def _evalCross(self, m):
if self.crossgrad == False:
return 0.0
elif self.crossgrad == True:
M = (self.mapping * m).reshape((self.regmesh.nC, self.nModels), order="F")
ax = self.regmesh.aveFx2CC * self.regmesh.wx[0] * M[:, 0]
ay = self.regmesh.aveFy2CC * self.regmesh.wy[0] * M[:, 0]
az = self.regmesh.aveFz2CC * self.regmesh.wz[0] * M[:, 0]
bx = self.regmesh.aveFx2CC * self.regmesh.wx[1] * M[:, 1]
by = self.regmesh.aveFy2CC * self.regmesh.wy[1] * M[:, 1]
bz = self.regmesh.aveFz2CC * self.regmesh.wz[1] * M[:, 1]
# ab
out_ab = cross([ax, ay, az], [bx, by, bz])
r = np.r_[out_ab[0], out_ab[1], out_ab[2]] * np.sqrt(self.betacross)
if self.nModels == 3:
cx = self.regmesh.aveFx2CC * self.regmesh.wx[1] * M[:, 1]
cy = self.regmesh.aveFy2CC * self.regmesh.wy[1] * M[:, 1]
cz = self.regmesh.aveFz2CC * self.regmesh.wz[1] * M[:, 1]
# ac
out_ac = cross([ax, ay, az], [cx, cy, cz])
# bc
out_bc = cross([bx, by, bz], [cx, cy, cz])
r = np.r_[r, np.hstack(out_ac) * np.sqrt(self.betacross), np.hstack(out_bc) * np.sqrt(self.betacross)]
return 0.5 * r.dot(r)
def readUBC_DC2DLoc(fileName):
from SimPEG import np
"""
Read UBC GIF 2D observation file and generate arrays for tx-rx location
Input:
:param fileName, path to the UBC GIF 2D model file
Output:
:param rx, tx
:return
Created on Thu Nov 12 13:14:10 2015
@author: dominiquef
"""
# Open fileand skip header... assume that we know the mesh already
#==============================================================================
# fopen = open(fileName,'r')
# lines = fopen.readlines()
# fopen.close()
#==============================================================================
# Load file
obsfile = np.genfromtxt(fileName,delimiter=' \n',dtype=np.str,comments='!')
# Check first line and figure out if 2D or 3D file format
line = np.array(obsfile[0].split(),dtype=float)
tx_A = []
tx_B = []
rx_M = []
rx_N = []
d = []
wd = []
for ii in range(obsfile.shape[0]):
# If len==3, then simple format where tx-rx is listed on each line
if len(line) == 4:
temp = np.fromstring(obsfile[ii], dtype=float,sep=' ')
tx_A = np.hstack((tx_A,temp[0]))
tx_B = np.hstack((tx_B,temp[1]))
rx_M = np.hstack((rx_M,temp[2]))
rx_N = np.hstack((rx_N,temp[3]))
rx = np.transpose(np.array((rx_M,rx_N)))
tx = np.transpose(np.array((tx_A,tx_B)))
return tx, rx, d, wd
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 S_eDeriv_m(self, problem, v, adjoint=False):
"""
Get the derivative of S_e wrt to sigma (m)
"""
# Need to deal with
if problem.mesh.dim == 1:
# Need to use the faceInnerProduct
MsigmaDeriv = (
problem.mesh.getFaceInnerProductDeriv(problem.curModel.sigma)(self.ePrimary(problem)[:, 1])
* problem.curModel.sigmaDeriv
)
# MsigmaDeriv = ( MsigmaDeriv * MsigmaDeriv.T)**2
if problem.mesh.dim == 2:
pass
if problem.mesh.dim == 3:
# Need to take the derivative of both u_px and u_py
ePri = self.ePrimary(problem)
# MsigmaDeriv = problem.MeSigmaDeriv(ePri[:,0]) + problem.MeSigmaDeriv(ePri[:,1])
# MsigmaDeriv = problem.MeSigmaDeriv(np.sum(ePri,axis=1))
if adjoint:
return sp.hstack((problem.MeSigmaDeriv(ePri[:, 0]).T, problem.MeSigmaDeriv(ePri[:, 1]).T)) * v
else:
return np.hstack(
(mkvc(problem.MeSigmaDeriv(ePri[:, 0]) * v, 2), mkvc(problem.MeSigmaDeriv(ePri[:, 1]) * v, 2))
)
if adjoint:
#
return MsigmaDeriv.T * v
else:
# v should be nC size
return MsigmaDeriv * v
def Wsmall(self):
"""Regularization matrix Wsmall"""
if getattr(self, "_Wsmall", None) is None:
vecs = []
for imodel in range(self.nModels):
vecs.append((self.regmesh.vol * self.alpha_s * self.wght * self.ratios[imodel]) ** 0.5)
self._Wsmall = Utils.sdiag(np.hstack(vecs))
return self._Wsmall
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 getADeriv_m(self, freq, u, v, adjoint=False):
"""
Calculate the derivative of A wrt m.
"""
# This considers both polarizations and returns a nE,2 matrix for each polarization
if adjoint:
dMe_dsigV = sp.hstack(( self.MeSigmaDeriv( u['e_pxSolution'] ).T, self.MeSigmaDeriv(u['e_pySolution'] ).T ))*v
else:
# Need a nE,2 matrix to be returned
dMe_dsigV = np.hstack(( mkvc(self.MeSigmaDeriv( u['e_pxSolution'] )*v,2), mkvc( self.MeSigmaDeriv(u['e_pySolution'] )*v,2) ))
return 1j * omega(freq) * dMe_dsigV
def fromRecArray(cls, recArray, srcType='primary'):
"""
Class method that reads in a numpy record array to MTdata object.
Only imports the impedance data.
"""
if srcType == 'primary':
src = simpegMT.SurveyMT.srcMT_polxy_1Dprimary
elif srcType == 'total':
src = sdsimpegMT.SurveyMT.srcMT_polxy_1DhomotD
else:
raise NotImplementedError(
'{:s} is not a valid source type for MTdata')
# Find all the frequencies in recArray
uniFreq = np.unique(recArray['freq'])
srcList = []
dataList = []
for freq in uniFreq:
# Initiate rxList
rxList = []
# Find that data for freq
dFreq = recArray[recArray['freq'] == freq].copy()
# Find the impedance rxTypes in the recArray.
rxTypes = [
comp for comp in recArray.dtype.names
if (len(comp) == 4 or len(comp) == 3) and 'z' in comp
]
for rxType in rxTypes:
# Find index of not nan values in rxType
notNaNind = ~np.isnan(dFreq[rxType])
if np.any(
notNaNind): # Make sure that there is any data to add.
locs = rec2ndarr(dFreq[['x', 'y', 'z']][notNaNind].copy())
if dFreq[rxType].dtype.name in 'complex128':
rxList.append(
simpegMT.SurveyMT.RxMT(locs, rxType + 'r'))
dataList.append(dFreq[rxType][notNaNind].real.copy())
rxList.append(
simpegMT.SurveyMT.RxMT(locs, rxType + 'i'))
dataList.append(dFreq[rxType][notNaNind].imag.copy())
else:
rxList.append(simpegMT.SurveyMT.RxMT(locs, rxType))
dataList.append(dFreq[rxType][notNaNind].copy())
srcList.append(src(rxList, freq))
# Make a survey
survey = simpegMT.SurveyMT.SurveyMT(srcList)
dataVec = np.hstack(dataList)
return cls(survey, dataVec)
def unpackdx(fid,nrows):
for ii in range(nrows):
line = fid.readline()
var = np.array(line.split(),dtype=float)
if ii==0:
x0= var[0]
xvec = np.ones(int(var[2])) * (var[1] - var[0]) / int(var[2])
xend = var[1]
else:
xvec = np.hstack((xvec,np.ones(int(var[1])) * (var[0] - xend) / int(var[1])))
xend = var[0]
return x0, xvec
def getADeriv_m(self, freq, u, v, adjoint=False):
"""
Calculate the derivative of A wrt m.
"""
# This considers both polarizations and returns a nE,2 matrix for each polarization
if adjoint:
dMe_dsigV = sp.hstack((self.MeSigmaDeriv(u['e_pxSolution']).T,
self.MeSigmaDeriv(u['e_pySolution']).T)) * v
else:
# Need a nE,2 matrix to be returned
dMe_dsigV = np.hstack(
(mkvc(self.MeSigmaDeriv(u['e_pxSolution']) * v,
2), mkvc(self.MeSigmaDeriv(u['e_pySolution']) * v, 2)))
return 1j * omega(freq) * dMe_dsigV
def unpackdx(fid,nrows):
for ii in range(nrows):
line = fid.readline()
var = np.array(line.split(),dtype=float)
if ii==0:
x0= var[0]
xvec = np.ones(int(var[2])) * (var[1] - var[0]) / int(var[2])
xend = var[1]
else:
xvec = np.hstack((xvec,np.ones(int(var[1])) * (var[0] - xend) / int(var[1])))
xend = var[0]
return x0, xvec
def fromRecArray(cls, recArray, srcType='primary'):
"""
Class method that reads in a numpy record array to MTdata object.
Only imports the impedance data.
"""
if srcType=='primary':
src = SrcMT.polxy_1Dprimary
elif srcType=='total':
src = SrcMT.polxy_1DhomotD
else:
raise NotImplementedError('{:s} is not a valid source type for MTdata')
# Find all the frequencies in recArray
uniFreq = np.unique(recArray['freq'])
srcList = []
dataList = []
for freq in uniFreq:
# Initiate rxList
rxList = []
# Find that data for freq
dFreq = recArray[recArray['freq'] == freq].copy()
# Find the impedance rxTypes in the recArray.
rxTypes = [ comp for comp in recArray.dtype.names if (len(comp)==4 or len(comp)==3) and 'z' in comp]
for rxType in rxTypes:
# Find index of not nan values in rxType
notNaNind = ~np.isnan(dFreq[rxType])
if np.any(notNaNind): # Make sure that there is any data to add.
locs = rec2ndarr(dFreq[['x','y','z']][notNaNind].copy())
if dFreq[rxType].dtype.name in 'complex128':
rxList.append(Rx(locs,rxType+'r'))
dataList.append(dFreq[rxType][notNaNind].real.copy())
rxList.append(Rx(locs,rxType+'i'))
dataList.append(dFreq[rxType][notNaNind].imag.copy())
else:
rxList.append(Rx(locs,rxType))
dataList.append(dFreq[rxType][notNaNind].copy())
srcList.append(src(rxList,freq))
# Make a survey
survey = Survey(srcList)
dataVec = np.hstack(dataList)
return cls(survey,dataVec)
def run(plotIt=True):
"""
Maps: Parametrized Block in a Layer
===================================
Parametrized description of a block confined to a layer in a
wholespace. The mapping can be applied in 2D or 3D. Here we show a 2D
example.
