def test_inv_mref_setting(self):
reg1 = regularization.Tikhonov(self.mesh)
reg2 = regularization.Tikhonov(self.mesh)
reg = reg1 + reg2
opt = optimization.InexactGaussNewton(maxIter=10)
invProb = inverse_problem.BaseInvProblem(self.dmiscobmo, reg, opt)
directives_list = [directives.BetaEstimate_ByEig(beta0_ratio=1e-2)]
inv = inversion.BaseInversion(invProb, directiveList=directives_list)
m0 = self.model.mean() * np.ones_like(self.model)
mrec = inv.run(m0)
self.assertTrue(np.all(reg1.mref == m0))
self.assertTrue(np.all(reg2.mref == m0))
def setUp(self):
ntx = 31
xtemp_txP = np.logspace(1, 3, ntx)
xtemp_txN = -xtemp_txP
ytemp_tx = np.zeros(ntx)
xtemp_rxP = -5
xtemp_rxN = 5
ytemp_rx = 0.0
abhalf = abs(xtemp_txP - xtemp_txN) * 0.5
a = xtemp_rxN - xtemp_rxP
b = ((xtemp_txN - xtemp_txP) - a) * 0.5
# We generate tx and rx lists:
srclist = []
for i in range(ntx):
rx = dc.receivers.Dipole(np.r_[xtemp_rxP, ytemp_rx, -12.5],
np.r_[xtemp_rxN, ytemp_rx, -12.5])
locA = np.r_[xtemp_txP[i], ytemp_tx[i], -12.5]
locB = np.r_[xtemp_txN[i], ytemp_tx[i], -12.5]
src = dc.sources.Dipole([rx], locA, locB)
srclist.append(src)
survey = dc.survey.Survey(srclist)
rho = np.r_[10, 10, 10]
dummy_hz = 100.0
hz = np.r_[10, 10, dummy_hz]
mesh = TensorMesh([hz])
simulation = dc.simulation_1d.Simulation1DLayers(
survey=survey,
rhoMap=maps.ExpMap(mesh),
thicknesses=hz[:-1],
data_type="apparent_resistivity",
)
simulation.dpred(np.log(rho))
mSynth = np.log(rho)
dobs = simulation.make_synthetic_data(mSynth, add_noise=True)
# Now set up the problem to do some minimization
dmis = data_misfit.L2DataMisfit(simulation=simulation, data=dobs)
reg = regularization.Tikhonov(mesh)
opt = optimization.InexactGaussNewton(maxIterLS=20,
maxIter=10,
tolF=1e-6,
tolX=1e-6,
tolG=1e-6,
maxIterCG=6)
invProb = inverse_problem.BaseInvProblem(dmis, reg, opt, beta=0.0)
inv = inversion.BaseInversion(invProb)
self.inv = inv
self.reg = reg
self.p = simulation
self.mesh = mesh
self.m0 = mSynth
self.survey = survey
self.dmis = dmis
self.dobs = dobs
def test_linked_properties(self):
mesh = discretize.TensorMesh([8, 7, 6])
reg = regularization.Tikhonov(mesh)
[self.assertTrue(reg.regmesh is fct.regmesh) for fct in reg.objfcts]
[self.assertTrue(reg.mapping is fct.mapping) for fct in reg.objfcts]
D = reg.regmesh.cellDiffx
reg.regmesh._cellDiffx = 4 * D
v = np.random.rand(D.shape[1])
[
self.assertTrue(
np.all(reg.regmesh._cellDiffx * v == fct.regmesh.cellDiffx *
v)) for fct in reg.objfcts
]
indActive = mesh.gridCC[:, 2] < 0.4
reg.indActive = indActive
self.assertTrue(np.all(reg.regmesh.indActive == indActive))
[
self.assertTrue(np.all(reg.indActive == fct.indActive))
for fct in reg.objfcts
]
[
self.assertTrue(np.all(reg.indActive == fct.regmesh.indActive))
for fct in reg.objfcts
]
def setUp(self, parallel=True):
frequency = np.array([900, 7200, 56000], dtype=float)
hz = get_vertical_discretization_frequency(frequency,
sigma_background=1. / 10.)
n_sounding = 10
dx = 20.
hx = np.ones(n_sounding) * dx
mesh = Mesh.TensorMesh([hx, hz], x0='00')
inds = mesh.gridCC[:, 1] < 25
inds_1 = mesh.gridCC[:, 1] < 50
sigma = np.ones(mesh.nC) * 1. / 100.
sigma[inds_1] = 1. / 10.
sigma[inds] = 1. / 50.
sigma_em1d = sigma.reshape(mesh.vnC, order='F').flatten()
mSynth = np.log(sigma_em1d)
x = mesh.vectorCCx
y = np.zeros_like(x)
z = np.ones_like(x) * 30.
rx_locations = np.c_[x, y, z]
src_locations = np.c_[x, y, z]
topo = np.c_[x, y, z - 30.].astype(float)
mapping = Maps.ExpMap(mesh)
survey = GlobalEM1DSurveyFD(rx_locations=rx_locations,
src_locations=src_locations,
frequency=frequency,
offset=np.ones_like(frequency) * 8.,
src_type="VMD",
rx_type="Hz",
field_type='secondary',
topo=topo)
problem = GlobalEM1DProblemFD([],
sigmaMap=mapping,
hz=hz,
parallel=parallel,
n_cpu=2)
problem.pair(survey)
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=0.)
