def generateSurvey(rx, tx, min_dipole_size, max_dipole_size):
"""
Generates a survey to through into a forward model
INPUT:
rx_dx = array of Rx x spacings
rx_dy = array of Rx y spacings
Tx_dx = array of Tx x spacings
Tx_dy = array of Tx y spacings
"""
SrcList = []
rx_length = rx.shape[0]
for idk in range(tx.shape[0]):
rx1 = []
rx2 = []
for idx in range(rx_length):
node1 = rx[idx, :]
for idj in range(idx, rx_length):
node2 = rx[idj, :]
dist = np.sqrt(np.sum((node1 - node2)**2))
distE = np.abs(node1[0] - tx[idk, 0])
if distE < 350:
if (min_dipole_size) < dist < (max_dipole_size):
rx1.append(node1)
rx2.append(node2)
# print(dist)
rx1 = np.asarray(rx1)
rx2 = np.asarray(rx2)
rxClass = DC.Rx.Dipole(rx1, rx2)
srcClass = DC.Src.Pole([rxClass], tx[idk, :])
SrcList.append(srcClass)
survey = DC.Survey(SrcList)
return survey
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)
print(topo)
def setUp(self):
self.plotIt = False
np.random.seed(1)
# Initiate I/O class for DC
self.IO = DC.IO()
# Obtain ABMN locations
xmin, xmax = 0., 200.
ymin, ymax = 0., 0.
zmin, zmax = 0, 0
self.endl = np.array([[xmin, ymin, zmin], [xmax, ymax, zmax]])
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"):
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",
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="pole-dipole"):
np.random.seed(1)
# Initiate I/O class for DC
IO = DC.IO()
# Obtain ABMN locations
fileName1 = "C:/Users/johnk/Projects/Seabridge/fmdataDC.con" # output mod
fileName1_ = "C:/Users/johnk/Projects/Seabridge/fmdataIP.chg" # output mod
fileName2 = "C:/Users/johnk/Projects/Seabridge/forwardmodel.msh" # in mesh
mesh = Mesh.TensorMesh._readUBC_3DMesh(fileName2) # Read in/create mesh
print("Starting forward modeling")
start = clock()
# Define model Background
rx = getRxData() # rx locations
tx = getTxData() # tx locations
survey_dc = generateSurvey(rx, tx, 45, 65) # create survey object
survey_dc.getABMN_locations() # get 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'
# )
uniq = Utils.uniqueRows(np.vstack((survey_dc.a_locations,
survey_dc.b_locations,
survey_dc.m_locations,
survey_dc.n_locations)))
electrode_locations = uniq[0] # assign
actinds = Utils.surface2ind_topo(mesh,
electrode_locations,
method='cubic') # active indicies
survey_dc.drapeTopo(mesh, actinds) # drape topo
# =============================================================================
# create sphere for ice representation
x0 = (np.max(mesh.gridCC[:, 0]) +
np.min(mesh.gridCC[:, 0])) / 2. + 50 # x0 center point of sphere
y0 = (np.max(mesh.gridCC[:, 1]) +
np.min(mesh.gridCC[:, 1])) / 2. - 50 # y0 center point of sphere
z0 = 2350 # x0 center point of sphere
# (np.max(mesh.gridCC[:, 2]) + np.min(mesh.gridCC[:, 2])) / 2.
r0 = 500 # radius of sphere
print(x0, y0, z0)
csph = (np.sqrt((mesh.gridCC[:, 0] - x0)**2. +
(mesh.gridCC[:, 1] - y0)**2. +
(mesh.gridCC[:, 2] - z0)**2.)) < r0 # indicies of sphere
# sphere done =================================================================
# ============================================================================
# Create model
mx = np.ones(mesh.nC) * 0.020 # chargeability
sigma = np.ones(mesh.nC) * 1. / 15000.