The model is given by
.. code::
m = np.r_[
'value of the background',
'value in the layer',
'value in the block',
'center of the layer (depth)',
'thickness of the layer',
'x-center of block',
'width of the block'
]
"""
mesh = Mesh.TensorMesh([50, 50], x0='CC') # 2D Tensor Mesh
mapping = Maps.ParametrizedBlockInLayer(mesh) # mapping
m = np.hstack(np.r_[1., # value of the background
2., # value in the layer
3., # value in the block
-0.1, # center of the layer (depth)
0.2, # thickness of the layer
0.3, # x-center of block
0.2 # width of the block
])
# apply the mapping to define the physical property on the mesh
rho = mapping * m
if plotIt is True:
fig, ax = plt.subplots(1, 1, figsize=(4, 6))
mesh.plotImage(rho, ax=ax)
def getADeriv_m(self, freq, u, v, adjoint=False):
# Nee to account for both the polarizations
# dMe_dsig = (self.MeSigmaDeriv( u['e_pxSolution'] ) + self.MeSigmaDeriv( u['e_pySolution'] ))
# dMe_dsig = (self.MeSigmaDeriv( u['e_pxSolution'] + u['e_pySolution'] ))
# # dMe_dsig = self.MeSigmaDeriv( u )
# if adjoint:
# return 1j * omega(freq) * ( dMe_dsig.T * v ) # As in simpegEM
# return 1j * omega(freq) * ( dMe_dsig * v ) # As in simpegEM
# This considers both polarizations and returns a nE,2 matrix for each polarization
if adjoint:
dMe_dsigV = sp.hstack((self.MeSigmaDeriv(u['e_pxSolution']).T,
self.MeSigmaDeriv(u['e_pySolution']).T)) * v
else:
# Need a nE,2 matrix to be returned
dMe_dsigV = np.hstack(
(mkvc(self.MeSigmaDeriv(u['e_pxSolution']) * v,
2), mkvc(self.MeSigmaDeriv(u['e_pySolution']) * v, 2)))
return 1j * omega(freq) * dMe_dsigV
def Jvec(self, m, v, f=None):
"""
Sensitivity times a vector.
:param numpy.array m: inversion model (nP,)
:param numpy.array v: vector which we take sensitivity product with (nP,)
:param SimPEG.EM.FDEM.FieldsFDEM.FieldsFDEM u: fields object
:rtype: numpy.array
:return: Jv (ndata,)
"""
if f is None:
f = self.fields(m)
self.curModel = m
# Jv = self.dataPair(self.survey)
Jv = []
for freq in self.survey.freqs:
A = self.getA(freq)
Ainv = self.Solver(A, **self.solverOpts) # create the concept of Ainv (actually a solve)
for src in self.survey.getSrcByFreq(freq):
u_src = f[src, self._solutionType]
dA_dm_v = self.getADeriv(freq, u_src, v)
dRHS_dm_v = self.getRHSDeriv(freq, src, v)
du_dm_v = Ainv * ( - dA_dm_v + dRHS_dm_v )
for rx in src.rxList:
df_dmFun = getattr(f, '_{0}Deriv'.format(rx.projField), None)
df_dm_v = df_dmFun(src, du_dm_v, v, adjoint=False)
# Jv[src, rx] = rx.evalDeriv(src, self.mesh, f, df_dm_v)
Jv.append(rx.evalDeriv(src, self.mesh, f, df_dm_v))
Ainv.clean()
# return Utils.mkvc(Jv)
return np.hstack(Jv)
def run(plotIt=True):
"""
Maps: Parametrized Layer
========================
Build a model of a parametrized layer in a wholespace. If you want to
build a model of a parametrized layer in a halfspace, also use
Maps.InjectActiveCell.
The model is
.. code::
m = [
'background physical property value',
'layer physical property value',
'layer center',
'layer thickness'
]
"""
mesh = Mesh.TensorMesh([50, 50], x0='CC') # 2D tensor mesh
mapping = Maps.ParametrizedLayer(mesh) # parametrized layer in wholespace
# model
m = np.hstack(np.r_[1., # background value
2., # layer value
-0.1, # layer center
0.2 # layer thickness
])
rho = mapping * m # apply the mapping
if plotIt is True:
fig, ax = plt.subplots(1, 1, figsize=(4, 6))
mesh.plotImage(rho, ax=ax)
def evalDeriv(self, src, mesh, f, v, adjoint=False):
"""
The derivative of the projection wrt u
:param MTsrc src: MT source
:param TensorMesh mesh: Mesh defining the topology of the problem
:param MTfields f: MT fields object of the source
:param numpy.ndarray v: Random vector of size
"""
real_or_imag = self.projComp
if not adjoint:
if self.projType is 'Z1D':
Pex = mesh.getInterpolationMat(self.locs[:,-1],'Fx')
Pbx = mesh.getInterpolationMat(self.locs[:,-1],'Ex')
# ex = Pex*mkvc(f[src,'e_1d'],2)
# bx = Pbx*mkvc(f[src,'b_1d'],2)/mu_0
dP_de = -mkvc(Utils.sdiag(1./(Pbx*mkvc(f[src,'b_1d'],2)/mu_0))*(Pex*v),2)
dP_db = mkvc( Utils.sdiag(Pex*mkvc(f[src,'e_1d'],2))*(Utils.sdiag(1./(Pbx*mkvc(f[src,'b_1d'],2)/mu_0)).T*Utils.sdiag(1./(Pbx*mkvc(f[src,'b_1d'],2)/mu_0)))*(Pbx*f._bDeriv_u(src,v)/mu_0),2)
PDeriv_complex = np.sum(np.hstack((dP_de,dP_db)),1)
elif self.projType is 'Z2D':
raise NotImplementedError('Has not been implement for 2D impedance tensor')
elif self.projType is 'Z3D':
if self.locs.ndim == 3:
eFLocs = self.locs[:,:,0]
bFLocs = self.locs[:,:,1]
else:
eFLocs = self.locs
bFLocs = self.locs
# Get the projection
Pex = mesh.getInterpolationMat(eFLocs,'Ex')
Pey = mesh.getInterpolationMat(eFLocs,'Ey')
Pbx = mesh.getInterpolationMat(bFLocs,'Fx')
Pby = mesh.getInterpolationMat(bFLocs,'Fy')
# Get the fields at location
# px: x-polaration and py: y-polaration.
ex_px = Pex*f[src,'e_px']
ey_px = Pey*f[src,'e_px']
ex_py = Pex*f[src,'e_py']
ey_py = Pey*f[src,'e_py']
hx_px = Pbx*f[src,'b_px']/mu_0
hy_px = Pby*f[src,'b_px']/mu_0
hx_py = Pbx*f[src,'b_py']/mu_0
hy_py = Pby*f[src,'b_py']/mu_0
# Derivatives as lambda functions
# The size of the diratives should be nD,nU
ex_px_u = lambda vec: Pex*f._e_pxDeriv_u(src,vec)
ey_px_u = lambda vec: Pey*f._e_pxDeriv_u(src,vec)
ex_py_u = lambda vec: Pex*f._e_pyDeriv_u(src,vec)
ey_py_u = lambda vec: Pey*f._e_pyDeriv_u(src,vec)
# NOTE: Think b_p?Deriv_u should return a 2*nF size matrix
hx_px_u = lambda vec: Pbx*f._b_pxDeriv_u(src,vec)/mu_0
hy_px_u = lambda vec: Pby*f._b_pxDeriv_u(src,vec)/mu_0
hx_py_u = lambda vec: Pbx*f._b_pyDeriv_u(src,vec)/mu_0
hy_py_u = lambda vec: Pby*f._b_pyDeriv_u(src,vec)/mu_0
# Update the input vector
sDiag = lambda t: Utils.sdiag(mkvc(t,2))
# Define the components of the derivative
Hd = sDiag(1./(sDiag(hx_px)*hy_py - sDiag(hx_py)*hy_px))
Hd_uV = sDiag(hy_py)*hx_px_u(v) + sDiag(hx_px)*hy_py_u(v) - sDiag(hx_py)*hy_px_u(v) - sDiag(hy_px)*hx_py_u(v)
# Calculate components
if 'zxx' in self.rxType:
Zij = sDiag(Hd*( sDiag(ex_px)*hy_py - sDiag(ex_py)*hy_px ))
ZijN_uV = sDiag(hy_py)*ex_px_u(v) + sDiag(ex_px)*hy_py_u(v) - sDiag(ex_py)*hy_px_u(v) - sDiag(hy_px)*ex_py_u(v)
elif 'zxy' in self.rxType:
Zij = sDiag(Hd*(-sDiag(ex_px)*hx_py + sDiag(ex_py)*hx_px ))
ZijN_uV = -sDiag(hx_py)*ex_px_u(v) - sDiag(ex_px)*hx_py_u(v) + sDiag(ex_py)*hx_px_u(v) + sDiag(hx_px)*ex_py_u(v)
elif 'zyx' in self.rxType:
Zij = sDiag(Hd*( sDiag(ey_px)*hy_py - sDiag(ey_py)*hy_px ))
ZijN_uV = sDiag(hy_py)*ey_px_u(v) + sDiag(ey_px)*hy_py_u(v) - sDiag(ey_py)*hy_px_u(v) - sDiag(hy_px)*ey_py_u(v)
elif 'zyy' in self.rxType:
Zij = sDiag(Hd*(-sDiag(ey_px)*hx_py + sDiag(ey_py)*hx_px ))
ZijN_uV = -sDiag(hx_py)*ey_px_u(v) - sDiag(ey_px)*hx_py_u(v) + sDiag(ey_py)*hx_px_u(v) + sDiag(hx_px)*ey_py_u(v)
# Calculate the complex derivative
PDeriv_complex = Hd * (ZijN_uV - Zij * Hd_uV )
elif self.projType is 'T3D':
if self.locs.ndim == 3:
eFLocs = self.locs[:,:,0]
bFLocs = self.locs[:,:,1]
else:
eFLocs = self.locs
bFLocs = self.locs
# Get the projection
Pbx = mesh.getInterpolationMat(bFLocs,'Fx')
Pby = mesh.getInterpolationMat(bFLocs,'Fy')
Pbz = mesh.getInterpolationMat(bFLocs,'Fz')
# Get the fields at location
# px: x-polaration and py: y-polaration.
bx_px = Pbx*f[src,'b_px']
by_px = Pby*f[src,'b_px']
bz_px = Pbz*f[src,'b_px']
bx_py = Pbx*f[src,'b_py']
by_py = Pby*f[src,'b_py']
bz_py = Pbz*f[src,'b_py']
# Derivatives as lambda functions
# NOTE: Think b_p?Deriv_u should return a 2*nF size matrix
bx_px_u = lambda vec: Pbx*f._b_pxDeriv_u(src,vec)
by_px_u = lambda vec: Pby*f._b_pxDeriv_u(src,vec)
bz_px_u = lambda vec: Pbz*f._b_pxDeriv_u(src,vec)
bx_py_u = lambda vec: Pbx*f._b_pyDeriv_u(src,vec)
by_py_u = lambda vec: Pby*f._b_pyDeriv_u(src,vec)
bz_py_u = lambda vec: Pbz*f._b_pyDeriv_u(src,vec)
# Update the input vector
sDiag = lambda t: Utils.sdiag(mkvc(t,2))
# Define the components of the derivative
Hd = sDiag(1./(sDiag(bx_px)*by_py - sDiag(bx_py)*by_px))
Hd_uV = sDiag(by_py)*bx_px_u(v) + sDiag(bx_px)*by_py_u(v) - sDiag(bx_py)*by_px_u(v) - sDiag(by_px)*bx_py_u(v)
if 'tzx' in self.rxType:
Tij = sDiag(Hd*( - sDiag(by_px)*bz_py + sDiag(by_py)*bz_px ))
TijN_uV = -sDiag(by_px)*bz_py_u(v) - sDiag(bz_py)*by_px_u(v) + sDiag(by_py)*bz_px_u(v) + sDiag(bz_px)*by_py_u(v)
elif 'tzy' in self.rxType:
Tij = sDiag(Hd*( sDiag(bx_px)*bz_py - sDiag(bx_py)*bz_px ))
TijN_uV = sDiag(bz_py)*bx_px_u(v) + sDiag(bx_px)*bz_py_u(v) - sDiag(bx_py)*bz_px_u(v) - sDiag(bz_px)*bx_py_u(v)
# Calculate the complex derivative
PDeriv_complex = Hd * (TijN_uV - Tij * Hd_uV )