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 setUp(self, parallel=True):
frequency = np.array([900, 7200, 56000], dtype=float)
hz = np.r_[1.]
n_sounding = 10
dx = 20.
hx = np.ones(n_sounding) * dx
e = np.ones(n_sounding)
mSynth = np.r_[e * np.log(1. / 100.), e * 20]
x = np.arange(n_sounding)
y = np.zeros_like(x)
z = np.ones_like(x) * 30.
rx_locations = np.c_[x, y, z]
src_locations = np.c_[x, y, z]
topo = np.c_[x, y, z - 30.].astype(float)
wires = Maps.Wires(('sigma', n_sounding), ('h', n_sounding))
expmap = Maps.ExpMap(nP=n_sounding)
sigmaMap = expmap * wires.sigma
survey = GlobalEM1DSurveyFD(rx_locations=rx_locations,
src_locations=src_locations,
frequency=frequency,
offset=np.ones_like(frequency) * 8.,
src_type="VMD",
rx_type="ppm",
field_type='secondary',
topo=topo,
half_switch=True)
problem = GlobalEM1DProblemFD([],
sigmaMap=sigmaMap,
hMap=wires.h,
hz=hz,
parallel=parallel,
n_cpu=2)
problem.pair(survey)
survey.makeSyntheticData(mSynth)
# Now set up the problem to do some minimization
mesh = Mesh.TensorMesh([int(n_sounding * 2)])
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=0.)
inv = Inversion.BaseInversion(invProb)
self.inv = inv
self.reg = reg
self.p = problem
self.mesh = mesh
self.m0 = mSynth * 1.2
self.survey = survey
self.dmis = dmis
def run_inversion(
m0,
simulation,
data,
actind,
mesh,
maxIter=15,
beta0_ratio=1e0,
coolingFactor=5,
coolingRate=2,
upper=np.inf,
lower=-np.inf,
use_sensitivity_weight=True,
alpha_s=1e-4,
alpha_x=1.0,
alpha_y=1.0,
alpha_z=1.0,
):
"""
Run DC inversion
"""
dmisfit = data_misfit.L2DataMisfit(simulation=simulation, data=data)
# Map for a regularization
regmap = maps.IdentityMap(nP=int(actind.sum()))
# Related to inversion
if use_sensitivity_weight:
reg = regularization.Sparse(mesh, indActive=actind, mapping=regmap)
reg.alpha_s = alpha_s
reg.alpha_x = alpha_x
reg.alpha_y = alpha_y
reg.alpha_z = alpha_z
else:
reg = regularization.Tikhonov(mesh, indActive=actind, mapping=regmap)
reg.alpha_s = alpha_s
reg.alpha_x = alpha_x
reg.alpha_y = alpha_y
reg.alpha_z = alpha_z
opt = optimization.ProjectedGNCG(maxIter=maxIter, upper=upper, lower=lower)
invProb = inverse_problem.BaseInvProblem(dmisfit, reg, opt)
beta = directives.BetaSchedule(coolingFactor=coolingFactor,
coolingRate=coolingRate)
betaest = directives.BetaEstimate_ByEig(beta0_ratio=beta0_ratio)
target = directives.TargetMisfit()
# Need to have basice saving function
update_Jacobi = directives.UpdatePreconditioner()
if use_sensitivity_weight:
updateSensW = directives.UpdateSensitivityWeights()
directiveList = [beta, target, updateSensW, update_Jacobi, betaest]
else:
directiveList = [beta, target, update_Jacobi, betaest]
inv = inversion.BaseInversion(invProb, directiveList=directiveList)
opt.LSshorten = 0.5
opt.remember("xc")
# Run inversion
mopt = inv.run(m0)
return mopt, invProb.dpred
def test_inv(self):
reg = regularization.Tikhonov(self.mesh)
opt = optimization.InexactGaussNewton(maxIter=10)
invProb = inverse_problem.BaseInvProblem(self.dmiscobmo, reg, opt)
directives_list = [directives.BetaEstimate_ByEig(beta0_ratio=1e-2)]
print(len(directives_list))
inv = inversion.BaseInversion(invProb, directiveList=directives_list)
m0 = self.model.mean() * np.ones_like(self.model)
mrec = inv.run(m0)
def test_inv_mref_setting(self):
reg1 = regularization.Tikhonov(self.mesh)
reg2 = regularization.Tikhonov(self.mesh)
reg = reg1 + reg2
opt = optimization.ProjectedGNCG(
maxIter=10, lower=-10, upper=10, maxIterLS=20, maxIterCG=50, tolCG=1e-4
)
invProb = inverse_problem.BaseInvProblem(self.dmiscombo, reg, opt)
directives_list = [
directives.ScalingMultipleDataMisfits_ByEig(chi0_ratio=[0.01, 1.0], verbose=True),
directives.AlphasSmoothEstimate_ByEig(verbose=True),
directives.BetaEstimate_ByEig(beta0_ratio=1e-2),
directives.BetaSchedule(),
]
inv = inversion.BaseInversion(invProb, directiveList=directives_list)
m0 = self.model.mean() * np.ones_like(self.model)
mrec = inv.run(m0)
self.assertTrue(np.all(reg1.mref == m0))
self.assertTrue(np.all(reg2.mref == m0))
def setUp(self):
cs = 12.5
hx = [(cs, 7, -1.3), (cs, 61), (cs, 7, 1.3)]
hy = [(cs, 7, -1.3), (cs, 20)]
mesh = discretize.TensorMesh([hx, hy], x0="CN")
# x = np.linspace(-200, 200., 20)
x = np.linspace(-200, 200.0, 2)
M = utils.ndgrid(x - 12.5, np.r_[0.0])
N = utils.ndgrid(x + 12.5, np.r_[0.0])
A0loc = np.r_[-150, 0.0]
A1loc = np.r_[-130, 0.0]
B0loc = np.r_[-130, 0.0]
B1loc = np.r_[-110, 0.0]
rx = dc.Rx.Dipole(M, N)
src0 = dc.Src.Dipole([rx], A0loc, B0loc)
src1 = dc.Src.Dipole([rx], A1loc, B1loc)
survey = ip.Survey([src0, src1])
