def setUp(self):
cs = 25.
hx = [(cs, 0, -1.3), (cs, 21), (cs, 0, 1.3)]
hy = [(cs, 0, -1.3), (cs, 21), (cs, 0, 1.3)]
hz = [(cs, 0, -1.3), (cs, 20)]
mesh = Mesh.TensorMesh([hx, hy, hz], x0="CCN")
blkind0 = Utils.ModelBuilder.getIndicesSphere(
np.r_[-100., -100., -200.], 75., mesh.gridCC
)
blkind1 = Utils.ModelBuilder.getIndicesSphere(
np.r_[100., 100., -200.], 75., mesh.gridCC
)
sigma = np.ones(mesh.nC)*1e-2
eta = np.zeros(mesh.nC)
tau = np.ones_like(sigma)*1.
eta[blkind0] = 0.1
eta[blkind1] = 0.1
tau[blkind0] = 0.1
tau[blkind1] = 0.01
x = mesh.vectorCCx[(mesh.vectorCCx > -155.) & (mesh.vectorCCx < 155.)]
y = mesh.vectorCCx[(mesh.vectorCCy > -155.) & (mesh.vectorCCy < 155.)]
Aloc = np.r_[-200., 0., 0.]
Bloc = np.r_[200., 0., 0.]
M = Utils.ndgrid(x-25., y, np.r_[0.])
N = Utils.ndgrid(x+25., y, np.r_[0.])
times = np.arange(10)*1e-3 + 1e-3
rx = SIP.Rx.Dipole(M, N, times)
src = SIP.Src.Dipole([rx], Aloc, Bloc)
survey = SIP.Survey([src])
wires = Maps.Wires(('eta', mesh.nC), ('taui', mesh.nC))
problem = SIP.Problem3D_N(
mesh,
sigma=sigma,
etaMap=wires.eta,
tauiMap=wires.taui
)
problem.Solver = Solver
problem.pair(survey)
mSynth = np.r_[eta, 1./tau]
survey.makeSyntheticData(mSynth)
# Now set up the problem to do some minimization
dmis = DataMisfit.l2_DataMisfit(survey)
reg = Regularization.Tikhonov(mesh)
opt = Optimization.InexactGaussNewton(
maxIterLS=20, maxIter=10, tolF=1e-6,
tolX=1e-6, tolG=1e-6, maxIterCG=6
)
invProb = InvProblem.BaseInvProblem(dmis, reg, opt, beta=1e4)
inv = Inversion.BaseInversion(invProb)
self.inv = inv
self.reg = reg
self.p = problem
self.mesh = mesh
self.m0 = mSynth
self.survey = survey
self.dmis = dmis
def halfSpaceProblemAnaVMDDiff(showIt=False, waveformType="STEPOFF"):
cs, ncx, ncz, npad = 20., 25, 25, 15
hx = [(cs, ncx), (cs, npad, 1.3)]
hz = [(cs, npad, -1.3), (cs, ncz), (cs, npad, 1.3)]
mesh = Mesh.CylMesh([hx, 1, hz], '00C')
sighalf = 1e-2
siginf = np.ones(mesh.nC) * 1e-8
siginf[mesh.gridCC[:, -1] < 0.] = sighalf
eta = np.ones(mesh.nC) * 0.2
tau = np.ones(mesh.nC) * 0.005
c = np.ones(mesh.nC) * 0.7
m = np.r_[siginf, eta, tau, c]
iMap = Maps.IdentityMap(nP=int(mesh.nC))
maps = [('sigmaInf', iMap), ('eta', iMap), ('tau', iMap), ('c', iMap)]
prb = ProblemATEMIP_b(mesh, mapping=maps)
if waveformType == "GENERAL":
# timeon = np.cumsum(np.r_[np.ones(10)*1e-3, np.ones(10)*5e-4, np.ones(10)*1e-4])
timeon = np.cumsum(np.r_[np.ones(10) * 1e-3,
np.ones(10) * 5e-4,
np.ones(10) * 1e-4])
timeon -= timeon.max()
timeoff = np.cumsum(np.r_[np.ones(20) * 1e-5,
np.ones(20) * 1e-4,
np.ones(20) * 1e-3])
time = np.r_[timeon, timeoff]
current_on = np.ones_like(timeon)
current_on[[0, -1]] = 0.
current = np.r_[current_on, np.zeros_like(timeoff)]
wave = np.c_[time, current]
prb.waveformType = "GENERAL"
prb.currentwaveform(wave)
prb.t0 = time.min()
elif waveformType == "STEPOFF":
prb.timeSteps = [(1e-5, 20), (1e-4, 20), (1e-3, 10)]
offset = 20.