# Extract the real number for the real/imag components.
Pv = np.array(getattr(PDeriv_complex, real_or_imag))
elif adjoint:
# Note: The v vector is real and the return should be complex
if self.projType is 'Z1D':
Pex = mesh.getInterpolationMat(self.locs[:,-1],'Fx')
Pbx = mesh.getInterpolationMat(self.locs[:,-1],'Ex')
# ex = Pex*mkvc(f[src,'e_1d'],2)
# bx = Pbx*mkvc(f[src,'b_1d'],2)/mu_0
dP_deTv = -mkvc(Pex.T*Utils.sdiag(1./(Pbx*mkvc(f[src,'b_1d'],2)/mu_0)).T*v,2)
db_duv = Pbx.T/mu_0*Utils.sdiag(1./(Pbx*mkvc(f[src,'b_1d'],2)/mu_0))*(Utils.sdiag(1./(Pbx*mkvc(f[src,'b_1d'],2)/mu_0))).T*Utils.sdiag(Pex*mkvc(f[src,'e_1d'],2)).T*v
dP_dbTv = mkvc(f._bDeriv_u(src,db_duv,adjoint=True),2)
PDeriv_real = np.sum(np.hstack((dP_deTv,dP_dbTv)),1)
elif self.projType is 'Z2D':
raise NotImplementedError('Has not be implement for 2D impedance tensor')
elif self.projType is 'Z3D':
if self.locs.ndim == 3:
eFLocs = self.locs[:,:,0]
bFLocs = self.locs[:,:,1]
else:
eFLocs = self.locs
bFLocs = self.locs
# Get the projection
Pex = mesh.getInterpolationMat(eFLocs,'Ex')
Pey = mesh.getInterpolationMat(eFLocs,'Ey')
Pbx = mesh.getInterpolationMat(bFLocs,'Fx')
Pby = mesh.getInterpolationMat(bFLocs,'Fy')
# Get the fields at location
# px: x-polaration and py: y-polaration.
aex_px = mkvc(mkvc(f[src,'e_px'],2).T*Pex.T)
aey_px = mkvc(mkvc(f[src,'e_px'],2).T*Pey.T)
aex_py = mkvc(mkvc(f[src,'e_py'],2).T*Pex.T)
aey_py = mkvc(mkvc(f[src,'e_py'],2).T*Pey.T)
ahx_px = mkvc(mkvc(f[src,'b_px'],2).T/mu_0*Pbx.T)
ahy_px = mkvc(mkvc(f[src,'b_px'],2).T/mu_0*Pby.T)
ahx_py = mkvc(mkvc(f[src,'b_py'],2).T/mu_0*Pbx.T)
ahy_py = mkvc(mkvc(f[src,'b_py'],2).T/mu_0*Pby.T)
# Derivatives as lambda functions
aex_px_u = lambda vec: f._e_pxDeriv_u(src,Pex.T*vec,adjoint=True)
aey_px_u = lambda vec: f._e_pxDeriv_u(src,Pey.T*vec,adjoint=True)
aex_py_u = lambda vec: f._e_pyDeriv_u(src,Pex.T*vec,adjoint=True)
aey_py_u = lambda vec: f._e_pyDeriv_u(src,Pey.T*vec,adjoint=True)
ahx_px_u = lambda vec: f._b_pxDeriv_u(src,Pbx.T*vec,adjoint=True)/mu_0
ahy_px_u = lambda vec: f._b_pxDeriv_u(src,Pby.T*vec,adjoint=True)/mu_0
ahx_py_u = lambda vec: f._b_pyDeriv_u(src,Pbx.T*vec,adjoint=True)/mu_0
ahy_py_u = lambda vec: f._b_pyDeriv_u(src,Pby.T*vec,adjoint=True)/mu_0
# Update the input vector
# Define shortcuts
sDiag = lambda t: Utils.sdiag(mkvc(t,2))
sVec = lambda t: Utils.sp.csr_matrix(mkvc(t,2))
# Define the components of the derivative
aHd = sDiag(1./(sDiag(ahx_px)*ahy_py - sDiag(ahx_py)*ahy_px))
aHd_uV = lambda x: ahx_px_u(sDiag(ahy_py)*x) + ahx_px_u(sDiag(ahy_py)*x) - ahy_px_u(sDiag(ahx_py)*x) - ahx_py_u(sDiag(ahy_px)*x)
# Need to fix this to reflect the adjoint
if 'zxx' in self.rxType:
Zij = sDiag(aHd*( sDiag(ahy_py)*aex_px - sDiag(ahy_px)*aex_py))
ZijN_uV = lambda x: aex_px_u(sDiag(ahy_py)*x) + ahy_py_u(sDiag(aex_px)*x) - ahy_px_u(sDiag(aex_py)*x) - aex_py_u(sDiag(ahy_px)*x)
elif 'zxy' in self.rxType:
Zij = sDiag(aHd*(-sDiag(ahx_py)*aex_px + sDiag(ahx_px)*aex_py))
ZijN_uV = lambda x:-aex_px_u(sDiag(ahx_py)*x) - ahx_py_u(sDiag(aex_px)*x) + ahx_px_u(sDiag(aex_py)*x) + aex_py_u(sDiag(ahx_px)*x)
elif 'zyx' in self.rxType:
Zij = sDiag(aHd*( sDiag(ahy_py)*aey_px - sDiag(ahy_px)*aey_py))
ZijN_uV = lambda x: aey_px_u(sDiag(ahy_py)*x) + ahy_py_u(sDiag(aey_px)*x) - ahy_px_u(sDiag(aey_py)*x) - aey_py_u(sDiag(ahy_px)*x)
elif 'zyy' in self.rxType:
Zij = sDiag(aHd*(-sDiag(ahx_py)*aey_px + sDiag(ahx_px)*aey_py))
ZijN_uV = lambda x:-aey_px_u(sDiag(ahx_py)*x) - ahx_py_u(sDiag(aey_px)*x) + ahx_px_u(sDiag(aey_py)*x) + aey_py_u(sDiag(ahx_px)*x)
# Calculate the complex derivative
PDeriv_real = ZijN_uV(aHd*v) - aHd_uV(Zij.T*aHd*v)#
# NOTE: Need to reshape the output to go from 2*nU array to a (nU,2) matrix for each polarization
# PDeriv_real = np.hstack((mkvc(PDeriv_real[:len(PDeriv_real)/2],2),mkvc(PDeriv_real[len(PDeriv_real)/2::],2)))
PDeriv_real = PDeriv_real.reshape((2,mesh.nE)).T
elif self.projType is 'T3D':
if self.locs.ndim == 3:
bFLocs = self.locs[:,:,1]
else:
bFLocs = self.locs
# Get the projection
Pbx = mesh.getInterpolationMat(bFLocs,'Fx')
Pby = mesh.getInterpolationMat(bFLocs,'Fy')
Pbz = mesh.getInterpolationMat(bFLocs,'Fz')
# Get the fields at location
# px: x-polaration and py: y-polaration.
abx_px = mkvc(mkvc(f[src,'b_px'],2).T*Pbx.T)
aby_px = mkvc(mkvc(f[src,'b_px'],2).T*Pby.T)
abz_px = mkvc(mkvc(f[src,'b_px'],2).T*Pbz.T)
abx_py = mkvc(mkvc(f[src,'b_py'],2).T*Pbx.T)
aby_py = mkvc(mkvc(f[src,'b_py'],2).T*Pby.T)
abz_py = mkvc(mkvc(f[src,'b_py'],2).T*Pbz.T)
# Derivatives as lambda functions
abx_px_u = lambda vec: f._b_pxDeriv_u(src,Pbx.T*vec,adjoint=True)
aby_px_u = lambda vec: f._b_pxDeriv_u(src,Pby.T*vec,adjoint=True)
abz_px_u = lambda vec: f._b_pxDeriv_u(src,Pbz.T*vec,adjoint=True)
abx_py_u = lambda vec: f._b_pyDeriv_u(src,Pbx.T*vec,adjoint=True)
aby_py_u = lambda vec: f._b_pyDeriv_u(src,Pby.T*vec,adjoint=True)
abz_py_u = lambda vec: f._b_pyDeriv_u(src,Pbz.T*vec,adjoint=True)
# Update the input vector
# Define shortcuts
sDiag = lambda t: Utils.sdiag(mkvc(t,2))
sVec = lambda t: Utils.sp.csr_matrix(mkvc(t,2))
# Define the components of the derivative
aHd = sDiag(1./(sDiag(abx_px)*aby_py - sDiag(abx_py)*aby_px))
aHd_uV = lambda x: abx_px_u(sDiag(aby_py)*x) + abx_px_u(sDiag(aby_py)*x) - aby_px_u(sDiag(abx_py)*x) - abx_py_u(sDiag(aby_px)*x)
# Need to fix this to reflect the adjoint
if 'tzx' in self.rxType:
Tij = sDiag(aHd*( -sDiag(abz_py)*aby_px + sDiag(abz_px)*aby_py))
TijN_uV = lambda x: -abz_py_u(sDiag(aby_px)*x) - aby_px_u(sDiag(abz_py)*x) + aby_py_u(sDiag(abz_px)*x) + abz_px_u(sDiag(aby_py)*x)
elif 'tzy' in self.rxType:
Tij = sDiag(aHd*( sDiag(abz_py)*abx_px - sDiag(abz_px)*abx_py))
TijN_uV = lambda x: abx_px_u(sDiag(abz_py)*x) + abz_py_u(sDiag(abx_px)*x) - abx_py_u(sDiag(abz_px)*x) - abz_px_u(sDiag(abx_py)*x)
# Calculate the complex derivative
PDeriv_real = TijN_uV(aHd*v) - aHd_uV(Tij.T*aHd*v)#
# NOTE: Need to reshape the output to go from 2*nU array to a (nU,2) matrix for each polarization
# PDeriv_real = np.hstack((mkvc(PDeriv_real[:len(PDeriv_real)/2],2),mkvc(PDeriv_real[len(PDeriv_real)/2::],2)))
PDeriv_real = PDeriv_real.reshape((2,mesh.nE)).T
# Extract the data
if real_or_imag == 'imag':
Pv = 1j*PDeriv_real
elif real_or_imag == 'real':
Pv = PDeriv_real.astype(complex)
return Pv
def plot_pseudoSection(DCsurvey, axs, stype):
"""
Read list of 2D tx-rx location and plot a speudo-section of apparent
resistivity.
Assumes flat topo for now...
Input:
:param d2D, z0
:switch stype -> Either 'pdp' (pole-dipole) | 'dpdp' (dipole-dipole)
Output:
:figure scatter plot overlayed on image
Edited Feb 17th, 2016
@author: dominiquef
"""
from SimPEG import np
from scipy.interpolate import griddata
import pylab as plt
# Set depth to 0 for now
z0 = 0.