sigma = np.ones(mesh.nC) * 1.0
problem = ip.Simulation2DCellCentered(
mesh,
survey=survey,
sigma=sigma,
etaMap=maps.IdentityMap(mesh),
verbose=False,
)
mSynth = np.ones(mesh.nC) * 0.1
dobs = problem.make_synthetic_data(mSynth, add_noise=True)
# Now set up the problem to do some minimization
dmis = data_misfit.L2DataMisfit(data=dobs, simulation=problem)
reg = regularization.Tikhonov(mesh)
opt = optimization.InexactGaussNewton(maxIterLS=20,
maxIter=10,
tolF=1e-6,
tolX=1e-6,
tolG=1e-6,
maxIterCG=6)
invProb = inverse_problem.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 test_inv(self):
reg = regularization.Tikhonov(self.mesh)
opt = optimization.InexactGaussNewton(maxIter=10, use_WolfeCurvature=True)
invProb = inverse_problem.BaseInvProblem(self.dmiscombo, reg, opt)
directives_list = [
directives.ScalingMultipleDataMisfits_ByEig(verbose=True),
directives.AlphasSmoothEstimate_ByEig(verbose=True),
directives.BetaEstimate_ByEig(beta0_ratio=1e-2),
directives.BetaSchedule(),
]
inv = inversion.BaseInversion(invProb, directiveList=directives_list)
m0 = self.model.mean() * np.ones_like(self.model)
mrec = inv.run(m0)
def run_inversion_direct(
self,
m0=0.0,
mref=0.0,
percentage=0,
floor=3e-2,
chi_fact=1.0,
beta_min=1e-4,
beta_max=1e5,
n_beta=81,
alpha_s=1.0,
alpha_x=0,
):
self.uncertainty = percentage * abs(self.data_vec) * 0.01 + floor
survey_obj, simulation_obj = self.get_problem_survey()
data_obj = data.Data(survey_obj,
dobs=self.data_vec,
noise_floor=self.uncertainty)
dmis = data_misfit.L2DataMisfit(simulation=simulation_obj,
data=data_obj)
m0 = np.ones(self.M) * m0
mref = np.ones(self.M) * mref
reg = regularization.Tikhonov(self.mesh_prop,
alpha_s=alpha_s,
alpha_x=alpha_x,
mref=mref)
betas = np.logspace(np.log10(beta_min), np.log10(beta_max),
n_beta)[::-1]
phi_d = np.zeros(n_beta, dtype=float)
phi_m = np.zeros(n_beta, dtype=float)
models = []
preds = []
G = dmis.W.dot(self.G)
for ii, beta in enumerate(betas):
A = G.T.dot(G) + beta * reg.deriv2(m0)
b = -(dmis.deriv(m0) + beta * reg.deriv(m0))
m = np.linalg.solve(A, b)
phi_d[ii] = dmis(m) * 2.0
phi_m[ii] = reg(m) * 2.0
models.append(m)
preds.append(simulation_obj.dpred(m))
return phi_d, phi_m, models, preds, betas
def setUp(self):
aSpacing = 2.5
nElecs = 10
surveySize = nElecs * aSpacing - aSpacing
cs = surveySize / nElecs / 4
mesh = discretize.TensorMesh(
[
[(cs, 10, -1.3), (cs, surveySize / cs), (cs, 10, 1.3)],
[(cs, 3, -1.3), (cs, 3, 1.3)],
# [(cs, 5, -1.3), (cs, 10)]
],
"CN",
)
source_list = dc.utils.WennerSrcList(nElecs, aSpacing, in2D=True)
survey = dc.survey.Survey(source_list)
simulation = dc.simulation.Simulation3DNodal(
mesh=mesh,
survey=survey,
rhoMap=maps.IdentityMap(mesh),
storeJ=True,
bc_type="Robin",
)
mSynth = np.ones(mesh.nC)
dobs = simulation.make_synthetic_data(mSynth, add_noise=True)
# Now set up the problem to do some minimization
dmis = data_misfit.L2DataMisfit(simulation=simulation, data=dobs)
reg = regularization.Tikhonov(mesh)
opt = optimization.InexactGaussNewton(maxIterLS=20,
maxIter=10,
tolF=1e-6,
tolX=1e-6,
tolG=1e-6,
maxIterCG=6)
invProb = inverse_problem.BaseInvProblem(dmis, reg, opt, beta=1e4)
inv = inversion.BaseInversion(invProb)
self.inv = inv
self.reg = reg
self.p = simulation
self.mesh = mesh
self.m0 = mSynth
self.survey = survey
self.dmis = dmis
self.dobs = dobs
def setUp(self):
print("\n ---- Testing {} ---- \n".format(self.formulation))
cs = 12.5
hx = [(cs, 2, -1.3), (cs, 61), (cs, 2, 1.3)]
hy = [(cs, 2, -1.3), (cs, 20)]
mesh = discretize.TensorMesh([hx, hy], x0="CN")
x = np.linspace(-135, 250.0, 20)
M = utils.ndgrid(x - 12.5, np.r_[0.0])
N = utils.ndgrid(x + 12.5, np.r_[0.0])
A0loc = np.r_[-150, 0.0]
A1loc = np.r_[-130, 0.0]
# rxloc = [np.c_[M, np.zeros(20)], np.c_[N, np.zeros(20)]]
rx1 = dc.receivers.Dipole(M, N)
rx2 = dc.receivers.Dipole(M, N, data_type="apparent_resistivity")
src0 = dc.sources.Pole([rx1, rx2], A0loc)
src1 = dc.sources.Pole([rx1, rx2], A1loc)
survey = dc.survey.Survey([src0, src1])
survey.set_geometric_factor()
simulation = getattr(dc, self.formulation)(
mesh,
rhoMap=maps.IdentityMap(mesh),
storeJ=self.storeJ,
solver=Solver,
survey=survey,
bc_type=self.bc_type,
)
mSynth = np.ones(mesh.nC) * 1.0
data = simulation.make_synthetic_data(mSynth, add_noise=True)
# Now set up the problem to do some minimization
dmis = data_misfit.L2DataMisfit(simulation=simulation, data=data)
reg = regularization.Tikhonov(mesh)
opt = optimization.InexactGaussNewton(maxIterLS=20,
maxIter=10,
tolF=1e-6,
tolX=1e-6,
tolG=1e-6,
maxIterCG=6)
invProb = inverse_problem.BaseInvProblem(dmis, reg, opt, beta=1e0)
