def test_adjoint(self):
# Adjoint Test
u = np.random.rand(self.mesh.nC*self.survey.nSrc)
v = np.random.rand(self.mesh.nC*2)
w = np.random.rand(self.survey.dobs.shape[0])
wtJv = w.dot(self.p.Jvec(self.m0, v))
vtJtw = v.dot(self.p.Jtvec(self.m0, w))
passed = np.abs(wtJv - vtJtw) < 1e-10
print('Adjoint Test', np.abs(wtJv - vtJtw), passed)
self.assertTrue(passed)
def test_adjoint(self):
# Adjoint Test
u = np.random.rand(self.mesh.nC * self.survey.nSrc)
v = np.random.rand(self.mesh.nC * 2)
w = np.random.rand(self.survey.dobs.shape[0])
wtJv = w.dot(self.p.Jvec(self.m0, v))
vtJtw = v.dot(self.p.Jtvec(self.m0, w))
passed = np.abs(wtJv - vtJtw) < 1e-10
print 'Adjoint Test', np.abs(wtJv - vtJtw), passed
self.assertTrue(passed)
def mycmp(c1,c2):
if c1.x0.size == 2:
if np.abs(c1.x0[1] - c2.x0[1]) < eps:
return c1.x0[0] - c2.x0[0]
return c1.x0[1] - c2.x0[1]
elif c1.x0.size == 3:
if np.abs(c1.x0[2] - c2.x0[2]) < eps:
if np.abs(c1.x0[1] - c2.x0[1]) < eps:
return c1.x0[0] - c2.x0[0]
return c1.x0[1] - c2.x0[1]
return c1.x0[2] - c2.x0[2]
def appResNorm(sigmaHalf):
nFreq = 26
m1d = Mesh.TensorMesh([[(100,5,1.5),(100.,10),(100,5,1.5)]], x0=['C'])
sigma = np.zeros(m1d.nC) + sigmaHalf
sigma[m1d.gridCC[:]>200] = 1e-8
# Calculate the analytic fields
freqs = np.logspace(4,-4,nFreq)
Z = []
for freq in freqs:
Ed, Eu, Hd, Hu = NSEM.Utils.getEHfields(m1d,sigma,freq,np.array([200]))
Z.append((Ed + Eu)/(Hd + Hu))
Zarr = np.concatenate(Z)
app_r, app_p = NSEM.Utils.appResPhs(freqs,Zarr)
return np.linalg.norm(np.abs(app_r - np.ones(nFreq)/sigmaHalf)) / np.log10(sigmaHalf)
def testOnes(self):
Adiagtest = diagEst(self.A, self.n, self.n)
r = np.abs(Adiagtest - self.Adiag)
self.assertTrue(r.dot(r) < TOL)
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 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)))
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(plotIt=True):
"""
MT: 1D: Inversion
=================
Forward model 1D MT data.
Setup and run a MT 1D inversion.
"""
## Setup the forward modeling
# Setting up 1D mesh and conductivity models to forward model data.
# Frequency
nFreq = 26
freqs = np.logspace(2,-3,nFreq)
# Set mesh parameters
ct = 10
air = simpeg.Utils.meshTensor([(ct,25,1.4)])
core = np.concatenate( ( np.kron(simpeg.Utils.meshTensor([(ct,10,-1.3)]),np.ones((5,))) , simpeg.Utils.meshTensor([(ct,5)]) ) )
bot = simpeg.Utils.meshTensor([(core[0],25,-1.4)])
x0 = -np.array([np.sum(np.concatenate((core,bot)))])
# Make the model
m1d = simpeg.Mesh.TensorMesh([np.concatenate((bot,core,air))], x0=x0)
# Setup model varibles
active = m1d.vectorCCx<0.
layer1 = (m1d.vectorCCx<-500.) & (m1d.vectorCCx>=-800.)
layer2 = (m1d.vectorCCx<-3500.) & (m1d.vectorCCx>=-5000.)