# Pre-allocate
midx = []
midz = []
rho = []
count = 0 # Counter for data
for ii in range(DCsurvey.nSrc):
Tx = DCsurvey.srcList[ii].loc
Rx = DCsurvey.srcList[ii].rxList[0].locs
nD = DCsurvey.srcList[ii].rxList[0].nD
data = DCsurvey.dobs[count:count+nD]
count += nD
# Get distances between each poles A-B-M-N
MA = np.abs(Tx[0][0] - Rx[0][:,0])
MB = np.abs(Tx[1][0] - Rx[0][:,0])
NB = np.abs(Tx[1][0] - Rx[1][:,0])
NA = np.abs(Tx[0][0] - Rx[1][:,0])
MN = np.abs(Rx[1][:,0] - Rx[0][:,0])
# Create mid-point location
Cmid = (Tx[0][0] + Tx[1][0])/2
Pmid = (Rx[0][:,0] + Rx[1][:,0])/2
# Compute pant leg of apparent rho
if stype == 'pdp':
leg = data * 2*np.pi * MA * ( MA + MN ) / MN
leg = np.log10(abs(1/leg))
elif stype == 'dpdp':
leg = data * 2*np.pi / ( 1/MA - 1/MB - 1/NB + 1/NA )
midx = np.hstack([midx, ( Cmid + Pmid )/2 ])
midz = np.hstack([midz, -np.abs(Cmid-Pmid)/2 + z0 ])
rho = np.hstack([rho,leg])
ax = axs
# Grid points
grid_x, grid_z = np.mgrid[np.min(midx):np.max(midx), np.min(midz):np.max(midz)]
grid_rho = griddata(np.c_[midx,midz], rho.T, (grid_x, grid_z), method='linear')
plt.imshow(grid_rho.T, extent = (np.min(midx),np.max(midx),np.min(midz),np.max(midz)), origin='lower', alpha=0.8, vmin = np.min(rho), vmax = np.max(rho))
cbar = plt.colorbar(format = '%.2f',fraction=0.04,orientation="horizontal")
cmin,cmax = cbar.get_clim()
ticks = np.linspace(cmin,cmax,3)
cbar.set_ticks(ticks)
# Plot apparent resistivity
plt.scatter(midx,midz,s=50,c=rho.T)
ax.set_xticklabels([])
ax.set_ylabel('Z')
ax.yaxis.tick_right()
ax.yaxis.set_label_position('right')
plt.gca().set_aspect('equal', adjustable='box')
return ax
def plot_pseudoSection(DCsurvey, axs, stype='dpdp', dtype="appc", clim=None):
"""
Read list of 2D tx-rx location and plot a speudo-section of apparent
resistivity.
Assumes flat topo for now...
Input:
:param d2D, z0
:switch stype -> Either 'pdp' (pole-dipole) | 'dpdp' (dipole-dipole)
:switch dtype=-> Either 'appr' (app. res) | 'appc' (app. con) | 'volt' (potential)
Output:
:figure scatter plot overlayed on image
Edited Feb 17th, 2016
@author: dominiquef
"""
from SimPEG import np
from scipy.interpolate import griddata
import pylab as plt
# Set depth to 0 for now
z0 = 0.
# Pre-allocate
midx = []
midz = []
rho = []
LEG = []
count = 0 # Counter for data
for ii in range(DCsurvey.nSrc):
Tx = DCsurvey.srcList[ii].loc
Rx = DCsurvey.srcList[ii].rxList[0].locs
nD = DCsurvey.srcList[ii].rxList[0].nD
data = DCsurvey.dobs[count:count + nD]
count += nD
# Get distances between each poles A-B-M-N
if stype == 'pdp':
MA = np.abs(Tx[0] - Rx[0][:, 0])
NA = np.abs(Tx[0] - Rx[1][:, 0])
MN = np.abs(Rx[1][:, 0] - Rx[0][:, 0])
# Create mid-point location
Cmid = Tx[0]
Pmid = (Rx[0][:, 0] + Rx[1][:, 0]) / 2
if DCsurvey.mesh.dim == 2:
zsrc = Tx[1]
elif DCsurvey.mesh.dim == 3:
zsrc = Tx[2]
elif stype == 'dpdp':
MA = np.abs(Tx[0][0] - Rx[0][:, 0])
MB = np.abs(Tx[1][0] - Rx[0][:, 0])
NA = np.abs(Tx[0][0] - Rx[1][:, 0])
NB = np.abs(Tx[1][0] - Rx[1][:, 0])
# Create mid-point location
Cmid = (Tx[0][0] + Tx[1][0]) / 2
Pmid = (Rx[0][:, 0] + Rx[1][:, 0]) / 2
if DCsurvey.mesh.dim == 2:
zsrc = (Tx[0][1] + Tx[1][1]) / 2
elif DCsurvey.mesh.dim == 3:
zsrc = (Tx[0][2] + Tx[1][2]) / 2
# Change output for dtype
if dtype == 'volt':
rho = np.hstack([rho, data])
else:
# Compute pant leg of apparent rho
if stype == 'pdp':
leg = data * 2 * np.pi * MA * (MA + MN) / MN
elif stype == 'dpdp':
leg = data * 2 * np.pi / (1 / MA - 1 / MB + 1 / NB - 1 / NA)
LEG.append(1. / (2 * np.pi) *
(1 / MA - 1 / MB + 1 / NB - 1 / NA))
else:
print """dtype must be 'pdp'(pole-dipole) | 'dpdp' (dipole-dipole) """
break
if dtype == 'appc':
leg = np.log10(abs(1. / leg))
rho = np.hstack([rho, leg])
elif dtype == 'appr':
leg = np.log10(abs(leg))
rho = np.hstack([rho, leg])
else:
print """dtype must be 'appr' | 'appc' | 'volt' """
break
midx = np.hstack([midx, (Cmid + Pmid) / 2])
if DCsurvey.mesh.dim == 3:
midz = np.hstack([midz, -np.abs(Cmid - Pmid) / 2 + zsrc])
elif DCsurvey.mesh.dim == 2:
midz = np.hstack([midz, -np.abs(Cmid - Pmid) / 2 + zsrc])
ax = axs
# Grid points
grid_x, grid_z = np.mgrid[np.min(midx):np.max(midx),
np.min(midz):np.max(midz)]
grid_rho = griddata(np.c_[midx, midz],
rho.T, (grid_x, grid_z),
method='linear')
if clim == None:
vmin, vmax = rho.min(), rho.max()
else:
vmin, vmax = clim[0], clim[1]
grid_rho = np.ma.masked_where(np.isnan(grid_rho), grid_rho)
ph = plt.pcolormesh(grid_x[:, 0],
grid_z[0, :],
grid_rho.T,
clim=(vmin, vmax),
vmin=vmin,
vmax=vmax)
cbar = plt.colorbar(format="$10^{%.1f}$",
fraction=0.04,
orientation="horizontal")
cmin, cmax = cbar.get_clim()
ticks = np.linspace(cmin, cmax, 3)
cbar.set_ticks(ticks)
cbar.ax.tick_params(labelsize=10)
if dtype == 'appc':
cbar.set_label("App.Cond", size=12)
elif dtype == 'appr':
cbar.set_label("App.Res.", size=12)
elif dtype == 'volt':
cbar.set_label("Potential (V)", size=12)
# Plot apparent resistivity
ax.scatter(midx,
midz,
s=10,
c=rho.T,
vmin=vmin,
vmax=vmax,
clim=(vmin, vmax))
#ax.set_xticklabels([])
#ax.set_yticklabels([])
plt.gca().set_aspect('equal', adjustable='box')
return ph, LEG
def run(loc=None, sig=None, radi=None, param=None, stype='dpdp', plotIt=True):
"""
DC Forward Simulation
=====================
Forward model conductive spheres in a half-space and plot a pseudo-section
Created by @fourndo on Mon Feb 01 19:28:06 2016
"""
assert stype in ['pdp', 'dpdp'], "Source type (stype) must be pdp or dpdp (pole dipole or dipole dipole)"
if loc is None:
loc = np.c_[[-50.,0.,-50.],[50.,0.,-50.]]
if sig is None:
sig = np.r_[1e-2,1e-1,1e-3]
if radi is None:
radi = np.r_[25.,25.]
if param is None:
param = np.r_[30.,30.,5]
# First we need to create a mesh and a model.
# This is our mesh
dx = 5.
hxind = [(dx,15,-1.3), (dx, 75), (dx,15,1.3)]
hyind = [(dx,15,-1.3), (dx, 10), (dx,15,1.3)]
hzind = [(dx,15,-1.3),(dx, 15)]
mesh = Mesh.TensorMesh([hxind, hyind, hzind], 'CCN')
# Set background conductivity
model = np.ones(mesh.nC) * sig[0]
# First anomaly
ind = Utils.ModelBuilder.getIndicesSphere(loc[:,0],radi[0],mesh.gridCC)
model[ind] = sig[1]
# Second anomaly
ind = Utils.ModelBuilder.getIndicesSphere(loc[:,1],radi[1],mesh.gridCC)
model[ind] = sig[2]
# Get index of the center
indy = int(mesh.nCy/2)
# Plot the model for reference
# Define core mesh extent
xlim = 200
zlim = 125
# Specify the survey type: "pdp" | "dpdp"
# Then specify the end points of the survey. Let's keep it simple for now and survey above the anomalies, top of the mesh
ends = [(-175,0),(175,0)]
ends = np.c_[np.asarray(ends),np.ones(2).T*mesh.vectorNz[-1]]
