def setUpPDE(self):
"""
Creates and returns the underlying PDE.
:rtype: `lpde.LinearPDE`
"""
if self.__pde is None:
if not HAVE_DIRECT:
raise ValueError(
"Either this build of escript or the current MPI configuration does not support direct solvers."
)
pde = lpde.LinearPDE(self.__domain, numEquations=2)
D = pde.createCoefficient('D')
A = pde.createCoefficient('A')
A[0, :, 0, :] = escript.kronecker(self.__domain.getDim())
A[1, :, 1, :] = escript.kronecker(self.__domain.getDim())
pde.setValue(A=A, D=D)
if self.__fixAtBottom:
DIM = self.__domain.getDim()
z = self.__domain.getX()[DIM - 1]
pde.setValue(q=whereZero(z - self.__BX[DIM - 1][0]) * [1, 1])
pde.getSolverOptions().setSolverMethod(lpde.SolverOptions.DIRECT)
pde.getSolverOptions().setTolerance(self.__tol)
pde.setSymmetryOff()
else:
pde = self.__pde
pde.resetRightHandSideCoefficients()
return pde
def _setCoefficients(self, pde, system):
"""sets PDE coefficients"""
FAC_DIAG = 1.
FAC_OFFDIAG = -0.4
x = Solution(self.domain).getX()
mask = whereZero(x[0])
dim = self.domain.getDim()
u_ex = self._getSolution(system)
g_ex = self._getGrad(system)
if system:
A = Tensor4(0., Function(self.domain))
for i in range(dim):
A[i,:,i,:] = kronecker(dim)
Y = Vector(0., Function(self.domain))
if dim == 2:
Y[0] = u_ex[0]*FAC_DIAG+u_ex[1]*FAC_OFFDIAG
Y[1] = u_ex[1]*FAC_DIAG+u_ex[0]*FAC_OFFDIAG
else:
Y[0] = u_ex[0]*FAC_DIAG+u_ex[2]*FAC_OFFDIAG+u_ex[1]*FAC_OFFDIAG
Y[1] = u_ex[1]*FAC_DIAG+u_ex[0]*FAC_OFFDIAG+u_ex[2]*FAC_OFFDIAG
Y[2] = u_ex[2]*FAC_DIAG+u_ex[1]*FAC_OFFDIAG+u_ex[0]*FAC_OFFDIAG
pde.setValue(r=u_ex, q=mask*numpy.ones(dim,),
A=A,
D=kronecker(dim)*(FAC_DIAG-FAC_OFFDIAG)+numpy.ones((dim,dim))*FAC_OFFDIAG,
Y=Y,
y=matrixmult(g_ex,self.domain.getNormal()))
else:
pde.setValue(r=u_ex, q=mask, A=kronecker(dim),
y=inner(g_ex, self.domain.getNormal()))
def setCoefficients(self, pde, system):
"""sets PDE coefficients"""
FAC_DIAG = self.FAC_DIAG
FAC_OFFDIAG =self.FAC_OFFDIAG
x = Solution(self.domain).getX()
mask = whereZero(x[0])
dim = self.domain.getDim()
u_ex = self.getSolution(system)
g_ex = self.getGrad(system)
if system:
A = Tensor4(0., Function(self.domain))
for i in range(dim):
A[i,:,i,:] = kronecker(dim)
Y = Vector(0., Function(self.domain))
if dim == 2:
Y[0] = u_ex[0]*FAC_DIAG+u_ex[1]*FAC_OFFDIAG-20
Y[1] = u_ex[1]*FAC_DIAG+u_ex[0]*FAC_OFFDIAG-10
else:
Y[0] = u_ex[0]*FAC_DIAG+u_ex[2]*FAC_OFFDIAG+u_ex[1]*FAC_OFFDIAG-60
Y[1] = u_ex[1]*FAC_DIAG+u_ex[0]*FAC_OFFDIAG+u_ex[2]*FAC_OFFDIAG-20
Y[2] = u_ex[2]*FAC_DIAG+u_ex[1]*FAC_OFFDIAG+u_ex[0]*FAC_OFFDIAG-22
pde.setValue(r=u_ex, q=mask*numpy.ones(dim,),
A=A,
D=kronecker(dim)*(FAC_DIAG-FAC_OFFDIAG)+numpy.ones((dim,dim))*FAC_OFFDIAG,
Y=Y,
y=matrixmult(g_ex,self.domain.getNormal()))
else:
pde.setValue(r=u_ex, q=mask, A=kronecker(dim),
y=inner(g_ex, self.domain.getNormal()))
if dim == 2:
pde.setValue(Y=-20.)
else:
pde.setValue(Y=-60.)
def getPotentialNumeric(self):
"""
Returns 3 list each made up of a number of list containing primary, secondary and total
potentials diferences. Each of the lists contain a list for each value of n.
"""
primCon=self.primaryConductivity
coords=self.domain.getX()
tol=1e-8
pde=LinearPDE(self.domain, numEquations=1)
pde.getSolverOptions().setTolerance(tol)
pde.setSymmetryOn()
primaryPde=LinearPDE(self.domain, numEquations=1)
primaryPde.getSolverOptions().setTolerance(tol)
primaryPde.setSymmetryOn()
DIM=self.domain.getDim()
x=self.domain.getX()
q=whereZero(x[DIM-1]-inf(x[DIM-1]))
for i in xrange(DIM-1):
xi=x[i]
q+=whereZero(xi-inf(xi))+whereZero(xi-sup(xi))
A = self.secondaryConductivity * kronecker(self.domain)
APrimary = self.primaryConductivity * kronecker(self.domain)
pde.setValue(A=A,q=q)
primaryPde.setValue(A=APrimary,q=q)
delPhiSecondaryList = []
delPhiPrimaryList = []
delPhiTotalList = []
for i in range(1,self.n+1): # 1 to n
maxR = self.numElectrodes - 1 - (2*i) #max amount of readings that will fit in the survey
delPhiSecondary = []
delPhiPrimary = []
delPhiTotal = []
for j in range(maxR):
y_dirac=Scalar(0,DiracDeltaFunctions(self.domain))
y_dirac.setTaggedValue(self.electrodeTags[j],self.current)
y_dirac.setTaggedValue(self.electrodeTags[j + ((2*i) + 1)],-self.current)
self.sources.append([self.electrodeTags[j], self.electrodeTags[j + ((2*i) + 1)]])
primaryPde.setValue(y_dirac=y_dirac)
numericPrimaryPot = primaryPde.getSolution()
X=(primCon-self.secondaryConductivity) * grad(numericPrimaryPot)
pde.setValue(X=X)
u=pde.getSolution()
loc=Locator(self.domain,[self.electrodes[j+i],self.electrodes[j+i+1]])
self.samples.append([self.electrodeTags[j+i],self.electrodeTags[j+i+1]])
valPrimary=loc.getValue(numericPrimaryPot)
valSecondary=loc.getValue(u)
delPhiPrimary.append(valPrimary[1]-valPrimary[0])
delPhiSecondary.append(valSecondary[1]-valSecondary[0])
delPhiTotal.append(delPhiPrimary[j]+delPhiSecondary[j])
delPhiPrimaryList.append(delPhiPrimary)
delPhiSecondaryList.append(delPhiSecondary)
delPhiTotalList.append(delPhiTotal)
self.delPhiPrimaryList=delPhiPrimaryList
self.delPhiSecondaryList=delPhiSecondaryList
self.delPhiTotalList = delPhiTotalList
return [delPhiPrimaryList, delPhiSecondaryList, delPhiTotalList]
def getPotentialNumeric(self):
"""
Returns 3 list each made up of a number of list containing primary, secondary and total
potentials diferences. Each of the lists contain a list for each value of n.
"""
primCon=self.primaryConductivity
coords=self.domain.getX()
tol=1e-8
pde=LinearPDE(self.domain, numEquations=1)
pde.getSolverOptions().setTolerance(tol)
pde.setSymmetryOn()
primaryPde=LinearPDE(self.domain, numEquations=1)
primaryPde.getSolverOptions().setTolerance(tol)
primaryPde.setSymmetryOn()
DIM=self.domain.getDim()
x=self.domain.getX()
q=es.whereZero(x[DIM-1]-es.inf(x[DIM-1]))
for i in xrange(DIM-1):
xi=x[i]
q+=es.whereZero(xi-es.inf(xi))+es.whereZero(xi-es.sup(xi))
A = self.secondaryConductivity * es.kronecker(self.domain)
APrimary = self.primaryConductivity * es.kronecker(self.domain)
pde.setValue(A=A,q=q)
primaryPde.setValue(A=APrimary,q=q)
delPhiSecondaryList = []
delPhiPrimaryList = []
delPhiTotalList = []
for i in range(1,self.n+1): # 1 to n
maxR = self.numElectrodes - 1 - (2*i) #max amount of readings that will fit in the survey
delPhiSecondary = []
delPhiPrimary = []
delPhiTotal = []
for j in range(maxR):
y_dirac=es.Scalar(0,es.DiracDeltaFunctions(self.domain))
y_dirac.setTaggedValue(self.electrodeTags[j],self.current)
y_dirac.setTaggedValue(self.electrodeTags[j + ((2*i) + 1)],-self.current)
self.sources.append([self.electrodeTags[j], self.electrodeTags[j + ((2*i) + 1)]])
primaryPde.setValue(y_dirac=y_dirac)
numericPrimaryPot = primaryPde.getSolution()
X=(primCon-self.secondaryConductivity) * es.grad(numericPrimaryPot)
pde.setValue(X=X)
u=pde.getSolution()
loc=Locator(self.domain,[self.electrodes[j+i],self.electrodes[j+i+1]])
self.samples.append([self.electrodeTags[j+i],self.electrodeTags[j+i+1]])
valPrimary=loc.getValue(numericPrimaryPot)
valSecondary=loc.getValue(u)
delPhiPrimary.append(valPrimary[1]-valPrimary[0])
delPhiSecondary.append(valSecondary[1]-valSecondary[0])
delPhiTotal.append(delPhiPrimary[j]+delPhiSecondary[j])
delPhiPrimaryList.append(delPhiPrimary)
delPhiSecondaryList.append(delPhiSecondary)
delPhiTotalList.append(delPhiTotal)
self.delPhiPrimaryList=delPhiPrimaryList
self.delPhiSecondaryList=delPhiSecondaryList
self.delPhiTotalList = delPhiTotalList
return [delPhiPrimaryList, delPhiSecondaryList, delPhiTotalList]
def getGradient(self, sigma, Ex, dExdz):
"""
Returns the gradient of the defect with respect to density.
:param sigma: a suggestion for conductivity
:type sigma: ``Data`` of shape ()
:param Ex: electric field
:type Ex: ``Data`` of shape (2,)
:param dExdz: vertical derivative of electric field
:type dExdz: ``Data`` of shape (2,)
"""
pde = self.setUpPDE()
DIM = self.getDomain().getDim()
x = dExdz.getFunctionSpace().getX()
Ex = escript.interpolate(Ex, x.getFunctionSpace())
u0 = Ex[0]
u1 = Ex[1]
u01 = dExdz[0]
u11 = dExdz[1]
D = pde.getCoefficient('D')
Y = pde.getCoefficient('Y')
X = pde.getCoefficient('X')
A = pde.getCoefficient('A')
A[0, :, 0, :] = escript.kronecker(DIM)
A[1, :, 1, :] = escript.kronecker(DIM)
f = self._omega_mu * sigma
D[0, 1] = f
D[1, 0] = -f
Z = self._Z
scale = 1. / (u01**2 + u11**2)
scale2 = scale**2
scale *= self._weight
scale2 *= self._weight
Y[0] = scale * (u0 - u01 * Z[0] + u11 * Z[1])
Y[1] = scale * (u1 - u01 * Z[1] - u11 * Z[0])
X[0,1] = scale2 * (2*u01*u11*(Z[0]*u1-Z[1]*u0) \
+ (Z[0]*u0+Z[1]*u1)*(u01**2-u11**2)
- u01*(u0**2 + u1**2))
X[1,1] = scale2 * (2*u01*u11*(Z[1]*u1+Z[0]*u0) \
+ (Z[1]*u0-Z[0]*u1)*(u01**2-u11**2)
- u11*(u0**2 + u1**2))
pde.setValue(A=A, D=D, X=X, Y=Y)
Zstar = pde.getSolution()
return (-self._omega_mu) * (Zstar[1] * u0 - Zstar[0] * u1)
def update_solute_transport_pde(mesh,
solute_pde,
concentration_old,
v,
dt,
solute_source,
dispersion_tensor,
diffusivity,
l_disp,
t_disp,
rho_f,
verbose=False):
"""
Solve the solute transport equation.
"""
# calculate hydrodynamic dispersivity tensor from molecular diffusivity
# and longitudinal and transverse dispersivity
# calculate absolute velocity
v_abs = (v[0]**2 + v[1]**2)**0.5
# get rid of 0 values of velocity
v_abs_1 = es.whereZero(v_abs) * 1e-20 + es.whereNonZero(v_abs) * v_abs
Dxx = l_disp * (v[0]**2) / v_abs_1 + diffusivity
Dyy = t_disp * (v[1]**2) / v_abs_1 + diffusivity
# and set dispersion tensor to 0 where 0 absolute velocity
Dxx = (Dxx * es.whereNonZero(v_abs) + es.whereZero(v_abs) * diffusivity)
Dyy = (Dyy * es.whereNonZero(v_abs) + es.whereZero(v_abs) * diffusivity)
# horizontal and vertical values of dispersion (Dxx and Dyy)
dispersion_tensor[0, 0] = Dxx
dispersion_tensor[1, 1] = Dyy
# off-diagonal terms in tensor (Dxy and Dyx)
# set to 0 for now, model becomes numerically unstable
# testing with fixed values did not result in significant cahnges in solute conc...
# todo, figure out why this is unstable or check the potential error
dispersion_tensor[0, 1] = (l_disp - t_disp) * (v[0] * v[1]) / v_abs_1
dispersion_tensor[1, 0] = (l_disp - t_disp) * (v[0] * v[1]) / v_abs_1
u_old = concentration_old
a_coeff = dt * dispersion_tensor * es.kronecker(mesh)
c_coeff = dt * v
d_coeff = 1
y_coeff = u_old + solute_source * dt
if verbose is True:
print('solute transport coefficients')
print('A: ', a_coeff.getShape(), a_coeff)
print('C: ', c_coeff.getShape(), c_coeff)
print('D: ', d_coeff)
print('Y: ', y_coeff.getShape(), y_coeff)
solute_pde.setValue(A=a_coeff, C=c_coeff, D=d_coeff, Y=y_coeff)
return solute_pde
def doStep(self,dt):
"""
performs an iteration step of the penalty method.