# Set the conductivity values
sig_half = 1e-2
sig_air = 1e-8
sig_layer1 = .2
sig_layer2 = .2
# Make the true model
sigma_true = np.ones(m1d.nCx)*sig_air
sigma_true[active] = sig_half
sigma_true[layer1] = sig_layer1
sigma_true[layer2] = sig_layer2
# Extract the model
m_true = np.log(sigma_true[active])
# Make the background model
sigma_0 = np.ones(m1d.nCx)*sig_air
sigma_0[active] = sig_half
m_0 = np.log(sigma_0[active])
# Set the mapping
actMap = simpeg.Maps.InjectActiveCells(m1d, active, np.log(1e-8), nC=m1d.nCx)
mappingExpAct = simpeg.Maps.ExpMap(m1d) * actMap
## Setup the layout of the survey, set the sources and the connected receivers
# Receivers
rxList = []
rxList.append(NSEM.Rx.Point_impedance1D(simpeg.mkvc(np.array([-0.5]),2).T,'real'))
rxList.append(NSEM.Rx.Point_impedance1D(simpeg.mkvc(np.array([-0.5]),2).T,'imag'))
# Source list
srcList =[]
for freq in freqs:
srcList.append(NSEM.Src.Planewave_xy_1Dprimary(rxList,freq))
# Make the survey
survey = NSEM.Survey(srcList)
survey.mtrue = m_true
## Set the problem
problem = NSEM.Problem1D_ePrimSec(m1d,sigmaPrimary=sigma_0,mapping=mappingExpAct)
problem.pair(survey)
## Forward model data
# Project the data
survey.dtrue = survey.dpred(m_true)
survey.dobs = survey.dtrue + 0.01*abs(survey.dtrue)*np.random.randn(*survey.dtrue.shape)
if plotIt:
fig = NSEM.Utils.dataUtils.plotMT1DModelData(problem,[])
fig.suptitle('Target - smooth true')
# Assign uncertainties
std = 0.05 # 5% std
survey.std = np.abs(survey.dobs*std)
# Assign the data weight
Wd = 1./survey.std
## Setup the inversion proceedure
# Define a counter
C = simpeg.Utils.Counter()
# Set the optimization
opt = simpeg.Optimization.ProjectedGNCG(maxIter = 25)
opt.counter = C
opt.lower = np.log(1e-4)
opt.upper = np.log(5)
opt.LSshorten = 0.1
opt.remember('xc')
# Data misfit
dmis = simpeg.DataMisfit.l2_DataMisfit(survey)
dmis.Wd = Wd
# Regularization - with a regularization mesh
regMesh = simpeg.Mesh.TensorMesh([m1d.hx[active]],m1d.x0)
reg = simpeg.Regularization.Tikhonov(regMesh)
reg.mrefInSmooth = True
reg.alpha_s = 1e-1
reg.alpha_x = 1.
# Inversion problem
invProb = simpeg.InvProblem.BaseInvProblem(dmis, reg, opt)
invProb.counter = C
# Beta cooling
beta = simpeg.Directives.BetaSchedule()
beta.coolingRate = 4.
beta.coolingFactor = 4.
betaest = simpeg.Directives.BetaEstimate_ByEig(beta0_ratio=100.)
betaest.beta0 = 1.
targmis = simpeg.Directives.TargetMisfit()
targmis.target = survey.nD
# Create an inversion object
inv = simpeg.Inversion.BaseInversion(invProb, directiveList=[beta,betaest,targmis])
## Run the inversion
mopt = inv.run(m_0)
if plotIt:
fig = NSEM.Utils.dataUtils.plotMT1DModelData(problem,[mopt])
fig.suptitle('Target - smooth true')
fig.axes[0].set_ylim([-10000,500])
plt.show()
def 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 xy_2_lineID(DCsurvey):
"""
Read DC survey class and append line ID.
