def run(plotIt=True, survey_type="dipole-dipole", p=0., qx=2., qz=2.):
np.random.seed(1)
# Initiate I/O class for DC
IO = DC.IO()
# Obtain ABMN locations
xmin, xmax = 0., 200.
ymin, ymax = 0., 0.
zmin, zmax = 0, 0
endl = np.array([[xmin, ymin, zmin], [xmax, ymax, zmax]])
# Generate DC survey object
survey = DC.Utils.gen_DCIPsurvey(endl,
survey_type=survey_type,
dim=2,
a=10,
b=10,
n=10)
survey.getABMN_locations()
survey = IO.from_ambn_locations_to_survey(survey.a_locations,
survey.b_locations,
survey.m_locations,
survey.n_locations,
survey_type,
data_dc_type='volt')
# Obtain 2D TensorMesh
mesh, actind = IO.set_mesh()
topo, mesh1D = DC.Utils.genTopography(mesh, -10, 0, its=100)
actind = Utils.surface2ind_topo(mesh, np.c_[mesh1D.vectorCCx, topo])
survey.drapeTopo(mesh, actind, option="top")
# Build a conductivity model
blk_inds_c = Utils.ModelBuilder.getIndicesSphere(np.r_[60., -25.], 12.5,
mesh.gridCC)
blk_inds_r = Utils.ModelBuilder.getIndicesSphere(np.r_[140., -25.], 12.5,
mesh.gridCC)
layer_inds = mesh.gridCC[:, 1] > -5.
sigma = np.ones(mesh.nC) * 1. / 100.
sigma[blk_inds_c] = 1. / 10.
sigma[blk_inds_r] = 1. / 1000.
sigma[~actind] = 1. / 1e8
rho = 1. / sigma
# Show the true conductivity model
if plotIt:
fig = plt.figure(figsize=(12, 3))
ax = plt.subplot(111)
temp = rho.copy()
temp[~actind] = np.nan
out = mesh.plotImage(temp,
grid=True,
ax=ax,
gridOpts={'alpha': 0.2},
clim=(10, 1000),
pcolorOpts={
"cmap": "viridis",
"norm": colors.LogNorm()
})
ax.plot(survey.electrode_locations[:, 0],
survey.electrode_locations[:, 1], 'k.')
ax.set_xlim(IO.grids[:, 0].min(), IO.grids[:, 0].max())
ax.set_ylim(-IO.grids[:, 1].max(), IO.grids[:, 1].min())
cb = plt.colorbar(out[0])
cb.set_label("Resistivity (ohm-m)")
ax.set_aspect('equal')
plt.show()
# Use Exponential Map: m = log(rho)
actmap = Maps.InjectActiveCells(mesh,
indActive=actind,
valInactive=np.log(1e8))
mapping = Maps.ExpMap(mesh) * actmap
# Generate mtrue
mtrue = np.log(rho[actind])
# Generate 2.5D DC problem
# "N" means potential is defined at nodes
prb = DC.Problem2D_N(mesh,
rhoMap=mapping,
storeJ=True,
Solver=Solver,
verbose=True)
# Pair problem with survey
try:
prb.pair(survey)
except:
survey.unpair()
prb.pair(survey)
# Make synthetic DC data with 5% Gaussian noise
dtrue = survey.makeSyntheticData(mtrue, std=0.05, force=True)
IO.data_dc = dtrue
# Show apparent resisitivty pseudo-section
if plotIt:
IO.plotPseudoSection(data=survey.dobs / IO.G,
data_type='apparent_resistivity')
# Show apparent resisitivty histogram
if plotIt:
fig = plt.figure()
out = hist(survey.dobs / IO.G, bins=20)
plt.xlabel("Apparent Resisitivty ($\Omega$m)")
plt.show()
# Set initial model based upon histogram
m0 = np.ones(actmap.nP) * np.log(100.)