tobs = np.logspace(-4, -2, 21)
rx = EM.TDEM.RxTDEM(np.array([[offset, 0., 0.]]), tobs, "bz")
src = EM.TDEM.SrcTDEM_VMD_MVP([rx],
np.array([[0., 0., 0.]]),
waveformType=waveformType)
survey = EM.TDEM.SurveyTDEM([src])
prb.Solver = MumpsSolver
prb.pair(survey)
out = survey.dpred(m)
bz_ana = mu_0 * hzAnalyticDipoleT_CC(
offset, rx.times, sigmaInf=sighalf, eta=eta[0], tau=tau[0], c=c[0])
err = np.linalg.norm(bz_ana - out) / np.linalg.norm(bz_ana)
print '>> Relative error = ', err
if showIt:
plt.loglog(rx.times, abs(bz_ana), 'k')
plt.loglog(rx.times, abs(out), 'b.')
plt.show()
return err
def setUp(self):
cs = 25.
hx = [(cs,0, -1.3),(cs,21),(cs,0, 1.3)]
hy = [(cs,0, -1.3),(cs,21),(cs,0, 1.3)]
hz = [(cs,0, -1.3),(cs,20),(cs,0, 1.3)]
mesh = Mesh.TensorMesh([hx, hy, hz],x0="CCC")
blkind0 = Utils.ModelBuilder.getIndicesSphere(np.r_[-100., -100., -200.], 75., mesh.gridCC)
blkind1 = Utils.ModelBuilder.getIndicesSphere(np.r_[100., 100., -200.], 75., mesh.gridCC)
sigma = np.ones(mesh.nC)*1e-2
airind = mesh.gridCC[:,2]>0.
sigma[airind] = 1e-8
eta = np.zeros(mesh.nC)
tau = np.ones_like(sigma)*1.
eta[blkind0] = 0.1
eta[blkind1] = 0.1
tau[blkind0] = 0.1
tau[blkind1] = 0.01
actmapeta = Maps.InjectActiveCells(mesh, ~airind, 0.)
actmaptau = Maps.InjectActiveCells(mesh, ~airind, 1.)
x = mesh.vectorCCx[(mesh.vectorCCx>-155.)&(mesh.vectorCCx<155.)]
y = mesh.vectorCCx[(mesh.vectorCCy>-155.)&(mesh.vectorCCy<155.)]
Aloc = np.r_[-200., 0., 0.]
Bloc = np.r_[200., 0., 0.]
M = Utils.ndgrid(x-25.,y, np.r_[0.])
N = Utils.ndgrid(x+25.,y, np.r_[0.])
times = np.arange(10)*1e-3 + 1e-3
rx = SIP.Rx.Dipole(M, N, times)
src = SIP.Src.Dipole([rx], Aloc, Bloc)
survey = SIP.Survey([src])
colemap = [("eta", Maps.IdentityMap(mesh)*actmapeta), ("taui", Maps.IdentityMap(mesh)*actmaptau)]
problem = SIP.Problem3D_N(mesh, sigma=sigma, mapping=colemap)
problem.Solver = Solver
problem.pair(survey)
mSynth = np.r_[eta[~airind], 1./tau[~airind]]
survey.makeSyntheticData(mSynth)
# Now set up the problem to do some minimization
dmis = DataMisfit.l2_DataMisfit(survey)
regmap = Maps.IdentityMap(nP=int(mSynth[~airind].size*2))
reg = SIP.MultiRegularization(mesh, mapping=regmap, nModels=2, indActive=~airind)
opt = Optimization.InexactGaussNewton(maxIterLS=20, maxIter=10, tolF=1e-6, tolX=1e-6, tolG=1e-6, maxIterCG=6)
invProb = InvProblem.BaseInvProblem(dmis, reg, opt, beta=1e4)
inv = Inversion.BaseInversion(invProb)
self.inv = inv
self.reg = reg
self.p = problem
self.mesh = mesh
self.m0 = mSynth
self.survey = survey
self.dmis = dmis
def halfSpaceProblemAnaVMDDiff(showIt=False, waveformType="STEPOFF"):
cs, ncx, ncz, npad = 20., 25, 25, 15
hx = [(cs, ncx), (cs, npad, 1.3)]
hz = [(cs, npad, -1.3), (cs, ncz), (cs, npad, 1.3)]
mesh = Mesh.CylMesh([hx, 1, hz], '00C')
prb = ProblemATEM_b(mesh)
if waveformType == "GENERAL":
timeon = np.cumsum(np.r_[np.ones(10) * 1e-3,
np.ones(10) * 5e-4,
np.ones(10) * 1e-4])
timeon -= timeon.max()
timeoff = np.cumsum(np.r_[np.ones(10) * 5e-5,
np.ones(10) * 1e-4,
np.ones(10) * 5e-4,
np.ones(10) * 1e-3,
np.ones(10) * 5e-3])
time = np.r_[timeon, timeoff]
current_on = np.ones_like(timeon)
current_on[[0, -1]] = 0.
