def solveERT(mesh, concentration, verbose=0):
"""Simulate resistivity distribution for given nonsteady concentration."""
if verbose:
print("Solve for ERT ...")
ertScheme = pg.physics.ert.createERTData(pg.utils.grange(-20, 20, dx=1.0),
schemeName='dd')
meshERT = mt.createParaMesh(ertScheme, quality=33, paraMaxCellSize=0.2,
boundaryMaxCellSize=50, smooth=[1, 2])
scale = 0.001
concentration *= scale # mg/m²
# apply saturation model to simulate unsaturated topsoil
sat = np.zeros(mesh.cellCount())
for c in mesh.cells():
if c.center()[1] < -8:
sat[c.id()] = 1.
elif c.center()[1] < -2:
sat[c.id()] = 1.
else:
sat[c.id()] = .5
cWater = 1./100.
conductivity = concentration * 0.1 + cWater
rArchie = resistivityArchie(rFluid=1. / conductivity,
porosity=0.3, sat=sat, m=1.3,
mesh=mesh, meshI=meshERT, fill=1)
# apply background resistivity model
rho0 = np.zeros(meshERT.cellCount())
for c in meshERT.cells():
if c.center()[1] < -8:
rho0[c.id()] = 150.
elif c.center()[1] < -2:
rho0[c.id()] = 500.
else:
rho0[c.id()] = 1000.
resis = pg.Matrix(rArchie)
for i, rbI in enumerate(rArchie):
resis[i] = 1. / ((1./rbI) + 1./rho0)
ert = pg.physics.ert.ERTManager(verbose=False)
ertScheme.set('k', ert.fop.calcGeometricFactors(ertScheme))
errPerc = 0.01
errVolt = 1e-5
rhoa = ert.simulate(meshERT, resis, ertScheme, verbose=0, returnArray=True)
voltage = rhoa / ertScheme('k')
err = np.abs(errVolt / voltage) + errPerc
dRhoa = rhoa[1:] / rhoa[0]
dErr = err[1:]
return meshERT, ertScheme, resis, rhoa, dRhoa, dErr
ertScheme = ert.createERTData(pg.utils.grange(-20, 20, dx=1.0),
schemeName='dd')
# Create suitable mesh for ert forward calculation
meshERT = mt.createParaMesh(ertScheme,
quality=33,
paraMaxCellSize=0.2,
boundaryMaxCellSize=50,
smooth=[1, 2])
# Select 10 time frame to simulate ERT data
timesERT = pg.core.IndexArray(np.floor(np.linspace(0, len(c) - 1, 10)))
# Create conductivity of fluid for salt concentration $c$
sigmaFluid = c[timesERT] * 0.1 + 0.01
# Calculate bulk resistivity based on Archie's Law
resBulk = petro.resistivityArchie(rFluid=1. / sigmaFluid,
porosity=0.3,
m=1.3,
mesh=mesh,
meshI=meshERT,
fill=1)
# apply background resistivity model
rho0 = np.zeros(meshERT.cellCount()) + 1000.
for c in meshERT.cells():
if c.center()[1] < -8:
rho0[c.id()] = 150.
elif c.center()[1] < -2:
rho0[c.id()] = 500.
resis = pg.Matrix(resBulk)
for i, rbI in enumerate(resBulk):
resis[i] = 1. / ((1. / rbI) + 1. / rho0)
# Initialize ert method manager
ERT = ERTManager(verbose=False)
# Run simulation for the apparent resistivities
def solveERT(mesh, concentration, verbose=0):
"""Simulate resistivity distribution for given nonsteady concentration."""
if verbose:
print("Solve for ERT ...")
ertScheme = pg.physics.ert.createERTData(pg.utils.grange(-20, 20, dx=1.0),
schemeName='dd')
meshERT = mt.createParaMesh(ertScheme,
quality=33,
paraMaxCellSize=0.2,
boundaryMaxCellSize=50,
smooth=[1, 2])
scale = 0.001
concentration *= scale # mg/m²
# apply saturation model to simulate unsaturated topsoil
sat = np.zeros(mesh.cellCount())
for c in mesh.cells():
if c.center()[1] < -8:
sat[c.id()] = 1.
elif c.center()[1] < -2:
sat[c.id()] = 1.
else:
sat[c.id()] = .5
cWater = 1. / 100.
conductivity = concentration * 0.1 + cWater
rArchie = resistivityArchie(rFluid=1. / conductivity,
porosity=0.3,
sat=sat,
m=1.3,
mesh=mesh,
meshI=meshERT,
fill=1)
# apply background resistivity model
rho0 = np.zeros(meshERT.cellCount())
for c in meshERT.cells():
if c.center()[1] < -8:
rho0[c.id()] = 150.
elif c.center()[1] < -2:
rho0[c.id()] = 500.
else:
rho0[c.id()] = 1000.
resis = pg.Matrix(rArchie)
for i, rbI in enumerate(rArchie):
resis[i] = 1. / ((1. / rbI) + 1. / rho0)
ert = pg.physics.ert.ERTManager(verbose=False)
ertScheme.set('k', ert.fop.calcGeometricFactor(ertScheme))
errPerc = 0.01
errVolt = 1e-5
rhoa = ert.simulate(meshERT, resis, ertScheme, verbose=0, returnArray=True)
voltage = rhoa / ertScheme('k')
err = np.abs(errVolt / voltage) + errPerc
dRhoa = rhoa[1:] / rhoa[0]
dErr = err[1:]
return meshERT, ertScheme, resis, rhoa, dRhoa, dErr
label='Concentration $c$ in g$/$l')
print('Solve ERT modelling ...')
# Create survey measurement scheme
ertScheme = ert.createERTData(pg.utils.grange(-20, 20, dx=1.0),
schemeName='dd')
# Create suitable mesh for ert forward calculation
meshERT = mt.createParaMesh(ertScheme, quality=33, paraMaxCellSize=0.2,
boundaryMaxCellSize=50, smooth=[1, 2])
# Select 10 time frame to simulate ERT data
timesERT = pg.IndexArray(np.floor(np.linspace(0, len(c)-1, 10)))
# Create conductivity of fluid for salt concentration $c$
sigmaFluid = c[timesERT] * 0.1 + 0.01
# Calculate bulk resistivity based on Archie's Law
resBulk = petro.resistivityArchie(rFluid=1. / sigmaFluid,
porosity=0.3, m=1.3,
mesh=mesh, meshI=meshERT, fill=1)
# apply background resistivity model
rho0 = np.zeros(meshERT.cellCount()) + 1000.
for c in meshERT.cells():
if c.center()[1] < -8:
rho0[c.id()] = 150.
elif c.center()[1] < -2:
rho0[c.id()] = 500.
resis = pg.RMatrix(resBulk)
for i, rbI in enumerate(resBulk):
resis[i] = 1. / ((1./rbI) + 1./rho0)
# Initialize ert method manager
ERT = ERTManager(verbose=False)
# Run simulation for the apparent resistivities
rhoa = ERT.simulate(meshERT, resis, ertScheme, verbose=0, returnArray=True)