# Set uncertainty
# floor
eps = 10**(-3.2)
# percentage
std = 0.05
dmisfit = DataMisfit.l2_DataMisfit(survey)
uncert = abs(survey.dobs) * std + eps
dmisfit.W = 1. / uncert
# Map for a regularization
regmap = Maps.IdentityMap(nP=int(actind.sum()))
# Related to inversion
reg = Regularization.Sparse(mesh,
indActive=actind,
mapping=regmap,
gradientType='components')
# gradientType = 'components'
reg.norms = np.c_[p, qx, qz, 0.]
IRLS = Directives.Update_IRLS(maxIRLSiter=20,
minGNiter=1,
betaSearch=False,
fix_Jmatrix=True)
opt = Optimization.InexactGaussNewton(maxIter=40)
invProb = InvProblem.BaseInvProblem(dmisfit, reg, opt)
beta = Directives.BetaSchedule(coolingFactor=5, coolingRate=2)
betaest = Directives.BetaEstimate_ByEig(beta0_ratio=1e0)
target = Directives.TargetMisfit()
update_Jacobi = Directives.UpdatePreconditioner()
inv = Inversion.BaseInversion(invProb, directiveList=[betaest, IRLS])
prb.counter = opt.counter = Utils.Counter()
opt.LSshorten = 0.5
opt.remember('xc')
# Run inversion
mopt = inv.run(m0)
rho_est = mapping * mopt
rho_est_l2 = mapping * invProb.l2model
rho_est[~actind] = np.nan
rho_est_l2[~actind] = np.nan
rho_true = rho.copy()
rho_true[~actind] = np.nan
# show recovered conductivity
if plotIt:
vmin, vmax = rho.min(), rho.max()
fig, ax = plt.subplots(3, 1, figsize=(20, 9))
out1 = mesh.plotImage(rho_true,
clim=(10, 1000),
pcolorOpts={
"cmap": "viridis",
"norm": colors.LogNorm()
},
ax=ax[0])
out2 = mesh.plotImage(rho_est_l2,
clim=(10, 1000),
pcolorOpts={
"cmap": "viridis",
"norm": colors.LogNorm()
},
ax=ax[1])
out3 = mesh.plotImage(rho_est,
clim=(10, 1000),
pcolorOpts={
"cmap": "viridis",
"norm": colors.LogNorm()
},
ax=ax[2])
out = [out1, out2, out3]
titles = ["True", "L2", ("L%d, Lx%d, Lz%d") % (p, qx, qz)]
for i in range(3):
ax[i].plot(survey.electrode_locations[:, 0],
survey.electrode_locations[:, 1], 'kv')
ax[i].set_xlim(IO.grids[:, 0].min(), IO.grids[:, 0].max())
ax[i].set_ylim(-IO.grids[:, 1].max(), IO.grids[:, 1].min())
cb = plt.colorbar(out[i][0], ax=ax[i])
cb.set_label("Resistivity ($\Omega$m)")
ax[i].set_xlabel("Northing (m)")
ax[i].set_ylabel("Elevation (m)")
ax[i].set_aspect('equal')
ax[i].set_title(titles[i])
plt.tight_layout()
plt.show()
def run(plotIt=True,
survey_type="dipole-dipole",
rho_background=1e3,
rho_block=1e2,
block_x0=100,
block_dx=10,
block_y0=-10,
block_dy=5):
np.random.seed(1)
# Initiate I/O class for DC
IO = DC.IO()
# Obtain ABMN locations
xmin, xmax = 0., 200.
ymin, ymax = 0., 0.
zmin, zmax = 0, 0
endl = np.array([[xmin, ymin, zmin], [xmax, ymax, zmax]])
# Generate DC survey object
survey = DC.Utils.gen_DCIPsurvey(endl,
survey_type=survey_type,
dim=2,
a=10,
b=10,
n=10)
survey.getABMN_locations()
survey = IO.from_ambn_locations_to_survey(survey.a_locations,
survey.b_locations,
survey.m_locations,
survey.n_locations,
survey_type,
data_dc_type='volt')
# Obtain 2D TensorMesh
mesh, actind = IO.set_mesh()
# Flat topography
actind = Utils.surface2ind_topo(mesh, np.c_[mesh.vectorCCx,
mesh.vectorCCx * 0.])