IterationDivergenceError is raised if pressure error cannot be reduced or max_iter is reached.
"""
penalty=self.viscosity/self.relaxation
self.__pde.setValue(lame_mu=self.viscosity, \
lame_lambda=penalty, \
F=self.internal_force, \
sigma=self.pressure*kronecker(self.__pde.getDomain()), \
r=self.prescribed_velocity, \
q=self.location_prescribed_velocity)
self.__pde.getSolverOptions().setTolerance(self.rel_tol/10.)
self.velocity=self.__pde.getSolution()
update=penalty*div(self.velocity)
self.pressure=self.pressure-update
self.__diff,diff_old=Lsup(update),self.__diff
self.__iter+=1
self.trace("velocity range %e:%e"%(inf(self.velocity),sup(self.velocity)))
self.trace("pressure range %e:%e"%(inf(self.pressure),sup(self.pressure)))
self.trace("pressure correction: %e"%self.__diff)
if self.__iter>2 and diff_old<self.__diff:
self.trace("Pressure iteration failed!")
raise IterationDivergenceError("no improvement in pressure iteration")
if self.__iter>self.max_iter:
raise IterationDivergenceError("Maximum number of iterations steps reached")
def doStep(self, dt):
"""
performs an iteration step of the penalty method.
IterationDivergenceError is raised if pressure error cannot be reduced or max_iter is reached.
"""
penalty = self.viscosity / self.relaxation
self.__pde.setValue(lame_mu=self.viscosity, \
lame_lambda=penalty, \
F=self.internal_force, \
sigma=self.pressure*es.kronecker(self.__pde.getDomain()), \
r=self.prescribed_velocity, \
q=self.location_prescribed_velocity)
self.__pde.getSolverOptions().setTolerance(self.rel_tol / 10.)
self.velocity = self.__pde.getSolution()
update = penalty * es.div(self.velocity)
self.pressure = self.pressure - update
self.__diff, diff_old = es.Lsup(update), self.__diff
self.__iter += 1
self.trace("velocity range %e:%e" %
(es.inf(self.velocity), es.sup(self.velocity)))
self.trace("pressure range %e:%e" %
(es.inf(self.pressure), es.sup(self.pressure)))
self.trace("pressure correction: %e" % self.__diff)
if self.__iter > 2 and diff_old < self.__diff:
self.trace("Pressure iteration failed!")
raise esmf.IterationDivergenceError(
"no improvement in pressure iteration")
if self.__iter > self.max_iter:
raise esmf.IterationDivergenceError(
"Maximum number of iterations steps reached")
def getPotential(self):
"""
returns a list containing 3 lists one for each the primary, secondary
and total potential.
"""
primCon=self.primaryConductivity
coords=self.domain.getX()
pde=LinearPDE(self.domain, numEquations=1)
tol=1e-8
pde.getSolverOptions().setTolerance(tol)
pde.setSymmetryOn()
DIM=self.domain.getDim()
x=self.domain.getX()
q=whereZero(x[DIM-1]-inf(x[DIM-1]))
for i in xrange(DIM-1):
xi=x[i]
q+=whereZero(xi-inf(xi))+whereZero(xi-sup(xi))
A = self.secondaryConductivity * kronecker(self.domain)
pde.setValue(A=A,q=q)
delPhiSecondary = []
delPhiPrimary = []
delPhiTotal = []
if(len(self.electrodes[0])==3):
for i in range(self.numElectrodes-1):
analyticRs=Data(0,(3,),ContinuousFunction(self.domain))
analyticRs[0]=(coords[0]-self.electrodes[i][0])
analyticRs[1]=(coords[1]-self.electrodes[i][1])
analyticRs[2]=(coords[2])
rsMag=(analyticRs[0]**2+analyticRs[1]**2+analyticRs[2]**2)**0.5
analyticPrimaryPot=(self.current*(1./primCon))/(2*pi*(rsMag+(whereZero(rsMag)*0.0000001))) #the magic number 0.0000001 is to avoid devide by 0
analyticRsPolePower=(analyticRs[0]**2+analyticRs[1]**2+analyticRs[2]**2)**1.5
analyticRsPolePower = analyticRsPolePower+(whereZero(analyticRsPolePower)*0.0000001)
gradUPrimary = Data(0,(3,),ContinuousFunction(self.domain))
gradUPrimary[0] =(self.current/(2*pi*primCon)) * (analyticRs[0]/analyticRsPolePower)
gradUPrimary[1] =(self.current/(2*pi*primCon)) * (analyticRs[1]/analyticRsPolePower)
gradUPrimary[2] =(self.current/(2*pi*primCon)) * (analyticRs[2]/analyticRsPolePower)
gradUPrimary=-gradUPrimary
X=(primCon-self.secondaryConductivity) * gradUPrimary
pde.setValue(X=X)
u=pde.getSolution()
loc=Locator(self.domain,self.electrodes[i+1])
delPhiSecondary.append(loc.getValue(u))
delPhiPrimary.append(loc.getValue(analyticPrimaryPot))
else:
raise NotImplementedError("2d forward model is not yet implemented")
self.delPhiSecondary = delPhiSecondary
self.delPhiPrimary = delPhiPrimary
for i in range(len(delPhiPrimary)):
delPhiTotal.append(delPhiPrimary[i] + delPhiSecondary[i])
self.delPhiTotal=delPhiTotal
return [delPhiPrimary, delPhiSecondary, delPhiTotal]
def getPotential(self):
"""
returns a list containing 3 lists one for each the primary, secondary
and total potential.
"""
primCon=self.primaryConductivity
coords=self.domain.getX()
pde=LinearPDE(self.domain, numEquations=1)
tol=1e-8
pde.getSolverOptions().setTolerance(tol)
pde.setSymmetryOn()
DIM=self.domain.getDim()
x=self.domain.getX()
q=es.whereZero(x[DIM-1]-es.inf(x[DIM-1]))
for i in xrange(DIM-1):
xi=x[i]
q+=es.whereZero(xi-es.inf(xi))+es.whereZero(xi-es.sup(xi))
A = self.secondaryConductivity * es.kronecker(self.domain)
pde.setValue(A=A,q=q)
delPhiSecondary = []
delPhiPrimary = []
delPhiTotal = []
if(len(self.electrodes[0])==3):
for i in range(self.numElectrodes-1):
analyticRs=es.Data(0,(3,),es.ContinuousFunction(self.domain))
analyticRs[0]=(coords[0]-self.electrodes[i][0])
analyticRs[1]=(coords[1]-self.electrodes[i][1])
analyticRs[2]=(coords[2])
rsMag=(analyticRs[0]**2+analyticRs[1]**2+analyticRs[2]**2)**0.5
analyticPrimaryPot=(self.current*(1./primCon))/(2*pi*(rsMag+(es.whereZero(rsMag)*0.0000001))) #the magic number 0.0000001 is to avoid devide by 0
analyticRsPolePower=(analyticRs[0]**2+analyticRs[1]**2+analyticRs[2]**2)**1.5
analyticRsPolePower = analyticRsPolePower+(es.whereZero(analyticRsPolePower)*0.0000001)
gradUPrimary = es.Data(0,(3,),es.ContinuousFunction(self.domain))
gradUPrimary[0] =(self.current/(2*pi*primCon)) * (analyticRs[0]/analyticRsPolePower)
gradUPrimary[1] =(self.current/(2*pi*primCon)) * (analyticRs[1]/analyticRsPolePower)
gradUPrimary[2] =(self.current/(2*pi*primCon)) * (analyticRs[2]/analyticRsPolePower)
gradUPrimary=-gradUPrimary
X=(primCon-self.secondaryConductivity) * gradUPrimary
pde.setValue(X=X)
u=pde.getSolution()
loc=Locator(self.domain,self.electrodes[i+1])
delPhiSecondary.append(loc.getValue(u))
delPhiPrimary.append(loc.getValue(analyticPrimaryPot))
else:
raise NotImplementedError("2d forward model is not yet implemented")
self.delPhiSecondary = delPhiSecondary
self.delPhiPrimary = delPhiPrimary
for i in range(len(delPhiPrimary)):
delPhiTotal.append(delPhiPrimary[i] + delPhiSecondary[i])
self.delPhiTotal=delPhiTotal
return [delPhiPrimary, delPhiSecondary, delPhiTotal]
def getArguments(self, sigma):
"""
Returns precomputed values shared by `getDefect()` and `getGradient()`.
:param sigma: conductivity
:type sigma: ``Data`` of shape (2,)
:return: E_x, E_z
:rtype: ``Data`` of shape (2,)
"""
DIM = self.getDomain().getDim()
pde = self.setUpPDE()
D = pde.getCoefficient('D')
f = self._omega_mu * sigma
D[0, 1] = -f
D[1, 0] = f
A = pde.getCoefficient('A')
A[0, :, 0, :] = escript.kronecker(DIM)
A[1, :, 1, :] = escript.kronecker(DIM)
pde.setValue(A=A, D=D, r=self._r)
u = pde.getSolution()
return u, escript.grad(u)[:, 1]
def getPotentialAnalytic(self):
"""
Returns 3 list each made up of a number of list containing primary, secondary and total
potentials diferences. Each of the lists contain a list for each value of n.
"""
coords=self.domain.getX()
pde=LinearPDE(self.domain, numEquations=1)
tol=1e-8
pde.getSolverOptions().setTolerance(tol)
pde.setSymmetryOn()
primCon=self.primaryConductivity
DIM=self.domain.getDim()
x=self.domain.getX()
q=es.whereZero(x[DIM-1]-es.inf(x[DIM-1]))
for i in xrange(DIM-1):
xi=x[i]
q+=es.whereZero(xi-es.inf(xi))+es.whereZero(xi-es.sup(xi))
A = self.secondaryConductivity * es.kronecker(self.domain)
pde.setValue(A=A,q=q)
delPhiSecondaryList = []
delPhiPrimaryList = []
delPhiTotalList = []
for i in range(1,self.n+1): # 1 to n
maxR = self.numElectrodes - 1 - (2*i) #max amount of readings that will fit in the survey
delPhiSecondary = []
delPhiPrimary = []
delPhiTotal = []
for j in range(maxR):
analyticRsOne=es.Data(0,(3,),es.ContinuousFunction(self.domain))
analyticRsOne[0]=(coords[0]-self.electrodes[j][0])
analyticRsOne[1]=(coords[1]-self.electrodes[j][1])
analyticRsOne[2]=(coords[2])
rsMagOne=(analyticRsOne[0]**2+analyticRsOne[1]**2+analyticRsOne[2]**2)**0.5
analyticRsTwo=es.Data(0,(3,),es.ContinuousFunction(self.domain))
analyticRsTwo[0]=(coords[0]-self.electrodes[j + ((2*i) + 1)][0])
analyticRsTwo[1]=(coords[1]-self.electrodes[j + ((2*i) + 1)][1])
analyticRsTwo[2]=(coords[2])
rsMagTwo=(analyticRsTwo[0]**2+analyticRsTwo[1]**2+analyticRsTwo[2]**2)**0.5
self.sources.append([self.electrodeTags[j], self.electrodeTags[j + ((2*i) + 1)]])
rsMagOne+=(es.whereZero(rsMagOne)*0.0000001)
rsMagTwo+=(es.whereZero(rsMagTwo)*0.0000001)
analyticPrimaryPot=(self.current/(2*pi*primCon*rsMagOne))-(self.current/(2*pi*primCon*rsMagTwo))
analyticRsOnePower=(analyticRsOne[0]**2+analyticRsOne[1]**2+analyticRsOne[2]**2)**1.5
analyticRsOnePower = analyticRsOnePower+(es.whereZero(analyticRsOnePower)*0.0001)
analyticRsTwoPower=(analyticRsTwo[0]**2+analyticRsTwo[1]**2+analyticRsTwo[2]**2)**1.5
analyticRsTwoPower = analyticRsTwoPower+(es.whereZero(analyticRsTwoPower)*0.0001)
gradAnalyticPrimaryPot = es.Data(0,(3,),es.ContinuousFunction(self.domain))
gradAnalyticPrimaryPot[0] =(self.current/(2*pi*primCon)) * ((-analyticRsOne[0]/analyticRsOnePower) + (analyticRsTwo[0]/analyticRsTwoPower))
gradAnalyticPrimaryPot[1] =(self.current/(2*pi*primCon)) * ((-analyticRsOne[1]/analyticRsOnePower) + (analyticRsTwo[1]/analyticRsTwoPower))
gradAnalyticPrimaryPot[2] =(self.current/(2*pi*primCon)) * ((-analyticRsOne[2]/analyticRsOnePower) + (analyticRsTwo[2]/analyticRsTwoPower))
X=(primCon-self.secondaryConductivity) * (gradAnalyticPrimaryPot)
pde.setValue(X=X)
u=pde.getSolution()
loc=Locator(self.domain,[self.electrodes[j+i],self.electrodes[j+i+1]])
self.samples.append([self.electrodeTags[j+i],self.electrodeTags[j+i+1]])
valPrimary=loc.getValue(analyticPrimaryPot)
valSecondary=loc.getValue(u)
delPhiPrimary.append(valPrimary[1]-valPrimary[0])
delPhiSecondary.append(valSecondary[1]-valSecondary[0])
delPhiTotal.append(delPhiPrimary[j]+delPhiSecondary[j])
delPhiPrimaryList.append(delPhiPrimary)
delPhiSecondaryList.append(delPhiSecondary)
delPhiTotalList.append(delPhiTotal)
self.delPhiPrimaryList=delPhiPrimaryList
self.delPhiSecondaryList=delPhiSecondaryList
self.delPhiTotalList = delPhiTotalList
return [delPhiPrimaryList, delPhiSecondaryList, delPhiTotalList]
def setup(self,
domainbuilder,
rho0=None,
drho=None,
rho_z0=None,
rho_beta=None,
k0=None,
dk=None,
k_z0=None,
k_beta=None,
w0=None,
w1=None,
w_gc=None,
rho_at_depth=None,
k_at_depth=None):
"""
Sets up the inversion from an instance ``domainbuilder`` of a
`DomainBuilder`. Gravity and magnetic data attached to the
``domainbuilder`` are considered in the inversion.
If magnetic data are given as scalar it is assumed that values are
collected in direction of the background magnetic field.
