nFreq = 33
freqs = np.logspace(3,-3,nFreq)
# Make the mesh
ct = 5
air = meshTensor([(ct,25,1.3)])
# coreT0 = meshTensor([(ct,15,1.2)])
# coreT1 = np.kron(meshTensor([(coreT0[-1],15,1.3)]),np.ones((7,)))
core = np.concatenate( ( np.kron(meshTensor([(ct,15,-1.2)]),np.ones((10,))) , meshTensor([(ct,20)]) ) )
bot = meshTensor([(core[0],10,-1.3)])
x0 = -np.array([np.sum(np.concatenate((core,bot)))])
m1d = simpeg.Mesh.TensorMesh([np.concatenate((bot,core,air))], x0=x0)
# Make the model
sigma = np.zeros(m1d.nC) + sigmaHalf
sigma[m1d.gridCC > 0 ] = 1e-8
rxList = []
for rxType in ['z1dr','z1di']:
rxList.append(simpegmt.SurveyMT.RxMT(simpeg.mkvc(np.array([0.0]),2).T,rxType))
# Source list
srcList =[]
if tD:
for freq in freqs:
srcList.append(simpegmt.SurveyMT.srcMT_polxy_1DhomotD(rxList,freq))
else:
for freq in freqs:
srcList.append(simpegmt.SurveyMT.srcMT_polxy_1Dprimary(rxList,freq))
survey = simpegmt.SurveyMT.SurveyMT(srcList)
return survey, sigma, m1d
def fun(u):
f = problem.fieldsPair(survey.mesh, survey)
f[src, 'e_pxSolution'] = u[:len(u) / 2]
f[src, 'e_pySolution'] = u[len(u) / 2::]
return rx.eval(
src, survey.mesh,
f), lambda t: rx.evalDeriv(src, survey.mesh, f0, simpeg.mkvc(t, 2))
def setupSurvey(sigmaHalf,tD=True):
# Frequency
nFreq = 33
freqs = np.logspace(3,-3,nFreq)
# Make the mesh
ct = 5
air = meshTensor([(ct,25,1.3)])
# coreT0 = meshTensor([(ct,15,1.2)])
# coreT1 = np.kron(meshTensor([(coreT0[-1],15,1.3)]),np.ones((7,)))
core = np.concatenate( ( np.kron(meshTensor([(ct,15,-1.2)]),np.ones((10,))) , meshTensor([(ct,20)]) ) )
bot = meshTensor([(core[0],10,-1.3)])
x0 = -np.array([np.sum(np.concatenate((core,bot)))])
m1d = simpeg.Mesh.TensorMesh([np.concatenate((bot,core,air))], x0=x0)
# Make the model
sigma = np.zeros(m1d.nC) + sigmaHalf
sigma[m1d.gridCC > 0 ] = 1e-8
rxList = []
for rxType in ['z1dr','z1di']:
rxList.append(MT.Rx(simpeg.mkvc(np.array([0.0]),2).T,rxType))
# Source list
srcList =[]
if tD:
for freq in freqs:
srcList.append(MT.SrcMT.polxy_1DhomotD(rxList,freq))
else:
for freq in freqs:
srcList.append(MT.SrcMT.polxy_1Dprimary(rxList,freq))
survey = MT.Survey(srcList)
return survey, sigma, m1d
def 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, Solver=Solver)
problem.pair(survey)
# Calculate the data
fields = problem.fields(sig)
dataVec = survey.eval(fields)
# Make the data
mtData = MT.Data(survey, dataVec)
# Add plots
if plotIt:
pass
def setup1DSurvey(sigmaHalf, tD=False, structure=False):
# Frequency
nFreq = 33
freqs = np.logspace(3, -3, nFreq)
# Make the mesh
ct = 5
air = meshTensor([(ct, 25, 1.3)])
# coreT0 = meshTensor([(ct,15,1.2)])
# coreT1 = np.kron(meshTensor([(coreT0[-1],15,1.3)]),np.ones((7,)))
core = np.concatenate((np.kron(meshTensor([(ct, 15, -1.2)]), np.ones(
(10, ))), meshTensor([(ct, 20)])))
bot = meshTensor([(core[0], 20, -1.3)])
x0 = -np.array([np.sum(np.concatenate((core, bot)))])
m1d = simpeg.Mesh.TensorMesh([np.concatenate((bot, core, air))], x0=x0)
# Make the model
sigma = np.zeros(m1d.nC) + sigmaHalf
sigma[m1d.gridCC > 0] = 1e-8
sigmaBack = sigma.copy()
# Add structure
if structure:
shallow = (m1d.gridCC < -200) * (m1d.gridCC > -600)
deep = (m1d.gridCC < -3000) * (m1d.gridCC > -5000)
sigma[shallow] = 1
sigma[deep] = 0.1
rxList = []