survey.drapeTopo(mesh, actind, option="top")
# Use Exponential Map: m = log(rho)
actmap = Maps.InjectActiveCells(mesh,
indActive=actind,
valInactive=np.log(1e8))
parametric_block = Maps.ParametricBlock(mesh, slopeFact=1e2)
mapping = Maps.ExpMap(mesh) * parametric_block
# Set true model
# val_background,val_block, block_x0, block_dx, block_y0, block_dy
mtrue = np.r_[np.log(1e3), np.log(10), 100, 10, -20, 10]
# Set initial model
m0 = np.r_[np.log(rho_background),
np.log(rho_block), block_x0, block_dx, block_y0, block_dy]
rho = mapping * mtrue
rho0 = mapping * m0
# Show the true conductivity model
fig = plt.figure(figsize=(12, 3))
ax = plt.subplot(111)
temp = rho.copy()
temp[~actind] = np.nan
out = mesh.plotImage(temp,
grid=False,
ax=ax,
gridOpts={'alpha': 0.2},
clim=(10, 1000),
pcolorOpts={
"cmap": "viridis",
"norm": colors.LogNorm()
})
ax.plot(survey.electrode_locations[:, 0], survey.electrode_locations[:, 1],
'k.')
ax.set_xlim(IO.grids[:, 0].min(), IO.grids[:, 0].max())
ax.set_ylim(-IO.grids[:, 1].max(), IO.grids[:, 1].min())
cb = plt.colorbar(out[0])
cb.set_label("Resistivity (ohm-m)")
ax.set_aspect('equal')
ax.set_title("True resistivity model")
plt.show()
# Show the true conductivity model
fig = plt.figure(figsize=(12, 3))
ax = plt.subplot(111)
temp = rho0.copy()
temp[~actind] = np.nan
out = mesh.plotImage(temp,
grid=False,
ax=ax,
gridOpts={'alpha': 0.2},
clim=(10, 1000),
pcolorOpts={
"cmap": "viridis",
"norm": colors.LogNorm()
})
ax.plot(survey.electrode_locations[:, 0], survey.electrode_locations[:, 1],
'k.')
ax.set_xlim(IO.grids[:, 0].min(), IO.grids[:, 0].max())
ax.set_ylim(-IO.grids[:, 1].max(), IO.grids[:, 1].min())
cb = plt.colorbar(out[0])
cb.set_label("Resistivity (ohm-m)")
ax.set_aspect('equal')
ax.set_title("Initial resistivity model")
plt.show()
# Generate 2.5D DC problem
# "N" means potential is defined at nodes
prb = DC.Problem2D_N(mesh, rhoMap=mapping, storeJ=True, Solver=Solver)
# Pair problem with survey
try:
prb.pair(survey)
except:
survey.unpair()
prb.pair(survey)
# Make synthetic DC data with 5% Gaussian noise
dtrue = survey.makeSyntheticData(mtrue, std=0.05, force=True)
# Show apparent resisitivty pseudo-section
IO.plotPseudoSection(data=survey.dobs / IO.G,
data_type='apparent_resistivity')
# Show apparent resisitivty histogram
fig = plt.figure()
out = hist(survey.dobs / IO.G, bins=20)
plt.show()
# Set uncertainty
# floor
eps = 10**(-3.2)
# percentage
std = 0.05
dmisfit = DataMisfit.l2_DataMisfit(survey)
uncert = abs(survey.dobs) * std + eps
dmisfit.W = 1. / uncert
# Map for a regularization
mesh_1d = Mesh.TensorMesh([parametric_block.nP])
# Related to inversion
reg = Regularization.Simple(mesh_1d, alpha_x=0.)