:param domainbuilder: Domain builder object with gravity source(s)
:type domainbuilder: `DomainBuilder`
:param rho0: reference density, see `DensityMapping`. If not specified,
zero is used.
:type rho0: ``float`` or `Scalar`
:param drho: density scale, see `DensityMapping`. If not specified,
2750 kg/m^3 is used.
:type drho: ``float`` or `Scalar`
:param rho_z0: reference depth for depth weighting for density, see
`DensityMapping`. If not specified, zero is used.
:type rho_z0: ``float`` or `Scalar`
:param rho_beta: exponent for density depth weighting, see
`DensityMapping`. If not specified, zero is used.
:type rho_beta: ``float`` or `Scalar`
:param k0: reference susceptibility, see `SusceptibilityMapping`.
If not specified, zero is used.
:type k0: ``float`` or `Scalar`
:param dk: susceptibility scale, see `SusceptibilityMapping`. If not
specified, 1. is used.
:type dk: ``float`` or `Scalar`
:param k_z0: reference depth for susceptibility depth weighting, see
`SusceptibilityMapping`. If not specified, zero is used.
:type k_z0: ``float`` or `Scalar`
:param k_beta: exponent for susceptibility depth weighting, see
`SusceptibilityMapping`. If not specified, zero is used.
:type k_beta: ``float`` or `Scalar`
:param w0: weighting factor for level set term in the regularization.
If not set zero is assumed.
:type w0: ``Scalar`` or ``float``
:param w1: weighting factor for the gradient term in the regularization
see `Regularization`. If not set zero is assumed.
:type w1: `es.Data` or ``ndarray`` of shape (DIM,)
:param w_gc: weighting factor for the cross gradient term in the
regularization, see `Regularization`. If not set one is
assumed.
:type w_gc: `Scalar` or `float`
:param k_at_depth: value for susceptibility at depth, see `DomainBuilder`.
:type k_at_depth: ``float`` or ``None``
:param rho_at_depth: value for density at depth, see `DomainBuilder`.
:type rho_at_depth: ``float`` or ``None``
"""
self.logger.info('Retrieving domain...')
dom = domainbuilder.getDomain()
DIM = dom.getDim()
trafo = makeTransformation(dom, domainbuilder.getReferenceSystem())
rock_mask = wherePositive(domainbuilder.getSetDensityMask() +
domainbuilder.getSetSusceptibilityMask())
#========================
self.logger.info('Creating mappings ...')
if rho_at_depth:
rho2 = rock_mask * rho_at_depth + (1 - rock_mask) * rho0
elif rho0:
rho2 = (1 - rock_mask) * rho0
else:
rho2 = 0
if k_at_depth:
k2 = rock_mask * k_at_depth + (1 - rock_mask) * k0
elif k0:
k2 = (1 - rock_mask) * k0
else:
k2 = 0
rho_mapping = DensityMapping(dom,
rho0=rho2,
drho=drho,
z0=rho_z0,
beta=rho_beta)
rho_scale_mapping = rho_mapping.getTypicalDerivative()
self.logger.debug("rho_scale_mapping = %s" % rho_scale_mapping)
k_mapping = SusceptibilityMapping(dom,
k0=k2,
dk=dk,
z0=k_z0,
beta=k_beta)
k_scale_mapping = k_mapping.getTypicalDerivative()
self.logger.debug("k_scale_mapping = %s" % k_scale_mapping)
#========================
self.logger.info("Setting up regularization...")
if w1 is None:
w1 = [1.] * DIM
regularization = Regularization(dom,
numLevelSets=1,
w0=w0,
w1=w1,
location_of_set_m=rock_mask,
coordinates=trafo)
#====================================================================
self.logger.info("Retrieving gravity surveys...")
surveys = domainbuilder.getGravitySurveys()
g = []
w = []
for g_i, sigma_i in surveys:
w_i = es.safeDiv(1., sigma_i)
if g_i.getRank() == 0:
g_i = g_i * es.kronecker(DIM)[DIM - 1]
if w_i.getRank() == 0:
w_i = w_i * es.kronecker(DIM)[DIM - 1]
g.append(g_i)
w.append(w_i)
self.logger.debug("Added gravity survey:")
self.logger.debug("g = %s" % g_i)
self.logger.debug("sigma = %s" % sigma_i)
self.logger.debug("w = %s" % w_i)
self.logger.info("Setting up gravity model...")
gravity_model = GravityModel(
dom,
w,
g,
fixPotentialAtBottom=self._fixGravityPotentialAtBottom,
coordinates=trafo)
gravity_model.rescaleWeights(rho_scale=rho_scale_mapping)
#====================================================================
self.logger.info("Retrieving magnetic field surveys...")
d_b = es.normalize(domainbuilder.getBackgroundMagneticFluxDensity())
surveys = domainbuilder.getMagneticSurveys()
B = []
w = []
for B_i, sigma_i in surveys:
w_i = es.safeDiv(1., sigma_i)
if self.magnetic_intensity_data:
if not B_i.getRank() == 0:
B_i = es.length(B_i)
if not w_i.getRank() == 0:
w_i = length(w_i)
else:
if B_i.getRank() == 0:
B_i = B_i * d_b
if w_i.getRank() == 0:
w_i = w_i * d_b
B.append(B_i)
w.append(w_i)
self.logger.debug("Added magnetic survey:")
self.logger.debug("B = %s" % B_i)
self.logger.debug("sigma = %s" % sigma_i)
self.logger.debug("w = %s" % w_i)
self.logger.info("Setting up magnetic model...")
if self.self_demagnetization:
magnetic_model = SelfDemagnetizationModel(
dom,
w,
B,
domainbuilder.getBackgroundMagneticFluxDensity(),
fixPotentialAtBottom=self._fixMagneticPotentialAtBottom,
coordinates=trafo)
else:
if self.magnetic_intensity_data:
magnetic_model = MagneticIntensityModel(
dom,
w,
B,
domainbuilder.getBackgroundMagneticFluxDensity(),
fixPotentialAtBottom=self._fixMagneticPotentialAtBottom,
coordinates=trafo)
else:
magnetic_model = MagneticModel(
dom,
w,
B,
domainbuilder.getBackgroundMagneticFluxDensity(),
fixPotentialAtBottom=self._fixMagneticPotentialAtBottom,
coordinates=trafo)
magnetic_model.rescaleWeights(k_scale=k_scale_mapping)
#====================================================================
self.logger.info("Setting cost function...")
self.setCostFunction(
InversionCostFunction(regularization, (rho_mapping, k_mapping),
((gravity_model, 0), (magnetic_model, 1))))
def getInverseHessianApproximationAtPoint(self, r, solve=True):
"""
"""
# substituting cached values
m = self.__pre_input
grad_m = self.__pre_args
if self._new_mu or self._update_Hessian:
self._new_mu = False
self._update_Hessian = False
mu = self.__mu
mu_c = self.__mu_c
DIM = self.getDomain().getDim()
numLS = self.getNumLevelSets()
if self.__w0 is not None:
if numLS == 1:
D = self.__w0 * mu
else:
D = self.getPDE().getCoefficient("D")
D.setToZero()
for k in range(numLS):
D[k, k] = self.__w0[k] * mu[k]
self.getPDE().setValue(D=D)
A = self.getPDE().getCoefficient("A")
A.setToZero()
if self.__w1 is not None:
if numLS == 1:
for i in range(DIM):
A[i, i] = self.__w1[i] * mu
else:
for k in range(numLS):
for i in range(DIM):
A[k, i, k, i] = self.__w1[k, i] * mu[k]
if numLS > 1:
# this could be make faster by creating caches for grad_m_k, l2_grad_m_k and o_kk
for k in range(numLS):
grad_m_k = grad_m[k, :]
l2_grad_m_k = escript.length(grad_m_k)**2
o_kk = escript.outer(grad_m_k, grad_m_k)
for l in range(k):
grad_m_l = grad_m[l, :]
l2_grad_m_l = escript.length(grad_m_l)**2
i_lk = escript.inner(grad_m_l, grad_m_k)
o_lk = escript.outer(grad_m_l, grad_m_k)
o_kl = escript.outer(grad_m_k, grad_m_l)
o_ll = escript.outer(grad_m_l, grad_m_l)
f = mu_c[l, k] * self.__wc[l, k]
Z = f * (2 * o_lk - o_kl -
i_lk * escript.kronecker(DIM))
A[l, :,
l, :] += f * (l2_grad_m_k * escript.kronecker(DIM) -
o_kk)
A[l, :, k, :] += Z
A[k, :, l, :] += escript.transpose(Z)
A[k, :,
k, :] += f * (l2_grad_m_l * escript.kronecker(DIM) -
o_ll)
self.getPDE().setValue(A=A)
#self.getPDE().resetRightHandSideCoefficients()
#self.getPDE().setValue(X=r[1])
#print "X only: ",self.getPDE().getSolution()
#self.getPDE().resetRightHandSideCoefficients()
#self.getPDE().setValue(Y=r[0])
#print "Y only: ",self.getPDE().getSolution()
self.getPDE().resetRightHandSideCoefficients()
self.getPDE().setValue(X=r[1], Y=r[0])
if not solve:
return self.getPDE()
return self.getPDE().getSolution()
def getInverseHessianApproximationAtPoint(self, r, solve=True):
"""
"""
# substituting cached values
m = self.__pre_input
grad_m = self.__pre_args
if self._new_mu or self._update_Hessian:
self._new_mu = False
self._update_Hessian = False
mu = self.__mu
mu_c = self.__mu_c
DIM = self.getDomain().getDim()
numLS = self.getNumLevelSets()
if self.__w0 is not None:
if numLS == 1:
D = self.__w0 * mu
else:
D = self.getPDE().getCoefficient("D")
D.setToZero()
for k in range(numLS):
D[k, k] = self.__w0[k] * mu[k]
self.getPDE().setValue(D=D)
A = self.getPDE().getCoefficient("A")
A.setToZero()
if self.__w1 is not None:
if numLS == 1:
for i in range(DIM):
A[i, i] = self.__w1[i] * mu
else:
for k in range(numLS):
for i in range(DIM):
A[k, i, k, i] = self.__w1[k, i] * mu[k]
if numLS > 1:
# this could be make faster by creating caches for grad_m_k, l2_grad_m_k and o_kk
for k in range(numLS):
grad_m_k = grad_m[k, :]
l2_grad_m_k = length(grad_m_k) ** 2
o_kk = outer(grad_m_k, grad_m_k)
for l in range(k):
grad_m_l = grad_m[l, :]
l2_grad_m_l = length(grad_m_l) ** 2
i_lk = inner(grad_m_l, grad_m_k)
o_lk = outer(grad_m_l, grad_m_k)
o_kl = outer(grad_m_k, grad_m_l)
o_ll = outer(grad_m_l, grad_m_l)
f = mu_c[l, k] * self.__wc[l, k]
Z = f * (2 * o_lk - o_kl - i_lk * kronecker(DIM))
A[l, :, l, :] += f * (l2_grad_m_k * kronecker(DIM) - o_kk)
A[l, :, k, :] += Z
A[k, :, l, :] += transpose(Z)
A[k, :, k, :] += f * (l2_grad_m_l * kronecker(DIM) - o_ll)
self.getPDE().setValue(A=A)
# self.getPDE().resetRightHandSideCoefficients()
# self.getPDE().setValue(X=r[1])
# print "X only: ",self.getPDE().getSolution()
# self.getPDE().resetRightHandSideCoefficients()
# self.getPDE().setValue(Y=r[0])
# print "Y only: ",self.getPDE().getSolution()
self.getPDE().resetRightHandSideCoefficients()
self.getPDE().setValue(X=r[1], Y=r[0])
if not solve:
return self.getPDE()
return self.getPDE().getSolution()
def iterate_coupled_flow_eqs(mesh,
topo_gradient,
pressure_pde,
solute_pde,
pressure_convergence_criterion,
concentration_convergence_criterion,
min_iterations,
max_iterations,
dt,
g_vector,
pressure,
concentration,
rho_f,
phi,
diffusivity,
l_disp,
t_disp,
solute_source,
specific_storage,
k_tensor,
k_vector,
dispersion_tensor,
viscosity,
gamma,
alpha,
fluid_source,
rho_f_0,
specified_pressure_bnd,
specified_pressure,
specified_concentration_bnd,
specified_concentration,
specified_concentration_rho_f,
rch_bnd_loc,
recharge_mass_flux,
coupled_iterations=True,
solute_transport=True,
heat_transport=False,
steady_state=False,
proj=None,
drain_loc=None,
seepage_bnd=False,
recalculate_seepage_bnd=True,
active_seepage_bnd=None,
concentration_bnd_inflow_only=False,
concentration_bnd_inflow_direction='up',
max_allowed_CFL_number=None,
force_CFL_timestep=False,
dt_max=None,
calculate_viscosity=False,
verbose=False,
iterate_seepage_in_one_timestep=False,
max_seepage_iterations=50,
ignore_convergence_failure=False):
"""
Iterative solve groundwater flow, solute transport and heat flow equations.
solves either steady state or 1 timestep in implicit or explicit mode
iterative coupling scheme of solute transport, pressure & flow eqs. and
eqs of state follows Ackerer (2004), Geophysical Research Letters 31(12)
Parameters
---------
mesh :
escript mesh object
pressure_pde :
groundwater flow PDE
solute_pde
solute transport PDE
pressure_convergence_criterion : float
convergence criterion groundwater flow eq. (Pa)
concentration_convergence_criterion : float
convergence criterion solute transport eq. (kg/kg)
max_iterations : int
max number of iterations
dt : int
timestep
g_vector :
gravity vector (0,g)
pressure :
pressure (Pa)
concentration :
solute concentration (kg/kg)
rho_f :
fluid density (kg / m3)
phi :
porosity
D :
solute diffusivity (...)
l_disp :
longitudinal dispersivity (...)
t_disp :
transverse dispersivity (...)
solute_source :
solute source (units...)
specific_storage :
specific storativity (...)
k :
permeability (m2)
anisotropy :
permeability anisotropy = horizontal/vertical permeability
(dimensionless)
viscosity :
viscosity (...)
gamma :
?
alpha :
?
fluid_source :
fluid source term (...)
rho_f_0
fluid density at solute concentration C=0 (kg/m3)
specified_pressure_bnd
location of specified pressure boundary
specified_pressure
specified pressure (Pa)
specified_concentration_bnd
location of specified concentration boundary
specified_concentration
specified concentration (kg/kg)
rch_bnd_loc :
recharge_mass_flux : float
coupled_iterations : bool, optional
couple groundwater and solute transport equations iteratively
by adjusting density term
solute_transport : bool, optional
if True, simulate solute transport
heat_transport : bool, optional
if True, simulate heat transport
steady_state : bool, optional
True for steady state groundwater flow, False for transient
verbose : bool, optional
verbose text output
drain_loc :
location of drain boundary nodes
debug : bool, optional
debugging
dt_max : float?