for rxType in ['z1d', 'z1d']:
rxList.append(
Point_impedance1D(simpeg.mkvc(np.array([0.0]), 2).T, 'real'))
rxList.append(
Point_impedance1D(simpeg.mkvc(np.array([0.0]), 2).T, 'imag'))
# Source list
srcList = []
if tD:
for freq in freqs:
srcList.append(Planewave_xy_1DhomotD(rxList, freq))
else:
for freq in freqs:
srcList.append(Planewave_xy_1Dprimary(rxList, freq))
survey = Survey(srcList)
return (survey, sigma, sigmaBack, m1d)
def setup1DSurvey(sigmaHalf, tD=False, structure=False):
# Frequency
nFreq = 33
freqs = np.logspace(3, -3, nFreq)
# Make the mesh
ct = 5
air = meshTensor([(ct, 25, 1.3)])
# coreT0 = meshTensor([(ct,15,1.2)])
# coreT1 = np.kron(meshTensor([(coreT0[-1],15,1.3)]),np.ones((7,)))
core = np.concatenate((np.kron(meshTensor([(ct, 15, -1.2)]), np.ones((10,))), meshTensor([(ct, 20)])))
bot = meshTensor([(core[0], 20, -1.3)])
x0 = -np.array([np.sum(np.concatenate((core, bot)))])
m1d = simpeg.Mesh.TensorMesh([np.concatenate((bot, core, air))], x0=x0)
# Make the model
sigma = np.zeros(m1d.nC) + sigmaHalf
sigma[m1d.gridCC > 0] = 1e-8
sigmaBack = sigma.copy()
# Add structure
if structure:
shallow = (m1d.gridCC < -200) * (m1d.gridCC > -600)
deep = (m1d.gridCC < -3000) * (m1d.gridCC > -5000)
sigma[shallow] = 1
sigma[deep] = 0.1
rxList = []
for rxType in ["z1d", "z1d"]:
rxList.append(Point_impedance1D(simpeg.mkvc(np.array([0.0]), 2).T, "real"))
rxList.append(Point_impedance1D(simpeg.mkvc(np.array([0.0]), 2).T, "imag"))
# Source list
srcList = []
if tD:
for freq in freqs:
srcList.append(Planewave_xy_1DhomotD(rxList, freq))
else:
for freq in freqs:
srcList.append(Planewave_xy_1Dprimary(rxList, freq))
survey = Survey(srcList)
return (survey, sigma, sigmaBack, m1d)
def DerivProjfieldsTest(inputSetup, comp="All", freq=False):
survey, problem = NSEM.Utils.testUtils.setupSimpegNSEM_ePrimSec(inputSetup, comp, freq)
print("Derivative test of data projection for eFormulation primary/secondary\n")
# problem.mapping = simpeg.Maps.ExpMap(problem.mesh)
# Initate things for the derivs Test
src = survey.srcList[0]
np.random.seed(1983)
u0x = np.random.randn(survey.mesh.nE) + np.random.randn(survey.mesh.nE) * 1j
u0y = np.random.randn(survey.mesh.nE) + np.random.randn(survey.mesh.nE) * 1j
u0 = np.vstack((simpeg.mkvc(u0x, 2), simpeg.mkvc(u0y, 2)))
f0 = problem.fieldsPair(survey.mesh, survey)
# u0 = np.hstack((simpeg.mkvc(u0_px,2),simpeg.mkvc(u0_py,2)))
f0[src, "e_pxSolution"] = u0[: len(u0) / 2] # u0x
f0[src, "e_pySolution"] = u0[len(u0) / 2 : :] # u0y
def fun(u):
f = problem.fieldsPair(survey.mesh, survey)
f[src, "e_pxSolution"] = u[: len(u) / 2]
f[src, "e_pySolution"] = u[len(u) / 2 : :]
return rx.eval(src, survey.mesh, f), lambda t: rx.evalDeriv(src, survey.mesh, f0, simpeg.mkvc(t, 2))
return simpeg.Tests.checkDerivative(fun, u0, num=4, plotIt=False, eps=FLR)
def dataMis_AnalyticPrimarySecondary(sigmaHalf):
# Make the survey
# Primary secondary
surveyPS, sigmaPS, mesh = setupSurvey(sigmaHalf,tD=False)
problemPS = MT.Problem1D.eForm_psField(mesh)
problemPS.sigmaPrimary = sigmaPS
problemPS.pair(surveyPS)
# Analytic data
dataAnaObj = calculateAnalyticSolution(surveyPS.srcList,mesh,sigmaPS)
dataPS = surveyPS.dpred(sigmaPS)
dataAna = simpeg.mkvc(dataAnaObj)
return np.all((dataPS - dataAna)/dataAna < 2.)
