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
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
verbose=0)
# Stack results together
c = np.vstack((c1, c2))
#ax, _ = pg.show(mesh, data=c[400]*0.001, label='Concentration $c$ in g$/$l',
#cMin=0, cMax=2.5)
print('Solve ERT modelling ...')
# Create survey measurement scheme
ertScheme = pg.physics.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 = pg.physics.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.
# Create more realistic data set
ertScheme = pb.createData(sensors, "dd", spacings=[1, 2, 4])
k = pb.geometricFactors(ertScheme)
ertScheme.markInvalid(pg.abs(k) > 5000)
ertScheme.removeInvalid()
ert = ERTManager()
# Create suitable mesh for ert forward calculation
# NOTE: In the published results paraMaxCellSize=1.0 was used, which is
# increased here to allow testing on Continuous Integration services.
meshERTFWD = mt.createParaMesh(ertScheme,
quality=33.5,
paraMaxCellSize=2.0,
paraDX=0.2,
boundaryMaxCellSize=50,
smooth=[1, 10],
paraBoundary=30)
pg.show(meshERTFWD)
res = pg.RVector()
pg.interpolate(mesh, rhotrue, meshERTFWD.cellCenters(), res)
res = mt.fillEmptyToCellArray(meshERTFWD, res, slope=True)
ert.setMesh(meshERTFWD)
ert.fop.createRefinedForwardMesh()
ertData = ert.simulate(meshERTFWD,
res,
ertScheme,
noiseLevel=0.05,
noiseAbs=0.0)
# Solve without injection starting with last result
c2 = pg.solver.solveFiniteVolume(mesh, a=dispersion, f=0, vel=vel,
u0=c1[-1], times=t, uB=[1, 0],
scheme='PS', verbose=0)
# Stack results together
c = np.vstack((c1, c2))
ax, _ = pg.show(mesh, data=c[400]*0.001, cMin=0, cMax=2.5,
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.