=None ...
proj :
escript PDE for projecting element data to nodes
seepage_optimization_automated : boolean
Returns
-------
pressure_t2_i2 :
pressure at next timestep (t2) and last iteration (i2)
concentration_t2_i2 :
solute concentration (kg/kg)
rho_f_t2_i2 :
fluid density
iteration : int
number of iterations
dt_max :
max timestep size
"""
# calculate transverse dispersivity
#t_disp = l_disp * disp_ratio
year = 365.25 * 24 * 60 * 60.
if verbose is True:
print('running iterative solver for pressure and concentration PDEs')
if coupled_iterations is False:
print('pressure and concentration are not coupled')
#pressure_new = pressure
pressure_old_ts = pressure
concentration_old_ts = concentration
fluid_density_new = fluid_density_old = rho_f
#pressure_t1 = pressure.copy()
#concentration_t1 = concentration.copy()
# added 22 jun 2016, not sure if this is ok:
active_rch_bnd = rch_bnd_loc
if coupled_iterations is True and calculate_viscosity is True:
viscosity_new = calculate_viscosity_simple(concentration)
else:
viscosity_new = viscosity
active_specified_concentration_bnd = specified_concentration_bnd
iteration = 0
converged = False
non_convergence = False
ele_size = None
q = None
v = None
while converged is False and non_convergence is False:
if verbose is True:
print('iteration ', iteration)
if iteration > 0:
print('pressure convergence ', es.Lsup(pressure_conv))
if solute_transport is True:
# get flux
q = calculate_q(k_vector, viscosity_new, pressure_old_ts,
fluid_density_new, g_vector)
v = q / phi
# calculate new solute concentration
concentration_old_iteration = concentration
# finite element solute transport
if concentration_bnd_inflow_only is True and iteration == 0:
# only apply concentration bnd for inflow into model domain
# assumes a horizontal model bnd
# TODO: calculate flux normal to model boundary to account
# for non-horizontal upper boundaries
proj.setValue(D=es.kronecker(mesh), Y=q)
try:
nodal_q = proj.getSolution()
except RuntimeError(msg):
print('error, non-convergence')
print(msg)
non_convergence = True
nodal_q_norm = rotate_vector_escript(nodal_q, topo_gradient)
nodal_v = nodal_q / phi
if concentration_bnd_inflow_direction == 'up':
inflow_bnd = (es.whereNegative(nodal_q_norm[1]) *
specified_concentration_bnd)
elif concentration_bnd_inflow_direction == 'down':
inflow_bnd = (es.wherePositive(nodal_q_norm[1]) *
specified_concentration_bnd)
elif concentration_bnd_inflow_direction == 'left':
inflow_bnd = (es.wherePositive(nodal_q[0]) *
specified_concentration_bnd)
elif concentration_bnd_inflow_direction == 'right':
inflow_bnd = (es.whereNegative(nodal_q[0]) *
specified_concentration_bnd)
if es.sup(inflow_bnd) > 0:
active_specified_concentration_bnd = inflow_bnd
else:
min_x = es.inf(
specified_concentration_bnd *
specified_concentration_bnd.getDomain().getX()[0])
active_specified_concentration_bnd = \
(specified_concentration_bnd *
es.whereZero(
specified_concentration_bnd.getDomain().getX()[0]
- min_x))
if verbose is True:
print('warning, outflow for all specified ' \
'concentration boundary nodes')
#print 'using entire bnd instead'
#active_specified_concentration_bnd = \
# specified_concentration_bnd
print('using first node as fixed conc bnd instead')
print('number of active conc bnd nodes:')
print(
np.sum(
np.array(active_specified_concentration_bnd.
toListOfTuples())))
if verbose is True:
import grompy_lib
xyi, ia = grompy_lib.convert_to_array(
active_specified_concentration_bnd)
xyc, ca = grompy_lib.convert_to_array(
specified_concentration_bnd)
print('inflow conc bnd nodes = %0.0f / %0.0f' \
% (ia.sum(), ca.sum()))
print('x = %0.3f - %0.3f' %
(xyi[ia == 1, 0].min(), xyi[ia == 1, 0].max()))
print('qv conc bnd: ',
(nodal_q[1] * specified_concentration_bnd))
#solute_pde.setValue(D=1,
# r=specified_concentration_rho_f,
# q=active_specified_concentration_bnd)
solute_pde.setValue(D=1,
r=specified_concentration,
q=active_specified_concentration_bnd)
solute_pde = update_solute_transport_pde(mesh, solute_pde,
concentration_old_ts, v,
dt, solute_source,
dispersion_tensor,
diffusivity, l_disp,
t_disp, fluid_density_old)
try:
#solute_mass = solute_pde.getSolution()
concentration = solute_pde.getSolution()
except RuntimeError(error_msg):
print('!! runtime error ', error_msg)
print('solver options: ')
print(solute_pde.getSolverOptions().getSummary())
non_convergence = True
#raise RuntimeError(error_msg)
# calculate concentration, using new solute mass and eq of state
#concentration_new = calculate_concentration(
# solute_mass, rho_f_0, gamma)
#concentration_new = solve_solute_transport_v2(
# solute_pde, mesh,
# steady_state,
# concentration_t1, v, dt, solute_source,
# diffusivity, l_disp, t_disp, fluid_density_old,
# rho_f_0, gamma)
concentration_change_rate = \
(concentration - concentration_old_ts) / dt
else:
# no solute transport:
concentration_change_rate = 0
if heat_transport is True:
# no temperature in models yet:
temperature_change_rate = 0
else:
# no heat transport:
temperature_change_rate = 0
if coupled_iterations is True:
if verbose is True:
print('recalculating fluid density and viscosity')
# recalculate fluid density
fluid_density_old = fluid_density_new
fluid_density_new = \
calculate_fluid_density(concentration, gamma, rho_f_0)
if calculate_viscosity is True:
viscosity_new = \
calculate_viscosity_simple(concentration)
else:
# leave fluid density unchanged
concentration_change_rate = 0
temperature_change_rate = 0
# store old pressure
pressure_old_iteration = pressure
if drain_loc is None or es.sup(drain_loc) == 0:
# calculate pressure, no drain or seepage bnd
pressure_pde = \
update_pressure_pde(pressure_pde,
pressure_old_ts,
phi, specific_storage,
k_tensor, k_vector,
fluid_density_new,
viscosity_new, dt,
rch_bnd_loc,
recharge_mass_flux,
fluid_source, g_vector,
gamma, concentration_change_rate,
alpha, temperature_change_rate)
try:
pressure = pressure_pde.getSolution()
except RuntimeError(msg):
print('error, non-convergence')
print(msg)
non_convergence = True
#print 'no seepage bnd'
else:
# implement drain or seepage boundary
if seepage_bnd is True:
## use seepage boundary:
if active_seepage_bnd is None:
# calculate pressure without any drain boundary
pressure_pde.setValue(r=specified_pressure,
q=specified_pressure_bnd)
active_rch_bnd = rch_bnd_loc
else:
# incorporate active drain bnd of previous timestep
specified_pressure_bnd_mod = \
es.wherePositive(
specified_pressure_bnd + active_seepage_bnd)
pressure_pde.setValue(r=specified_pressure,
q=specified_pressure_bnd_mod)
# do not change active rch bnd
active_rch_bnd = rch_bnd_loc
#active_rch_bnd = rch_bnd_loc * \
# es.whereZero(specified_pressure_bnd)
#specified_flux = rch_bnd_loc * dt * recharge_mass_flux
# calculate pressure with existing seepage bnd
pressure_pde = \
update_pressure_pde(pressure_pde,
pressure_old_ts,
phi, specific_storage,
k_tensor, k_vector,
fluid_density_new,
viscosity_new, dt,
active_rch_bnd, recharge_mass_flux,
fluid_source, g_vector,
gamma, concentration_change_rate,
alpha, temperature_change_rate)
try:
pressure = pressure_pde.getSolution()
except RuntimeError:
print("error, pressure PDE solver failed")
converged = True
non_convergence = True
#if pressure_new not in locals():
# pressure_new = pressure_t1
# assign drain bnd nodes
if active_seepage_bnd is None:
active_seepage_bnd = \
es.wherePositive(drain_loc * pressure)
if iteration < max_seepage_iterations and recalculate_seepage_bnd is True:
# adjust seepage boundary, but only for first x iterations
# to avoid instability
if verbose is True:
seepage_xy = active_seepage_bnd.getDomain().getX()
seepage_nodes_xy = \
np.array(seepage_xy.toListOfTuples())
seepage_array = np.array(
active_seepage_bnd.toListOfTuples())
ind = seepage_array > 0
print('\tbefore adjustment:')
print('\tactive seepage bnd from x=%0.0f to %0.0f m' \
% (seepage_nodes_xy[ind, 0].min(),
seepage_nodes_xy[ind, 0].max()))
# remove seepage nodes that have become source of water
q = calculate_q(k_vector, viscosity_new, pressure,
fluid_density_new, g_vector)
proj.setValue(D=es.kronecker(mesh), Y=q)
try:
nodal_q = proj.getSolution()
except RuntimeError(msg):
print('error, non-convergence')
print(msg)
non_convergence = True
# calculate max vertical flux into the model domain at
# drain bnd nodes
# -> not possible, cannot mix face elements and normal elements
# later on to adjust seepage...
#nodal_q_norm = nodal_q * nodal_q.getDomain().getNormal()
#
nodal_q_norm = rotate_vector_escript(
nodal_q, topo_gradient)
#flux_seepage_bnd = active_seepage_bnd * nodal_q[1]
flux_seepage_bnd = active_seepage_bnd * nodal_q_norm[1]
#flux_seepage_bnd_corr = flux_seepage_bnd +
seepage_change_buffer = 1e-3 / year
seepage_inflow_nodes = \
es.whereNegative(flux_seepage_bnd
+ recharge_mass_flux
/ fluid_density_new)
if verbose is True:
print('\tflux seepage bnd (m/yr): ',
flux_seepage_bnd * year)
print('recharge ')
print('\tseepage inflow nodes: ', seepage_inflow_nodes)
#seepage_inflow_nodes = \
# es.whereNegative(flux_seepage_bnd)
removed_seepage_inflow_nodes = seepage_inflow_nodes
# add boundary nodes with P>0 to seepage bnd
new_seepage_nodes = \
es.wherePositive(drain_loc
* (1 - active_seepage_bnd)
* pressure)
# update the seepage bnd
active_seepage_bnd = (active_seepage_bnd +
new_seepage_nodes -
removed_seepage_inflow_nodes)
if verbose is True:
seepage_xy = active_seepage_bnd.getDomain().getX()
seepage_nodes_xy = \
np.array(seepage_xy.toListOfTuples())
seepage_array = np.array(
active_seepage_bnd.toListOfTuples())
ind = np.array(seepage_array > 0)
print('\tafter adjustment:')
print('\tN=%i active seepage bnd x=%0.0f to %0.0f m' \
% (np.sum(ind.astype(int)),
seepage_nodes_xy[ind, 0].min(),
seepage_nodes_xy[ind, 0].max()))
if iterate_seepage_in_one_timestep is True:
# update the specified pressure boundary to include
# new seepage nodes
specified_pressure_bnd_mod = \
es.wherePositive(
specified_pressure_bnd + active_seepage_bnd)
#active_rch_bnd = rch_bnd_loc * es.whereZero(specified_pressure_bnd_mod)
# changed to have steady recharge bnd regardless of seepage bnd,
# 11 apr 2016, Elco
active_rch_bnd = rch_bnd_loc
# experiment, adjust recharge to have 0 rehcarge at seepage nodes
# not sure if this makes sense...
#specified_flux_adj = active_rch_bnd * dt * recharge_mass_flux
#
#pressure_pde.setValue(r=specified_pressure,
# q=specified_pressure_bnd_mod,
# y=specified_flux_adj)
pressure_pde.setValue(r=specified_pressure,
q=specified_pressure_bnd_mod)
# recalculate pressure
#pressure_pde = \
# update_pressure_pde(pressure_pde,
# pressure_t1,
# phi, specific_storage,
# k_tensor, k_vector,
# fluid_density_new,
# viscosity_new, dt,
# rch_bnd_loc, recharge_mass_flux,
# fluid_source, g_vector,
# gamma, concentration_change_rate,
# alpha, temperature_change_rate)
# recalculate pressure
try:
pressure = pressure_pde.getSolution()
except RuntimeError(msg):
print('error, non-convergence')
print(msg)
non_convergence = True
# remove inflow nodes again
#q = (k_vector / viscosity_new *
# -(es.grad(pressure_new)
# - fluid_density_new * g_vector)
# / phi)
q = calculate_q(k_vector, viscosity_new, pressure,
fluid_density_new, g_vector)
proj.setValue(D=es.kronecker(mesh), Y=q)
nodal_q = proj.getSolution()
# calculate max vertical flux into the model domain at
# drain bnd nodes
#nodal_q_norm = nodal_q * nodal_q.getDomain().getNormal()
nodal_q_norm = rotate_vector_escript(
nodal_q, topo_gradient)
flux_seepage_bnd = active_seepage_bnd * nodal_q_norm[1]
#removed_seepage_inflow_nodes = \
# es.whereNegative(flux_seepage_bnd -
# seepage_inflow_threshold)
#removed_seepage_inflow_nodes = \
# es.whereNegative(flux_seepage_bnd
# + recharge_mass_flux
# / fluid_density_new)
removed_seepage_inflow_nodes = \
es.whereNegative(flux_seepage_bnd)
active_seepage_bnd = (active_seepage_bnd -
removed_seepage_inflow_nodes)
if verbose is True:
seepage_xy = active_seepage_bnd.getDomain().getX()
seepage_nodes_xy = \
np.array(seepage_xy.toListOfTuples())
seepage_array = np.array(
active_seepage_bnd.toListOfTuples())
ind = seepage_array > 0
print(
'\tafter 2nd adjustment (removing inflow nodes):'
)
print('\tN=%i active seepage bnd from ' \
'x=%0.0f to %0.0f m' \
% (np.sum(ind.astype(int)),
seepage_nodes_xy[ind, 0].min(),
seepage_nodes_xy[ind, 0].max()))
if iterate_seepage_in_one_timestep is True:
# assign updated seepage nodes:
specified_pressure_bnd_mod = \
es.wherePositive(
specified_pressure_bnd + active_seepage_bnd)
#active_rch_bnd = rch_bnd_loc * es.whereZero(specified_pressure_bnd_mod)