def dataMis_AnalyticTotalDomain(sigmaHalf):
# Make the survey
# Total domain solution
surveyTD, sigma, mesh = setupSurvey(sigmaHalf)
problemTD = MT.Problem1D.eForm_TotalField(mesh)
problemTD.pair(surveyTD)
# Analytic data
dataAnaObj = calculateAnalyticSolution(surveyTD.srcList,mesh,sigma)
# dataTDObj = MT.DataMT.DataMT(surveyTD, surveyTD.dpred(sigma))
dataTD = surveyTD.dpred(sigma)
dataAna = simpeg.mkvc(dataAnaObj)
return np.all((dataTD - dataAna)/dataAna < 2.)
def dataMis_AnalyticPrimarySecondary(sigmaHalf):
# Make the survey
# Primary secondary
surveyPS, sigmaPS, mesh = setupSurvey(sigmaHalf, tD=False)
problemPS = simpegmt.ProblemMT1D.eForm_psField(mesh)
problemPS.sigmaPrimary = sigmaPS
problemPS.pair(surveyPS)
# Analytic data
dataAnaObj = calculateAnalyticSolution(surveyPS.srcList, mesh, sigmaPS)
dataPS = surveyPS.dpred(sigmaPS)
dataAna = simpeg.mkvc(dataAnaObj)
return np.all((dataPS - dataAna) / dataAna < 2.)
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.eval(fields)
# Make the data
mtData = MT.Data(survey,dataVec)
# Add plots
if plotIt:
pass
def dataMis_AnalyticPrimarySecondary(sigmaHalf):
# Make the survey
# Primary secondary
survey, sig, sigBG, mesh = NSEM.Utils.testUtils.setup1DSurvey(sigmaHalf,False,structure=True)
# Analytic data
problem = NSEM.Problem1D_ePrimSec(mesh, sigmaPrimary = sig)
problem.pair(survey)
dataAnaObj = calculateAnalyticSolution(survey.srcList,mesh,sig)
data = survey.dpred(sig)
dataAna = simpeg.mkvc(dataAnaObj)
return np.all((data - dataAna)/dataAna < 2.)
def dataMis_AnalyticTotalDomain(sigmaHalf):
# Make the survey
# Total domain solution
surveyTD, sigma, mesh = setupSurvey(sigmaHalf)
problemTD = simpegmt.ProblemMT1D.eForm_TotalField(mesh)
problemTD.pair(surveyTD)
# Analytic data
dataAnaObj = calculateAnalyticSolution(surveyTD.srcList, mesh, sigma)
# dataTDObj = simpegmt.DataMT.DataMT(surveyTD, surveyTD.dpred(sigma))
dataTD = surveyTD.dpred(sigma)
dataAna = simpeg.mkvc(dataAnaObj)
return np.all((dataTD - dataAna) / dataAna < 2.)