opt = Optimization.InexactGaussNewton(maxIter=10)
invProb = InvProblem.BaseInvProblem(dmisfit, reg, opt)
beta = Directives.BetaSchedule(coolingFactor=5, coolingRate=2)
betaest = Directives.BetaEstimate_ByEig(beta0_ratio=1e0)
target = Directives.TargetMisfit()
updateSensW = Directives.UpdateSensitivityWeights()
update_Jacobi = Directives.UpdatePreconditioner()
invProb.beta = 0.
inv = Inversion.BaseInversion(invProb, directiveList=[target])
prb.counter = opt.counter = Utils.Counter()
opt.LSshorten = 0.5
opt.remember('xc')
# Run inversion
mopt = inv.run(m0)
# Convert obtained inversion model to resistivity
# rho = M(m), where M(.) is a mapping
rho_est = mapping * mopt
rho_true = rho.copy()
# show recovered conductivity
vmin, vmax = rho.min(), rho.max()
fig, ax = plt.subplots(2, 1, figsize=(20, 6))
out1 = mesh.plotImage(rho_true,
clim=(10, 1000),
pcolorOpts={
"cmap": "viridis",
"norm": colors.LogNorm()
},
ax=ax[0])
out2 = mesh.plotImage(rho_est,
clim=(10, 1000),
pcolorOpts={
"cmap": "viridis",
"norm": colors.LogNorm()
},
ax=ax[1])
out = [out1, out2]
for i in range(2):
ax[i].plot(survey.electrode_locations[:, 0],
survey.electrode_locations[:, 1], 'kv')
ax[i].set_xlim(IO.grids[:, 0].min(), IO.grids[:, 0].max())
ax[i].set_ylim(-IO.grids[:, 1].max(), IO.grids[:, 1].min())
cb = plt.colorbar(out[i][0], ax=ax[i])
cb.set_label("Resistivity ($\Omega$m)")
ax[i].set_xlabel("Northing (m)")
ax[i].set_ylabel("Elevation (m)")
ax[i].set_aspect('equal')
ax[0].set_title("True resistivity model")
ax[1].set_title("Recovered resistivity model")
plt.tight_layout()
plt.show()
def run(plotIt=True, survey_type="dipole-dipole"):
np.random.seed(1)
# Initiate I/O class for DC
IO = DC.IO()
# Obtain ABMN locations
xmin, xmax = 0., 200.
ymin, ymax = 0., 0.
zmin, zmax = 0, 0
endl = np.array([[xmin, ymin, zmin], [xmax, ymax, zmax]])
# Generate DC survey object
survey_dc = DC.Utils.gen_DCIPsurvey(endl,
survey_type=survey_type,
dim=2,
a=10,
b=10,
n=10)
survey_dc.getABMN_locations()
survey_dc = IO.from_ambn_locations_to_survey(survey_dc.a_locations,
survey_dc.b_locations,
survey_dc.m_locations,
survey_dc.n_locations,
survey_type,
data_dc_type='volt',
data_ip_type='volt')
# Obtain 2D TensorMesh
mesh, actind = IO.set_mesh()
topo, mesh1D = DC.Utils.genTopography(mesh, -10, 0, its=100)
actind = Utils.surface2ind_topo(mesh, np.c_[mesh1D.vectorCCx, topo])
survey_dc.drapeTopo(mesh, actind, option="top")
# Build conductivity and chargeability model
blk_inds_c = Utils.ModelBuilder.getIndicesSphere(np.r_[60., -25.], 12.5,
mesh.gridCC)
blk_inds_r = Utils.ModelBuilder.getIndicesSphere(np.r_[140., -25.], 12.5,
mesh.gridCC)
blk_inds_charg = Utils.ModelBuilder.getIndicesSphere(
np.r_[100., -25], 12.5, mesh.gridCC)
sigma = np.ones(mesh.nC) * 1. / 100.
sigma[blk_inds_c] = 1. / 10.
sigma[blk_inds_r] = 1. / 1000.