# Snap the endpoints to the grid. Easier to create 2D section.
indx = Utils.closestPoints(mesh, ends )
locs = np.c_[mesh.gridCC[indx,0],mesh.gridCC[indx,1],np.ones(2).T*mesh.vectorNz[-1]]
# We will handle the geometry of the survey for you and create all the combination of tx-rx along line
# [Tx, Rx] = DC.gen_DCIPsurvey(locs, mesh, stype, param[0], param[1], param[2])
survey, Tx, Rx = DC.gen_DCIPsurvey(locs, mesh, stype, param[0], param[1], param[2])
# Define some global geometry
dl_len = np.sqrt( np.sum((locs[0,:] - locs[1,:])**2) )
dl_x = ( Tx[-1][0,1] - Tx[0][0,0] ) / dl_len
dl_y = ( Tx[-1][1,1] - Tx[0][1,0] ) / dl_len
azm = np.arctan(dl_y/dl_x)
#Set boundary conditions
mesh.setCellGradBC('neumann')
# Define the differential operators needed for the DC problem
Div = mesh.faceDiv
Grad = mesh.cellGrad
Msig = Utils.sdiag(1./(mesh.aveF2CC.T*(1./model)))
A = Div*Msig*Grad
# Change one corner to deal with nullspace
A[0,0] = 1
A = sp.csc_matrix(A)
# We will solve the system iteratively, so a pre-conditioner is helpful
# This is simply a Jacobi preconditioner (inverse of the main diagonal)
dA = A.diagonal()
P = sp.spdiags(1/dA,0,A.shape[0],A.shape[0])
# Now we can solve the system for all the transmitters
# We want to store the data
data = []
# There is probably a more elegant way to do this, but we can just for-loop through the transmitters
for ii in range(len(Tx)):
start_time = time.time() # Let's time the calculations
#print("Transmitter %i / %i\r" % (ii+1,len(Tx)))
# Select dipole locations for receiver
rxloc_M = np.asarray(Rx[ii][:,0:3])
rxloc_N = np.asarray(Rx[ii][:,3:])
# For usual cases "dpdp" or "gradient"
if stype == 'pdp':
# Create an "inifinity" pole
tx = np.squeeze(Tx[ii][:,0:1])
tinf = tx + np.array([dl_x,dl_y,0])*dl_len*2
inds = Utils.closestPoints(mesh, np.c_[tx,tinf].T)
RHS = mesh.getInterpolationMat(np.asarray(Tx[ii]).T, 'CC').T*( [-1] / mesh.vol[inds] )
else:
inds = Utils.closestPoints(mesh, np.asarray(Tx[ii]).T )
RHS = mesh.getInterpolationMat(np.asarray(Tx[ii]).T, 'CC').T*( [-1,1] / mesh.vol[inds] )
# Iterative Solve
Ainvb = sp.linalg.bicgstab(P*A,P*RHS, tol=1e-5)
# We now have the potential everywhere
phi = Utils.mkvc(Ainvb[0])
# Solve for phi on pole locations
P1 = mesh.getInterpolationMat(rxloc_M, 'CC')
P2 = mesh.getInterpolationMat(rxloc_N, 'CC')
# Compute the potential difference
dtemp = (P1*phi - P2*phi)*np.pi
data.append( dtemp )
print '\rTransmitter {0} of {1} -> Time:{2} sec'.format(ii,len(Tx),time.time()- start_time),
print 'Transmitter {0} of {1}'.format(ii,len(Tx))
print 'Forward completed'
# Let's just convert the 3D format into 2D (distance along line) and plot
# [Tx2d, Rx2d] = DC.convertObs_DC3D_to_2D(survey, np.ones(survey.nSrc))
survey2D = DC.convertObs_DC3D_to_2D(survey, np.ones(survey.nSrc))
survey2D.dobs =np.hstack(data)
# Here is an example for the first tx-rx array
if plotIt:
import matplotlib.pyplot as plt
fig = plt.figure()
ax = plt.subplot(2,1,1, aspect='equal')
mesh.plotSlice(np.log10(model), ax =ax, normal = 'Y', ind = indy,grid=True)
ax.set_title('E-W section at '+str(mesh.vectorCCy[indy])+' m')
plt.gca().set_aspect('equal', adjustable='box')
plt.scatter(Tx[0][0,:],Tx[0][2,:],s=40,c='g', marker='v')
plt.scatter(Rx[0][:,0::3],Rx[0][:,2::3],s=40,c='y')
plt.xlim([-xlim,xlim])
plt.ylim([-zlim,mesh.vectorNz[-1]+dx])
ax = plt.subplot(2,1,2, aspect='equal')
# Plot the location of the spheres for reference
circle1=plt.Circle((loc[0,0]-Tx[0][0,0],loc[2,0]),radi[0],color='w',fill=False, lw=3)
circle2=plt.Circle((loc[0,1]-Tx[0][0,0],loc[2,1]),radi[1],color='k',fill=False, lw=3)
ax.add_artist(circle1)
ax.add_artist(circle2)
# Add the speudo section
DC.plot_pseudoSection(survey2D,ax,stype)
# plt.scatter(Tx2d[0][:],Tx[0][2,:],s=40,c='g', marker='v')
# plt.scatter(Rx2d[0][:],Rx[0][:,2::3],s=40,c='y')
# plt.plot(np.r_[Tx2d[0][0],Rx2d[-1][-1,-1]],np.ones(2)*mesh.vectorNz[-1], color='k')
plt.ylim([-zlim,mesh.vectorNz[-1]+dx])
plt.show()
return fig, ax
def animate(ii):
#for ii in range(1):
removeFrame()
# Grab current line and
indx = np.where(lineID == ii)[0]
srcLeft = []
obs_l = []
obs = []
srcRight = []
obs_r = []
srcList = []
# Split the obs file into left and right
# Split the obs file into left and right
for jj in range(len(indx)):
# Grab corresponding data
obs = np.hstack([obs, DCdobs2D.dobs[dataID == indx[jj]]])
#std = dobs2D.std[dataID==indx[jj]]
srcList.append(DCdobs2D.srcList[indx[jj]])
Tx = DCdobs2D.srcList[indx[jj]].loc
Rx = DCdobs2D.srcList[indx[jj]].rxList[0].locs
# Create mid-point location
Cmid = (Tx[0][0] + Tx[1][0]) / 2
Pmid = (Rx[0][:, 0] + Rx[1][:, 0]) / 2
ileft = Pmid < Cmid
iright = Pmid >= Cmid
temp = np.zeros(len(ileft))
temp[ileft] = 1
obs_l = np.hstack([obs_l, temp])
temp = np.zeros(len(iright))
temp[iright] = 1
obs_r = np.hstack([obs_r, temp])
if np.any(ileft):
rx = DC.RxDipole(Rx[0][ileft, :], Rx[1][ileft, :])
srcLeft.append(DC.SrcDipole([rx], Tx[0], Tx[1]))
#std_l = np.hstack([std_l,std[ileft]])
if np.any(iright):
rx = DC.RxDipole(Rx[0][iright, :], Rx[1][iright, :])
srcRight.append(DC.SrcDipole([rx], Tx[0], Tx[1]))
#obs_r = np.hstack([obs_r,iright])
#std_r = np.hstack([std_r,std[iright]])
DC2D_full = DC.SurveyDC(srcList)
DC2D_full.dobs = np.asarray(obs)
DC2D_full.std = DC2D_full.dobs * 0.
DC2D_full.std[obs_l ==
1] = np.abs(DC2D_full.dobs[obs_l == 1]) * 0.02 + 2e-5
DC2D_full.std[obs_r ==
1] = np.abs(DC2D_full.dobs[obs_r == 1]) * 0.06 + 4e-5
# DC2D_l = DC.SurveyDC(srcLeft)
# DC2D_l.dobs = np.asarray(obs[obs_l==1])
# DC2D_l.std = np.abs(np.asarray(DC2D_l.dobs))*0.05 + 2e-5
#
# DC2D_r = DC.SurveyDC(srcRight)
# DC2D_r.dobs = np.asarray(obs[obs_r==1])
# DC2D_r.std = np.abs(np.asarray(DC2D_r.dobs))*0.05 + 2e-5
survey = DC2D_full
# Export data file
DC.writeUBC_DCobs(inv_dir + dsep + obsfile2d, survey, '2D', 'SIMPLE')
# Write input file
fid = open(inv_dir + dsep + inp_file, 'w')
fid.write('OBS LOC_X %s \n' % obsfile2d)
fid.write('MESH FILE %s \n' % mshfile2d)
fid.write('CHIFACT 1 \n')
fid.write('TOPO DEFAULT \n')
fid.write('INIT_MOD VALUE %e\n' % ini_mod)
fid.write('REF_MOD VALUE %e\n' % ref_mod)
fid.write('ALPHA VALUE %f %f %F\n' % (1. / dx**4., 1, 1))
fid.write('WEIGHT DEFAULT\n')
fid.write('STORE_ALL_MODELS FALSE\n')
fid.write('INVMODE CG\n')
#fid.write('CG_PARAM 200 1e-4\n')
fid.write('USE_MREF FALSE\n')
#fid.write('BOUNDS VALUE 1e-4 1e+2\n')
fid.close()
os.chdir(inv_dir)
os.system('dcinv2d ' + inp_file)
#%% Load DC model and predicted data
minv = DC.readUBC_DC2DModel(inv_dir + dsep + 'dcinv2d.con')
minv = np.reshape(minv, (mesh2d.nCy, mesh2d.nCx))
#%% Repeat for IP data
indx = np.where(IPlineID == ii)[0]
srcLeft = []
obs_l = []
std_l = []
srcRight = []
obs_r = []
std_r = []
obs_full = []
std_full = []
srcList = []
# Split the obs file into left and right
for jj in range(len(indx)):
srcList.append(IPdobs2D.srcList[indx[jj]])
# Grab corresponding data
obs = IPdobs2D.dobs[IPdataID == indx[jj]]
std = IPdobs2D.std[IPdataID == indx[jj]]
obs_full = np.hstack([obs_full, obs])
std_full = np.hstack([std_full, std])
Tx = IPdobs2D.srcList[indx[jj]].loc
Rx = IPdobs2D.srcList[indx[jj]].rxList[0].locs
# Create mid-point location
Cmid = (Tx[0][0] + Tx[1][0]) / 2
Pmid = (Rx[0][:, 0] + Rx[1][:, 0]) / 2
ileft = Pmid < Cmid
iright = Pmid >= Cmid
temp = np.zeros(len(ileft))
temp[ileft] = 1
obs_l = np.hstack([obs_l, temp])
temp = np.zeros(len(iright))
temp[iright] = 1
obs_r = np.hstack([obs_r, temp])
if np.any(ileft):
rx = DC.RxDipole(Rx[0][ileft, :], Rx[1][ileft, :])
srcLeft.append(DC.SrcDipole([rx], Tx[0], Tx[1]))
#std_l = np.hstack([std_l,std[ileft]])
if np.any(iright):
rx = DC.RxDipole(Rx[0][iright, :], Rx[1][iright, :])
srcRight.append(DC.SrcDipole([rx], Tx[0], Tx[1]))
IP2D_full = DC.SurveyDC(srcList)
IP2D_full.dobs = np.asarray(obs_full)
IP2D_full.std = np.asarray(std_full)
IP2D_l = DC.SurveyDC(srcLeft)
IP2D_l.dobs = np.asarray(obs_full[obs_l == 1])
#IP2D_l.std = np.abs(np.asarray(obs_l))*0.03 + 2e-2
IP2D_r = DC.SurveyDC(srcRight)
IP2D_r.dobs = np.asarray(obs_full[obs_r == 1])
#IP2D_r.std = np.abs(np.asarray(obs_r))*0.03 + 1e-2
id_lbe = int(IPsurvey.srcList[indx[jj]].loc[0][1])
mesh3d = Mesh.TensorMesh([hx, np.ones(1) * 100., hz],
x0=(-np.sum(padx) + np.min(srcMat[0][:, 0]),