current = np.r_[current_on, np.zeros_like(timeoff)]
wave = np.c_[time, current]
prb.waveformType = "GENERAL"
prb.currentwaveform(wave)
prb.t0 = time.min()
elif waveformType == "STEPOFF":
prb.timeSteps = [(1e-5, 10), (5e-5, 10), (1e-4, 10), (5e-4, 10),
(1e-3, 10), (5e-3, 10)]
offset = 20.
tobs = np.logspace(-4, -2, 21)
rx = EM.TDEM.RxTDEM(np.array([[offset, 0., 0.]]), tobs, "bz")
src = EM.TDEM.SrcTDEM_VMD_MVP([rx],
np.array([[0., 0., 0.]]),
waveformType=waveformType)
survey = EM.TDEM.SurveyTDEM([src])
prb.Solver = MumpsSolver
sigma = np.ones(mesh.nC) * 1e-8
active = mesh.gridCC[:, 2] < 0.
sig_half = 1e-2
sigma[active] = sig_half
prb.pair(survey)
out = survey.dpred(sigma)
bz_ana = mu_0 * hzAnalyticDipoleT(offset, rx.times, sig_half)
err = np.linalg.norm(bz_ana - out) / np.linalg.norm(bz_ana)
print '>> Relative error = ', err
if showIt:
plt.loglog(rx.times, bz_ana, 'k')
plt.loglog(rx.times, out, 'b.')
plt.show()
return err
def setUp(self):
cs = 25.
hx = [(cs,0, -1.3),(cs,21),(cs,0, 1.3)]
hy = [(cs,0, -1.3),(cs,21),(cs,0, 1.3)]
hz = [(cs,0, -1.3),(cs,20)]
mesh = Mesh.TensorMesh([hx, hy, hz],x0="CCN")
blkind0 = Utils.ModelBuilder.getIndicesSphere(np.r_[-100., -100., -200.], 75., mesh.gridCC)
blkind1 = Utils.ModelBuilder.getIndicesSphere(np.r_[100., 100., -200.], 75., mesh.gridCC)
sigma = np.ones(mesh.nC)*1e-2
eta = np.zeros(mesh.nC)
tau = np.ones_like(sigma)*1.
eta[blkind0] = 0.1
eta[blkind1] = 0.1
tau[blkind0] = 0.1
tau[blkind1] = 0.01
x = mesh.vectorCCx[(mesh.vectorCCx>-155.)&(mesh.vectorCCx<155.)]
y = mesh.vectorCCx[(mesh.vectorCCy>-155.)&(mesh.vectorCCy<155.)]
Aloc = np.r_[-200., 0., 0.]
Bloc = np.r_[200., 0., 0.]
M = Utils.ndgrid(x-25.,y, np.r_[0.])
N = Utils.ndgrid(x+25.,y, np.r_[0.])
times = np.arange(10)*1e-3 + 1e-3
rx = SIP.Rx.Dipole(M, N, times)
src = SIP.Src.Dipole([rx], Aloc, Bloc)
survey = SIP.Survey([src])
colemap = [("eta", Maps.IdentityMap(mesh)), ("taui", Maps.IdentityMap(mesh))]
problem = SIP.Problem3D_CC(mesh, rho=1./sigma, mapping=colemap)
problem.Solver = MumpsSolver
problem.pair(survey)
mSynth = np.r_[eta, 1./tau]
survey.makeSyntheticData(mSynth)
# Now set up the problem to do some minimization
dmis = DataMisfit.l2_DataMisfit(survey)
reg = Regularization.Tikhonov(mesh)
opt = Optimization.InexactGaussNewton(maxIterLS=20, maxIter=10, tolF=1e-6, tolX=1e-6, tolG=1e-6, maxIterCG=6)
invProb = InvProblem.BaseInvProblem(dmis, reg, opt, beta=1e4)
inv = Inversion.BaseInversion(invProb)
self.inv = inv
self.reg = reg
self.p = problem
self.mesh = mesh
self.m0 = mSynth
self.survey = survey
self.dmis = dmis
def halfSpaceProblemAnaVMDDiff(showIt=False, waveformType="STEPOFF"):
cs, ncx, ncz, npad = 20., 25, 25, 15
hx = [(cs,ncx), (cs,npad,1.3)]
hz = [(cs,npad,-1.3), (cs,ncz), (cs,npad,1.3)]
mesh = Mesh.CylMesh([hx,1,hz], '00C')
sighalf = 1e-2
siginf = np.ones(mesh.nC)*1e-8
siginf[mesh.gridCC[:,-1]<0.] = sighalf
eta = np.ones(mesh.nC)*0.2
tau = np.ones(mesh.nC)*0.005
c = np.ones(mesh.nC)*0.7
m = np.r_[siginf, eta, tau, c]
iMap = Maps.IdentityMap(nP=int(mesh.nC))
maps = [('sigmaInf', iMap), ('eta', iMap), ('tau', iMap), ('c', iMap)]
prb = ProblemATEMIP_b(mesh, mapping = maps)
if waveformType =="GENERAL":
# timeon = np.cumsum(np.r_[np.ones(10)*1e-3, np.ones(10)*5e-4, np.ones(10)*1e-4])
timeon = np.cumsum(np.r_[np.ones(10)*1e-3, np.ones(10)*5e-4, np.ones(10)*1e-4])
timeon -= timeon.max()
timeoff = np.cumsum(np.r_[np.ones(20)*1e-5, np.ones(20)*1e-4, np.ones(20)*1e-3])
time = np.r_[timeon, timeoff]
current_on = np.ones_like(timeon)
current_on[[0,-1]] = 0.