def DerivProjfieldsTest(inputSetup,comp='All',freq=False):
survey, problem = setupSimpegMTfwd_eForm_ps(inputSetup,comp,freq)
print 'Derivative test of data projection for eFormulation primary/secondary\n\n'
# problem.mapping = simpeg.Maps.ExpMap(problem.mesh)
# Initate things for the derivs Test
src = survey.srcList[0]
rx = src.rxList[0]
u0x = np.random.randn(survey.mesh.nE)+np.random.randn(survey.mesh.nE)*1j
u0y = np.random.randn(survey.mesh.nE)+np.random.randn(survey.mesh.nE)*1j
u0 = np.vstack((simpeg.mkvc(u0x,2),simpeg.mkvc(u0y,2)))
f0 = problem.fieldsPair(survey.mesh,survey)
# u0 = np.hstack((simpeg.mkvc(u0_px,2),simpeg.mkvc(u0_py,2)))
f0[src,'e_pxSolution'] = u0[:len(u0)/2]#u0x
f0[src,'e_pySolution'] = u0[len(u0)/2::]#u0y
def fun(u):
f = problem.fieldsPair(survey.mesh,survey)
f[src,'e_pxSolution'] = u[:len(u)/2]
f[src,'e_pySolution'] = u[len(u)/2::]
return rx.projectFields(src,survey.mesh,f), lambda t: rx.projectFieldsDeriv(src,survey.mesh,f0,simpeg.mkvc(t,2))
return simpeg.Tests.checkDerivative(fun, u0, num=3, plotIt=False, eps=FLR)
def read_modem_models(model_file, ref_loc):
'''
Function to read in ModEM models into SimPEG/VTK
Inputs:
model_file - path to the modEM model file
ref_loc - xyz reference location for the model and
mesh has to be in a metric reference frame
Returns:
(mesh, mod_dict) - tuple containing the mesh and a model dict
with resistivity model.
'''
# Note: using UTM xyz convention
# Read all the lines
file_lines = np.genfromtxt(model_file, dtype=str, delimiter='\n')
# Make the mesh
nr_y, nr_x, nr_z, temp, val_type = file_lines[0].split()
hy = np.array(file_lines[1].split(), float)[::-1]
hx = np.array(file_lines[2].split(), float)
hz = np.array(file_lines[3].split(), float)[::-1]
# Calculate the SimPEG reference (SW - bottom point)
x0 = ref_loc - np.array([np.sum(hx) / 2., np.sum(hy) / 2., np.sum(hz)])
mesh = discretize.TensorMesh([hx, hy, hz], x0)
# Read the model
nr_mod_lines = int(nr_x) * int(nr_z)
mod_modem_convention = np.concatenate(
[np.array(line.split(), float)
for line in file_lines[4:4 + nr_mod_lines]])
mod_mat = mod_modem_convention.reshape(
int(nr_y), int(nr_x), int(nr_z), order='F')[::-1, :, ::-1]
mod_mat = np.transpose(mod_mat, (1, 0, 2))
mod_vec = simpeg.mkvc(np.exp(mod_mat))
# Write the vtk model
mesh.writeVTK(model_file.split('.')[0] + '.vtr', {'Ohm*m': mod_vec})
# Return the SimPEG mesh and model
return (mesh, {'Ohm*m': mod_vec})
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.
"""
from . 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 fun(u):
f = problem.fieldsPair(survey.mesh, survey)
f[src, "e_pxSolution"] = u[: len(u) / 2]
f[src, "e_pySolution"] = u[len(u) / 2 : :]
return rx.eval(src, survey.mesh, f), lambda t: rx.evalDeriv(src, survey.mesh, f0, simpeg.mkvc(t, 2))
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()
def plotMT1DModelData(problem, models, symList=None):
# 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)
# Loop through the models.
modelList = [problem.survey.mtrue]
modelList.extend(models)
if False:
modelList = [problem.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.sigmaMap * model), np.ones(2, ))
axM.semilogx(modelPts, meshPts, color=col)
## Data
loc = rec_to_ndarr(np.unique(data1D[['x', 'y']]).copy())
# Appres
pDt.plotIsoStaImpedance(axR, loc, data1D, 'zyx', 'res', pColor=col)
# Appphs
pDt.plotIsoStaImpedance(axP, loc, 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)
if False:
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 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.
