def test_sphericalInclusions(self):
mesh = Mesh.TensorMesh([4, 5, 3])
mapping = Maps.SelfConsistentEffectiveMedium(
mesh, sigma0=1e-1, sigma1=1.
)
m = np.abs(np.random.rand(mesh.nC))
mapping.test(m=m, dx=0.05, num=3)
def test_spheroidalInclusions(self):
mesh = Mesh.TensorMesh([4, 3, 2])
mapping = Maps.SelfConsistentEffectiveMedium(
mesh, sigma0=1e-1, sigma1=1., alpha0=0.8, alpha1=0.9, rel_tol=1e-8
)
m = np.abs(np.random.rand(mesh.nC))
mapping.test(m=m, dx=0.05, num=3)
def run(plotIt=True):
nC = 40
de = 1.
h = np.ones(nC) * de / nC
M = Mesh.TensorMesh([h, h])
y = np.linspace(M.vectorCCy[0], M.vectorCCx[-1], int(np.floor(nC / 4)))
rlocs = np.c_[0 * y + M.vectorCCx[-1], y]
rx = StraightRay.Rx(rlocs, None)
srcList = [
StraightRay.Src(loc=np.r_[M.vectorCCx[0], yi], rxList=[rx]) for yi in y
]
# phi model
phi0 = 0
phi1 = 0.65
phitrue = Utils.ModelBuilder.defineBlock(M.gridCC, [0.4, 0.6], [0.6, 0.4],
[phi1, phi0])
knownVolume = np.sum(phitrue * M.vol)
print('True Volume: {}'.format(knownVolume))
# Set up true conductivity model and plot the model transform
sigma0 = np.exp(1)
sigma1 = 1e4
if plotIt:
fig, ax = plt.subplots(1, 1)
sigmaMapTest = Maps.SelfConsistentEffectiveMedium(nP=1000,
sigma0=sigma0,
sigma1=sigma1,
rel_tol=1e-1,
maxIter=150)
testphis = np.linspace(0., 1., 1000)
sigetest = sigmaMapTest * testphis
ax.semilogy(testphis, sigetest)
ax.set_title('Model Transform')
ax.set_xlabel('$\\varphi$')
ax.set_ylabel('$\sigma$')
sigmaMap = Maps.SelfConsistentEffectiveMedium(M,
sigma0=sigma0,
sigma1=sigma1)
# scale the slowness so it is on a ~linear scale
slownessMap = Maps.LogMap(M) * sigmaMap
# set up the true sig model and log model dobs
sigtrue = sigmaMap * phitrue
# modt = Model.BaseModel(M);
slownesstrue = slownessMap * phitrue # true model (m = log(sigma))
# set up the problem and survey
survey = StraightRay.Survey(srcList)
problem = StraightRay.Problem(M, slownessMap=slownessMap)
problem.pair(survey)
if plotIt:
fig, ax = plt.subplots(1, 1)
cb = plt.colorbar(M.plotImage(phitrue, ax=ax)[0], ax=ax)
survey.plot(ax=ax)
cb.set_label('$\\varphi$')
# get observed data
dobs = survey.makeSyntheticData(phitrue, std=0.03, force=True)
dpred = survey.dpred(np.zeros(M.nC))
# objective function pieces
reg = Regularization.Tikhonov(M)
dmis = DataMisfit.l2_DataMisfit(survey)
dmisVol = Volume(mesh=M, knownVolume=knownVolume)
beta = 0.25
maxIter = 15
# without the volume regularization
opt = Optimization.ProjectedGNCG(maxIter=maxIter, lower=0.0, upper=1.0)
opt.remember('xc')
invProb = InvProblem.BaseInvProblem(dmis, reg, opt, beta=beta)
inv = Inversion.BaseInversion(invProb)
mopt1 = inv.run(np.zeros(M.nC) + 1e-16)
print('\nTotal recovered volume (no vol misfit term in inversion): '
'{}'.format(dmisVol(mopt1)))
# with the volume regularization
vol_multiplier = 9e4
reg2 = reg
dmis2 = dmis + vol_multiplier * dmisVol
opt2 = Optimization.ProjectedGNCG(maxIter=maxIter, lower=0.0, upper=1.0)
opt2.remember('xc')
invProb2 = InvProblem.BaseInvProblem(dmis2, reg2, opt2, beta=beta)
inv2 = Inversion.BaseInversion(invProb2)
mopt2 = inv2.run(np.zeros(M.nC) + 1e-16)
print('\nTotal volume (vol misfit term in inversion): {}'.format(
dmisVol(mopt2)))
# plot results
if plotIt:
fig, ax = plt.subplots(1, 1)
ax.plot(dobs)
ax.plot(dpred)
ax.plot(survey.dpred(mopt1), 'o')
ax.plot(survey.dpred(mopt2), 's')
ax.legend(['dobs', 'dpred0', 'dpred w/o Vol', 'dpred with Vol'])
fig, ax = plt.subplots(1, 3, figsize=(16, 4))
cb0 = plt.colorbar(M.plotImage(phitrue, ax=ax[0])[0], ax=ax[0])
cb1 = plt.colorbar(M.plotImage(mopt1, ax=ax[1])[0], ax=ax[1])
cb2 = plt.colorbar(M.plotImage(mopt2, ax=ax[2])[0], ax=ax[2])
for cb in [cb0, cb1, cb2]:
cb.set_clim([0., phi1])
ax[0].set_title('true, vol: {:1.3e}'.format(knownVolume))
ax[1].set_title('recovered(no Volume term), vol: {:1.3e} '.format(
dmisVol(mopt1)))
ax[2].set_title('recovered(with Volume term), vol: {:1.3e} '.format(
dmisVol(mopt2)))
plt.tight_layout()
#
sigma_fluid = 3
sigma1 = np.logspace(1, 5, 5) # look at a range of particle conductivities
phi = np.linspace(0.0, 1, 1000) # vary the volume of particles
###############################################################################
# Construct the Mapping
# ---------------------
#
# We set the conductivity of the phase-0 material to the conductivity of the
# fluid. The mapping will then take a concentration (by volume), of phase-1
# material and compute the effective conductivity
#
scemt = Maps.SelfConsistentEffectiveMedium(sigma0=sigma_fluid, sigma1=1)
###############################################################################
# Loop over a range of particle conductivities
# --------------------------------------------
#
# We loop over the values defined as `sigma1` and compute the effective
# conductivity of the mixture for each concentration in the `phi` vector
#
sige = np.zeros([phi.size, sigma1.size])
for i, s in enumerate(sigma1):
scemt.sigma1 = s
sige[:, i] = scemt * phi