# create dipping structure parameters
theta = 45. * np.pi / 180. # dipping angle
x0_d = 374700.
x1_d = 375000.
y0_d = 6275850.
y0_1d = 500. * np.sin(theta) + y0_d
y1_d = 6275900.
y1_1d = 500. * np.sin(theta) + y1_d
z0_d = 1860.
z1_d = z0_d - (500. * np.cos(theta))
m_ = (z0_d - z1_d) / (y0_1d - y0_d) # slope of dip
# loop through mesh and assign dipping structure conductivity
for idx in range(mesh.nC):
if z1_d <= mesh.gridCC[idx, 2] <= z0_d:
if (x0_d <= mesh.gridCC[idx, 0] <= x1_d):
yslope1 = y0_d + (1. / m_) * (mesh.gridCC[idx, 2] - z0_d)
yslope2 = y1_d + (1. / m_) * (mesh.gridCC[idx, 2] - z0_d)
if yslope1 <= mesh.gridCC[idx, 1] <= yslope2:
mx[idx] = 0.03
sigma[idx] = 1. / 300.
# mx[csph] = ((0.025) *
# np.ones_like(mx[csph])) # set sphere values
mx[~actinds] = 1. / 1e8 # flag air values
# sigma[csph] = ((5000.) *
# np.ones_like(sigma[csph])) # set sphere values
sigma[~actinds] = 1. / 1e8 # flag air values
rho = 1. / sigma
stop = clock()
print(stop)
# plot results
# Show the true conductivity model
if plotIt:
ncy = mesh.nCy
ncz = mesh.nCz
ncx = mesh.nCx
mtrue = mx
print(mtrue.min(), mtrue.max())
clim = [0, 0.04]
fig, ax = plt.subplots(2, 2, figsize=(12, 6))
ax = Utils.mkvc(ax)
dat = mesh.plotSlice(((mx)), ax=ax[0], normal='Z', clim=clim,
ind=int(ncz / 2), pcolorOpts={"cmap": "jet"})
ax[0].plot(rx[:, 0], rx[:, 1], 'or')
ax[0].plot(tx[:, 0], tx[:, 1], 'dk')
mesh.plotSlice(((mx)), ax=ax[1], normal='Y', clim=clim,
ind=int(ncy / 2 + 2), pcolorOpts={"cmap": "jet"})
mesh.plotSlice(((mx)), ax=ax[2], normal='X', clim=clim,
ind=int(ncx / 2 + 4), pcolorOpts={"cmap": "jet"})
mesh.plotSlice(((mx)), ax=ax[3], normal='X', clim=clim,
ind=int(ncx / 2 + 8), pcolorOpts={"cmap": "jet"})
cbar_ax = fig.add_axes([0.82, 0.15, 0.05, 0.7])
cb = plt.colorbar(dat[0], ax=cbar_ax)
fig.subplots_adjust(right=0.85)
cb.set_label('V/V')
cbar_ax.axis('off')
plt.show()
mtrue = 1. / sigma
print(mtrue.min(), mtrue.max())
clim = [0, 20000]
fig, ax = plt.subplots(2, 2, figsize=(12, 6))
ax = Utils.mkvc(ax)
dat = mesh.plotSlice(((mtrue)), ax=ax[0], normal='Z', clim=clim,
ind=int(ncz / 2 - 4), pcolorOpts={"cmap": "jet"})
ax[0].plot(rx[:, 0], rx[:, 1], 'or')
ax[0].plot(tx[:, 0], tx[:, 1], 'dk')
mesh.plotSlice(((mtrue)), ax=ax[1], normal='Y', clim=clim,
ind=int(ncy / 2), pcolorOpts={"cmap": "jet"})
mesh.plotSlice(((mtrue)), ax=ax[2], normal='X', clim=clim,
ind=int(ncx / 2 + 4), pcolorOpts={"cmap": "jet"})
mesh.plotSlice(((mtrue)), ax=ax[3], normal='X', clim=clim,
ind=int(ncx / 2 + 8), pcolorOpts={"cmap": "jet"})
cbar_ax = fig.add_axes([0.82, 0.15, 0.05, 0.7])
cb = plt.colorbar(dat[0], ax=cbar_ax)
fig.subplots_adjust(right=0.85)
cb.set_label('rho')
cbar_ax.axis('off')
plt.show()
# Use Exponential Map: m = log(rho)
actmap = Maps.InjectActiveCells(
mesh, indActive=actinds, valInactive=np.log(1e8)
)
mapping = Maps.ExpMap(mesh) * actmap