"""
from . 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 run(plotIt=True):
# 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, 15, -1.2)]), np.ones((8, ))),
simpeg.Utils.meshTensor([(ct, 5)])))
bot = simpeg.Utils.meshTensor([(core[0], 20, -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 variables
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, sigmaMap=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))
# Assign uncertainties
std = 0.025 # 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()
# Optimization
opt = simpeg.Optimization.InexactGaussNewton(maxIter=25)
opt.counter = C
opt.LSshorten = 0.1
opt.remember('xc')
# Data misfit
dmis = simpeg.DataMisfit.l2_DataMisfit(survey)
dmis.W = 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-2
reg.alpha_x = 1.
reg.mrefInSmooth = True
# Inversion problem
invProb = simpeg.InvProblem.BaseInvProblem(dmis, reg, opt)
invProb.counter = C
# Beta schedule
beta = simpeg.Directives.BetaSchedule()
beta.coolingRate = 4.
beta.coolingFactor = 4.
# Initial estimate of beta
betaest = simpeg.Directives.BetaEstimate_ByEig(beta0_ratio=10.)
# Target misfit stop
targmis = simpeg.Directives.TargetMisfit()
targmis.target = survey.nD
# Create an inversion object
directives = [beta, betaest, targmis]
inv = simpeg.Inversion.BaseInversion(invProb, directiveList=directives)
# 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])
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'
]:
rxList.append(simpegmt.SurveyMT.RxMT(simpeg.mkvc(loc, 2).T, rxType))
# Source list
srcList = []
for freq in np.logspace(3, -3, 7):
srcList.append(simpegmt.SurveyMT.srcMT(freq, rxList))
# Survey MT
survey = simpegmt.SurveyMT.SurveyMT(srcList)
## Setup the problem object
problem = simpegmt.ProblemMT.MTProblem(M)
problem.pair(survey)
fields = problem.fields(sig, sigBG)
mtData = survey.projectFields(fields)
def run(plotIt=True):
"""
MT: 3D: Forward
===============
Forward model 3D MT data.
"""
# Make a mesh
M = simpeg.Mesh.TensorMesh([[
(100, 9, -1.5), (100., 13), (100, 9, 1.5)
], [(100, 9, -1.5), (100., 13),
(100, 9, 1.5)], [(50, 10, -1.6), (50., 10), (50, 6, 2)]],
x0=['C', 'C', -14926.8217])
# Setup the model
conds = [1, 1e-2]
sig = simpeg.Utils.ModelBuilder.defineBlock(M.gridCC, [-100, -100, -350],
[100, 100, -150], conds)
sig[M.gridCC[:, 2] > 0] = 1e-8
sig[M.gridCC[:, 2] < -1000] = 1e-1
sigBG = np.zeros(M.nC) + conds[1]
sigBG[M.gridCC[:, 2] > 0] = 1e-8
if plotIt:
collect_obj, line_obj = M.plotSlice(np.log10(sig),
grid=True,
normal='X')
color_bar = plt.colorbar(collect_obj)
# Setup the the survey object
# Receiver locations
rx_x, rx_y = np.meshgrid(np.arange(-600, 601, 100),
np.arange(-600, 601, 100))
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 rx_orientation in ['xx', 'xy', 'yx', 'yy']:
rxList.append(NSEM.Rx.Point_impedance3D(rx_loc, rx_orientation,
'real'))
rxList.append(NSEM.Rx.Point_impedance3D(rx_loc, rx_orientation,
'imag'))
for rx_orientation in ['zx', 'zy']:
rxList.append(NSEM.Rx.Point_tipper3D(rx_loc, rx_orientation, 'real'))
rxList.append(NSEM.Rx.Point_tipper3D(rx_loc, rx_orientation, 'imag'))
# Source list
srcList = [
NSEM.Src.Planewave_xy_1Dprimary(rxList, freq)
for freq in np.logspace(4, -2, 13)
]
# Survey MT
survey = NSEM.Survey(srcList)
# Setup the problem object
problem = NSEM.Problem3D_ePrimSec(M, sigma=sig, sigmaPrimary=sigBG)
problem.pair(survey)
problem.Solver = Solver
# Calculate the data
fields = problem.fields()
dataVec = survey.eval(fields)
# Add uncertainty to the data - 10% standard
# devation and 0 floor
dataVec.standard_deviation.fromvec(
np.ones_like(simpeg.mkvc(dataVec)) * 0.1)