Assumes that the locations are listed in the order
they were collected. May need to generalize for random
point locations, but will be more expensive
Input:
:param DCdict Vectors of station location
Output:
:param LineID Vector of integers
:return
Created on Thu Feb 11, 2015
@author: dominiquef
"""
# Compute unit vector between two points
nstn = DCsurvey.nSrc
# Pre-allocate space
lineID = np.zeros(nstn)
linenum = 0
indx = 0
for ii in range(nstn):
if ii == 0:
A = DCsurvey.srcList[ii].loc[0]
B = DCsurvey.srcList[ii].loc[1]
xout = np.mean([A[0:2],B[0:2]], axis = 0)
xy0 = A[:2]
xym = xout
# Deal with replicate pole location
if np.all(xy0==xym):
xym[0] = xym[0] + 1e-3
continue
A = DCsurvey.srcList[ii].loc[0]
B = DCsurvey.srcList[ii].loc[1]
xin = np.mean([A[0:2],B[0:2]], axis = 0)
# Compute vector between neighbours
vec1, r1 = r_unit(xout,xin)
# Compute vector between current stn and mid-point
vec2, r2 = r_unit(xym,xin)
# Compute vector between current stn and start line
vec3, r3 = r_unit(xy0,xin)
# Compute vector between mid-point and start line
vec4, r4 = r_unit(xym,xy0)
# Compute dot product
ang1 = np.abs(vec1.dot(vec2))
ang2 = np.abs(vec3.dot(vec4))
# If the angles are smaller then 45d, than next point is on a new line
if ((ang1 < np.cos(np.pi/4.)) | (ang2 < np.cos(np.pi/4.))) & (np.all(np.r_[r1,r2,r3,r4] > 0)):
# Re-initiate start and mid-point location
xy0 = A[:2]
xym = xin
# Deal with replicate pole location
if np.all(xy0==xym):
xym[0] = xym[0] + 1e-3
linenum += 1
indx = ii
else:
xym = np.mean([xy0,xin], axis = 0)
lineID[ii] = linenum
xout = xin
return lineID
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 run(plotIt=True):
"""
MT: 1D: Inversion
=================
Forward model 1D MT data.
Setup and run a MT 1D inversion.
"""
## Setup the forward modeling
# Setting up 1D mesh and conductivity models to forward model data.
# Frequency
nFreq = 26
freqs = np.logspace(2, -3, nFreq)
# Set mesh parameters
ct = 10
air = simpeg.Utils.meshTensor([(ct, 25, 1.4)])
core = np.concatenate(
(np.kron(simpeg.Utils.meshTensor([(ct, 10, -1.3)]), np.ones(
(5, ))), simpeg.Utils.meshTensor([(ct, 5)])))
bot = simpeg.Utils.meshTensor([(core[0], 25, -1.4)])
x0 = -np.array([np.sum(np.concatenate((core, bot)))])
# Make the model
m1d = simpeg.Mesh.TensorMesh([np.concatenate((bot, core, air))], x0=x0)
# Setup model varibles
active = m1d.vectorCCx < 0.
layer1 = (m1d.vectorCCx < -500.) & (m1d.vectorCCx >= -800.)
layer2 = (m1d.vectorCCx < -3500.) & (m1d.vectorCCx >= -5000.)