# Generate mtrue_dc for resistivity
mtrue_dc = np.log(rho[actinds])
# Generate 3D DC problem
# "CC" means potential is defined at center
prb = DC.Problem3D_CC(
mesh, rhoMap=mapping, storeJ=False,
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 = mx[actinds]
# Generate 3D DC problem
# "CC" means potential is defined at center
prb_ip = IP.Problem3D_CC(
mesh, etaMap=actmap, storeJ=False, rho=rho,
Solver=Solver
)
survey_ip = IP.from_dc_to_ip_survey(survey_dc, dim="3D")
prb_ip.pair(survey_ip)
dtrue_ip = survey_ip.makeSyntheticData(mtrue_ip, std=0.05)
IO.data_ip = dtrue_ip
# 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(10000.)
# Set uncertainty
# floor
eps_dc = 10**(-3.2)
# percentage
std_dc = 0.05
mopt_dc, pred_dc = DC.run_inversion(
m0_dc, survey_dc, actinds, mesh, std_dc, eps_dc,
use_sensitivity_weight=False)
# Convert obtained inversion model to resistivity
# rho = M(m), where M(.) is a mapping
rho_est = mapping * mopt_dc
# rho_est[~actinds] = np.nan
rho_true = rho.copy()
rho_true[~actinds] = np.nan
# write data to file
out_file = open(fileName1, "w")
for i in range(rho_est.size):
out_file.write("%0.5e\n" % rho_est[i])
# 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, actinds, mesh, std_ip, eps_ip,
upper=np.Inf, lower=0.,
use_sensitivity_weight=False)
# 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[~actinds] = np.nan
charg_true = charg.copy()
charg_true[~actinds] = np.nan
# write IP data to file
out_file = open(fileName1_, "w")
for i in range(charg_est.size):
out_file.write("%0.5e\n" % charg_est[i])
def run(plotIt=True, survey_type="pole-dipole"):
np.random.seed(1)
# Initiate I/O class for DC
IO = DC.IO()
# Obtain ABMN locations
fileName1 = "/Users/juan/Documents/testData/fmdata-daf.con" # output mod
fileName2 = "/Users/juan/Documents/testData/forwardmodel.msh" # input mesh
mesh = Mesh.TensorMesh._readUBC_3DMesh(fileName2) # Read in/create mesh
print("Starting forward modeling")
start = clock()
# Define model Background
rx = getRxData() # rx locations
tx = getTxData() # tx locations
survey_dc = generateSurvey(rx, tx, 45, 55) # create survey object
survey_dc.survey_type = "pole-dipole"
survey_dc.getABMN_locations() # get 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'
# )
uniq = Utils.uniqueRows(
np.vstack((survey_dc.a_locations, survey_dc.b_locations,
survey_dc.m_locations, survey_dc.n_locations)))
electrode_locations = uniq[0] # assign
actinds = Utils.surface2ind_topo(mesh, electrode_locations,
method='cubic') # active indicies
# survey_dc.drapeTopo(mesh, actinds)
IO.a_locations = survey_dc.a_locations.copy()
IO.b_locations = survey_dc.b_locations.copy()
IO.m_locations = survey_dc.m_locations.copy()
IO.n_locations = survey_dc.n_locations.copy() # drape topo
IO.data_dc_type = 'volt'
IO.G = IO.geometric_factor(survey_dc)