active_rch_bnd = rch_bnd_loc
# experiment, adjust recharge to have 0 rehcarge at seepage nodes
# not sure if this makes sense...
# ! probably the source of long timescale instability of seepage/rch bnd
#specified_flux_adj = active_rch_bnd * dt * recharge_mass_flux
#pressure_pde.setValue(r=specified_pressure,
# q=specified_pressure_bnd_mod,
# y=specified_flux_adj)
pressure_pde.setValue(r=specified_pressure,
q=specified_pressure_bnd_mod)
# recalculate final pressure
#pressure_pde = \
# update_pressure_pde(pressure_pde,
# pressure_t1,
# phi, specific_storage,
# k_tensor, k_vector,
# fluid_density_new,
# viscosity_new, dt,
# rch_bnd_loc, recharge_mass_flux,
# fluid_source, g_vector,
# gamma, concentration_change_rate,
# alpha, temperature_change_rate)
try:
pressure = pressure_pde.getSolution()
except RuntimeError(msg):
print('error, non-convergence')
print(msg)
non_convergence = True
# calculate convergence criteria
pressure_conv = pressure - pressure_old_iteration
if solute_transport is True:
conc_conv = concentration - concentration_old_iteration
else:
conc_conv = 0.0
# check whether iterations have converged or not:
if (es.Lsup(pressure_conv) < pressure_convergence_criterion) and \
(es.Lsup(conc_conv) < concentration_convergence_criterion)\
and iteration + 1 >= min_iterations:
if iteration > 0 and verbose is True:
print('iterations converged after %i iterations' % iteration)
converged = True
else:
if verbose is True:
print('iteration %i, max. pressure change %0.3e ' \
% (iteration, es.Lsup(pressure_conv)))
print(' max. C change %0.3e ' \
% (es.Lsup(conc_conv)))
if iteration + 1 >= max_iterations:
print('warning, reached maximum number of %i iterations' \
% (iteration + 1))
print('iteration %i, max. pressure change %0.3e Pa, ' \
'convergence at %0.2e Pa' \
% (iteration, es.Lsup(pressure_conv),
pressure_convergence_criterion))
print(' max. C change %0.3e kg/kg, ' \
'convergence at %0.2e kg/kg' \
% (es.Lsup(conc_conv), concentration_convergence_criterion))
converged = True
non_convergence = True
# check CFL number
#max_CFL_number = calculate_CFL_number(q, dt)
if ele_size is None:
ele_size = q.getDomain().getSize()
#print ele_size - q.getDomain().getSize()
CFL_number = q * dt / ele_size
max_CFL_number = es.Lsup(CFL_number)
if max_CFL_number > 0.5 and verbose is True:
print('warning, max CFL number = %0.2f, exceeds 0.5' \
% max_CFL_number)
# recaclulcate timestep if max timestep exceeds CFL number
if (max_allowed_CFL_number is not None
and max_CFL_number > max_allowed_CFL_number
and iteration == 0) \
or (force_CFL_timestep is True and iteration <= 1):
# make sure iteration is repeated
converged = False
#CFL_number / flux * flux.getDomain().getSize() = dtc /
dtc = max_allowed_CFL_number / q * ele_size
new_timestep = es.inf((dtc**2)**0.5)
if dt_max is not None and new_timestep > dt_max:
new_timestep = dt_max
dt = new_timestep
if verbose is True:
print('max CFL number = ', max_CFL_number)
print('changing timestep from %0.2e sec to %0.2e sec' \
% (dt, new_timestep))
if coupled_iterations is False:
converged = True
iteration += 1
return (pressure, concentration, fluid_density_new, viscosity_new, q, v,
active_specified_concentration_bnd, active_seepage_bnd,
active_rch_bnd, iteration, es.Lsup(pressure_conv),
es.Lsup(conc_conv), max_CFL_number, non_convergence, dt)
def solve_steady_state_pressure_eq_new(mesh,
topo_gradient,
pressure_pde,
rho_f,
k_tensor,
k_vector,
viscosity,
g_vector,
fluid_source,
rch_bnd_loc,
recharge_mass_flux,
specified_pressure_bnd,
specified_pressure,
drain_bnd_loc,
fluid_density,
proj,
debug=True):
"""
Solve the steady-state fluid flow equation for fluid pressure using escript with optional seepage bnd condition.
"""
year = 365.25 * 24 * 60 * 60.0
# calculate boundary flux
specified_flux = rch_bnd_loc * recharge_mass_flux
a = rho_f * k_tensor / viscosity * es.kronecker(mesh)
d = 0.0
x = rho_f**2 * k_vector / viscosity * g_vector
y = fluid_source
#
pressure_pde.setValue(A=a,
D=d,
X=x,
Y=y,
y=specified_flux,
q=specified_pressure_bnd,
r=specified_pressure)
# calculate pressure, without seepage bnd
pressure = pressure_pde.getSolution()
debug = True
if debug is True:
print('initial calculated steady-state pressure: ', pressure)
if es.sup(drain_bnd_loc) == 0:
print('no drain or seepage bnd')
active_seepage_bnd = es.wherePositive(drain_bnd_loc)
return pressure, active_seepage_bnd
# check if h > surface elevation
#pressure_threshold = 0.01 * 9.81 * 1000.0
pressure_threshold = 0.0
active_seepage_bnd = es.wherePositive(drain_bnd_loc * pressure -
pressure_threshold)
if debug is True:
print('active seepage nodes: ',
np.sum(np.array(active_seepage_bnd.toListOfTuples())))
print('potential seepage nodes: ',
np.sum(np.array(drain_bnd_loc.toListOfTuples())))
n_seepage_change = 9999
n_seepage_nodes = 99999
n_iter = 0
max_seepage_iter = 2000
while n_seepage_change > 0 and n_iter < max_seepage_iter:
# add seepage to specified pressure bnd and update bnd conditions
specified_pressure_bnd_mod = \
es.wherePositive(
specified_pressure_bnd + active_seepage_bnd)
#active_rch_bnd = rch_bnd_loc * es.whereZero(specified_pressure_bnd)
active_rch_bnd = rch_bnd_loc
specified_flux = active_rch_bnd * recharge_mass_flux
pressure_pde.setValue(r=specified_pressure,
q=specified_pressure_bnd_mod,
y=specified_flux)
# recalculate pressure
pressure = pressure_pde.getSolution()
if debug is True:
print('new pressure: ', pressure)
# calculate flux
q = calculate_q(k_vector, viscosity, pressure, fluid_density, g_vector)
proj.setValue(D=es.kronecker(mesh), Y=q)
try:
nodal_q = proj.getSolution()
except RuntimeError(msg):
print('error, non-convergence')
print(msg)
non_convergence = True
# calculate max vertical flux into the model domain at
# drain bnd nodes
# using outer norm to calculate correct bnd flux does not work because
# flux cannot be interpolated to same functionspace as pressure variable
#nodal_q_norm_bnd = nodal_q * nodal_q.getDomain().getNormal()
#nodal_q_norm = es.interpolate(nodal_q_norm_bnd, active_seepage_bnd.getFunctionSpace())
nodal_q_norm = rotate_vector_escript(nodal_q, topo_gradient)
flux_seepage_bnd = active_seepage_bnd * nodal_q_norm[1]
# remove inlfow nodes that are <= recharge
flux_seepage_bnd_corr = flux_seepage_bnd + recharge_mass_flux / fluid_density
# changed back to old method to speed up seepage bnd calc
#flux_seepage_bnd_corr = flux_seepage_bnd
# and remove only the worst x % of seepage nodes to avoid oscillations:
seepage_threshold = es.inf(flux_seepage_bnd_corr) * 0.5
#seepage_threshold = 0.0
seepage_inflow_nodes = \
es.whereNegative(flux_seepage_bnd_corr - seepage_threshold)
removed_seepage_inflow_nodes = seepage_inflow_nodes
if debug is True:
print('number of seepage inflow nodes: ', \
np.sum(np.array(seepage_inflow_nodes.toListOfTuples())))
xmin_seep = es.inf(seepage_inflow_nodes *
seepage_inflow_nodes.getDomain().getX()[0] +
(1 - seepage_inflow_nodes) * 999999)
xmax_seep = es.sup(seepage_inflow_nodes *
seepage_inflow_nodes.getDomain().getX()[0])
print('from x= %0.2f m to x= %0.2f m' % (xmin_seep, xmax_seep))
# add boundary nodes with P>0 to seepage bnd
new_seepage_nodes = \
es.wherePositive(drain_bnd_loc
* (1 - active_seepage_bnd)
* pressure)
if debug is True:
print('number of new seepage nodes: ', \
np.sum(np.array(new_seepage_nodes.toListOfTuples())))
# update the seepage bnd
active_seepage_bnd = (active_seepage_bnd + new_seepage_nodes -
removed_seepage_inflow_nodes)
n_seepage_nodes_old = n_seepage_nodes
n_seepage_nodes = np.sum(np.array(active_seepage_bnd.toListOfTuples()))
n_seepage_change = np.abs(n_seepage_nodes_old - n_seepage_nodes)
if debug is True:
print('final active seepage nodes: ',
np.sum(np.array(active_seepage_bnd.toListOfTuples())))
print('potential seepage nodes: ',
np.sum(np.array(drain_bnd_loc.toListOfTuples())))
if n_seepage_nodes_old < n_seepage_nodes:
print(
'lowest number of seepage nodes reached, stopping iterations')
n_seepage_change = 0
print('seepage iteration %i' % n_iter)
print('seepage threshold ', seepage_threshold * year)
print('change in seepage nodes from %0.0f to %0.0f' %
(n_seepage_nodes_old, n_seepage_nodes))
n_iter += 1
# update specified pressure bnd condition
specified_pressure_bnd_mod = \
es.wherePositive(
specified_pressure_bnd + active_seepage_bnd)
#active_rch_bnd = rch_bnd_loc * es.whereZero(specified_pressure_bnd)
active_rch_bnd = rch_bnd_loc
specified_flux = active_rch_bnd * recharge_mass_flux
pressure_pde.setValue(r=specified_pressure,
q=specified_pressure_bnd_mod,
y=specified_flux)
# recalculate pressure
pressure = pressure_pde.getSolution()
if debug is True:
print('final pressure: ', pressure)
return pressure, active_seepage_bnd
def getPotential(self):
"""
Returns 3 list each made up of a number of list containing primary, secondary and total
potentials diferences. Each of the lists contain a list for each value of n.
"""
coords=self.domain.getX()
pde=LinearPDE(self.domain, numEquations=1)
tol=1e-8
pde.getSolverOptions().setTolerance(tol)
pde.setSymmetryOn()
primCon=self.primaryConductivity
DIM=self.domain.getDim()
x=self.domain.getX()
q=whereZero(x[DIM-1]-inf(x[DIM-1]))
for i in xrange(DIM-1):
xi=x[i]
q+=whereZero(xi-inf(xi))+whereZero(xi-sup(xi))
A = self.secondaryConductivity * kronecker(self.domain)
pde.setValue(A=A,q=q)
delPhiSecondaryList = []
delPhiPrimaryList = []
delPhiTotalList = []
for i in range(1,self.n+1): # 1 to n
maxR = self.numElectrodes - 2 - (i) #max amount of readings that will fit in the survey
delPhiSecondary = []
delPhiPrimary = []
delPhiTotal = []
for j in range(maxR):
analyticRsOne=Data(0,(3,),ContinuousFunction(self.domain))
analyticRsOne[0]=(coords[0]-self.electrodes[j][0])
analyticRsOne[1]=(coords[1]-self.electrodes[j][1])
analyticRsOne[2]=(coords[2])
rsMagOne=(analyticRsOne[0]**2+analyticRsOne[1]**2+analyticRsOne[2]**2)**0.5
analyticRsTwo=Data(0,(3,),ContinuousFunction(self.domain))
analyticRsTwo[0]=(coords[0]-self.electrodes[j + 1][0])
analyticRsTwo[1]=(coords[1]-self.electrodes[j + 1][1])
analyticRsTwo[2]=(coords[2])
rsMagTwo=(analyticRsTwo[0]**2+analyticRsTwo[1]**2+analyticRsTwo[2]**2)**0.5
rsMagOne+=(whereZero(rsMagOne)*0.0000001)
rsMagTwo+=(whereZero(rsMagTwo)*0.0000001)
analyticPrimaryPot=(self.current/(2*pi*primCon*rsMagTwo))-(self.current/(2*pi*primCon*rsMagOne))
analyticRsOnePower=(analyticRsOne[0]**2+analyticRsOne[1]**2+analyticRsOne[2]**2)**1.5
analyticRsOnePower = analyticRsOnePower+(whereZero(analyticRsOnePower)*0.0001)
analyticRsTwoPower=(analyticRsTwo[0]**2+analyticRsTwo[1]**2+analyticRsTwo[2]**2)**1.5
analyticRsTwoPower = analyticRsTwoPower+(whereZero(analyticRsTwoPower)*0.0001)
gradAnalyticPrimaryPot = Data(0,(3,),ContinuousFunction(self.domain))
gradAnalyticPrimaryPot[0] =(self.current/(2*pi*primCon)) * ((analyticRsOne[0]/analyticRsOnePower) - (analyticRsTwo[0]/analyticRsTwoPower))
gradAnalyticPrimaryPot[1] =(self.current/(2*pi*primCon)) * ((analyticRsOne[1]/analyticRsOnePower) - (analyticRsTwo[1]/analyticRsTwoPower))
gradAnalyticPrimaryPot[2] =(self.current/(2*pi*primCon)) * ((analyticRsOne[2]/analyticRsOnePower) - (analyticRsTwo[2]/analyticRsTwoPower))
X=(primCon-self.secondaryConductivity) * (gradAnalyticPrimaryPot)
pde.setValue(X=X)
u=pde.getSolution()
loc=Locator(self.domain,[self.electrodes[1+j+i],self.electrodes[j+i+2]])
valPrimary=loc.getValue(analyticPrimaryPot)
valSecondary=loc.getValue(u)
delPhiPrimary.append(valPrimary[1]-valPrimary[0])
delPhiSecondary.append(valSecondary[1]-valSecondary[0])
delPhiTotal.append(delPhiPrimary[j]+delPhiSecondary[j])
delPhiPrimaryList.append(delPhiPrimary)
delPhiSecondaryList.append(delPhiSecondary)
delPhiTotalList.append(delPhiTotal)
self.delPhiPrimaryList=delPhiPrimaryList
self.delPhiSecondaryList=delPhiSecondaryList
self.delPhiTotalList = delPhiTotalList
return [delPhiPrimaryList, delPhiSecondaryList, delPhiTotalList]
def setup(self,
domainbuilder,
rho0=None,
drho=None,
z0=None,
beta=None,
w0=None,
w1=None,
rho_at_depth=None):
"""
Sets up the inversion parameters from a `DomainBuilder`.