# Set the conductivity values
sig_half = 1e-2
sig_air = 1e-8
sig_layer1 = .2
sig_layer2 = .2
# Make the true model
sigma_true = np.ones(m1d.nCx) * sig_air
sigma_true[active] = sig_half
sigma_true[layer1] = sig_layer1
sigma_true[layer2] = sig_layer2
# Extract the model
m_true = np.log(sigma_true[active])
# Make the background model
sigma_0 = np.ones(m1d.nCx) * sig_air
sigma_0[active] = sig_half
m_0 = np.log(sigma_0[active])
# Set the mapping
actMap = simpeg.Maps.InjectActiveCells(m1d,
active,
np.log(1e-8),
nC=m1d.nCx)
mappingExpAct = simpeg.Maps.ExpMap(m1d) * actMap
## Setup the layout of the survey, set the sources and the connected receivers
# Receivers
rxList = []
rxList.append(
NSEM.Rx.Point_impedance1D(simpeg.mkvc(np.array([-0.5]), 2).T, 'real'))
rxList.append(
NSEM.Rx.Point_impedance1D(simpeg.mkvc(np.array([-0.5]), 2).T, 'imag'))
# Source list
srcList = []
for freq in freqs:
srcList.append(NSEM.Src.Planewave_xy_1Dprimary(rxList, freq))
# Make the survey
survey = NSEM.Survey(srcList)
survey.mtrue = m_true
## Set the problem
problem = NSEM.Problem1D_ePrimSec(m1d,
sigmaPrimary=sigma_0,
mapping=mappingExpAct)
problem.pair(survey)
## Forward model data
# Project the data
survey.dtrue = survey.dpred(m_true)
survey.dobs = survey.dtrue + 0.01 * abs(
survey.dtrue) * np.random.randn(*survey.dtrue.shape)
if plotIt:
fig = NSEM.Utils.dataUtils.plotMT1DModelData(problem, [])
fig.suptitle('Target - smooth true')
# Assign uncertainties
std = 0.05 # 5% std
survey.std = np.abs(survey.dobs * std)
# Assign the data weight
Wd = 1. / survey.std
## Setup the inversion proceedure
# Define a counter
C = simpeg.Utils.Counter()
# Set the optimization
opt = simpeg.Optimization.ProjectedGNCG(maxIter=25)
opt.counter = C
opt.lower = np.log(1e-4)
opt.upper = np.log(5)
opt.LSshorten = 0.1
opt.remember('xc')
# Data misfit
dmis = simpeg.DataMisfit.l2_DataMisfit(survey)
dmis.Wd = Wd
# Regularization - with a regularization mesh
regMesh = simpeg.Mesh.TensorMesh([m1d.hx[active]], m1d.x0)
reg = simpeg.Regularization.Tikhonov(regMesh)
reg.mrefInSmooth = True
reg.alpha_s = 1e-1
reg.alpha_x = 1.
# Inversion problem
invProb = simpeg.InvProblem.BaseInvProblem(dmis, reg, opt)
invProb.counter = C
# Beta cooling
beta = simpeg.Directives.BetaSchedule()
beta.coolingRate = 4.
beta.coolingFactor = 4.
betaest = simpeg.Directives.BetaEstimate_ByEig(beta0_ratio=100.)
betaest.beta0 = 1.
targmis = simpeg.Directives.TargetMisfit()
targmis.target = survey.nD
# Create an inversion object
inv = simpeg.Inversion.BaseInversion(
invProb, directiveList=[beta, betaest, targmis])
## Run the inversion
mopt = inv.run(m_0)
if plotIt:
fig = NSEM.Utils.dataUtils.plotMT1DModelData(problem, [mopt])
fig.suptitle('Target - smooth true')
fig.axes[0].set_ylim([-10000, 500])
plt.show()
LD = sp.tril(A,k=0)
phi = mkvc(Ainvb[0])
elif re.match(slvr,'LU'):
#Direct Solve
phi = Ainv.solve(RHS)
# Compute potential at each electrode
dtemp = (P1*phi - P2*phi)*np.pi
data.append( dtemp )
unct.append( np.abs(dtemp) * pct + flr)
print("--- %s seconds ---" % (time.time() - start_time))
#%% Run 2D inversion if pdp or dpdp survey
# Otherwise just plot and apparent susceptibility map
if not re.match(stype,'gradient'):
#%% Write data file in UBC-DCIP3D format
DC.writeUBC_DCobs(home_dir+'\FWR_data3D.dat',Tx,Rx,data,unct,'3D')
#%% Load 3D data
[Tx, Rx, data, wd] = DC.readUBC_DC3Dobs(home_dir + '\FWR_data3D.dat')
def testOnes(self):
Adiagtest = diagEst(self.A,self.n,self.n)
r = np.abs(Adiagtest-self.Adiag)
self.assertTrue(r.dot(r) < TOL)