sigma[~actind] = 1. / 1e8
rho = 1. / sigma
charg = np.zeros(mesh.nC)
charg[blk_inds_charg] = 0.1
# Show the true conductivity model
if plotIt:
fig, axs = plt.subplots(2, 1, figsize=(12, 6))
temp_rho = rho.copy()
temp_rho[~actind] = np.nan
temp_charg = charg.copy()
temp_charg[~actind] = np.nan
out1 = mesh.plotImage(temp_rho,
grid=True,
ax=axs[0],
gridOpts={'alpha': 0.2},
clim=(10, 1000),
pcolorOpts={
"cmap": "viridis",
"norm": colors.LogNorm()
})
out2 = mesh.plotImage(temp_charg,
grid=True,
ax=axs[1],
gridOpts={'alpha': 0.2},
clim=(0, 0.1),
pcolorOpts={"cmap": "magma"})
for i in range(2):
axs[i].plot(survey_dc.electrode_locations[:, 0],
survey_dc.electrode_locations[:, 1], 'kv')
axs[i].set_xlim(IO.grids[:, 0].min(), IO.grids[:, 0].max())
axs[i].set_ylim(-IO.grids[:, 1].max(), IO.grids[:, 1].min())
axs[i].set_aspect('equal')
cb = plt.colorbar(out1[0], ax=axs[0])
cb.set_label("Resistivity (ohm-m)")
cb = plt.colorbar(out2[0], ax=axs[1])
cb.set_label("Chargeability")
plt.show()
# Use Exponential Map: m = log(rho)
actmap = Maps.InjectActiveCells(mesh,
indActive=actind,
valInactive=np.log(1e8))
mapping = Maps.ExpMap(mesh) * actmap
# Generate mtrue_dc for resistivity
mtrue_dc = np.log(rho[actind])
# Generate 2.5D DC problem
# "N" means potential is defined at nodes
prb = DC.Problem2D_N(mesh, rhoMap=mapping, storeJ=True, Solver=Solver)
# Pair problem with survey
try:
prb.pair(survey_dc)
except:
survey_dc.unpair()
prb.pair(survey_dc)
# Make synthetic DC data with 5% Gaussian noise
dtrue_dc = survey_dc.makeSyntheticData(mtrue_dc, std=0.05, force=True)
IO.data_dc = dtrue_dc
# Generate mtrue_ip for chargability
mtrue_ip = charg[actind]
# Generate 2.5D DC problem
# "N" means potential is defined at nodes
prb_ip = IP.Problem2D_N(mesh,
etaMap=actmap,
storeJ=True,
rho=rho,
Solver=Solver)
survey_ip = IP.from_dc_to_ip_survey(survey_dc, dim="2.5D")
prb_ip.pair(survey_ip)
dtrue_ip = survey_ip.makeSyntheticData(mtrue_ip, std=0.05)
IO.data_ip = dtrue_ip
# Show apparent resisitivty pseudo-section
if plotIt:
IO.plotPseudoSection(data_type='apparent_resistivity',
scale='log',
cmap='viridis')
plt.show()
# Show apparent chargeability pseudo-section
if plotIt:
IO.plotPseudoSection(data_type='apparent_chargeability',
scale='linear',
cmap='magma')
plt.show()
# Show apparent resisitivty histogram
if plotIt:
fig = plt.figure(figsize=(10, 4))
ax1 = plt.subplot(121)
out = hist(np.log10(abs(IO.voltages)), bins=20)
ax1.set_xlabel("log10 DC voltage (V)")
ax2 = plt.subplot(122)
out = hist(IO.apparent_resistivity, bins=20)
ax2.set_xlabel("Apparent Resistivity ($\Omega$m)")
plt.tight_layout()
plt.show()
# Set initial model based upon histogram
m0_dc = np.ones(actmap.nP) * np.log(100.)