inv = inversion.BaseInversion(invProb)
self.inv = inv
self.reg = reg
self.p = simulation
self.mesh = mesh
self.m0 = mSynth
self.survey = survey
self.dmis = dmis
self.data = data
def run_inversion_direct(
self,
m0=0.0,
mref=0.0,
percentage=5,
floor=0.1,
chi_fact=1.0,
beta_min=1e-4,
beta_max=1e0,
n_beta=31,
alpha_s=1.0,
alpha_x=1.0,
):
simulation = self.get_simulation()
dobs = self.data.copy()
lin_data = Data(survey=simulation.survey, dobs=dobs)
self.uncertainty = percentage * abs(dobs) * 0.01 + floor
m0 = np.ones(self.M) * m0
mref = np.ones(self.M) * mref
reg = regularization.Tikhonov(self.mesh,
alpha_s=alpha_s,
alpha_x=alpha_x,
mref=mref)
dmis = data_misfit.L2DataMisfit(data=lin_data, simulation=simulation)
dmis.W = 1.0 / self.uncertainty
betas = np.logspace(np.log10(beta_min), np.log10(beta_max),
n_beta)[::-1]
phi_d = np.zeros(n_beta, dtype=float)
phi_m = np.zeros(n_beta, dtype=float)
models = []
preds = []
G = dmis.W.dot(self.G)
for ii, beta in enumerate(betas):
A = G.T.dot(G) + beta * reg.deriv2(m0)
b = -(dmis.deriv(m0) + beta * reg.deriv(m0))
m = np.linalg.solve(A, b)
phi_d[ii] = dmis(m) * 2.0
phi_m[ii] = reg(m) * 2.0
models.append(m)
preds.append(simulation.dpred(m))
return phi_d, phi_m, models, preds, betas
def test_addition(self):
mesh = discretize.TensorMesh([8, 7, 6])
m = np.random.rand(mesh.nC)
reg1 = regularization.Tikhonov(mesh)
reg2 = regularization.Simple(mesh)
reg_a = reg1 + reg2
self.assertTrue(len(reg_a) == 2)
self.assertTrue(reg1(m) + reg2(m) == reg_a(m))
reg_a.test(eps=TOL)
reg_b = 2 * reg1 + reg2
self.assertTrue(len(reg_b) == 2)
self.assertTrue(2 * reg1(m) + reg2(m) == reg_b(m))
reg_b.test(eps=TOL)
reg_c = reg1 + reg2 / 2
self.assertTrue(len(reg_c) == 2)
self.assertTrue(reg1(m) + 0.5 * reg2(m) == reg_c(m))
reg_c.test(eps=TOL)
def setUp(self):
time = np.logspace(-3, 0, 21)
n_loc = 5
wires = Maps.Wires(('eta', n_loc), ('tau', n_loc), ('c', n_loc))
taumap = Maps.ExpMap(nP=n_loc) * wires.tau
etamap = Maps.ExpMap(nP=n_loc) * wires.eta
cmap = Maps.ExpMap(nP=n_loc) * wires.c
survey = SEMultiSurvey(time=time, locs=np.zeros((n_loc, 3)), n_pulse=0)
mesh = Mesh.TensorMesh([np.ones(int(n_loc * 3))])
prob = SEMultiInvProblem(mesh, etaMap=etamap, tauMap=taumap, cMap=cmap)
prob.pair(survey)
eta0, tau0, c0 = 0.1, 10., 0.5
m0 = np.log(np.r_[eta0 * np.ones(n_loc), tau0 * np.ones(n_loc),
c0 * np.ones(n_loc)])
survey.makeSyntheticData(m0)
# 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=0.)
inv = Inversion.BaseInversion(invProb)
self.inv = inv
self.reg = reg
self.p = prob
self.survey = survey
self.m0 = m0
self.dmis = dmis
self.mesh = mesh
def run(plotIt=True):
nC = 40
de = 1.0
h = np.ones(nC) * de / nC
M = discretize.TensorMesh([h, h])
y = np.linspace(M.vectorCCy[0], M.vectorCCx[-1], int(np.floor(nC / 4)))
rlocs = np.c_[0 * y + M.vectorCCx[-1], y]
rx = tomo.Rx(rlocs)
source_list = [
tomo.Src(location=np.r_[M.vectorCCx[0], yi], receiver_list=[rx])
for yi in y
]
# phi model
phi0 = 0
phi1 = 0.65
phitrue = utils.model_builder.defineBlock(M.gridCC, [0.4, 0.6], [0.6, 0.4],
[phi1, phi0])
knownVolume = np.sum(phitrue * M.vol)
print("True Volume: {}".format(knownVolume))
# Set up true conductivity model and plot the model transform
sigma0 = np.exp(1)
sigma1 = 1e4
if plotIt:
fig, ax = plt.subplots(1, 1)
sigmaMapTest = maps.SelfConsistentEffectiveMedium(nP=1000,
sigma0=sigma0,
sigma1=sigma1,
rel_tol=1e-1,
maxIter=150)
testphis = np.linspace(0.0, 1.0, 1000)
sigetest = sigmaMapTest * testphis
ax.semilogy(testphis, sigetest)
ax.set_title("Model Transform")
ax.set_xlabel("$\\varphi$")
ax.set_ylabel("$\sigma$")
sigmaMap = maps.SelfConsistentEffectiveMedium(M,
sigma0=sigma0,
sigma1=sigma1)
# scale the slowness so it is on a ~linear scale
slownessMap = maps.LogMap(M) * sigmaMap
# set up the true sig model and log model dobs
sigtrue = sigmaMap * phitrue
# modt = Model.BaseModel(M);
slownesstrue = slownessMap * phitrue # true model (m = log(sigma))
# set up the problem and survey
survey = tomo.Survey(source_list)
problem = tomo.Simulation(M, survey=survey, slownessMap=slownessMap)
if plotIt:
fig, ax = plt.subplots(1, 1)
cb = plt.colorbar(M.plotImage(phitrue, ax=ax)[0], ax=ax)
survey.plot(ax=ax)
cb.set_label("$\\varphi$")
# get observed data
data = problem.make_synthetic_data(phitrue,
relative_error=0.03,
add_noise=True)
dpred = problem.dpred(np.zeros(M.nC))
# objective function pieces
reg = regularization.Tikhonov(M)
dmis = data_misfit.L2DataMisfit(simulation=problem, data=data)
dmisVol = Volume(mesh=M, knownVolume=knownVolume)
beta = 0.25
maxIter = 15