:param domainbuilder: Domain builder object with gravity source(s)
:type domainbuilder: `DomainBuilder`
:param rho0: reference density, see `DensityMapping`. If not specified, zero is used.
:type rho0: ``float`` or ``Scalar``
:param drho: density scale, see `DensityMapping`. If not specified, 2750kg/m^3 is used.
:type drho: ``float`` or ``Scalar``
:param z0: reference depth for depth weighting, see `DensityMapping`. If not specified, zero is used.
:type z0: ``float`` or ``Scalar``
:param beta: exponent for depth weighting, see `DensityMapping`. If not specified, zero is used.
:type beta: ``float`` or ``Scalar``
:param w0: weighting factor for level set term regularization. If not set zero is assumed.
:type w0: ``Scalar`` or ``float``
:param w1: weighting factor for the gradient term in the regularization. If not set zero is assumed
:type w1: ``Vector`` or list of ``float``
:param rho_at_depth: value for density at depth, see `DomainBuilder`.
:type rho_at_depth: ``float`` or ``None``
"""
self.logger.info('Retrieving domain...')
dom = domainbuilder.getDomain()
trafo = makeTransformation(dom, domainbuilder.getReferenceSystem())
DIM = dom.getDim()
rho_mask = domainbuilder.getSetDensityMask()
#========================
self.logger.info('Creating mapping...')
if rho_at_depth:
rho2 = rho_mask * rho_at_depth + (1 - rho_mask) * rho0
elif rho0:
rho2 = (1 - rho_mask) * rho0
else:
rho2 = 0.
rho_mapping = DensityMapping(dom,
rho0=rho2,
drho=drho,
z0=z0,
beta=beta)
scale_mapping = rho_mapping.getTypicalDerivative()
#========================
self.logger.info("Setting up regularization...")
if w1 is None:
w1 = [1.] * DIM
regularization=Regularization(dom, numLevelSets=1,\
w0=w0, w1=w1, location_of_set_m=rho_mask,
coordinates=trafo)
#====================================================================
self.logger.info("Retrieving gravity surveys...")
surveys = domainbuilder.getGravitySurveys()
g = []
w = []
for g_i, sigma_i in surveys:
w_i = es.safeDiv(1., sigma_i)
if g_i.getRank() == 0:
g_i = g_i * es.kronecker(DIM)[DIM - 1]
if w_i.getRank() == 0:
w_i = w_i * es.kronecker(DIM)[DIM - 1]
g.append(g_i)
w.append(w_i)
self.logger.debug("Added gravity survey:")
self.logger.debug("g = %s" % g_i)
self.logger.debug("sigma = %s" % sigma_i)
self.logger.debug("w = %s" % w_i)
#====================================================================
self.logger.info("Setting up model...")
forward_model = GravityModel(
dom,
w,
g,
fixPotentialAtBottom=self._fixGravityPotentialAtBottom,
coordinates=trafo)
forward_model.rescaleWeights(rho_scale=scale_mapping)
#====================================================================
self.logger.info("Setting cost function...")
self.setCostFunction(
InversionCostFunction(regularization, rho_mapping, forward_model))
def getPotential(self):
"""
returns a list containing 3 lists one for each the primary, secondary
and total potential.
"""
primCon=self.primaryConductivity
coords=self.domain.getX()
pde=LinearPDE(self.domain, numEquations=1)
tol=1e-8
pde.getSolverOptions().setTolerance(tol)
pde.setSymmetryOn()
DIM=self.domain.getDim()
x=self.domain.getX()
q=es.whereZero(x[DIM-1]-es.inf(x[DIM-1]))
for i in xrange(DIM-1):
xi=x[i]
q+=es.whereZero(xi-es.inf(xi))+es.whereZero(xi-es.sup(xi))
A = self.secondaryConductivity * es.kronecker(self.domain)
pde.setValue(A=A,q=q)
delPhiSecondary = []
delPhiPrimary = []
delPhiTotal = []
if(len(self.electrodes[0])==3):
for i in range(self.numElectrodes-3):
analyticRsOne=es.Data(0,(3,),es.ContinuousFunction(self.domain))
analyticRsOne[0]=(coords[0]-self.electrodes[i][0])
analyticRsOne[1]=(coords[1]-self.electrodes[i][1])
analyticRsOne[2]=(coords[2])
rsMagOne=(analyticRsOne[0]**2+analyticRsOne[1]**2+analyticRsOne[2]**2)**0.5
analyticRsTwo=es.Data(0,(3,),es.ContinuousFunction(self.domain))
analyticRsTwo[0]=(coords[0]-self.electrodes[i+3][0])
analyticRsTwo[1]=(coords[1]-self.electrodes[i+3][1])
analyticRsTwo[2]=(coords[2])
rsMagTwo=(analyticRsTwo[0]**2+analyticRsTwo[1]**2+analyticRsTwo[2]**2)**0.5
rsMagOne+=(es.whereZero(rsMagOne)*0.0000001)
rsMagTwo+=(es.whereZero(rsMagTwo)*0.0000001)
analyticPrimaryPot=(self.current/(2*pi*primCon*rsMagOne))-(self.current/(2*pi*primCon*rsMagTwo))
analyticRsOnePower=(analyticRsOne[0]**2+analyticRsOne[1]**2+analyticRsOne[2]**2)**1.5
analyticRsOnePower = analyticRsOnePower+(es.whereZero(analyticRsOnePower)*0.0001)
analyticRsTwoPower=(analyticRsTwo[0]**2+analyticRsTwo[1]**2+analyticRsTwo[2]**2)**1.5
analyticRsTwoPower = analyticRsTwoPower+(es.whereZero(analyticRsTwoPower)*0.0001)
gradAnalyticPrimaryPot = es.Data(0,(3,),es.ContinuousFunction(self.domain))
gradAnalyticPrimaryPot[0] =(self.current/(2*pi*primCon)) \
* ((-analyticRsOne[0]/analyticRsOnePower) \
+ (analyticRsTwo[0]/analyticRsTwoPower))
gradAnalyticPrimaryPot[1] =(self.current/(2*pi*primCon)) \
* ((-analyticRsOne[1]/analyticRsOnePower) \
+ (analyticRsTwo[1]/analyticRsTwoPower))
gradAnalyticPrimaryPot[2] =(self.current/(2*pi*primCon)) \
* ((-analyticRsOne[2]/analyticRsOnePower)
+ (analyticRsTwo[2]/analyticRsTwoPower))
X=(primCon-self.secondaryConductivity) * (gradAnalyticPrimaryPot)
pde.setValue(X=X)
u=pde.getSolution()
loc=Locator(self.domain,[self.electrodes[i+1],self.electrodes[i+2]])
valPrimary=loc.getValue(analyticPrimaryPot)
valSecondary=loc.getValue(u)
delPhiPrimary.append(valPrimary[1]-valPrimary[0])
delPhiSecondary.append(valSecondary[1]-valSecondary[0])
delPhiTotal.append(delPhiPrimary[i]+delPhiSecondary[i])
else:
raise NotImplementedError("2d forward model is not yet implemented")
self.delPhiSecondary = delPhiSecondary
self.delPhiPrimary = delPhiPrimary
self.delPhiTotal=delPhiTotal
return [delPhiPrimary, delPhiSecondary, delPhiTotal]
def __init__(self,
domain,
v_p,
v_s,
wavelet,
source_tag,
source_vector=[0., 1.],
eps=0.,
delta=0.,
theta=0.,
rho=1.,
dt=None,
u0=None,
v0=None,
absorption_zone=300 * U.m,
absorption_cut=1e-2,
lumping=True):
"""
initialize the TTI wave solver
:param domain: domain of the problem
:type domain: `Domain`
:param v_p: vertical p-velocity field
:type v_p: `escript.Scalar`
:param v_s: vertical s-velocity field
:type v_s: `escript.Scalar`
:param wavelet: wavelet to describe the time evolution of source term
:type wavelet: `Wavelet`
:param source_tag: tag of the source location
:type source_tag: 'str' or 'int'
:param source_vector: source orientation vector
:param eps: first Thompsen parameter
:param delta: second Thompsen parameter
:param theta: tilting (in Rad)
:param rho: density
:param dt: time step size. If not present a suitable time step size is calculated.
:param u0: initial solution. If not present zero is used.
:param v0: initial solution change rate. If not present zero is used.
:param absorption_zone: thickness of absorption zone
:param absorption_cut: boundary value of absorption decay factor
:param lumping: if True mass matrix lumping is being used. This is accelerates the computing but introduces some diffusion.
"""
cos = escript.cos
sin = escript.sin
DIM = domain.getDim()
if not DIM == 2:
raise ValueError("Only 2D is supported.")
f = createAbsorptionLayerFunction(
escript.Function(domain).getX(), absorption_zone, absorption_cut)
v_p = v_p * f
v_s = v_s * f
if u0 == None:
u0 = escript.Vector(0., escript.Solution(domain))
else:
u0 = escript.interpolate(p0, escript.Solution(domain))
if v0 == None:
v0 = escript.Vector(0., escript.Solution(domain))
else:
v0 = escript.interpolate(v0, escript.Solution(domain))
if dt == None:
dt = min((1. / 5.) * min(escript.inf(domain.getSize() / v_p),
escript.inf(domain.getSize() / v_s)),
wavelet.getTimeScale())
super(TTIWave, self).__init__(dt, u0=u0, v0=v0, t0=0.)
self.__wavelet = wavelet
self.__mypde = lpde.LinearPDESystem(domain)
if lumping:
self.__mypde.getSolverOptions().setSolverMethod(
lpde.SolverOptions.HRZ_LUMPING)
self.__mypde.setSymmetryOn()
self.__mypde.setValue(D=rho * escript.kronecker(DIM),
X=self.__mypde.createCoefficient('X'))
self.__source_tag = source_tag
self.__r = escript.Vector(
0, escript.DiracDeltaFunctions(self.__mypde.getDomain()))
self.__r.setTaggedValue(self.__source_tag, source_vector)
c0_33 = v_p**2 * rho
c0_66 = v_s**2 * rho
c0_11 = (1 + 2 * eps) * c0_33
c0_13 = escript.sqrt(2 * c0_33 * (c0_33 - c0_66) * delta +
(c0_33 - c0_66)**2) - c0_66
self.c11 = c0_11 * cos(theta)**4 - 2 * c0_13 * cos(
theta)**4 + 2 * c0_13 * cos(theta)**2 + c0_33 * sin(
theta)**4 - 4 * c0_66 * cos(theta)**4 + 4 * c0_66 * cos(
theta)**2
self.c13 = -c0_11 * cos(theta)**4 + c0_11 * cos(
theta)**2 + c0_13 * sin(theta)**4 + c0_13 * cos(
theta)**4 - c0_33 * cos(theta)**4 + c0_33 * cos(
theta)**2 + 4 * c0_66 * cos(theta)**4 - 4 * c0_66 * cos(
theta)**2
self.c16 = (-2 * c0_11 * cos(theta)**2 - 4 * c0_13 * sin(theta)**2 +
2 * c0_13 + 2 * c0_33 * sin(theta)**2 - 8 * c0_66 *
sin(theta)**2 + 4 * c0_66) * sin(theta) * cos(theta) / 2
self.c33 = c0_11 * sin(theta)**4 - 2 * c0_13 * cos(
theta)**4 + 2 * c0_13 * cos(theta)**2 + c0_33 * cos(
theta)**4 - 4 * c0_66 * cos(theta)**4 + 4 * c0_66 * cos(
theta)**2
self.c36 = (2 * c0_11 * cos(theta)**2 - 2 * c0_11 +
4 * c0_13 * sin(theta)**2 - 2 * c0_13 +
2 * c0_33 * cos(theta)**2 + 8 * c0_66 * sin(theta)**2 -
4 * c0_66) * sin(theta) * cos(theta) / 2
self.c66 = -c0_11 * cos(theta)**4 + c0_11 * cos(
theta)**2 + 2 * c0_13 * cos(theta)**4 - 2 * c0_13 * cos(
theta)**2 - c0_33 * cos(theta)**4 + c0_33 * cos(
theta)**2 + c0_66 * sin(theta)**4 + 3 * c0_66 * cos(
theta)**4 - 2 * c0_66 * cos(theta)**2
def __init__(self,
domain,
v_p,
v_s,
wavelet,
source_tag,
source_vector=[1., 0., 0.],
eps=0.,
gamma=0.,
delta=0.,
rho=1.,
dt=None,
u0=None,
v0=None,
absorption_zone=None,
absorption_cut=1e-2,
lumping=True,
disable_fast_assemblers=False):
"""
initialize the VTI wave solver
:param domain: domain of the problem
:type domain: `Domain`
:param v_p: vertical p-velocity field
:type v_p: `escript.Scalar`
:param v_s: vertical s-velocity field
:type v_s: `escript.Scalar`
:param wavelet: wavelet to describe the time evolution of source term
:type wavelet: `Wavelet`
:param source_tag: tag of the source location
:type source_tag: 'str' or 'int'
:param source_vector: source orientation vector
:param eps: first Thompsen parameter
:param delta: second Thompsen parameter
:param gamma: third Thompsen parameter
:param rho: density
:param dt: time step size. If not present a suitable time step size is calculated.
:param u0: initial solution. If not present zero is used.
:param v0: initial solution change rate. If not present zero is used.
:param absorption_zone: thickness of absorption zone
:param absorption_cut: boundary value of absorption decay factor
:param lumping: if True mass matrix lumping is being used. This is accelerates the computing but introduces some diffusion.
