def test_transforms_logMap_reciprocalMap(self):
# Note that log/reciprocal maps can be kinda finicky, so we are being
# explicit about the random seed.
v2 = np.r_[0.40077291, 0.1441044, 0.58452314, 0.96323738, 0.01198519,
0.79754415]
dv2 = np.r_[0.80653921, 0.13132446, 0.4901117, 0.03358737, 0.65473762,
0.44252488]
v3 = np.r_[0.96084865, 0.34385186, 0.39430044, 0.81671285, 0.65929109,
0.2235217, 0.87897526, 0.5784033, 0.96876393, 0.63535864,
0.84130763, 0.22123854]
dv3 = np.r_[0.96827838, 0.26072111, 0.45090749, 0.10573893, 0.65276365,
0.15646586, 0.51679682, 0.23071984, 0.95106218, 0.14201845,
0.25093564, 0.3732866]
maps = Maps.LogMap(self.mesh2)
self.assertTrue(maps.test(v2, dx=dv2))
maps = Maps.LogMap(self.mesh3)
self.assertTrue(maps.test(v3, dx=dv3))
maps = Maps.ReciprocalMap(self.mesh2)
self.assertTrue(maps.test(v2, dx=dv2))
maps = Maps.ReciprocalMap(self.mesh3)
self.assertTrue(maps.test(v3, dx=dv3))
ind_active = mesh.gridCC[:, 2] < 0.
active_map = Maps.InjectActiveCells(mesh, ind_active, air_value)
# Define the model
model = background_value * np.ones(ind_active.sum())
ind_layer = ((mesh.gridCC[ind_active, 2] > -20.) &
(mesh.gridCC[ind_active, 2] < -0))
model[ind_layer] = layer_value
ind_pipe = ((mesh.gridCC[ind_active, 0] < 10.) &
(mesh.gridCC[ind_active, 2] > -50.) &
(mesh.gridCC[ind_active, 2] < 0.))
model[ind_pipe] = pipe_value
# Define a single mapping from model to mesh
exponential_map = Maps.ExpMap()
reciprocal_map = Maps.ReciprocalMap()
model_map = Maps.ComboMap([active_map, reciprocal_map, exponential_map])
# Plotting
fig = plt.figure(figsize=(5, 5))
ax = fig.add_subplot(111)
mesh.plotImage(model_map * model, ax=ax, grid=True)
ax.set_title('Cylindrically Symmetric Model')
#############################################
# Parameterized pipe model
# ------------------------
#
# Instead of defining a model value for each sub-surface cell, we can define
# the model in terms of a small number of parameters. Here we parameterize the
# model as a block in a half-space. We then create a mapping which projects
def setupProblem(
mesh, muMod, sigmaMod, prbtype='e', invertMui=False,
sigmaInInversion=False, freq=1.
):
rxcomp = ['real', 'imag']
loc = Utils.ndgrid(
[mesh.vectorCCx, np.r_[0.], mesh.vectorCCz]
)
if prbtype in ['e', 'b']:
rxfields_y = ['e', 'j']
rxfields_xz = ['b', 'h']
elif prbtype in ['h', 'j']:
rxfields_y = ['b', 'h']
rxfields_xz = ['e', 'j']
rxList_edge = [
getattr(FDEM.Rx, 'Point_{f}'.format(f=f))(
loc, component=comp, orientation=orient
)
for f in rxfields_y
for comp in rxcomp
for orient in ['y']
]
rxList_face = [
getattr(FDEM.Rx, 'Point_{f}'.format(f=f))(
loc, component=comp, orientation=orient
)
for f in rxfields_xz
for comp in rxcomp
for orient in ['x', 'z']
]
rxList = rxList_edge + rxList_face
src_loc = np.r_[0., 0., 0.]
if prbtype in ['e', 'b']:
src = FDEM.Src.MagDipole(
rxList=rxList, loc=src_loc, freq=freq
)
elif prbtype in ['h', 'j']:
ind = Utils.closestPoints(mesh, src_loc, 'Fz') + mesh.vnF[0]
vec = np.zeros(mesh.nF)
vec[ind] = 1.
src = FDEM.Src.RawVec_e(rxList=rxList, freq=freq, s_e=vec)
survey = FDEM.Survey([src])
if sigmaInInversion:
wires = Maps.Wires(
('mu', mesh.nC),
('sigma', mesh.nC)
)
muMap = Maps.MuRelative(mesh) * wires.mu
sigmaMap = Maps.ExpMap(mesh) * wires.sigma
if invertMui:
muiMap = Maps.ReciprocalMap(mesh)*muMap
prob = getattr(FDEM, 'Problem3D_{}'.format(prbtype))(
mesh, muiMap=muiMap, sigmaMap=sigmaMap
)
# m0 = np.hstack([1./muMod, sigmaMod])
else:
prob = getattr(FDEM, 'Problem3D_{}'.format(prbtype))(
mesh, muMap=muMap, sigmaMap=sigmaMap
)
m0 = np.hstack([muMod, sigmaMod])
else:
muMap = Maps.MuRelative(mesh)
if invertMui:
muiMap = Maps.ReciprocalMap(mesh) * muMap
prob = getattr(FDEM, 'Problem3D_{}'.format(prbtype))(
mesh, sigma=sigmaMod, muiMap=muiMap
)
# m0 = 1./muMod
else:
prob = getattr(FDEM, 'Problem3D_{}'.format(prbtype))(
mesh, sigma=sigmaMod, muMap=muMap
)
m0 = muMod
prob.pair(survey)
return m0, prob, survey