# without the volume regularization
opt = optimization.ProjectedGNCG(maxIter=maxIter, lower=0.0, upper=1.0)
opt.remember("xc")
invProb = inverse_problem.BaseInvProblem(dmis, reg, opt, beta=beta)
inv = inversion.BaseInversion(invProb)
mopt1 = inv.run(np.zeros(M.nC) + 1e-16)
print("\nTotal recovered volume (no vol misfit term in inversion): "
"{}".format(dmisVol(mopt1)))
# with the volume regularization
vol_multiplier = 9e4
reg2 = reg
dmis2 = dmis + vol_multiplier * dmisVol
opt2 = optimization.ProjectedGNCG(maxIter=maxIter, lower=0.0, upper=1.0)
opt2.remember("xc")
invProb2 = inverse_problem.BaseInvProblem(dmis2, reg2, opt2, beta=beta)
inv2 = inversion.BaseInversion(invProb2)
mopt2 = inv2.run(np.zeros(M.nC) + 1e-16)
print("\nTotal volume (vol misfit term in inversion): {}".format(
dmisVol(mopt2)))
# plot results
if plotIt:
fig, ax = plt.subplots(1, 1)
ax.plot(data.dobs)
ax.plot(dpred)
ax.plot(problem.dpred(mopt1), "o")
ax.plot(problem.dpred(mopt2), "s")
ax.legend(["dobs", "dpred0", "dpred w/o Vol", "dpred with Vol"])
fig, ax = plt.subplots(1, 3, figsize=(16, 4))
im0 = M.plotImage(phitrue, ax=ax[0])[0]
im1 = M.plotImage(mopt1, ax=ax[1])[0]
im2 = M.plotImage(mopt2, ax=ax[2])[0]
for im in [im0, im1, im2]:
im.set_clim([0.0, phi1])
plt.colorbar(im0, ax=ax[0])
plt.colorbar(im1, ax=ax[1])
plt.colorbar(im2, ax=ax[2])
ax[0].set_title("true, vol: {:1.3e}".format(knownVolume))
ax[1].set_title("recovered(no Volume term), vol: {:1.3e} ".format(
dmisVol(mopt1)))
ax[2].set_title("recovered(with Volume term), vol: {:1.3e} ".format(
dmisVol(mopt2)))
plt.tight_layout()
def run(plotIt=True):
M = discretize.TensorMesh([np.ones(40)], x0="N")
M.setCellGradBC("dirichlet")
# We will use the haverkamp empirical model with parameters from Celia1990
k_fun, theta_fun = richards.empirical.haverkamp(
M,
A=1.1750e06,
gamma=4.74,
alpha=1.6110e06,
theta_s=0.287,
theta_r=0.075,
beta=3.96,
)
# Here we are making saturated hydraulic conductivity
# an exponential mapping to the model (defined below)
k_fun.KsMap = maps.ExpMap(nP=M.nC)
# Setup the boundary and initial conditions
bc = np.array([-61.5, -20.7])
h = np.zeros(M.nC) + bc[0]
prob = richards.SimulationNDCellCentered(
M,
hydraulic_conductivity=k_fun,
water_retention=theta_fun,
boundary_conditions=bc,
initial_conditions=h,
do_newton=False,
method="mixed",
debug=False,
)
prob.time_steps = [(5, 25, 1.1), (60, 40)]
# Create the survey
locs = -np.arange(2, 38, 4.0).reshape(-1, 1)
times = np.arange(30, prob.time_mesh.vectorCCx[-1], 60)
rxSat = richards.receivers.Saturation(locs, times)
survey = richards.Survey([rxSat])
prob.survey = survey
# Create a simple model for Ks
Ks = 1e-3
mtrue = np.ones(M.nC) * np.log(Ks)
mtrue[15:20] = np.log(5e-2)
mtrue[20:35] = np.log(3e-3)
mtrue[35:40] = np.log(1e-2)
m0 = np.ones(M.nC) * np.log(Ks)
# Create some synthetic data and fields
relative = 0.02 # The standard deviation for the noise
Hs = prob.fields(mtrue)
data = prob.make_synthetic_data(mtrue,
relative_error=relative,
f=Hs,
add_noise=True)
# Setup a pretty standard inversion
reg = regularization.Tikhonov(M, alpha_s=1e-1)
dmis = data_misfit.L2DataMisfit(simulation=prob, data=data)
opt = optimization.InexactGaussNewton(maxIter=20, maxIterCG=10)
invProb = inverse_problem.BaseInvProblem(dmis, reg, opt)
beta = directives.BetaSchedule(coolingFactor=4)
betaest = directives.BetaEstimate_ByEig(beta0_ratio=1e2)
target = directives.TargetMisfit()
dir_list = [beta, betaest, target]
inv = inversion.BaseInversion(invProb, directiveList=dir_list)
mopt = inv.run(m0)
Hs_opt = prob.fields(mopt)
if plotIt:
plt.figure(figsize=(14, 9))
ax = plt.subplot(121)
plt.semilogx(np.exp(np.c_[mopt, mtrue]), M.gridCC)
plt.xlabel("Saturated Hydraulic Conductivity, $K_s$")
plt.ylabel("Depth, cm")
plt.semilogx([10**-3.9] * len(locs), locs, "ro")
plt.legend(("$m_{rec}$", "$m_{true}$", "Data locations"), loc=4)
ax = plt.subplot(222)
mesh2d = discretize.TensorMesh([prob.time_mesh.hx / 60, prob.mesh.hx],
"0N")
sats = [theta_fun(_) for _ in Hs]
clr = mesh2d.plotImage(np.c_[sats][1:, :], ax=ax)
cmap0 = matplotlib.cm.RdYlBu_r
clr[0].set_cmap(cmap0)
c = plt.colorbar(clr[0])
c.set_label("Saturation $\\theta$")
plt.xlabel("Time, minutes")
plt.ylabel("Depth, cm")
plt.title("True saturation over time")
ax = plt.subplot(224)
mesh2d = discretize.TensorMesh([prob.time_mesh.hx / 60, prob.mesh.hx],
"0N")
sats = [theta_fun(_) for _ in Hs_opt]
clr = mesh2d.plotImage(np.c_[sats][1:, :], ax=ax)
cmap0 = matplotlib.cm.RdYlBu_r
clr[0].set_cmap(cmap0)
c = plt.colorbar(clr[0])
c.set_label("Saturation $\\theta$")
plt.xlabel("Time, minutes")
plt.ylabel("Depth, cm")