:param disable_fast_assemblers: if True, forces use of slower and more general PDE assemblers
"""
DIM = domain.getDim()
self.fastAssembler = hasattr(
domain, "createAssembler") and not disable_fast_assemblers
f = createAbsorptionLayerFunction(v_p.getFunctionSpace().getX(),
absorption_zone, absorption_cut)
v_p = v_p * f
v_s = v_s * f
if u0 == None:
u0 = escript.Vector(0., escript.Solution(domain))
else:
u0 = escript.interpolate(p0, escript.Solution(domain))
if v0 == None:
v0 = escript.Vector(0., escript.Solution(domain))
else:
v0 = escript.interpolate(v0, escript.Solution(domain))
if dt == None:
dt = min((1. / 5.) * min(escript.inf(domain.getSize() / v_p),
escript.inf(domain.getSize() / v_s)),
wavelet.getTimeScale())
super(HTIWave, self).__init__(dt, u0=u0, v0=v0, t0=0.)
self.__wavelet = wavelet
self.c33 = v_p**2 * rho
self.c44 = v_s**2 * rho
self.c11 = (1 + 2 * eps) * self.c33
self.c66 = (1 + 2 * gamma) * self.c44
self.c13 = escript.sqrt(2 * self.c33 * (self.c33 - self.c44) * delta +
(self.c33 - self.c44)**2) - self.c44
self.c23 = self.c33 - 2 * self.c66
if self.fastAssembler:
C = [("c11", self.c11), ("c23", self.c23), ("c13", self.c13),
("c33", self.c33), ("c44", self.c44), ("c66", self.c66)]
if "speckley" in domain.getDescription().lower():
C = [(n, escript.interpolate(d,
escript.ReducedFunction(domain)))
for n, d in C]
self.__mypde = lpde.WavePDE(domain, C)
else:
self.__mypde = lpde.LinearPDESystem(domain)
self.__mypde.setValue(X=self.__mypde.createCoefficient('X'))
if lumping:
self.__mypde.getSolverOptions().setSolverMethod(
lpde.SolverOptions.HRZ_LUMPING)
self.__mypde.setSymmetryOn()
self.__mypde.setValue(D=rho * escript.kronecker(DIM))
self.__source_tag = source_tag
if DIM == 2:
source_vector = [source_vector[0], source_vector[2]]
self.__r = escript.Vector(
0, escript.DiracDeltaFunctions(self.__mypde.getDomain()))
self.__r.setTaggedValue(self.__source_tag, source_vector)
def getPotential(self):
"""
Returns 3 list each made up of a number of list containing primary, secondary and total
potentials diferences. Each of the lists contain a list for each value of n.
"""
primCon=self.primaryConductivity
coords=self.domain.getX()
pde=LinearPDE(self.domain, numEquations=1)
tol=1e-8
pde.getSolverOptions().setTolerance(tol)
pde.setSymmetryOn()
DIM=self.domain.getDim()
x=self.domain.getX()
q=whereZero(x[DIM-1]-inf(x[DIM-1]))
for i in xrange(DIM-1):
xi=x[i]
q+=whereZero(xi-inf(xi))+whereZero(xi-sup(xi))
A = self.secondaryConductivity * kronecker(self.domain)
pde.setValue(A=A,q=q)
delPhiSecondaryList = []
delPhiPrimaryList = []
delPhiTotalList = []
for i in range(1,self.n+1): # 1 to n
maxR = self.numElectrodes - 1 - i #max amount of readings that will fit in the survey
delPhiSecondary = []
delPhiPrimary = []
delPhiTotal = []
for j in range(maxR):
analyticRs=Data(0,(3,),ContinuousFunction(self.domain))
analyticRs[0]=(coords[0]-self.electrodes[j][0])
analyticRs[1]=(coords[1]-self.electrodes[j][1])
analyticRs[2]=(coords[2])
rsMag=(analyticRs[0]**2+analyticRs[1]**2+analyticRs[2]**2)**0.5
analyticPrimaryPot=(self.current*(1./primCon))/(2*pi*(rsMag+(whereZero(rsMag)*0.0000001))) #the magic number 0.0000001 is to avoid devide by 0
analyticRsPolePower=(analyticRs[0]**2+analyticRs[1]**2+analyticRs[2]**2)**1.5
analyticRsPolePower = analyticRsPolePower+(whereZero(analyticRsPolePower)*0.0000001)
gradUPrimary = Data(0,(3,),ContinuousFunction(self.domain))
gradUPrimary[0] =(self.current/(2*pi*primCon)) * (analyticRs[0]/analyticRsPolePower)
gradUPrimary[1] =(self.current/(2*pi*primCon)) * (analyticRs[1]/analyticRsPolePower)
gradUPrimary[2] =(self.current/(2*pi*primCon)) * (analyticRs[2]/analyticRsPolePower)
gradUPrimary=-gradUPrimary
X=(primCon-self.secondaryConductivity) * gradUPrimary
pde.setValue(X=X)
u=pde.getSolution()
loc=Locator(self.domain,[self.electrodes[i+j],self.electrodes[i+j+1]])
valPrimary=loc.getValue(analyticPrimaryPot)
valSecondary=loc.getValue(u)
delPhiPrimary.append(valPrimary[1]-valPrimary[0])
delPhiSecondary.append(valSecondary[1]-valSecondary[0])
delPhiTotal.append(delPhiPrimary[j]+delPhiSecondary[j])
delPhiPrimaryList.append(delPhiPrimary)
delPhiSecondaryList.append(delPhiSecondary)
delPhiTotalList.append(delPhiTotal)
self.delPhiPrimaryList=delPhiPrimaryList
self.delPhiSecondaryList=delPhiSecondaryList
self.delPhiTotalList = delPhiTotalList
return [delPhiPrimaryList, delPhiSecondaryList, delPhiTotalList]
def RegionalCalculation(reg_mask):
"""
Calculates the "regional" from the entire FEILDS model excluding the
selected region and outputs gravity at the specified altitude...
see above for the "residual"
"""
# read in a gravity data grid to define data computation space
G_DATA = os.path.join(DATADIR,'Final_BouguerTC_UC15K_qrtdeg.nc')
FS=ReducedFunction(dom)
nValues=[NX, NY, 1]
first = [0, 0, cell_at_altitude]
multiplier = [1, 1, 1]
reverse = [0, 0, 0]
byteorder = BYTEORDER_NATIVE
gdata = readBinaryGrid(G_DATA, FS, shape=(),
fill=-999999, byteOrder=byteorder,
dataType=DATATYPE_FLOAT32, first=first, numValues=nValues,
multiplier=multiplier, reverse=reverse)
print("Grid successfully read")
# get the masking and units sorted out for the data-space
g_mask = whereNonZero(gdata+999999)
gdata=gdata*g_mask * GRAV_UNITS
# if people choose to have air in their region we exclude it from the
# specified gravity calculation region
if h_top < 0.:
reg_mask = reg_mask+mask_air
live_model = initial_model* whereNonPositive(reg_mask)
dead_model = initial_model* wherePositive(reg_mask)
if UseMean is True:
# calculate the mean density within the selected region
BackgroundDensity = integrate(dead_model)/integrate(wherePositive(reg_mask))
print("Density mean for selected region equals = %s"%BackgroundDensity)
live_model = live_model + BackgroundDensity * wherePositive(reg_mask)
# create mapping
rho_mapping = DensityMapping(dom, rho0=live_model)
# invert sign of gravity field to account for escript's coordinate system
gdata = -GRAV_UNITS * gdata
# turn the scalars into vectors (vertical direction)
d=kronecker(DIM)[DIM-1]
w=safeDiv(1., g_mask)
gravity_model=GravityModel(dom, w*d, gdata*d, fixPotentialAtBottom=False, coordinates=COORDINATES)
gravity_model.rescaleWeights(rho_scale=rho_mapping.getTypicalDerivative())
phi,_ = gravity_model.getArguments(live_model)
g_init = -gravity_model.getCoordinateTransformation().getGradient(phi)
g_init = interpolate(g_init, gdata.getFunctionSpace())
print("Computed gravity: %s"%(g_init[2]))
fn=os.path.join(OUTPUTDIR,'regional-gravity')
if SiloOutput is True:
saveSilo(fn, density=live_model, gravity_init=g_init, g_initz=-g_init[2], gravitymask=g_mask, modelmask=reg_mask)
print('SILO file written with the following fields: density (kg/m^3), gravity vector (m/s^2), gz (m/s^2), gravitymask, modelmask')
# to compare calculated data against input dataset.
# Not used by default but should work if the input dataset is correct
#gslice = g_init[2]*wherePositive(g_mask)
#g_dash = integrate(gslice)/integrate(wherePositive(g_mask))
#gdataslice = gdata*wherePositive(g_mask)
#gdata_dash = integrate(gdataslice)/integrate(wherePositive(g_mask))
#misfit=(gdataslice-gdata_dash)-(gslice-g_dash)
saveDataCSV(fn+".csv", mask=g_mask, gz=-g_init[2], Long=datacoords[0], Lat=datacoords[1], h=datacoords[2])
print('CSV file written with the following fields: Longitude (degrees) Latitude (degrees), h (100km), gz (m/s^2)')
def stress(self):
"""
returns current stress"""
return 2*self.viscosity*self.stretching-self.pressure*kronecker(self.domain)
def getPotential(self):
"""
Returns 3 list each made up of a number of list containing primary, secondary and total
potentials diferences. Each of the lists contain a list for each value of n.
"""
primCon=self.primaryConductivity
coords=self.domain.getX()
pde=LinearPDE(self.domain, numEquations=1)
tol=1e-8
pde.getSolverOptions().setTolerance(tol)
pde.setSymmetryOn()
DIM=self.domain.getDim()
x=self.domain.getX()
q=es.whereZero(x[DIM-1]-es.inf(x[DIM-1]))
for i in xrange(DIM-1):
xi=x[i]
q+=es.whereZero(xi-es.inf(xi))+es.whereZero(xi-es.sup(xi))
A = self.secondaryConductivity * es.kronecker(self.domain)
pde.setValue(A=A,q=q)
delPhiSecondaryList = []
delPhiPrimaryList = []
delPhiTotalList = []
for i in range(1,self.n+1): # 1 to n
maxR = self.numElectrodes - 1 - i #max amount of readings that will fit in the survey
delPhiSecondary = []
delPhiPrimary = []
delPhiTotal = []
for j in range(maxR):
analyticRs=es.Data(0,(3,),es.ContinuousFunction(self.domain))
analyticRs[0]=(coords[0]-self.electrodes[j][0])
analyticRs[1]=(coords[1]-self.electrodes[j][1])
analyticRs[2]=(coords[2])
rsMag=(analyticRs[0]**2+analyticRs[1]**2+analyticRs[2]**2)**0.5
analyticPrimaryPot=(self.current*(1./primCon))/(2*pi*(rsMag+(es.whereZero(rsMag)*0.0000001))) #the magic number 0.0000001 is to avoid devide by 0
analyticRsPolePower=(analyticRs[0]**2+analyticRs[1]**2+analyticRs[2]**2)**1.5
analyticRsPolePower = analyticRsPolePower+(es.whereZero(analyticRsPolePower)*0.0000001)
gradUPrimary = es.Data(0,(3,),es.ContinuousFunction(self.domain))
gradUPrimary[0] =(self.current/(2*pi*primCon)) * (analyticRs[0]/analyticRsPolePower)
gradUPrimary[1] =(self.current/(2*pi*primCon)) * (analyticRs[1]/analyticRsPolePower)
gradUPrimary[2] =(self.current/(2*pi*primCon)) * (analyticRs[2]/analyticRsPolePower)
gradUPrimary=-gradUPrimary
X=(primCon-self.secondaryConductivity) * gradUPrimary
pde.setValue(X=X)
u=pde.getSolution()
loc=Locator(self.domain,[self.electrodes[i+j],self.electrodes[i+j+1]])
valPrimary=loc.getValue(analyticPrimaryPot)
valSecondary=loc.getValue(u)
delPhiPrimary.append(valPrimary[1]-valPrimary[0])
delPhiSecondary.append(valSecondary[1]-valSecondary[0])
delPhiTotal.append(delPhiPrimary[j]+delPhiSecondary[j])
delPhiPrimaryList.append(delPhiPrimary)
delPhiSecondaryList.append(delPhiSecondary)
delPhiTotalList.append(delPhiTotal)
self.delPhiPrimaryList=delPhiPrimaryList
self.delPhiSecondaryList=delPhiSecondaryList
self.delPhiTotalList = delPhiTotalList
return [delPhiPrimaryList, delPhiSecondaryList, delPhiTotalList]
def getPotential(self):
"""
returns a list containing 3 lists one for each the primary, secondary
and total potential.