# Set uncertainty
# floor
eps_dc = 10**(-3.2)
# percentage
std_dc = 0.05
mopt_dc, pred_dc = DC.run_inversion(m0_dc,
survey_dc,
actind,
mesh,
std_dc,
eps_dc,
beta0_ratio=1e0,
use_sensitivity_weight=True)
# Convert obtained inversion model to resistivity
# rho = M(m), where M(.) is a mapping
rho_est = mapping * mopt_dc
rho_est[~actind] = np.nan
rho_true = rho.copy()
rho_true[~actind] = np.nan
# show recovered conductivity
if plotIt:
vmin, vmax = rho.min(), rho.max()
fig, ax = plt.subplots(2, 1, figsize=(20, 6))
out1 = mesh.plotImage(rho_true,
clim=(10, 1000),
pcolorOpts={
"cmap": "viridis",
"norm": colors.LogNorm()
},
ax=ax[0])
out2 = mesh.plotImage(rho_est,
clim=(10, 1000),
pcolorOpts={
"cmap": "viridis",
"norm": colors.LogNorm()
},
ax=ax[1])
out = [out1, out2]
for i in range(2):
ax[i].plot(survey_dc.electrode_locations[:, 0],
survey_dc.electrode_locations[:, 1], 'kv')
ax[i].set_xlim(IO.grids[:, 0].min(), IO.grids[:, 0].max())
ax[i].set_ylim(-IO.grids[:, 1].max(), IO.grids[:, 1].min())
cb = plt.colorbar(out[i][0], ax=ax[i])
cb.set_label("Resistivity ($\Omega$m)")
ax[i].set_xlabel("Northing (m)")
ax[i].set_ylabel("Elevation (m)")
ax[i].set_aspect('equal')
plt.tight_layout()
plt.show()
# Show apparent resisitivty histogram
if plotIt:
fig = plt.figure(figsize=(10, 4))
ax1 = plt.subplot(121)
out = hist(np.log10(abs(IO.voltages_ip)), bins=20)
ax1.set_xlabel("log10 IP voltage (V)")
ax2 = plt.subplot(122)
out = hist(IO.apparent_chargeability, bins=20)
ax2.set_xlabel("Apparent Chargeability (V/V)")
plt.tight_layout()
plt.show()
# Set initial model based upon histogram
m0_ip = np.ones(actmap.nP) * 1e-10
# Set uncertainty
# floor
eps_ip = 10**(-4)
# percentage
std_ip = 0.05
# Clean sensitivity function formed with true resistivity
prb_ip._Jmatrix = None
# Input obtained resistivity to form sensitivity
prb_ip.rho = mapping * mopt_dc
mopt_ip, _ = IP.run_inversion(m0_ip,
survey_ip,
actind,
mesh,
std_ip,
eps_ip,
upper=np.Inf,
lower=0.,
beta0_ratio=1e0,
use_sensitivity_weight=True)
# Convert obtained inversion model to chargeability
# charg = M(m), where M(.) is a mapping for cells below topography
charg_est = actmap * mopt_ip
charg_est[~actind] = np.nan
charg_true = charg.copy()
charg_true[~actind] = np.nan
# show recovered chargeability
if plotIt:
fig, ax = plt.subplots(2, 1, figsize=(20, 6))
out1 = mesh.plotImage(charg_true,
clim=(0, 0.1),
pcolorOpts={"cmap": "magma"},
ax=ax[0])
out2 = mesh.plotImage(charg_est,
clim=(0, 0.1),
pcolorOpts={"cmap": "magma"},
ax=ax[1])
out = [out1, out2]
for i in range(2):
ax[i].plot(survey_dc.electrode_locations[:, 0],
survey_dc.electrode_locations[:, 1], 'rv')
ax[i].set_xlim(IO.grids[:, 0].min(), IO.grids[:, 0].max())
ax[i].set_ylim(-IO.grids[:, 1].max(), IO.grids[:, 1].min())
cb = plt.colorbar(out[i][0], ax=ax[i])
cb.set_label("Resistivity ($\Omega$m)")
ax[i].set_xlabel("Northing (m)")
ax[i].set_ylabel("Elevation (m)")
ax[i].set_aspect('equal')
plt.tight_layout()
plt.show()
def run(plotIt=True, survey_type="dipole-dipole"):
np.random.seed(1)
# Initiate I/O class for DC
IO = DC.IO()
# Obtain ABMN locations
xmin, xmax = 0., 200.