plt.title("Recovered saturation over time")
plt.tight_layout()
petrodir = directives.PGI_UpdateParameters(update_gmm=False)
# Setup Inversion
inv = inversion.BaseInversion(
invProb,
directiveList=[
alphas, scales, beta, petrodir, targets, betaIt, scaling_schedule
],
)
mcluster_no_map = inv.run(minit)
# Tikhonov Inversion
reg1 = regularization.Tikhonov(mesh,
alpha_s=1.0,
alpha_x=1.0,
mapping=wires.m1)
reg1.cell_weights = wr1
reg2 = regularization.Tikhonov(mesh,
alpha_s=1.0,
alpha_x=1.0,
mapping=wires.m2)
reg2.cell_weights = wr2
reg = reg1 + reg2
opt = optimization.ProjectedGNCG(
maxIter=30,
tolX=1e-6,
maxIterCG=100,
tolCG=1e-3,
lower=-10,
# # The inverse problem is defined by 3 things: # # 1) Data Misfit: a measure of how well our recovered model explains the field data # 2) Regularization: constraints placed on the recovered model and a priori information # 3) Optimization: the numerical approach used to solve the inverse problem # # Define the data misfit. Here the data misfit is the L2 norm of the weighted # residual between the observed data and the data predicted for a given model. # Within the data misfit, the residual between predicted and observed data are # normalized by the data's standard deviation. dmis = data_misfit.L2DataMisfit(simulation=sim, data=data_obj) # Define the regularization (model objective function). reg = regularization.Tikhonov(mesh, alpha_s=1.0, alpha_x=1.0) # Define how the optimization problem is solved. opt = optimization.InexactGaussNewton(maxIter=50) # Here we define the inverse problem that is to be solved inv_prob = inverse_problem.BaseInvProblem(dmis, reg, opt) ####################################################################### # Define Inversion Directives # --------------------------- # # Here we define any directiveas that are carried out during the inversion. This # includes the cooling schedule for the trade-off parameter (beta), stopping # criteria for the inversion and saving inversion results at each iteration. #
def setUp(self, parallel=True):
time = np.logspace(-6, -3, 21)
time_input_currents = wave.current_times[-7:]
input_currents = wave.currents[-7:]
hz = get_vertical_discretization_time(time,
facter_tmax=0.5,
factor_tmin=10.)
hz = np.r_[1.]
n_sounding = 10
dx = 20.
hx = np.ones(n_sounding) * dx
e = np.ones(n_sounding)
mSynth = np.r_[e * np.log(1. / 100.), e * 20]
x = np.arange(n_sounding)
y = np.zeros_like(x)
z = np.ones_like(x) * 30.
rx_locations = np.c_[x, y, z]
src_locations = np.c_[x, y, z]
topo = np.c_[x, y, z - 30.].astype(float)
rx_type_global = np.array(["dBzdt"], dtype=str).repeat(n_sounding,
axis=0)
field_type_global = np.array(['secondary'],
dtype=str).repeat(n_sounding, axis=0)
wave_type_global = np.array(['general'], dtype=str).repeat(n_sounding,
axis=0)
time_global = [time for i in range(n_sounding)]
src_type_global = np.array(["CircularLoop"],
dtype=str).repeat(n_sounding, axis=0)
a_global = np.array([13.], dtype=float).repeat(n_sounding, axis=0)
input_currents_global = [input_currents for i in range(n_sounding)]
time_input_currents_global = [
time_input_currents for i in range(n_sounding)
]
wires = Maps.Wires(('sigma', n_sounding), ('h', n_sounding))
expmap = Maps.ExpMap(nP=n_sounding)
sigmaMap = expmap * wires.sigma
survey = GlobalEM1DSurveyTD(
rx_locations=rx_locations,
src_locations=src_locations,
topo=topo,
time=time_global,
src_type=src_type_global,
rx_type=rx_type_global,
field_type=field_type_global,
wave_type=wave_type_global,
a=a_global,
input_currents=input_currents_global,
time_input_currents=time_input_currents_global,
half_switch=True)
problem = GlobalEM1DProblemTD([],
sigmaMap=sigmaMap,
hMap=wires.h,
hz=hz,
parallel=parallel,
n_cpu=2)
problem.pair(survey)
survey.makeSyntheticData(mSynth)
# Now set up the problem to do some minimization
mesh = Mesh.TensorMesh([int(n_sounding * 2)])
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=0.)
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 setUp(self, parallel=True):
time = np.logspace(-6, -3, 21)
hz = get_vertical_discretization_time(time,
facter_tmax=0.5,
factor_tmin=10.)
time_input_currents = wave.current_times[-7:]
input_currents = wave.currents[-7:]
n_sounding = 5
dx = 20.
hx = np.ones(n_sounding) * dx
mesh = Mesh.TensorMesh([hx, hz], x0='00')
inds = mesh.gridCC[:, 1] < 25
inds_1 = mesh.gridCC[:, 1] < 50
sigma = np.ones(mesh.nC) * 1. / 100.
sigma[inds_1] = 1. / 10.
sigma[inds] = 1. / 50.
sigma_em1d = sigma.reshape(mesh.vnC, order='F').flatten()
mSynth = np.log(sigma_em1d)
x = mesh.vectorCCx
y = np.zeros_like(x)
z = np.ones_like(x) * 30.