"""
primCon=self.primaryConductivity
coords=self.domain.getX()
pde=LinearPDE(self.domain, numEquations=1)
tol=1e-8
pde.getSolverOptions().setTolerance(tol)
pde.setSymmetryOn()
DIM=self.domain.getDim()
x=self.domain.getX()
q=whereZero(x[DIM-1]-inf(x[DIM-1]))
for i in xrange(DIM-1):
xi=x[i]
q+=whereZero(xi-inf(xi))+whereZero(xi-sup(xi))
A = self.secondaryConductivity * kronecker(self.domain)
pde.setValue(A=A,q=q)
delPhiSecondary = []
delPhiPrimary = []
delPhiTotal = []
if(len(self.electrodes[0])==3):
for i in range(self.numElectrodes-3):
analyticRsOne=Data(0,(3,),ContinuousFunction(self.domain))
analyticRsOne[0]=(coords[0]-self.electrodes[i][0])
analyticRsOne[1]=(coords[1]-self.electrodes[i][1])
analyticRsOne[2]=(coords[2])
rsMagOne=(analyticRsOne[0]**2+analyticRsOne[1]**2+analyticRsOne[2]**2)**0.5
analyticRsTwo=Data(0,(3,),ContinuousFunction(self.domain))
analyticRsTwo[0]=(coords[0]-self.electrodes[i+3][0])
analyticRsTwo[1]=(coords[1]-self.electrodes[i+3][1])
analyticRsTwo[2]=(coords[2])
rsMagTwo=(analyticRsTwo[0]**2+analyticRsTwo[1]**2+analyticRsTwo[2]**2)**0.5
rsMagOne+=(whereZero(rsMagOne)*0.0000001)
rsMagTwo+=(whereZero(rsMagTwo)*0.0000001)
analyticPrimaryPot=(self.current/(2*pi*primCon*rsMagOne))-(self.current/(2*pi*primCon*rsMagTwo))
analyticRsOnePower=(analyticRsOne[0]**2+analyticRsOne[1]**2+analyticRsOne[2]**2)**1.5
analyticRsOnePower = analyticRsOnePower+(whereZero(analyticRsOnePower)*0.0001)
analyticRsTwoPower=(analyticRsTwo[0]**2+analyticRsTwo[1]**2+analyticRsTwo[2]**2)**1.5
analyticRsTwoPower = analyticRsTwoPower+(whereZero(analyticRsTwoPower)*0.0001)
gradAnalyticPrimaryPot = Data(0,(3,),ContinuousFunction(self.domain))
gradAnalyticPrimaryPot[0] =(self.current/(2*pi*primCon)) \
* ((-analyticRsOne[0]/analyticRsOnePower) \
+ (analyticRsTwo[0]/analyticRsTwoPower))
gradAnalyticPrimaryPot[1] =(self.current/(2*pi*primCon)) \
* ((-analyticRsOne[1]/analyticRsOnePower) \
+ (analyticRsTwo[1]/analyticRsTwoPower))
gradAnalyticPrimaryPot[2] =(self.current/(2*pi*primCon)) \
* ((-analyticRsOne[2]/analyticRsOnePower)
+ (analyticRsTwo[2]/analyticRsTwoPower))
X=(primCon-self.secondaryConductivity) * (gradAnalyticPrimaryPot)
pde.setValue(X=X)
u=pde.getSolution()
loc=Locator(self.domain,[self.electrodes[i+1],self.electrodes[i+2]])
valPrimary=loc.getValue(analyticPrimaryPot)
valSecondary=loc.getValue(u)
delPhiPrimary.append(valPrimary[1]-valPrimary[0])
delPhiSecondary.append(valSecondary[1]-valSecondary[0])
delPhiTotal.append(delPhiPrimary[i]+delPhiSecondary[i])
else:
raise NotImplementedError("2d forward model is not yet implemented")
self.delPhiSecondary = delPhiSecondary
self.delPhiPrimary = delPhiPrimary
self.delPhiTotal=delPhiTotal
return [delPhiPrimary, delPhiSecondary, delPhiTotal]
def __init__(self,
domain,
v_p,
wavelet,
source_tag,
source_vector=[1., 0.],
eps=0.,
delta=0.,
azimuth=0.,
dt=None,
p0=None,
v0=None,
absorption_zone=300 * U.m,
absorption_cut=1e-2,
lumping=True):
"""
initialize the HTI wave solver
:param domain: domain of the problem
:type domain: `Doamin`
:param v_p: vertical p-velocity field
:type v_p: `escript.Scalar`
:param v_s: vertical s-velocity field
:type v_s: `escript.Scalar`
:param wavelet: wavelet to describe the time evolution of source term
:type wavelet: `Wavelet`
:param source_tag: tag of the source location
:type source_tag: 'str' or 'int'
:param source_vector: source orientation vector
:param eps: first Thompsen parameter
:param azimuth: azimuth (rotation around verticle axis)
:param gamma: third Thompsen parameter
:param rho: density
:param dt: time step size. If not present a suitable time step size is calculated.
:param p0: initial solution (Q(t=0), P(t=0)). If not present zero is used.
:param v0: initial solution change rate. If not present zero is used.
:param absorption_zone: thickness of absorption zone
:param absorption_cut: boundary value of absorption decay factor
:param lumping: if True mass matrix lumping is being used. This is accelerates the computing but introduces some diffusion.
"""
DIM = domain.getDim()
f = createAbsorptionLayerFunction(v_p.getFunctionSpace().getX(),
absorption_zone, absorption_cut)
self.v2_p = v_p**2
self.v2_t = self.v2_p * escript.sqrt(1 + 2 * delta)
self.v2_n = self.v2_p * (1 + 2 * eps)
if p0 == None:
p0 = escript.Data(0., (2, ), escript.Solution(domain))
else:
p0 = escript.interpolate(p0, escript.Solution(domain))
if v0 == None:
v0 = escript.Data(0., (2, ), escript.Solution(domain))
else:
v0 = escript.interpolate(v0, escript.Solution(domain))
if dt == None:
dt = min(
min(escript.inf(domain.getSize() / escript.sqrt(self.v2_p)),
escript.inf(domain.getSize() / escript.sqrt(self.v2_t)),
escript.inf(domain.getSize() / escript.sqrt(self.v2_n))),
wavelet.getTimeScale()) * 0.2
super(SonicHTIWave, self).__init__(dt, u0=p0, v0=v0, t0=0.)
self.__wavelet = wavelet
self.__mypde = lpde.LinearPDESystem(domain)
if lumping:
self.__mypde.getSolverOptions().setSolverMethod(
lpde.SolverOptions.HRZ_LUMPING)
self.__mypde.setSymmetryOn()
self.__mypde.setValue(D=escript.kronecker(2),
X=self.__mypde.createCoefficient('X'))
self.__source_tag = source_tag
self.__r = escript.Vector(
0, escript.DiracDeltaFunctions(self.__mypde.getDomain()))
self.__r.setTaggedValue(self.__source_tag, source_vector)
def setup(self, domainbuilder,
rho0=None, drho=None, rho_z0=None, rho_beta=None,
k0=None, dk=None, k_z0=None, k_beta=None, w0=None, w1=None,
w_gc=None,rho_at_depth=None, k_at_depth=None):
"""
Sets up the inversion from an instance ``domainbuilder`` of a
`DomainBuilder`. Gravity and magnetic data attached to the
``domainbuilder`` are considered in the inversion.
If magnetic data are given as scalar it is assumed that values are
collected in direction of the background magnetic field.
:param domainbuilder: Domain builder object with gravity source(s)
:type domainbuilder: `DomainBuilder`
:param rho0: reference density, see `DensityMapping`. If not specified,
zero is used.
:type rho0: ``float`` or `Scalar`
:param drho: density scale, see `DensityMapping`. If not specified,
2750 kg/m^3 is used.
:type drho: ``float`` or `Scalar`
:param rho_z0: reference depth for depth weighting for density, see
`DensityMapping`. If not specified, zero is used.
:type rho_z0: ``float`` or `Scalar`
:param rho_beta: exponent for density depth weighting, see
`DensityMapping`. If not specified, zero is used.
:type rho_beta: ``float`` or `Scalar`
:param k0: reference susceptibility, see `SusceptibilityMapping`.
If not specified, zero is used.
:type k0: ``float`` or `Scalar`
:param dk: susceptibility scale, see `SusceptibilityMapping`. If not
specified, 1. is used.
:type dk: ``float`` or `Scalar`
:param k_z0: reference depth for susceptibility depth weighting, see
`SusceptibilityMapping`. If not specified, zero is used.
:type k_z0: ``float`` or `Scalar`
:param k_beta: exponent for susceptibility depth weighting, see
`SusceptibilityMapping`. If not specified, zero is used.
:type k_beta: ``float`` or `Scalar`
:param w0: weighting factor for level set term in the regularization.
If not set zero is assumed.
:type w0: ``Scalar`` or ``float``
:param w1: weighting factor for the gradient term in the regularization
see `Regularization`. If not set zero is assumed.
:type w1: `es.Data` or ``ndarray`` of shape (DIM,)
:param w_gc: weighting factor for the cross gradient term in the
regularization, see `Regularization`. If not set one is
assumed.
:type w_gc: `Scalar` or `float`
:param k_at_depth: value for susceptibility at depth, see `DomainBuilder`.
:type k_at_depth: ``float`` or ``None``
:param rho_at_depth: value for density at depth, see `DomainBuilder`.
:type rho_at_depth: ``float`` or ``None``
"""
self.logger.info('Retrieving domain...')
dom=domainbuilder.getDomain()
DIM=dom.getDim()
trafo=makeTransformation(dom, domainbuilder.getReferenceSystem())
rock_mask=wherePositive(domainbuilder.getSetDensityMask() + domainbuilder.getSetSusceptibilityMask())
#========================
self.logger.info('Creating mappings ...')
if rho_at_depth:
rho2= rock_mask * rho_at_depth + (1-rock_mask) * rho0
elif rho0:
rho2= (1-rock_mask) * rho0
else:
rho2=0
if k_at_depth:
k2= rock_mask * k_at_depth + (1-rock_mask) * k0
elif k0:
k2= (1-rock_mask) * k0
else:
k2=0
rho_mapping=DensityMapping(dom, rho0=rho2, drho=drho, z0=rho_z0, beta=rho_beta)
rho_scale_mapping=rho_mapping.getTypicalDerivative()
self.logger.debug("rho_scale_mapping = %s"%rho_scale_mapping)
k_mapping=SusceptibilityMapping(dom, k0=k2, dk=dk, z0=k_z0, beta=k_beta)
k_scale_mapping=k_mapping.getTypicalDerivative()
self.logger.debug("k_scale_mapping = %s"%k_scale_mapping)
#========================
self.logger.info("Setting up regularization...")
if w1 is None:
w1=[1.]*DIM
regularization=Regularization(dom, numLevelSets=1,w0=w0, w1=w1, location_of_set_m=rock_mask, coordinates=trafo)
#====================================================================
self.logger.info("Retrieving gravity surveys...")
surveys=domainbuilder.getGravitySurveys()
g=[]
w=[]
for g_i,sigma_i in surveys:
w_i=es.safeDiv(1., sigma_i)
if g_i.getRank()==0:
g_i=g_i*es.kronecker(DIM)[DIM-1]
if w_i.getRank()==0:
w_i=w_i*es.kronecker(DIM)[DIM-1]
g.append(g_i)
w.append(w_i)
self.logger.debug("Added gravity survey:")
self.logger.debug("g = %s"%g_i)
self.logger.debug("sigma = %s"%sigma_i)
self.logger.debug("w = %s"%w_i)
self.logger.info("Setting up gravity model...")
gravity_model=GravityModel(dom, w, g, fixPotentialAtBottom=self._fixGravityPotentialAtBottom, coordinates=trafo)
gravity_model.rescaleWeights(rho_scale=rho_scale_mapping)
#====================================================================
self.logger.info("Retrieving magnetic field surveys...")
d_b=es.normalize(domainbuilder.getBackgroundMagneticFluxDensity())
surveys=domainbuilder.getMagneticSurveys()
B=[]
w=[]
for B_i,sigma_i in surveys:
w_i=es.safeDiv(1., sigma_i)
if B_i.getRank()==0:
B_i=B_i*d_b
if w_i.getRank()==0:
w_i=w_i*d_b
B.append(B_i)
w.append(w_i)
self.logger.debug("Added magnetic survey:")
self.logger.debug("B = %s"%B_i)
self.logger.debug("sigma = %s"%sigma_i)
self.logger.debug("w = %s"%w_i)
self.logger.info("Setting up magnetic model...")
magnetic_model=MagneticModel(dom, w, B, domainbuilder.getBackgroundMagneticFluxDensity(), fixPotentialAtBottom=self._fixMagneticPotentialAtBottom, coordinates=trafo)
magnetic_model.rescaleWeights(k_scale=k_scale_mapping)
#====================================================================
self.logger.info("Setting cost function...")
self.setCostFunction(InversionCostFunction(regularization,
(rho_mapping, k_mapping),
((gravity_model,0), (magnetic_model,1)) ))
def stress(self):
"""
returns current stress"""
return 2 * self.viscosity * self.stretching - self.pressure * es.kronecker(
self.domain)
def setup(self, domainbuilder,
rho0=None, drho=None, z0=None, beta=None,
w0=None, w1=None, rho_at_depth=None):
"""
Sets up the inversion parameters from a `DomainBuilder`.
:param domainbuilder: Domain builder object with gravity source(s)
:type domainbuilder: `DomainBuilder`
:param rho0: reference density, see `DensityMapping`. If not specified, zero is used.
:type rho0: ``float`` or ``Scalar``
:param drho: density scale, see `DensityMapping`. If not specified, 2750kg/m^3 is used.
:type drho: ``float`` or ``Scalar``
:param z0: reference depth for depth weighting, see `DensityMapping`. If not specified, zero is used.
:type z0: ``float`` or ``Scalar``
:param beta: exponent for depth weighting, see `DensityMapping`. If not specified, zero is used.
:type beta: ``float`` or ``Scalar``
:param w0: weighting factor for level set term regularization. If not set zero is assumed.
:type w0: ``Scalar`` or ``float``
:param w1: weighting factor for the gradient term in the regularization. If not set zero is assumed
:type w1: ``Vector`` or list of ``float``
:param rho_at_depth: value for density at depth, see `DomainBuilder`.
:type rho_at_depth: ``float`` or ``None``
"""
self.logger.info('Retrieving domain...')
dom=domainbuilder.getDomain()
trafo=makeTransformation(dom, domainbuilder.getReferenceSystem())
DIM=dom.getDim()
rho_mask = domainbuilder.getSetDensityMask()
#========================
self.logger.info('Creating mapping...')
if rho_at_depth:
rho2 = rho_mask * rho_at_depth + (1-rho_mask) * rho0
elif rho0:
rho2 = (1-rho_mask) * rho0
else:
rho2 = 0.
rho_mapping=DensityMapping(dom, rho0=rho2, drho=drho, z0=z0, beta=beta)
scale_mapping=rho_mapping.getTypicalDerivative()
#========================
self.logger.info("Setting up regularization...")
if w1 is None:
w1=[1.]*DIM
regularization=Regularization(dom, numLevelSets=1,\
w0=w0, w1=w1, location_of_set_m=rho_mask,
coordinates=trafo)
#====================================================================
self.logger.info("Retrieving gravity surveys...")
surveys=domainbuilder.getGravitySurveys()
g=[]
w=[]
for g_i,sigma_i in surveys:
w_i=es.safeDiv(1., sigma_i)
if g_i.getRank()==0:
g_i=g_i*es.kronecker(DIM)[DIM-1]
if w_i.getRank()==0:
w_i=w_i*es.kronecker(DIM)[DIM-1]
g.append(g_i)
w.append(w_i)
self.logger.debug("Added gravity survey:")
self.logger.debug("g = %s"%g_i)
self.logger.debug("sigma = %s"%sigma_i)
self.logger.debug("w = %s"%w_i)
#====================================================================
self.logger.info("Setting up model...")
forward_model=GravityModel(dom, w, g, fixPotentialAtBottom=self._fixGravityPotentialAtBottom, coordinates=trafo)
forward_model.rescaleWeights(rho_scale=scale_mapping)
#====================================================================
self.logger.info("Setting cost function...")
self.setCostFunction(InversionCostFunction(regularization, rho_mapping, forward_model))