# =============================================================================
# create sphere for ice representation
x0 = (np.max(mesh.gridCC[:, 0]) +
np.min(mesh.gridCC[:, 0])) / 2. + 50 # x0 center point of sphere
y0 = (np.max(mesh.gridCC[:, 1]) +
np.min(mesh.gridCC[:, 1])) / 2. - 50 # y0 center point of sphere
z0 = 2350 # x0 center point of sphere
# (np.max(mesh.gridCC[:, 2]) + np.min(mesh.gridCC[:, 2])) / 2.
r0 = 500 # radius of sphere
print(x0, y0, z0)
csph = (np.sqrt((mesh.gridCC[:, 0] - x0)**2. +
(mesh.gridCC[:, 1] - y0)**2. +
(mesh.gridCC[:, 2] - z0)**2.)) < r0 # indicies of sphere
# sphere done =================================================================
# ============================================================================
# Create model
mx = np.ones(mesh.nC) * 0.018 # chargeability
sigma = np.ones(mesh.nC) * 1. / 15000.
# create dipping structure parameters
theta = 45. * np.pi / 180. # dipping angle
x0_d = 374700.
x1_d = 375000.
y0_d = 6275850.
y0_1d = 900. * np.sin(theta) + y0_d
y1_d = 6275900.
y1_1d = 900. * np.sin(theta) + y1_d
z0_d = 1900.
z1_d = z0_d - (900. * np.cos(theta))
m_ = (z0_d - z1_d) / (y0_1d - y0_d) # slope of dip
# loop through mesh and assign dipping structure conductivity
for idx in range(mesh.nC):
if z1_d <= mesh.gridCC[idx, 2] <= z0_d:
if (x0_d <= mesh.gridCC[idx, 0] <= x1_d):
yslope1 = y0_d + (1. / m_) * (mesh.gridCC[idx, 2] - z0_d)
yslope2 = y1_d + (1. / m_) * (mesh.gridCC[idx, 2] - z0_d)
if yslope1 <= mesh.gridCC[idx, 1] <= yslope2:
mx[idx] = 0.035
sigma[idx] = 1. / 300.
# mx[csph] = ((0.025) *
# np.ones_like(mx[csph])) # set sphere values
mx[~actinds] = 1. / 1e8 # flag air values
# sigma[csph] = ((5000.) *
# np.ones_like(sigma[csph])) # set sphere values
sigma[~actinds] = 1. / 1e8 # flag air values
rho = 1. / sigma
stop = clock()
print(stop)
# plot results
# Show the true conductivity model
if plotIt:
ncy = mesh.nCy
ncz = mesh.nCz
ncx = mesh.nCx
print(mesh.nC)
clim = [0, 0.04]
fig, ax = plt.subplots(2, 2, figsize=(12, 6))
ax = Utils.mkvc(ax)
dat = mesh.plotSlice(((mx)),
ax=ax[0],
normal='Z',
clim=clim,
ind=int(ncz / 2 - 14),
pcolorOpts={"cmap": "jet"})
ax[0].plot(rx[:, 0], rx[:, 1], 'or')
ax[0].plot(tx[:, 0], tx[:, 1], 'dk')
mesh.plotSlice(((mx)),
ax=ax[1],
normal='Y',
clim=clim,
ind=int(ncy / 2 + 2),
pcolorOpts={"cmap": "jet"})
mesh.plotSlice(((mx)),
ax=ax[2],
normal='X',
clim=clim,
ind=int(ncx / 2 + 4),
pcolorOpts={"cmap": "jet"})
mesh.plotSlice(((mx)),
ax=ax[3],
normal='X',
clim=clim,
ind=int(ncx / 2 + 8),
pcolorOpts={"cmap": "jet"})
cbar_ax = fig.add_axes([0.82, 0.15, 0.05, 0.7])
cb = plt.colorbar(dat[0], ax=cbar_ax)
fig.subplots_adjust(right=0.85)
cb.set_label('V/V')
cbar_ax.axis('off')
plt.show()
