def M(self):
"""
M: ndarray
Magnetization matrix
"""
if getattr(self, "_M", None) is None:
if self.modelType == "vector":
self._M = sp.identity(self.nC) * self.survey.source_field.parameters[0]
else:
mag = mat_utils.dip_azimuth2cartesian(
np.ones(self.nC) * self.survey.source_field.parameters[1],
np.ones(self.nC) * self.survey.source_field.parameters[2],
)
self._M = sp.vstack(
(
sdiag(mag[:, 0] * self.survey.source_field.parameters[0]),
sdiag(mag[:, 1] * self.survey.source_field.parameters[0]),
sdiag(mag[:, 2] * self.survey.source_field.parameters[0]),
)
)
return self._M
def tmi_projection(self):
if getattr(self, "_tmi_projection", None) is None:
# Convert from north to cartesian
self._tmi_projection = mat_utils.dip_azimuth2cartesian(
self.survey.source_field.parameters[1],
self.survey.source_field.parameters[2],
)
return self._tmi_projection
# Find cells active in the forward modeling (cells below surface)
ind_active = surface2ind_topo(mesh, xyz_topo)
# Define mapping from model to active cells
nC = int(ind_active.sum())
model_map = maps.IdentityMap(nP=3 * nC) # model has 3 parameters for each cell
# Define susceptibility for each cell
susceptibility_model = background_susceptibility * np.ones(ind_active.sum())
ind_sphere = model_builder.getIndicesSphere(np.r_[0.0, 0.0, -45.0], 15.0,
mesh.gridCC)
ind_sphere = ind_sphere[ind_active]
susceptibility_model[ind_sphere] = sphere_susceptibility
# Compute the unit direction of the inducing field in Cartesian coordinates
field_direction = mat_utils.dip_azimuth2cartesian(field_inclination,
field_declination)
# Multiply susceptibility model to obtain the x, y, z components of the
# effective susceptibility contribution from induced magnetization.
susceptibility_model = np.outer(susceptibility_model, field_direction)
# Define the effective susceptibility contribution for remanent magnetization to have a
# magnitude of 0.006 SI, with inclination -45 and declination 90
remanence_inclination = -45.0
remanence_declination = 90.0
remanence_susceptibility = 0.01
remanence_model = np.zeros(np.shape(susceptibility_model))
effective_susceptibility_sphere = (
remanence_susceptibility * mat_utils.dip_azimuth2cartesian(
remanence_inclination, remanence_declination))
# Find cells active in the forward modeling (cells below surface)
ind_active = surface2ind_topo(mesh, xyz_topo)
# Define mapping from model to active cells
nC = int(ind_active.sum())
model_map = maps.IdentityMap(nP=3 * nC) # model has 3 parameters for each cell
# Define susceptibility for each cell
susceptibility_model = background_susceptibility * np.ones(ind_active.sum())
ind_sphere = model_builder.getIndicesSphere(np.r_[0.0, 0.0, -45.0], 15.0, mesh.gridCC)
ind_sphere = ind_sphere[ind_active]
susceptibility_model[ind_sphere] = sphere_susceptibility
# Compute the unit direction of the inducing field in Cartesian coordinates
field_direction = mat_utils.dip_azimuth2cartesian(field_inclination, field_declination)
# Multiply susceptibility model to obtain the x, y, z components of the
# effective susceptibility contribution from induced magnetization.
susceptibility_model = np.outer(susceptibility_model, field_direction)
# Define the effective susceptibility contribution for remanent magnetization to have a
# magnitude of 0.006 SI, with inclination -45 and declination 90
remanence_inclination = -45.0
remanence_declination = 90.0
remanence_susceptibility = 0.01
remanence_model = np.zeros(np.shape(susceptibility_model))
effective_susceptibility_sphere = (
remanence_susceptibility
* mat_utils.dip_azimuth2cartesian(remanence_inclination, remanence_declination)