current = np.r_[current_on, np.zeros_like(timeoff)]
wave = np.c_[time, current]
prb.waveformType = "GENERAL"
prb.currentwaveform(wave)
prb.t0 = time.min()
elif waveformType =="STEPOFF":
prb.timeSteps = [(1e-5, 20), (1e-4, 20), (1e-3, 10)]
offset = 20.
tobs = np.logspace(-4, -2, 21)
rx = EM.TDEM.RxTDEM(np.array([[offset, 0., 0.]]), tobs, "bz")
src = EM.TDEM.SrcTDEM_VMD_MVP([rx], np.array([[0., 0., 0.]]), waveformType=waveformType)
survey = EM.TDEM.SurveyTDEM([src])
prb.Solver = MumpsSolver
prb.pair(survey)
out = survey.dpred(m)
bz_ana = mu_0*hzAnalyticDipoleT_CC(offset, rx.times, sigmaInf=sighalf, eta=eta[0], tau=tau[0], c=c[0])
err = np.linalg.norm(bz_ana-out)/np.linalg.norm(bz_ana)
print '>> Relative error = ', err
if showIt:
plt.loglog(rx.times, abs(bz_ana), 'k')
plt.loglog(rx.times, abs(out), 'b.')
plt.show()
return err
def halfSpaceProblemAnaVMDDiff(showIt=False, waveformType="STEPOFF"): cs, ncx, ncz, npad = 20., 25, 25, 15 hx = [(cs,ncx), (cs,npad,1.3)] hz = [(cs,npad,-1.3), (cs,ncz), (cs,npad,1.3)] mesh = Mesh.CylMesh([hx,1,hz], '00C') prb = ProblemATEM_b(mesh) if waveformType =="GENERAL": timeon = np.cumsum(np.r_[np.ones(10)*1e-3, np.ones(10)*5e-4, np.ones(10)*1e-4]) timeon -= timeon.max() timeoff = np.cumsum(np.r_[np.ones(10)*5e-5, np.ones(10)*1e-4, np.ones(10)*5e-4, np.ones(10)*1e-3, np.ones(10)*5e-3]) time = np.r_[timeon, timeoff] current_on = np.ones_like(timeon) current_on[[0,-1]] = 0. current = np.r_[current_on, np.zeros_like(timeoff)] wave = np.c_[time, current] prb.waveformType = "GENERAL" prb.currentwaveform(wave) prb.t0 = time.min() elif waveformType =="STEPOFF": prb.timeSteps = [(1e-5, 10), (5e-5, 10), (1e-4, 10), (5e-4, 10), (1e-3, 10),(5e-3, 10)] offset = 20. tobs = np.logspace(-4, -2, 21) rx = EM.TDEM.RxTDEM(np.array([[offset, 0., 0.]]), tobs, "bz") src = EM.TDEM.SrcTDEM_VMD_MVP([rx], np.array([[0., 0., 0.]]), waveformType=waveformType) survey = EM.TDEM.SurveyTDEM([src]) prb.Solver = MumpsSolver sigma = np.ones(mesh.nC)*1e-8 active = mesh.gridCC[:,2]<0. sig_half = 1e-2 sigma[active] = sig_half prb.pair(survey) out = survey.dpred(sigma) bz_ana = mu_0*hzAnalyticDipoleT(offset, rx.times, sig_half) err = np.linalg.norm(bz_ana-out)/np.linalg.norm(bz_ana) print '>> Relative error = ', err if showIt: plt.loglog(rx.times, bz_ana, 'k') plt.loglog(rx.times, out, 'b.') plt.show() return err