id_lbe - 50,
np.max(srcMat[0][0, 2]) - np.sum(hz)))
Mesh.TensorMesh.writeUBC(mesh3d,
home_dir + dsep + 'Mesh' + str(id_lbe) + '.msh')
global ax1, ax2, ax3, ax5, ax6, fig
ax2 = plt.subplot(3, 2, 2)
ph = DC.plot_pseudoSection(IP2D_r,
ax2,
stype='pdp',
dtype='volt',
colorbar=False)
ax2.set_title('Observed P-DP', fontsize=10)
plt.xlim([xmin, xmax])
plt.ylim([zmin, zmax])
plt.gca().set_aspect('equal', adjustable='box')
ax2.set_xticklabels([])
ax2.set_yticklabels([])
ax1 = plt.subplot(3, 2, 1)
DC.plot_pseudoSection(IP2D_l,
ax1,
stype='pdp',
dtype='volt',
clim=(ph[0].get_clim()[0], ph[0].get_clim()[1]),
colorbar=False)
ax1.set_title('Observed DP-P', fontsize=10)
plt.xlim([xmin, xmax])
plt.ylim([zmin, zmax])
plt.gca().set_aspect('equal', adjustable='box')
ax1.set_xticklabels([])
z = np.linspace(np.min(ph[2]), np.max(ph[2]), 5)
z_label = np.linspace(20, 1, 5)
ax1.set_yticks(map(int, z))
ax1.set_yticklabels(map(str, map(int, z_label)), size=8)
ax1.set_ylabel('n-spacing', fontsize=8)
#%% Add labels
bbox_props = dict(boxstyle="circle,pad=0.3", fc="r", ec="k", lw=1)
ax2.text(0.00,
1,
'A',
transform=ax2.transAxes,
ha="left",
va="center",
size=6,
bbox=bbox_props)
bbox_props = dict(boxstyle="circle,pad=0.3", fc="y", ec="k", lw=1)
ax2.text(0.1,
1,
'M',
transform=ax2.transAxes,
ha="left",
va="center",
size=6,
bbox=bbox_props)
bbox_props = dict(boxstyle="circle,pad=0.3", fc="g", ec="k", lw=1)
ax2.text(0.2,
1,
'N',
transform=ax2.transAxes,
ha="left",
va="center",
size=6,
bbox=bbox_props)
bbox_props = dict(boxstyle="circle,pad=0.3", fc="g", ec="k", lw=1)
ax1.text(0.00,
1,
'N',
transform=ax1.transAxes,
ha="left",
va="center",
size=6,
bbox=bbox_props)
bbox_props = dict(boxstyle="circle,pad=0.3", fc="y", ec="k", lw=1)
ax1.text(0.1,
1,
'M',
transform=ax1.transAxes,
ha="left",
va="center",
size=6,
bbox=bbox_props)
bbox_props = dict(boxstyle="circle,pad=0.3", fc="r", ec="k", lw=1)
ax1.text(0.2,
1,
'A',
transform=ax1.transAxes,
ha="left",
va="center",
size=6,
bbox=bbox_props)
survey = IP2D_full
# Export data file
DC.writeUBC_DCobs(inv_dir + dsep + ipfile2d,
survey,
'2D',
'SIMPLE',
iptype=1)
fid = open(inv_dir + dsep + inp_file, 'w')
fid.write('OBS LOC_X %s \n' % ipfile2d)
fid.write('MESH FILE %s \n' % mshfile2d)
fid.write('CHIFACT 4 \n')
fid.write('COND FILE dcinv2d.con\n')
fid.write('TOPO DEFAULT \n')
fid.write('INIT_MOD VALUE %e\n' % ini_mod)
fid.write('REF_MOD VALUE 0.0\n')
fid.write('ALPHA VALUE %f %f %F\n' % (1. / dx**4., 1, 1))
fid.write('WEIGHT DEFAULT\n')
fid.write('STORE_ALL_MODELS FALSE\n')
fid.write('INVMODE CG\n')
#fid.write('CG_PARAM 200 1e-4\n')
fid.write('USE_MREF FALSE\n')
#fid.write('BOUNDS VALUE 1e-4 1e+2\n')
fid.close()
os.chdir(inv_dir)
os.system('ipinv2d ' + inp_file)
#%% Load model and predicted data
minv = DC.readUBC_DC2DModel(inv_dir + dsep + 'ipinv2d.chg')
minv = np.reshape(minv, (mesh2d.nCy, mesh2d.nCx))
Mesh.TensorMesh.writeModelUBC(
mesh3d, home_dir + dsep + 'Model' + str(id_lbe) + '.chg', minv.T)
dpre = DC.readUBC_DC2Dpre(inv_dir + dsep + 'ipinv2d.pre')
DCpre = dpre['DCsurvey']
DCtemp = IP2D_l
DCtemp.dobs = DCpre.dobs[obs_l == 1]
ax5 = plt.subplot(3, 2, 3)
DC.plot_pseudoSection(DCtemp,
ax5,
stype='pdp',
dtype='volt',
clim=(ph[0].get_clim()[0], ph[0].get_clim()[1]),
colorbar=False)
ax5.set_title('Predicted', fontsize=10)
plt.xlim([xmin, xmax])
plt.ylim([zmin, zmax])
plt.gca().set_aspect('equal', adjustable='box')
ax5.set_xticklabels([])
z = np.linspace(np.min(ph[2]), np.max(ph[2]), 5)
z_label = np.linspace(20, 1, 5)
ax5.set_yticks(map(int, z))
ax5.set_yticklabels(map(str, map(int, z_label)), size=8)
ax5.set_ylabel('n-spacing', fontsize=8)
DCtemp = IP2D_r
DCtemp.dobs = DCpre.dobs[obs_r == 1]
ax6 = plt.subplot(3, 2, 4)
DC.plot_pseudoSection(DCtemp,
ax6,
stype='pdp',
dtype='volt',
clim=(ph[0].get_clim()[0], ph[0].get_clim()[1]),
colorbar=False)
ax6.set_title('Predicted', fontsize=10)
plt.xlim([xmin, xmax])
plt.ylim([zmin, zmax])
plt.gca().set_aspect('equal', adjustable='box')
ax6.set_xticklabels([])
ax6.set_yticklabels([])
pos = ax6.get_position()
cbarax = fig.add_axes([
pos.x0 + 0.325, pos.y0 + 0.2, pos.width * 0.1, pos.height * 0.5
]) ## the parameters are the specified position you set
cb = fig.colorbar(ph[0],
cax=cbarax,
orientation="vertical",
ax=ax6,
ticks=np.linspace(ph[0].get_clim()[0],
ph[0].get_clim()[1], 4),
format="$10^{%.1f}$")
cb.set_label("App. Charg.", size=8)
ax3 = plt.subplot(3, 1, 3)
ax3.set_title('2-D Model (S/m)', fontsize=10)
ax3.set_xticks(map(int, x))
ax3.set_xticklabels(map(str, map(int, x)))
ax3.set_xlabel('Easting (m)', fontsize=8)
ax3.set_yticks(map(int, z))
ax3.set_yticklabels(map(str, map(int, z)), rotation='vertical')
ax3.set_ylabel('Depth (m)', fontsize=8)
plt.xlim([xmin, xmax])
plt.ylim([zmin / 2, zmax])
plt.gca().set_aspect('equal', adjustable='box')
ph2 = plt.pcolormesh(mesh2d.vectorNx,
mesh2d.vectorNy, (minv),
vmin=vmin,
vmax=vmax)
plt.gca().tick_params(axis='both', which='major', labelsize=8)
plt.draw()
for ss in range(survey.nSrc):
Tx = survey.srcList[ss].loc[0]
plt.scatter(Tx[0], mesh2d.vectorNy[-1] + 10, s=10)
pos = ax3.get_position()
ax3.set_position([pos.x0 + 0.025, pos.y0, pos.width, pos.height])
pos = ax3.get_position()
cbarax = fig.add_axes([
pos.x0 + 0.65, pos.y0 + 0.01, pos.width * 0.05, pos.height * 0.75
]) ## the parameters are the specified position you set
cb = fig.colorbar(ph2,
cax=cbarax,
orientation="vertical",
ax=ax3,
ticks=np.linspace(vmin, vmax, 4),
format="%4.1f")
cb.set_label("Chargeability", size=8)
pos = ax1.get_position()
ax1.set_position([pos.x0 + 0.03, pos.y0, pos.width, pos.height])
pos = ax5.get_position()
ax5.set_position([pos.x0 + 0.03, pos.y0, pos.width, pos.height])
pos = ax2.get_position()
ax2.set_position([pos.x0 - 0.03, pos.y0, pos.width, pos.height])
pos = ax6.get_position()
ax6.set_position([pos.x0 - 0.03, pos.y0, pos.width, pos.height])
#%% Add the extra
bbox_props = dict(boxstyle="rarrow,pad=0.3", fc="w", ec="k", lw=2)
ax2.text(0.01, (float(ii) + 1.) / (len(uniqueID) + 2),
'N: ' + str(id_lbe),
transform=fig.transFigure,
ha="left",
va="center",
size=8,
bbox=bbox_props)
mrk_props = dict(boxstyle="square,pad=0.3", fc="w", ec="k", lw=2)
ax2.text(0.01,
0.9,
'Line ID#',
transform=fig.transFigure,
ha="left",
va="center",
size=8,
bbox=mrk_props)
mrk_props = dict(boxstyle="square,pad=0.3", fc="b", ec="k", lw=2)
for jj in range(len(uniqueID)):
ax2.text(0.1, (float(jj) + 1.) / (len(uniqueID) + 2),
".",
transform=fig.transFigure,
ha="right",
va="center",
size=8,
bbox=mrk_props)
mrk_props = dict(boxstyle="square,pad=0.3", fc="r", ec="k", lw=2)
ax2.text(0.1, (float(ii) + 1.) / (len(uniqueID) + 2),
".",
transform=fig.transFigure,
ha="right",
va="center",
size=8,
bbox=mrk_props)
def run(loc=None, sig=None, radi=None, param=None, stype='dpdp', plotIt=True):
"""
DC Forward Simulation
=====================
Forward model conductive spheres in a half-space and plot a pseudo-section
Created by @fourndo on Mon Feb 01 19:28:06 2016
"""
assert stype in [
'pdp', 'dpdp'
], "Source type (stype) must be pdp or dpdp (pole dipole or dipole dipole)"
if loc is None:
loc = np.c_[[-50., 0., -50.], [50., 0., -50.]]
if sig is None:
sig = np.r_[1e-2, 1e-1, 1e-3]
if radi is None:
radi = np.r_[25., 25.]
if param is None:
param = np.r_[30., 30., 5]
# First we need to create a mesh and a model.
# This is our mesh
dx = 5.
hxind = [(dx, 15, -1.3), (dx, 75), (dx, 15, 1.3)]
hyind = [(dx, 15, -1.3), (dx, 10), (dx, 15, 1.3)]
hzind = [(dx, 15, -1.3), (dx, 15)]
mesh = Mesh.TensorMesh([hxind, hyind, hzind], 'CCN')
# Set background conductivity
model = np.ones(mesh.nC) * sig[0]
# First anomaly
ind = Utils.ModelBuilder.getIndicesSphere(loc[:, 0], radi[0], mesh.gridCC)
model[ind] = sig[1]
# Second anomaly
ind = Utils.ModelBuilder.getIndicesSphere(loc[:, 1], radi[1], mesh.gridCC)
model[ind] = sig[2]
# Get index of the center
indy = int(mesh.nCy / 2)
# Plot the model for reference
# Define core mesh extent
xlim = 200
zlim = 125
# Specify the survey type: "pdp" | "dpdp"
# Then specify the end points of the survey. Let's keep it simple for now and survey above the anomalies, top of the mesh
ends = [(-175, 0), (175, 0)]
ends = np.c_[np.asarray(ends), np.ones(2).T * mesh.vectorNz[-1]]
