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, ]
mapping = maps.LogMap(self.mesh2)
self.assertTrue(mapping.test(v2, dx=dv2))
mapping = maps.LogMap(self.mesh3)
self.assertTrue(mapping.test(v3, dx=dv3))
mapping = maps.ReciprocalMap(self.mesh2)
self.assertTrue(mapping.test(v2, dx=dv2))
mapping = maps.ReciprocalMap(self.mesh3)
self.assertTrue(mapping.test(v3, dx=dv3))
# Starting/Reference Model and Mapping on Tensor Mesh # --------------------------------------------------- # # Here, we create starting and/or reference models for the inversion as # well as the mapping from the model space to the slowness. Starting and # reference models can be a constant background value or contain a-priori # structures. Here, the background is 3000 m/s. # # Define density contrast values for each unit in g/cc. Don't make this 0! # Otherwise the gradient for the 1st iteration is zero and the inversion will # not converge. background_velocity = 3000.0 # Define mapping from model space to the slowness on mesh cells model_mapping = maps.ReciprocalMap() # Define starting model starting_model = background_velocity * np.ones(mesh.nC) ############################################## # Define the Physics # ------------------ # # Here, we define the physics of the 2D straight ray tomography problem by # using the simulation class. # # Define the forward simulation. To do this we need the mesh, the survey and # the mapping from the model to the slowness value on each cell. simulation = tomo.Simulation(mesh, survey=survey, slownessMap=model_mapping)
# Define the model on subsurface cells
model = background_value * np.ones(ind_active.sum())
ind_dyke = (mesh.gridCC[ind_active, 0] > 20.0) & (mesh.gridCC[ind_active, 0] <
40.0)
model[ind_dyke] = dyke_value
ind_block = ((mesh.gridCC[ind_active, 0] > -40.0)
& (mesh.gridCC[ind_active, 0] < -10.0)
& (mesh.gridCC[ind_active, 1] > -30.0)
& (mesh.gridCC[ind_active, 1] < 30.0)
& (mesh.gridCC[ind_active, 2] > -40.0)
& (mesh.gridCC[ind_active, 2] < 0.0))
model[ind_block] = block_value
# Define a single mapping from model to mesh
exponential_map = maps.ExpMap()
reciprocal_map = maps.ReciprocalMap()
model_map = active_map * reciprocal_map * exponential_map
# Plot
fig = plt.figure(figsize=(5, 5))
ax = fig.add_subplot(111)
ind_slice = int(mesh.hy.size / 2)
mesh.plotSlice(model_map * model, normal="Y", ax=ax, ind=ind_slice, grid=True)
ax.set_title("Model slice at y = {} m".format(mesh.x0[1] +
np.sum(mesh.hy[0:ind_slice])))
plt.show()
#############################################
# Models with arbitrary shapes
# ----------------------------
#
def setupProblem(
mesh,
muMod,
sigmaMod,
prbtype="ElectricField",
invertMui=False,
sigmaInInversion=False,
freq=1.0,
):
rxcomp = ["real", "imag"]
loc = utils.ndgrid([mesh.vectorCCx, np.r_[0.0], mesh.vectorCCz])
if prbtype in ["ElectricField", "MagneticFluxDensity"]:
rxfields_y = ["ElectricField", "CurrentDensity"]
rxfields_xz = ["MagneticFluxDensity", "MagneticField"]
elif prbtype in ["MagneticField", "CurrentDensity"]:
rxfields_y = ["MagneticFluxDensity", "MagneticField"]
rxfields_xz = ["ElectricField", "CurrentDensity"]
receiver_list_edge = [
getattr(fdem.receivers, "Point{f}".format(f=f))(loc,
component=comp,
orientation=orient)
for f in rxfields_y for comp in rxcomp for orient in ["y"]
]
receiver_list_face = [
getattr(fdem.receivers, "Point{f}".format(f=f))(loc,
component=comp,
orientation=orient)
for f in rxfields_xz for comp in rxcomp for orient in ["x", "z"]
]
receiver_list = receiver_list_edge + receiver_list_face
src_loc = np.r_[0.0, 0.0, 0.0]
if prbtype in ["ElectricField", "MagneticFluxDensity"]:
src = fdem.sources.MagDipole(receiver_list=receiver_list,
location=src_loc,
frequency=freq)
elif prbtype in ["MagneticField", "CurrentDensity"]:
ind = utils.closestPoints(mesh, src_loc, "Fz") + mesh.vnF[0]
vec = np.zeros(mesh.nF)
vec[ind] = 1.0
src = fdem.sources.RawVec_e(receiver_list=receiver_list,
frequency=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,
"Simulation3D{}".format(prbtype))(mesh,
muiMap=muiMap,
sigmaMap=sigmaMap)
# m0 = np.hstack([1./muMod, sigmaMod])
else:
prob = getattr(fdem,
"Simulation3D{}".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,
"Simulation3D{}".format(prbtype))(mesh,
sigma=sigmaMod,
muiMap=muiMap)
# m0 = 1./muMod
else:
prob = getattr(fdem,
"Simulation3D{}".format(prbtype))(mesh,
sigma=sigmaMod,
muMap=muMap)
m0 = muMod
prob.survey = survey
return m0, prob, survey