rx_locations = np.c_[x, y, z]
src_locations = np.c_[x, y, z]
topo = np.c_[x, y, z - 30.].astype(float)
n_sounding = rx_locations.shape[0]
rx_type_global = np.array(["dBzdt"], dtype=str).repeat(n_sounding,
axis=0)
field_type_global = np.array(['secondary'],
dtype=str).repeat(n_sounding, axis=0)
wave_type_global = np.array(['general'], dtype=str).repeat(n_sounding,
axis=0)
time_global = [time for i in range(n_sounding)]
src_type_global = np.array(["CircularLoop"],
dtype=str).repeat(n_sounding, axis=0)
a_global = np.array([13.], dtype=float).repeat(n_sounding, axis=0)
input_currents_global = [input_currents for i in range(n_sounding)]
time_input_currents_global = [
time_input_currents for i in range(n_sounding)
]
mapping = Maps.ExpMap(mesh)
survey = GlobalEM1DSurveyTD(
rx_locations=rx_locations,
src_locations=src_locations,
topo=topo,
time=time_global,
src_type=src_type_global,
rx_type=rx_type_global,
field_type=field_type_global,
wave_type=wave_type_global,
a=a_global,
input_currents=input_currents_global,
time_input_currents=time_input_currents_global)
problem = GlobalEM1DProblemTD(mesh,
sigmaMap=mapping,
hz=hz,
parallel=parallel,
n_cpu=2)
problem.pair(survey)
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=0.)
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 setUp(self):
cs = 25.0
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 = discretize.TensorMesh([hx, hy, hz], x0="CCN")
blkind0 = utils.model_builder.getIndicesSphere(
np.r_[-100.0, -100.0, -200.0], 75.0, mesh.gridCC)
blkind1 = utils.model_builder.getIndicesSphere(
np.r_[100.0, 100.0, -200.0], 75.0, mesh.gridCC)
sigma = np.ones(mesh.nC) * 1e-2
eta = np.zeros(mesh.nC)
tau = np.ones_like(sigma) * 1.0
eta[blkind0] = 0.1
eta[blkind1] = 0.1
tau[blkind0] = 0.1
tau[blkind1] = 0.01
x = mesh.vectorCCx[(mesh.vectorCCx > -155.0)
& (mesh.vectorCCx < 155.0)]
y = mesh.vectorCCy[(mesh.vectorCCy > -155.0)
& (mesh.vectorCCy < 155.0)]
Aloc = np.r_[-200.0, 0.0, 0.0]
Bloc = np.r_[200.0, 0.0, 0.0]
M = utils.ndgrid(x - 25.0, y, np.r_[0.0])
N = utils.ndgrid(x + 25.0, y, np.r_[0.0])
times = np.arange(10) * 1e-3 + 1e-3
rx = sip.receivers.Dipole(M, N, times)
print(rx.nD)
print(rx.locations)
src = sip.sources.Dipole([rx], Aloc, Bloc)
survey = sip.Survey([src])
print(f"Survey ND = {survey.nD}")
print(f"Survey ND = {src.nD}")
wires = maps.Wires(("eta", mesh.nC), ("taui", mesh.nC))
problem = sip.Simulation3DCellCentered(
mesh,
survey=survey,
rho=1.0 / sigma,
etaMap=wires.eta,
tauiMap=wires.taui,
storeJ=False,
)
problem.solver = Solver
mSynth = np.r_[eta, 1.0 / tau]
problem.model = mSynth
dobs = problem.make_synthetic_data(mSynth, add_noise=True)
# Now set up the problem to do some minimization
dmis = data_misfit.L2DataMisfit(data=dobs, simulation=problem)
reg = regularization.Tikhonov(mesh)
opt = optimization.InexactGaussNewton(maxIterLS=20,
maxIter=10,
tolF=1e-6,
tolX=1e-6,
tolG=1e-6,
maxIterCG=6)
invProb = inverse_problem.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
self.dobs = dobs
def run_inversion(
self,
maxIter=60,
m0=0.0,
mref=0.0,
percentage=5,
floor=0.1,
chifact=1,
beta0_ratio=1.0,
coolingFactor=1,
n_iter_per_beta=1,
alpha_s=1.0,
alpha_x=1.0,
alpha_z=1.0,
use_target=False,
use_tikhonov=True,
use_irls=False,
p_s=2,
p_x=2,
p_y=2,
p_z=2,
beta_start=None,
):
self.uncertainty = percentage * abs(self.data_prop.dobs) * 0.01 + floor
m0 = np.ones(self.mesh_prop.nC) * m0
mref = np.ones(self.mesh_prop.nC) * mref
if ~use_tikhonov:
reg = regularization.Sparse(
self.mesh_prop,
alpha_s=alpha_s,
alpha_x=alpha_x,
alpha_y=alpha_z,
mref=mref,
mapping=maps.IdentityMap(self.mesh_prop),
cell_weights=self.mesh_prop.vol,
)
else:
reg = regularization.Tikhonov(
self.mesh_prop,
alpha_s=alpha_s,
alpha_x=alpha_x,
alpha_y=alpha_z,
mref=mref,
mapping=maps.IdentityMap(self.mesh_prop),
)
dataObj = data.Data(self.survey_prop,
dobs=self.dobs,
noise_floor=self.uncertainty)
dmis = data_misfit.L2DataMisfit(simulation=self.simulation_prop,
data=dataObj)
dmis.W = 1.0 / self.uncertainty
opt = optimization.ProjectedGNCG(maxIter=maxIter, maxIterCG=20)
opt.lower = 0.0
opt.remember("xc")
opt.tolG = 1e-10
opt.eps = 1e-10
invProb = inverse_problem.BaseInvProblem(dmis, reg, opt)
beta_schedule = directives.BetaSchedule(coolingFactor=coolingFactor,
coolingRate=n_iter_per_beta)
save = directives.SaveOutputEveryIteration()
print(chifact)
if use_irls:
IRLS = directives.Update_IRLS(
f_min_change=1e-4,
minGNiter=1,
silent=False,
max_irls_iterations=40,
beta_tol=5e-1,
coolEpsFact=1.3,
chifact_start=chifact,
)
if beta_start is None:
directives_list = [
directives.BetaEstimate_ByEig(beta0_ratio=beta0_ratio),
IRLS,
save,
]
else:
directives_list = [IRLS, save]
invProb.beta = beta_start
reg.norms = np.c_[p_s, p_x, p_z, 2]
else:
target = directives.TargetMisfit(chifact=chifact)
directives_list = [
directives.BetaEstimate_ByEig(beta0_ratio=beta0_ratio),
beta_schedule,
save,
]
if use_target:
directives_list.append(target)
inv = inversion.BaseInversion(invProb, directiveList=directives_list)
mopt = inv.run(m0)
model = opt.recall("xc")
model.append(mopt)
pred = []
for m in model:
pred.append(self.simulation_prop.dpred(m))
return model, pred, save
def run(plotIt=True):
cs, ncx, ncz, npad = 5.0, 25, 15, 15
hx = [(cs, ncx), (cs, npad, 1.3)]
hz = [(cs, npad, -1.3), (cs, ncz), (cs, npad, 1.3)]
mesh = discretize.CylMesh([hx, 1, hz], "00C")
active = mesh.vectorCCz < 0.0
layer = (mesh.vectorCCz < 0.0) & (mesh.vectorCCz >= -100.0)
actMap = maps.InjectActiveCells(mesh, active, np.log(1e-8), nC=mesh.nCz)
mapping = maps.ExpMap(mesh) * maps.SurjectVertical1D(mesh) * actMap
sig_half = 2e-3
sig_air = 1e-8
sig_layer = 1e-3
sigma = np.ones(mesh.nCz) * sig_air
sigma[active] = sig_half
sigma[layer] = sig_layer
mtrue = np.log(sigma[active])
rxOffset = 1e-3
rx = time_domain.Rx.PointMagneticFluxTimeDerivative(
np.array([[rxOffset, 0.0, 30]]), np.logspace(-5, -3, 31), "z"
)
src = time_domain.Src.MagDipole([rx], location=np.array([0.0, 0.0, 80]))
survey = time_domain.Survey([src])
time_steps = [(1e-06, 20), (1e-05, 20), (0.0001, 20)]
simulation = time_domain.Simulation3DElectricField(
mesh, sigmaMap=mapping, survey=survey, time_steps=time_steps
)
# d_true = simulation.dpred(mtrue)
# create observed data
rel_err = 0.05
data = simulation.make_synthetic_data(mtrue, relative_error=rel_err)
dmisfit = data_misfit.L2DataMisfit(simulation=simulation, data=data)
regMesh = discretize.TensorMesh([mesh.hz[mapping.maps[-1].indActive]])
reg = regularization.Tikhonov(regMesh, alpha_s=1e-2, alpha_x=1.0)
opt = optimization.InexactGaussNewton(maxIter=5, LSshorten=0.5)
invProb = inverse_problem.BaseInvProblem(dmisfit, reg, opt)
# Create an inversion object
beta = directives.BetaSchedule(coolingFactor=5, coolingRate=2)
betaest = directives.BetaEstimate_ByEig(beta0_ratio=1e0)
inv = inversion.BaseInversion(invProb, directiveList=[beta, betaest])
m0 = np.log(np.ones(mtrue.size) * sig_half)
simulation.counter = opt.counter = utils.Counter()
opt.remember("xc")
mopt = inv.run(m0)
if plotIt:
fig, ax = plt.subplots(1, 2, figsize=(10, 6))
ax[0].loglog(rx.times, -invProb.dpred, "b.-")
ax[0].loglog(rx.times, -data.dobs, "r.-")
ax[0].legend(("Noisefree", "$d^{obs}$"), fontsize=16)
ax[0].set_xlabel("Time (s)", fontsize=14)
ax[0].set_ylabel("$B_z$ (T)", fontsize=16)
ax[0].set_xlabel("Time (s)", fontsize=14)
ax[0].grid(color="k", alpha=0.5, linestyle="dashed", linewidth=0.5)
plt.semilogx(sigma[active], mesh.vectorCCz[active])
plt.semilogx(np.exp(mopt), mesh.vectorCCz[active])
ax[1].set_ylim(-600, 0)
ax[1].set_xlim(1e-4, 1e-2)
ax[1].set_xlabel("Conductivity (S/m)", fontsize=14)
ax[1].set_ylabel("Depth (m)", fontsize=14)
ax[1].grid(color="k", alpha=0.5, linestyle="dashed", linewidth=0.5)
plt.legend(["$\sigma_{true}$", "$\sigma_{pred}$"])
def run_inversion_cg(
self,
maxIter=60,
m0=0.0,
mref=0.0,
percentage=5,
floor=0.1,
chifact=1,
beta0_ratio=1.0,
coolingFactor=1,
coolingRate=1,
alpha_s=1.0,
alpha_x=1.0,
use_target=False,
):
sim = self.get_simulation()
data = Data(sim.survey,
dobs=self.data,
relative_error=percentage,
noise_floor=floor)
self.uncertainty = data.uncertainty
m0 = np.ones(self.M) * m0
mref = np.ones(self.M) * mref
reg = regularization.Tikhonov(self.mesh,
alpha_s=alpha_s,
alpha_x=alpha_x,
mref=mref)
dmis = data_misfit.L2DataMisfit(data=data, simulation=sim)
opt = optimization.InexactGaussNewton(maxIter=maxIter, maxIterCG=20)
opt.remember("xc")
opt.tolG = 1e-10
opt.eps = 1e-10
invProb = inverse_problem.BaseInvProblem(dmis, reg, opt)
save = directives.SaveOutputEveryIteration()
beta_schedule = directives.BetaSchedule(coolingFactor=coolingFactor,
coolingRate=coolingRate)
target = directives.TargetMisfit(chifact=chifact)
if use_target:
directs = [
directives.BetaEstimate_ByEig(beta0_ratio=beta0_ratio),
beta_schedule,
target,
save,
]
else:
directs = [
directives.BetaEstimate_ByEig(beta0_ratio=beta0_ratio),
beta_schedule,
save,
]
inv = inversion.BaseInversion(invProb, directiveList=directs)
mopt = inv.run(m0)
model = opt.recall("xc")
model.append(mopt)
pred = []
for m in model:
pred.append(sim.dpred(m))
return model, pred, save