# print(mtrue.min(), mtrue.max())
# clim = [0, 20000]
# fig, ax = plt.subplots(2, 2, figsize=(12, 6))
# ax = Utils.mkvc(ax)
# dat = mesh.plotSlice(((mtrue)), ax=ax[0], normal='Z', clim=clim,
# ind=int(ncz / 2 - 4), pcolorOpts={"cmap": "jet"})
# ax[0].plot(rx[:, 0], rx[:, 1], 'or')
# mesh.plotSlice(((mtrue)), ax=ax[1], normal='Y', clim=clim,
# ind=int(ncy / 2), pcolorOpts={"cmap": "jet"})
# mesh.plotSlice(((mtrue)), ax=ax[2], normal='X', clim=clim,
# ind=int(ncx / 2 + 4), pcolorOpts={"cmap": "jet"})
# mesh.plotSlice(((mtrue)), ax=ax[3], normal='X', clim=clim,
# ind=int(ncx / 2 + 8), pcolorOpts={"cmap": "jet"})
# cbar_ax = fig.add_axes([0.82, 0.15, 0.05, 0.7])
# cb = plt.colorbar(dat[0], ax=cbar_ax)
# fig.subplots_adjust(right=0.85)
# cb.set_label('rho')
# cbar_ax.axis('off')
# plt.show()
# print(error.size, survey_ip.obs.size)
# error = np.asarray(survey_ip.dobs) * (np.random.randint(-1, 2, survey_ip.dobs) / 20.)
# survey_ip.dobs = survey_ip.dobs + error
# Use Exponential Map: m = log(rho)
actmap = Maps.InjectActiveCells(mesh,
indActive=actinds,
valInactive=np.log(1e8))
mapping = Maps.ExpMap(mesh) * actmap
# Generate mtrue_dc for resistivity
mtrue_dc = np.log(rho[actinds])
# Generate 3D DC problem
# "CC" means potential is defined at center
prb = DC.Problem3D_CC(mesh, rhoMap=mapping, storeJ=False, Solver=Solver)
# Pair problem with survey
# try:
prb.pair(survey_dc)
# except:
# survey_dc.unpair()
# prb.pair(survey_dc)
survey_dc.dpred(mtrue_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 = mx[actinds]
# Generate 3D DC problem
# "CC" means potential is defined at center
prb_ip = IP.Problem3D_CC(mesh,
etaMap=actmap,
storeJ=False,
rho=rho,
Solver=Solver)
survey_ip = IP.from_dc_to_ip_survey(survey_dc, dim="3D")
survey_ip.survey_type = "pole-dipole"
survey_ip.getABMN_locations()
prb_ip.pair(survey_ip)
survey_ip.dpred(mtrue_ip)
dtrue_ip = survey_ip.makeSyntheticData(mtrue_ip, std=0.05)
survey_ip.std = np.ones_like(dtrue_ip) * 0.05
survey_ip.eps = np.ones_like(dtrue_ip) * 10**(-4)
IO.data_ip = dtrue_ip
DC.Utils.writeUBC_DCobs("fmip.obs", survey_ip, 3, 'GENERAL', 'pole-dipole')
# Convert file to DC.IO object
# ----------------------------
#
# Number of the data
ndata = df[header_loc[0]].values.size
# ABMN locations
a = np.c_[df[header_loc[0]].values, np.zeros(ndata)]
b = np.c_[df[header_loc[1]].values, np.zeros(ndata)]
m = np.c_[df[header_loc[2]].values, np.zeros(ndata)]
n = np.c_[df[header_loc[3]].values, np.zeros(ndata)]
# Apparent resistivity
apprho = df[header_apprho].values
# Create DC.IO survey Object object
IO = DC.IO()
# Generate DC survey using IO object
dc_survey = IO.from_ambn_locations_to_survey(
a,
b,
m,
n,
survey_type='dipole-dipole',
data_dc=apprho,
data_dc_type='apparent_resistivity')
###############################################################################
#
# Plot
# ----
#
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()
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()