dataVec.floor.fromvec(np.zeros_like(simpeg.mkvc(dataVec)))
# Add plots
if plotIt:
# Plot the data
# On and off diagonal (on left and right axis, respectively)
fig, axes = plt.subplots(2, 1, figsize=(7, 5))
plt.subplots_adjust(right=0.8)
[(ax.invert_xaxis(), ax.set_xscale('log')) for ax in axes]
ax_r, ax_p = axes
ax_r.set_yscale('log')
ax_r.set_ylabel('Apparent resistivity [xy-yx]')
ax_r_on = ax_r.twinx()
ax_r_on.set_yscale('log')
ax_r_on.set_ylabel('Apparent resistivity [xx-yy]')
ax_p.set_ylabel('Apparent phase')
ax_p.set_xlabel('Frequency [Hz]')
# Start plotting
ax_r = dataVec.plot_app_res(np.array([-200, 0]),
components=['xy', 'yx'],
ax=ax_r,
errorbars=True)
ax_r_on = dataVec.plot_app_res(np.array([-200, 0]),
components=['xx', 'yy'],
ax=ax_r_on,
errorbars=True)
ax_p = dataVec.plot_app_phs(np.array([-200, 0]),
components=['xx', 'xy', 'yx', 'yy'],
ax=ax_p,
errorbars=True)
ax_p.legend(bbox_to_anchor=(1.05, 1), loc=2)
def plotMT1DModelData(problem, models, symList=None):
# 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)
# Loop through the models.
modelList = [problem.survey.mtrue]
modelList.extend(models)
if False:
modelList = [problem.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.sigmaMap*model),np.ones(2,))
axM.semilogx(modelPts,meshPts,color=col)
## Data
loc = rec_to_ndarr(np.unique(data1D[['x','y']]))
# Appres
pDt.plotIsoStaImpedance(axR,loc,data1D,'zyx','res',pColor=col)
# Appphs
pDt.plotIsoStaImpedance(axP,loc,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)
if False:
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 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 simpegMT.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
# Load the model to the uniform cell mesh
modelUniCell = simpeg.Utils.meshutils.readUBCTensorModel(modelname,mesh3dCons)
# Load the model to the mesh with padding cells
modelT = simpeg.Utils.meshutils.readUBCTensorModel(modelname,mesh3d)
# Adjust the model to reflect changes in the mesh (fewer aircells)
modMat = mesh3d.r(modelT,'CC','CC','M')
modNewMat = np.ones((50,50,48))*modMat[0,0,0]
modNewMat[:,:,9::] = modMat[:,:,:-9]
modelTD = mesh3d.r(modNewMat,'CC','CC','V')
# Define the data locations
xG,yG = np.meshgrid(np.linspace(-700,700,8),np.linspace(-700,700,8))
zG = np.zeros_like(xG)
locs = np.hstack((simpeg.mkvc(xG.ravel(),2),simpeg.mkvc(yG.ravel(),2),simpeg.mkvc(zG.ravel(),2)))
# Make the receiver list
rxList = []
for rxType in ['zxxr','zxxi','zxyr','zxyi','zyxr','zyxi','zyyr','zyyi']:
rxList.append(simpegmt.SurveyMT.RxMT(locs,rxType))
# Source list
srcList =[]
freqs = np.logspace(4,0,17)
for freq in freqs:
srcList.append(simpegmt.SurveyMT.srcMT_polxy_1Dprimary(rxList,freq))
# Survey MT
survey = simpegmt.SurveyMT.SurveyMT(srcList)
# Setup the problem object
sigma1d = mesh3d.r(modelTD,'CC','CC','M')[0,0,:] # Use the edge column as a background model
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()
def run(plotIt=True):
# 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, 15, -1.2)]), np.ones(
(8, ))), simpeg.Utils.meshTensor([(ct, 5)])))
bot = simpeg.Utils.meshTensor([(core[0], 20, -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 variables
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,
sigmaMap=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))
# Assign uncertainties
std = 0.025 # 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()
# Optimization
opt = simpeg.Optimization.InexactGaussNewton(maxIter=25)
opt.counter = C
opt.LSshorten = 0.1
opt.remember('xc')
# Data misfit
dmis = simpeg.DataMisfit.l2_DataMisfit(survey)
dmis.W = 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-2
reg.alpha_x = 1.