# Snap the endpoints to the grid. Easier to create 2D section.
indx = Utils.closestPoints(mesh, ends)
locs = np.c_[mesh.gridCC[indx, 0], mesh.gridCC[indx, 1],
np.ones(2).T * mesh.vectorNz[-1]]
# We will handle the geometry of the survey for you and create all the combination of tx-rx along line
# [Tx, Rx] = DC.gen_DCIPsurvey(locs, mesh, stype, param[0], param[1], param[2])
survey, Tx, Rx = DC.gen_DCIPsurvey(locs, mesh, stype, param[0], param[1],
param[2])
# Define some global geometry
dl_len = np.sqrt(np.sum((locs[0, :] - locs[1, :])**2))
dl_x = (Tx[-1][0, 1] - Tx[0][0, 0]) / dl_len
dl_y = (Tx[-1][1, 1] - Tx[0][1, 0]) / dl_len
azm = np.arctan(dl_y / dl_x)
#Set boundary conditions
mesh.setCellGradBC('neumann')
# Define the differential operators needed for the DC problem
Div = mesh.faceDiv
Grad = mesh.cellGrad
Msig = Utils.sdiag(1. / (mesh.aveF2CC.T * (1. / model)))
A = Div * Msig * Grad
# Change one corner to deal with nullspace
A[0, 0] = 1
A = sp.csc_matrix(A)
# We will solve the system iteratively, so a pre-conditioner is helpful
# This is simply a Jacobi preconditioner (inverse of the main diagonal)
dA = A.diagonal()
P = sp.spdiags(1 / dA, 0, A.shape[0], A.shape[0])
# Now we can solve the system for all the transmitters
# We want to store the data
data = []
# There is probably a more elegant way to do this, but we can just for-loop through the transmitters
for ii in range(len(Tx)):
start_time = time.time() # Let's time the calculations
#print("Transmitter %i / %i\r" % (ii+1,len(Tx)))
# Select dipole locations for receiver
rxloc_M = np.asarray(Rx[ii][:, 0:3])
rxloc_N = np.asarray(Rx[ii][:, 3:])
# For usual cases "dpdp" or "gradient"
if stype == 'pdp':
# Create an "inifinity" pole
tx = np.squeeze(Tx[ii][:, 0:1])
tinf = tx + np.array([dl_x, dl_y, 0]) * dl_len * 2
inds = Utils.closestPoints(mesh, np.c_[tx, tinf].T)
RHS = mesh.getInterpolationMat(np.asarray(Tx[ii]).T,
'CC').T * ([-1] / mesh.vol[inds])
else:
inds = Utils.closestPoints(mesh, np.asarray(Tx[ii]).T)
RHS = mesh.getInterpolationMat(np.asarray(Tx[ii]).T,
'CC').T * ([-1, 1] / mesh.vol[inds])
# Iterative Solve
Ainvb = sp.linalg.bicgstab(P * A, P * RHS, tol=1e-5)
# We now have the potential everywhere
phi = Utils.mkvc(Ainvb[0])
# Solve for phi on pole locations
P1 = mesh.getInterpolationMat(rxloc_M, 'CC')
P2 = mesh.getInterpolationMat(rxloc_N, 'CC')
# Compute the potential difference
dtemp = (P1 * phi - P2 * phi) * np.pi
data.append(dtemp)
print '\rTransmitter {0} of {1} -> Time:{2} sec'.format(
ii, len(Tx),
time.time() - start_time),
print 'Transmitter {0} of {1}'.format(ii, len(Tx))
print 'Forward completed'
# Let's just convert the 3D format into 2D (distance along line) and plot
# [Tx2d, Rx2d] = DC.convertObs_DC3D_to_2D(survey, np.ones(survey.nSrc))
survey2D = DC.convertObs_DC3D_to_2D(survey, np.ones(survey.nSrc))
survey2D.dobs = np.hstack(data)
# Here is an example for the first tx-rx array
if plotIt:
import matplotlib.pyplot as plt
fig = plt.figure()
ax = plt.subplot(2, 1, 1, aspect='equal')
mesh.plotSlice(np.log10(model), ax=ax, normal='Y', ind=indy, grid=True)
ax.set_title('E-W section at ' + str(mesh.vectorCCy[indy]) + ' m')
plt.gca().set_aspect('equal', adjustable='box')
plt.scatter(Tx[0][0, :], Tx[0][2, :], s=40, c='g', marker='v')
plt.scatter(Rx[0][:, 0::3], Rx[0][:, 2::3], s=40, c='y')
plt.xlim([-xlim, xlim])
plt.ylim([-zlim, mesh.vectorNz[-1] + dx])
ax = plt.subplot(2, 1, 2, aspect='equal')
# Plot the location of the spheres for reference
circle1 = plt.Circle((loc[0, 0] - Tx[0][0, 0], loc[2, 0]),
radi[0],
color='w',
fill=False,
lw=3)
circle2 = plt.Circle((loc[0, 1] - Tx[0][0, 0], loc[2, 1]),
radi[1],
color='k',
fill=False,
lw=3)
ax.add_artist(circle1)
ax.add_artist(circle2)
# Add the speudo section
DC.plot_pseudoSection(survey2D, ax, stype)
# plt.scatter(Tx2d[0][:],Tx[0][2,:],s=40,c='g', marker='v')
# plt.scatter(Rx2d[0][:],Rx[0][:,2::3],s=40,c='y')
# plt.plot(np.r_[Tx2d[0][0],Rx2d[-1][-1,-1]],np.ones(2)*mesh.vectorNz[-1], color='k')
plt.ylim([-zlim, mesh.vectorNz[-1] + dx])
plt.show()
return fig, ax
def getUniqueTimes(self):
time_rx = []
for src in self.srcList:
for rx in src.rxList:
time_rx.append(rx.times)
self.times = np.unique(np.hstack(time_rx))
def Jvec(self, m, v, f=None):
"""
Jvec computes the sensitivity times a vector
.. math::
\mathbf{J} \mathbf{v} = \\frac{d\mathbf{P}}{d\mathbf{F}} \left(
\\frac{d\mathbf{F}}{d\mathbf{u}} \\frac{d\mathbf{u}}{d\mathbf{m}} +
\\frac{\partial\mathbf{F}}{\partial\mathbf{m}} \\right) \mathbf{v}
where
.. math::
\mathbf{A} \\frac{d\mathbf{u}}{d\mathbf{m}} +
\\frac{\partial \mathbf{A}(\mathbf{u}, \mathbf{m})}
{\partial\mathbf{m}} =
\\frac{d \mathbf{RHS}}{d \mathbf{m}}
"""
if f is None:
f = self.fields(m)
ftype = self._fieldType + 'Solution' # the thing we solved for
self.model = m
# mat to store previous time-step's solution deriv times a vector for
# each source
# size: nu x nSrc
# this is a bit silly
# if self._fieldType is 'b' or self._fieldType is 'j':
# ifields = np.zeros((self.mesh.nF, len(Srcs)))
# elif self._fieldType is 'e' or self._fieldType is 'h':
# ifields = np.zeros((self.mesh.nE, len(Srcs)))
# for i, src in enumerate(self.survey.srcList):
dun_dm_v = np.hstack([
Utils.mkvc(
self.getInitialFieldsDeriv(src, v), 2
)
for src in self.survey.srcList
]) # can over-write this at each timestep
# store the field derivs we need to project to calc full deriv
df_dm_v = Fields_Derivs(self.mesh, self.survey)
Adiaginv = None
for tInd, dt in zip(range(self.nT), self.timeSteps):
# keep factors if dt is the same as previous step b/c A will be the
# same
if Adiaginv is not None and (tInd > 0 and dt !=
self.timeSteps[tInd - 1]):
Adiaginv.clean()
Adiaginv = None
if Adiaginv is None:
A = self.getAdiag(tInd)
Adiaginv = self.Solver(A, **self.solverOpts)
Asubdiag = self.getAsubdiag(tInd)
for i, src in enumerate(self.survey.srcList):
# here, we are lagging by a timestep, so filling in as we go
for projField in set([rx.projField for rx in src.rxList]):
df_dmFun = getattr(f, '_%sDeriv' % projField, None)
# df_dm_v is dense, but we only need the times at
# (rx.P.T * ones > 0)
# This should be called rx.footprint
df_dm_v[src, '{}Deriv'.format(projField), tInd] = df_dmFun(
tInd, src, dun_dm_v[:, i], v
)
un_src = f[src, ftype, tInd+1]
# cell centered on time mesh
dA_dm_v = self.getAdiagDeriv(tInd, un_src, v)
# on nodes of time mesh
dRHS_dm_v = self.getRHSDeriv(tInd+1, src, v)
dAsubdiag_dm_v = self.getAsubdiagDeriv(
tInd, f[src, ftype, tInd], v
)
JRHS = dRHS_dm_v - dAsubdiag_dm_v - dA_dm_v
# step in time and overwrite
if tInd != len(self.timeSteps+1):
dun_dm_v[:, i] = Adiaginv * (
JRHS - Asubdiag * dun_dm_v[:, i]
)
Jv = []
for src in self.survey.srcList:
for rx in src.rxList:
Jv.append(
rx.evalDeriv(src, self.mesh, self.timeMesh, f, Utils.mkvc(
df_dm_v[src, '%sDeriv' % rx.projField, :]
)
)
)
Adiaginv.clean()
# del df_dm_v, dun_dm_v, Asubdiag
# return Utils.mkvc(Jv)
return np.hstack(Jv)
def plot_pseudoSection(DCsurvey, axs, stype='dpdp', dtype="appc", clim=None):
"""
Read list of 2D tx-rx location and plot a speudo-section of apparent
resistivity.
Assumes flat topo for now...
Input:
:param d2D, z0
:switch stype -> Either 'pdp' (pole-dipole) | 'dpdp' (dipole-dipole)
:switch dtype=-> Either 'appr' (app. res) | 'appc' (app. con) | 'volt' (potential)
Output:
:figure scatter plot overlayed on image
Edited Feb 17th, 2016
@author: dominiquef
"""
from SimPEG import np
from scipy.interpolate import griddata
import pylab as plt
# Set depth to 0 for now
z0 = 0.