ymin, ymax = 0., 0.
zmin, zmax = 0, 0
endl = np.array([[xmin, ymin, zmin], [xmax, ymax, zmax]])
# Generate DC survey object
survey = DC.Utils.gen_DCIPsurvey(endl, survey_type=survey_type, dim=2,
a=10, b=10, n=10)
survey.getABMN_locations()
survey = IO.from_ambn_locations_to_survey(
survey.a_locations, survey.b_locations,
survey.m_locations, survey.n_locations,
survey_type, data_dc_type='volt'
)
# Obtain 2D TensorMesh
mesh, actind = IO.set_mesh()
topo, mesh1D = DC.Utils.genTopography(mesh, -10, 0, its=100)
actind = Utils.surface2ind_topo(mesh, np.c_[mesh1D.vectorCCx, topo])
survey.drapeTopo(mesh, actind, option="top")
# Build a conductivity model
blk_inds_c = Utils.ModelBuilder.getIndicesSphere(
np.r_[60., -25.], 12.5, mesh.gridCC
)
blk_inds_r = Utils.ModelBuilder.getIndicesSphere(
np.r_[140., -25.], 12.5, mesh.gridCC
)
layer_inds = mesh.gridCC[:, 1] > -5.
sigma = np.ones(mesh.nC)*1./100.
sigma[blk_inds_c] = 1./10.
sigma[blk_inds_r] = 1./1000.
sigma[~actind] = 1./1e8
rho = 1./sigma
# Show the true conductivity model
if plotIt:
fig = plt.figure(figsize=(12, 3))
ax = plt.subplot(111)
temp = rho.copy()
temp[~actind] = np.nan
out = mesh.plotImage(
temp, grid=True, ax=ax, gridOpts={'alpha': 0.2},
clim=(10, 1000),
pcolorOpts={"cmap": "viridis", "norm": colors.LogNorm()}
)
ax.plot(
survey.electrode_locations[:, 0],
survey.electrode_locations[:, 1], 'k.'
)
ax.set_xlim(IO.grids[:, 0].min(), IO.grids[:, 0].max())
ax.set_ylim(-IO.grids[:, 1].max(), IO.grids[:, 1].min())
cb = plt.colorbar(out[0])
cb.set_label("Resistivity (ohm-m)")
ax.set_aspect('equal')
plt.show()
# Use Exponential Map: m = log(rho)
actmap = Maps.InjectActiveCells(
mesh, indActive=actind, valInactive=np.log(1e8)
)
mapping = Maps.ExpMap(mesh) * actmap
# Generate mtrue
mtrue = np.log(rho[actind])
# Generate 2.5D DC problem
# "N" means potential is defined at nodes
prb = DC.Problem2D_N(
mesh, rhoMap=mapping, storeJ=True,
Solver=Solver
)
# Pair problem with survey
try:
prb.pair(survey)
except:
survey.unpair()
prb.pair(survey)
geometric_factor = survey.set_geometric_factor(
data_type="apparent_resistivity",
survey_type='dipole-dipole',
space_type='half-space'
)
# Make synthetic DC data with 5% Gaussian noise
dtrue = survey.makeSyntheticData(mtrue, std=0.05, force=True)
IO.data_dc = dtrue
# Show apparent resisitivty pseudo-section
if plotIt:
IO.plotPseudoSection(
data=survey.dobs, data_type='apparent_resistivity'
)
# Show apparent resisitivty histogram
if plotIt:
fig = plt.figure()
out = hist(survey.dobs, bins=20)
plt.xlabel("Apparent Resisitivty ($\Omega$m)")
plt.show()
# Set initial model based upon histogram
m0 = np.ones(actmap.nP)*np.log(100.)
# Set uncertainty
# floor (10 ohm-m)
eps = 1.