reg.mrefInSmooth = True
# Inversion problem
invProb = simpeg.InvProblem.BaseInvProblem(dmis, reg, opt)
invProb.counter = C
# Beta schedule
beta = simpeg.Directives.BetaSchedule()
beta.coolingRate = 4.
beta.coolingFactor = 4.
# Initial estimate of beta
betaest = simpeg.Directives.BetaEstimate_ByEig(beta0_ratio=10.)
# Target misfit stop
targmis = simpeg.Directives.TargetMisfit()
targmis.target = survey.nD
# Create an inversion object
directives = [beta, betaest, targmis]
inv = simpeg.Inversion.BaseInversion(invProb, directiveList=directives)
# 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])
def fun(u):
f = problem.fieldsPair(survey.mesh,survey)
f[src,'e_pxSolution'] = u[:len(u)/2]
f[src,'e_pySolution'] = u[len(u)/2::]
return rx.projectFields(src,survey.mesh,f), lambda t: rx.projectFieldsDeriv(src,survey.mesh,f0,simpeg.mkvc(t,2))
def convert3Dto1Dobject(NSEMdata, rxType3D="yx"):
"""
Function that converts a 3D NSEMdata of a list of
1D NSEMdata objects for running 1D inversions for.
:param SimPEG.electromagnetics.natural_source.Data NSEMdata: NSEM data object to process
:param rxType3D: component of the NSEMdata to use.
Can be 'xy', 'yx' or 'det'
:type rxType3D: str, optional
"""
# Find the unique locations
# Need to find the locations
recDataTemp = NSEMdata.toRecArray().data.flatten()
# 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 - Zoff)
recData = recFunc.append_fields(
recDataTemp, ["zdetr", "zdeti"], [det.real, det.imag]
)
else:
recData = recDataTemp
uniLocs = rec_to_ndarr(np.unique(recData[["x", "y", "z"]].copy()))
mtData1DList = []
if "xy" 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 = []
rx1DList.append(Point1DImpedance(simpeg.mkvc(loc, 2).T, "real"))
rx1DList.append(Point1DImpedance(simpeg.mkvc(loc, 2).T, "imag"))
# Source list
locrecData = recData[
np.sqrt(
np.sum(
(rec_to_ndarr(recData[["x", "y", "z"]].copy()) - loc) ** 2, axis=1
)
)
< 1e-5
]
dat1DList = []
src1DList = []
for freq in locrecData["freq"]:
src1DList.append(Planewave_xy_1Dprimary(rx1DList, freq))
for comp in ["r", "i"]:
dat1DList.append(
corr * locrecData[rxType3D + comp][locrecData["freq"] == freq]
)
# Make the survey
sur1D = Survey(src1DList)
# Make the data
dataVec = np.hstack(dat1DList)
dat1D = Data(sur1D, dataVec)
sur1D.dobs = dataVec
# Need to take NSEMdata.survey.std and split it as well.
std = 0.05
sur1D.std = np.abs(sur1D.dobs * std)
mtData1DList.append(dat1D)
# Return the the list of data.
return mtData1DList
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 simpegMT.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
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']:
rxList.append(simpegmt.SurveyMT.RxMT(simpeg.mkvc(loc,2).T,rxType))
# Source list
srcList =[]
for freq in np.logspace(3,-3,7):
srcList.append(simpegmt.SurveyMT.srcMT(freq,rxList))
# Survey MT
survey = simpegmt.SurveyMT.SurveyMT(srcList)
## Setup the problem object
problem = simpegmt.ProblemMT.MTProblem(M)
problem.pair(survey)
fields = problem.fields(sig,sigBG)
mtData = survey.projectFields(fields)