# Pre-allocate
midx = []
midz = []
rho = []
LEG = []
count = 0 # Counter for data
for ii in range(DCsurvey.nSrc):
Tx = DCsurvey.srcList[ii].loc
Rx = DCsurvey.srcList[ii].rxList[0].locs
nD = DCsurvey.srcList[ii].rxList[0].nD
data = DCsurvey.dobs[count:count+nD]
count += nD
# Get distances between each poles A-B-M-N
if stype == 'pdp':
MA = np.abs(Tx[0] - Rx[0][:,0])
NA = np.abs(Tx[0] - Rx[1][:,0])
MN = np.abs(Rx[1][:,0] - Rx[0][:,0])
# Create mid-point location
Cmid = Tx[0]
Pmid = (Rx[0][:,0] + Rx[1][:,0])/2
if DCsurvey.mesh.dim == 2:
zsrc = Tx[1]
elif DCsurvey.mesh.dim ==3:
zsrc = Tx[2]
elif stype == 'dpdp':
MA = np.abs(Tx[0][0] - Rx[0][:,0])
MB = np.abs(Tx[1][0] - Rx[0][:,0])
NA = np.abs(Tx[0][0] - Rx[1][:,0])
NB = np.abs(Tx[1][0] - Rx[1][:,0])
# Create mid-point location
Cmid = (Tx[0][0] + Tx[1][0])/2
Pmid = (Rx[0][:,0] + Rx[1][:,0])/2
if DCsurvey.mesh.dim == 2:
zsrc = (Tx[0][1] + Tx[1][1])/2
elif DCsurvey.mesh.dim ==3:
zsrc = (Tx[0][2] + Tx[1][2])/2
# Change output for dtype
if dtype == 'volt':
rho = np.hstack([rho,data])
else:
# Compute pant leg of apparent rho
if stype == 'pdp':
leg = data * 2*np.pi * MA * ( MA + MN ) / MN
elif stype == 'dpdp':
leg = data * 2*np.pi / ( 1/MA - 1/MB + 1/NB - 1/NA )
LEG.append(1./(2*np.pi) *( 1/MA - 1/MB + 1/NB - 1/NA ))
else:
print("""dtype must be 'pdp'(pole-dipole) | 'dpdp' (dipole-dipole) """)
break
if dtype == 'appc':
leg = np.log10(abs(1./leg))
rho = np.hstack([rho,leg])
elif dtype == 'appr':
leg = np.log10(abs(leg))
rho = np.hstack([rho,leg])
else:
print("""dtype must be 'appr' | 'appc' | 'volt' """)
break
midx = np.hstack([midx, ( Cmid + Pmid )/2 ])
if DCsurvey.mesh.dim==3:
midz = np.hstack([midz, -np.abs(Cmid-Pmid)/2 + zsrc ])
elif DCsurvey.mesh.dim==2:
midz = np.hstack([midz, -np.abs(Cmid-Pmid)/2 + zsrc ])
ax = axs
# Grid points
grid_x, grid_z = np.mgrid[np.min(midx):np.max(midx), np.min(midz):np.max(midz)]
grid_rho = griddata(np.c_[midx,midz], rho.T, (grid_x, grid_z), method='linear')
if clim == None:
vmin, vmax = rho.min(), rho.max()
else:
vmin, vmax = clim[0], clim[1]
grid_rho = np.ma.masked_where(np.isnan(grid_rho), grid_rho)
ph = plt.pcolormesh(grid_x[:,0],grid_z[0,:],grid_rho.T, clim=(vmin, vmax), vmin=vmin, vmax=vmax)
cbar = plt.colorbar(format="$10^{%.1f}$",fraction=0.04,orientation="horizontal")
cmin,cmax = cbar.get_clim()
ticks = np.linspace(cmin,cmax,3)
cbar.set_ticks(ticks)
cbar.ax.tick_params(labelsize=10)
if dtype == 'appc':
cbar.set_label("App.Cond",size=12)
elif dtype == 'appr':
cbar.set_label("App.Res.",size=12)
elif dtype == 'volt':
cbar.set_label("Potential (V)",size=12)
# Plot apparent resistivity
ax.scatter(midx,midz,s=10,c=rho.T, vmin =vmin, vmax = vmax, clim=(vmin, vmax))
#ax.set_xticklabels([])
#ax.set_yticklabels([])
plt.gca().set_aspect('equal', adjustable='box')
return ph, LEG
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 Jvec(self, m, v, f=None):
"""
Jvec computes the sensitivity times a vector
.. math::
\mathbf{J} \mathbf{v} = \\frac{d\mathbf{P}}{d\mathbf{F}} \left(
\\frac{d\mathbf{F}}{d\mathbf{u}} \\frac{d\mathbf{u}}{d\mathbf{m}} +
\\frac{\partial\mathbf{F}}{\partial\mathbf{m}} \\right) \mathbf{v}
where
.. math::
\mathbf{A} \\frac{d\mathbf{u}}{d\mathbf{m}} +
\\frac{\partial \mathbf{A}(\mathbf{u}, \mathbf{m})}
{\partial\mathbf{m}} =
\\frac{d \mathbf{RHS}}{d \mathbf{m}}
"""
if f is None:
f = self.fields(m)
ftype = self._fieldType + 'Solution' # the thing we solved for
self.curModel = m
# mat to store previous time-step's solution deriv times a vector for
# each source
# size: nu x nSrc
# this is a bit silly
# if self._fieldType is 'b' or self._fieldType is 'j':
# ifields = np.zeros((self.mesh.nF, len(Srcs)))
# elif self._fieldType is 'e' or self._fieldType is 'h':
# ifields = np.zeros((self.mesh.nE, len(Srcs)))
# for i, src in enumerate(self.survey.srcList):
dun_dm_v = np.hstack([Utils.mkvc(self.getInitialFieldsDeriv(src, v), 2)
for src in self.survey.srcList]
) # can over-write this at each timestep
# store the field derivs we need to project to calc full deriv
df_dm_v = Fields_Derivs(self.mesh, self.survey)
Adiaginv = None
for tInd, dt in zip(range(self.nT), self.timeSteps):
# keep factors if dt is the same as previous step b/c A will be the
# same
if Adiaginv is not None and (tInd > 0 and dt !=
self.timeSteps[tInd - 1]):
Adiaginv.clean()
Adiaginv = None
if Adiaginv is None:
A = self.getAdiag(tInd)
Adiaginv = self.Solver(A, **self.solverOpts)
Asubdiag = self.getAsubdiag(tInd)
for i, src in enumerate(self.survey.srcList):
# here, we are lagging by a timestep, so filling in as we go
for projField in set([rx.projField for rx in src.rxList]):
# Seogi: df_duFun?
df_dmFun = getattr(f, '_%sDeriv' % projField, None)
# df_dm_v is dense, but we only need the times at
# (rx.P.T * ones > 0)
# This should be called rx.footprint
df_dm_v[src, '{}Deriv'.format(projField), tInd] = df_dmFun(
tInd, src, dun_dm_v[:, i], v
)
un_src = f[src, ftype, tInd+1]
# cell centered on time mesh
dA_dm_v = self.getAdiagDeriv(tInd, un_src, v)
# on nodes of time mesh
dRHS_dm_v = self.getRHSDeriv(tInd+1, src, v)
dAsubdiag_dm_v = self.getAsubdiagDeriv(tInd, f[src, ftype,
tInd], v)
JRHS = dRHS_dm_v - dAsubdiag_dm_v - dA_dm_v
# step in time and overwrite
if tInd != len(self.timeSteps+1):
dun_dm_v[:, i] = Adiaginv * (JRHS - Asubdiag *
dun_dm_v[:, i])
Jv = []
for src in self.survey.srcList:
for rx in src.rxList:
Jv.append(rx.evalDeriv(src, self.mesh, self.timeMesh,
Utils.mkvc(df_dm_v[src, '%sDeriv' % rx.projField, :])
))
Adiaginv.clean()
# del df_dm_v, dun_dm_v, Asubdiag
# return Utils.mkvc(Jv)
return np.hstack(Jv)
def getUniqueTimes(self):
time_rx = []
for src in self.srcList:
for rx in src.rxList:
time_rx.append(rx.times)
self.times = np.unique(np.hstack(time_rx))
def interpFFT(x, y, m):
"""
Load in a 2D grid and resample
OUTPUT:
m_out
"""
from SimPEG import np, sp
import scipy.signal as sn
# Add padding values by reflection (2**n)
lenx = np.round(np.log2(2 * len(x)))
npadx = int(np.floor((2**lenx - len(x)) / 2.))
#Create hemming taper
if np.mod(npadx * 2 + len(x), 2) != 0:
oddx = 1
else:
oddx = 0
tap0 = sn.hamming(npadx * 2)
tapl = sp.spdiags(tap0[0:npadx], 0, npadx, npadx)
tapr = sp.spdiags(tap0[npadx:], 0, npadx, npadx + oddx)
# Mirror the 2d data over the half lenght and apply 0-taper
mpad = np.hstack(
[np.fliplr(m[:, 0:npadx]) * tapl, m,
np.fliplr(m[:, -npadx:]) * tapr])
# Repeat along the second dimension
leny = np.round(np.log2(2 * len(y)))
npady = int(np.floor((2**leny - len(y)) / 2.))
#Create hemming taper
if np.mod(npady * 2 + len(y), 2) != 0:
oddy = 1
else:
oddy = 0
tap0 = sn.hamming(npady * 2)
tapu = sp.spdiags(tap0[0:npady], 0, npady, npady)
tapd = sp.spdiags(tap0[npady:], 0, npady + oddy, npady)
mpad = np.vstack([
tapu * np.flipud(mpad[0:npady, :]), mpad,
tapd * np.flipud(mpad[-npady:, :])
])
# Compute FFT
FFTm = np.fft.fft2(mpad)
# Do an FFT shift
FFTshift = np.fft.fftshift(FFTm)
# Pad high frequencies with zeros to increase the sampling rate
py = int(FFTm.shape[0] / 2)
px = int(FFTm.shape[1] / 2)
FFTshift = np.hstack([
np.zeros((FFTshift.shape[0], px)), FFTshift,
np.zeros((FFTshift.shape[0], px))
])
FFTshift = np.vstack([
np.zeros((py, FFTshift.shape[1])), FFTshift,
np.zeros((py, FFTshift.shape[1]))
])
# Inverse shift
FFTm = np.fft.ifftshift(FFTshift)
# Compute inverse FFT
IFFTm = np.fft.ifft2(FFTm) * FFTm.size / mpad.size
m_out = np.real(IFFTm)
# Extract core
#m_out = np.real(IFFTm[npady*2:-(npady*2+oddy+1),npadx*2:-(npadx*2+oddx+1)])
m_out = m_out[npady * 2:-(npady + oddy) * 2, npadx * 2:-(npadx + oddx) * 2]
if np.mod(m.shape[0], 2) != 0:
m_out = m_out[:-1, :]
if np.mod(m.shape[1], 2) != 0:
m_out = m_out[:, :-1]
return m_out
def plot_pseudoSection(Tx,Rx,data,z0, stype):
from SimPEG import np, mkvc
from scipy.interpolate import griddata
from matplotlib.colors import LogNorm
import pylab as plt
import re
"""
Read list of 2D tx-rx location and plot a speudo-section of apparent
resistivity.
Assumes flat topo for now...
Input:
:param d2D, z0
:switch stype -> Either 'pdp' (pole-dipole) | 'dpdp' (dipole-dipole)
Output:
:figure scatter plot overlayed on image
Created on Mon December 7th, 2015
@author: dominiquef
"""
#d2D = np.asarray(d2D)
midl = []
midz = []
rho = []
for ii in range(len(Tx)):
# Get distances between each poles
rC1P1 = np.abs(Tx[ii][0] - Rx[ii][:,0])
rC2P1 = np.abs(Tx[ii][1] - Rx[ii][:,0])
rC1P2 = np.abs(Tx[ii][1] - Rx[ii][:,1])
rC2P2 = np.abs(Tx[ii][0] - Rx[ii][:,1])
rP1P2 = np.abs(Rx[ii][:,1] - Rx[ii][:,0])
# Compute apparent resistivity
if re.match(stype,'pdp'):
rho = np.hstack([rho, data[ii] * 2*np.pi * rC1P1 * ( rC1P1 + rP1P2 ) / rP1P2] )
elif re.match(stype,'dpdp'):
rho = np.hstack([rho, data[ii] * 2*np.pi / ( 1/rC1P1 - 1/rC2P1 - 1/rC1P2 + 1/rC2P2 ) ])
Cmid = (Tx[ii][0] + Tx[ii][1])/2
Pmid = (Rx[ii][:,0] + Rx[ii][:,1])/2
midl = np.hstack([midl, ( Cmid + Pmid )/2 ])
midz = np.hstack([midz, -np.abs(Cmid-Pmid)/2 + z0 ])
# Grid points
grid_x, grid_z = np.mgrid[np.min(midl):np.max(midl), np.min(midz):np.max(midz)]
grid_rho = griddata(np.c_[midl,midz], np.log10(abs(1/rho.T)), (grid_x, grid_z), method='linear')
#plt.subplot(2,1,2)
plt.imshow(grid_rho.T, extent = (np.min(midl),np.max(midl),np.min(midz),np.max(midz)), origin='lower', alpha=0.8)
cbar = plt.colorbar(format = '%.2f',fraction=0.02)
cmin,cmax = cbar.get_clim()
ticks = np.linspace(cmin,cmax,3)
cbar.set_ticks(ticks)
# Plot apparent resistivity
plt.scatter(midl,midz,s=50,c=np.log10(abs(1/rho.T)))