# percentage
std = 0.05
dmisfit = DataMisfit.l2_DataMisfit(survey)
uncert = abs(survey.dobs) * std + eps
dmisfit.W = 1./uncert
# Map for a regularization
regmap = Maps.IdentityMap(nP=int(actind.sum()))
# Related to inversion
reg = Regularization.Sparse(mesh, indActive=actind, mapping=regmap)
opt = Optimization.InexactGaussNewton(maxIter=15)
invProb = InvProblem.BaseInvProblem(dmisfit, reg, opt)
beta = Directives.BetaSchedule(coolingFactor=5, coolingRate=2)
betaest = Directives.BetaEstimate_ByEig(beta0_ratio=1e0)
target = Directives.TargetMisfit()
updateSensW = Directives.UpdateSensitivityWeights()
update_Jacobi = Directives.UpdatePreconditioner()
inv = Inversion.BaseInversion(
invProb, directiveList=[
beta, betaest, target, updateSensW, update_Jacobi
]
)
prb.counter = opt.counter = Utils.Counter()
opt.LSshorten = 0.5
opt.remember('xc')
# Run inversion
mopt = inv.run(m0)
# Get diag(JtJ)
mask_inds = np.ones(mesh.nC, dtype=bool)
jtj = np.sqrt(updateSensW.JtJdiag[0])
jtj /= jtj.max()
temp = np.ones_like(jtj, dtype=bool)
temp[jtj > 0.005] = False
mask_inds[actind] = temp
actind_final = np.logical_and(actind, ~mask_inds)
jtj_cc = np.ones(mesh.nC)*np.nan
jtj_cc[actind] = jtj
# Show the sensitivity
if plotIt:
fig = plt.figure(figsize=(12, 3))
ax = plt.subplot(111)
temp = rho.copy()
temp[~actind] = np.nan
out = mesh.plotImage(
jtj_cc, grid=True, ax=ax,
gridOpts={'alpha': 0.2}, clim=(0.005, 0.5),
pcolorOpts={"cmap": "viridis", "norm": colors.LogNorm()}
)
ax.plot(
survey.electrode_locations[:, 0],
survey.electrode_locations[:, 1], 'k.'
)
ax.set_xlim(IO.grids[:, 0].min(), IO.grids[:, 0].max())
ax.set_ylim(-IO.grids[:, 1].max(), IO.grids[:, 1].min())
cb = plt.colorbar(out[0])
cb.set_label("Sensitivity")
ax.set_aspect('equal')
plt.show()
# Convert obtained inversion model to resistivity
# rho = M(m), where M(.) is a mapping
rho_est = mapping*mopt
rho_est[~actind_final] = np.nan
rho_true = rho.copy()
rho_true[~actind_final] = np.nan
# show recovered conductivity
if plotIt:
vmin, vmax = rho.min(), rho.max()
fig, ax = plt.subplots(2, 1, figsize=(20, 6))
out1 = mesh.plotImage(
rho_true, clim=(10, 1000),
pcolorOpts={"cmap": "viridis", "norm": colors.LogNorm()},
ax=ax[0]
)
out2 = mesh.plotImage(
rho_est, clim=(10, 1000),
pcolorOpts={"cmap": "viridis", "norm": colors.LogNorm()},
ax=ax[1]
)
out = [out1, out2]
for i in range(2):
ax[i].plot(
survey.electrode_locations[:, 0],
survey.electrode_locations[:, 1], 'kv'
)
ax[i].set_xlim(IO.grids[:, 0].min(), IO.grids[:, 0].max())
ax[i].set_ylim(-IO.grids[:, 1].max(), IO.grids[:, 1].min())
cb = plt.colorbar(out[i][0], ax=ax[i])
cb.set_label("Resistivity ($\Omega$m)")
ax[i].set_xlabel("Northing (m)")
ax[i].set_ylabel("Elevation (m)")
ax[i].set_aspect('equal')
plt.tight_layout()
plt.show()