simpeg.potential_fields.magnetics.Simulation3DDifferential

class simpeg.potential_fields.magnetics.Simulation3DDifferential(mesh, survey=None, mu=None, muMap=None, rem=None, remMap=None, storeJ=False, solver_dtype=<class 'numpy.float64'>, **kwargs)

Bases: BaseMagneticPDESimulation

A secondary field simulation for magnetic data.

Parameters:

meshdiscretize.base.BaseMesh

surveymagnetics.survey.Survey

mufloat, array_like

Magnetic Permeability Model (H/ m). Set this for forward modeling or to fix while inverting for remanence. This is used if muMap is None.

muMapsimpeg.maps.IdentityMap, optional

The mapping used to go from the simulation model to mu. Set this to invert for mu.

remfloat, array_like

Magnetic Polarization \(\mu_0 \mathbf{M}\) (nT). Set this for forward modeling or to fix remanent magnetization while inverting for permeability. This is used if remMap is None.

remMapsimpeg.maps.IdentityMap, optional

The mapping used to go from the simulation model to \(\mu_0 \mathbf{M}\). Set this to invert for \(\mu_0 \mathbf{M}\).

storeJ: bool

Whether to store the sensitivity matrix. If set to True

solver_dtype: dtype, optional

Data type to use for the matrix that gets passed to the solver. Default to numpy.float64.

Attributes

Mcc	Get cell inner product matrix.
MccI	Get inverse of cell inner product matrix.
MccMu	Get cell center property inner product matrix.
MccMuI	Get cell center property inner product inverse matrix.
MccMui	Get cell center property inner product matrix.
MccMuiI	Get cell center property inner product inverse matrix.
Me	Get edge inner product matrix.
MeI	Get inverse of edge inner product matrix.
MeMu	Get edge property inner product matrix.
MeMuI	Get edge property inner product inverse matrix.
MeMui	Get edge property inner product matrix.
MeMuiI	Get edge property inner product inverse matrix.
Mf	Get face inner product matrix.
MfI	Get inverse of face inner product matrix.
MfMu	Get face property inner product matrix.
MfMuI	Get face property inner product inverse matrix.
MfMui	Get face property inner product matrix.
MfMuiI	Get face property inner product inverse matrix.
Mn	Get node inner product matrix.
MnI	Get inverse of node inner product matrix.
MnMu	Get node property inner product matrix.
MnMuI	Get node property inner product inverse matrix.
MnMui	Get node property inner product matrix.
MnMuiI	Get node property inner product inverse matrix.
Vol	Get volumes.
clean_on_model_update	A list of solver objects to clean when the model is updated
counter	SimPEG Counter object to store iterations and run-times.
deleteTheseOnModelUpdate	HasModel.deleteTheseOnModelUpdate has been deprecated.
mesh	Mesh for the simulation.
model	The inversion model.
mu	Magnetic permeability (h/m) physical property model.
muDeriv	Derivative of Magnetic Permeability (H/m) wrt the model.
muMap	Mapping of the inversion model to Magnetic Permeability (H/m).
mui	Inverse magnetic permeability (m/h) physical property model.
muiDeriv	Derivative of Inverse Magnetic Permeability (m/H) wrt the model.
muiMap	Mapping of the inversion model to Inverse Magnetic Permeability (m/H).
needs_model	True if a model is necessary
rem	Magnetic polarization (nt) physical property model.
remDeriv	Derivative of Magnetic Polarization (nT) wrt the model.
remMap	Mapping of the inversion model to Magnetic Polarization (nT).
sensitivity_path	Path to directory where sensitivity file is stored.
solver	Numerical solver used in the forward simulation.
solver_dtype	Data type used by the solver.
solver_opts	Set solver-specific parameters.
storeJ	Whether to store the sensitivity matrix
survey	The magnetic survey object.
verbose	Verbose progress printout.

Methods

Jtvec(m, v[, f])	Compute the Jacobian transpose times a vector for the model provided.
Jtvec_approx(m, v[, f])	Approximation of the Jacobian transpose times a vector for the model provided.
Jvec(m, v[, f])	Compute the Jacobian times a vector for the model provided.
Jvec_approx(m, v[, f])	Approximation of the Jacobian times a vector for the model provided.
MccMuDeriv(u[, v, adjoint])	Get derivative of MccProperty with respect to the model.
MccMuIDeriv(u[, v, adjoint])	Get derivative of MccPropertyI with respect to the model.
MccMuiDeriv(u[, v, adjoint])	Get derivative of MccProperty with respect to the model.
MccMuiIDeriv(u[, v, adjoint])	Get derivative of MccPropertyI with respect to the model.
MeMuDeriv(u[, v, adjoint])	Get derivative of MeProperty with respect to the model.
MeMuIDeriv(u[, v, adjoint])	Get derivative of MePropertyI with respect to the model.
MeMuiDeriv(u[, v, adjoint])	Get derivative of MeProperty with respect to the model.
MeMuiIDeriv(u[, v, adjoint])	Get derivative of MePropertyI with respect to the model.
MfMuDeriv(u[, v, adjoint])	Get derivative of MfProperty with respect to the model.
MfMuIDeriv(u[, v, adjoint])	Get derivative of MfPropertyI with respect to the model.
MfMuiDeriv(u[, v, adjoint])	Get derivative of MfProperty with respect to the model.
MfMuiIDeriv(u[, v, adjoint])	Get derivative of MfPropertyI with respect to the model.
MnMuDeriv(u[, v, adjoint])	Get derivative of MnProperty with respect to the model.
MnMuIDeriv(u[, v, adjoint])	Get derivative of MnPropertyI with respect to the model.
MnMuiDeriv(u[, v, adjoint])	Get derivative of MnProperty with respect to the model.
MnMuiIDeriv(u[, v, adjoint])	Get derivative of MnPropertyI with respect to the model.
dpred([m, f])	Predicted data for the model provided.
fields(m)	Return the computed geophysical fields for the model provided.
magnetic_polarization([m])	Computes the total magnetic polarization \(\mu_0\mathbf{M}\).
make_synthetic_data(m[, relative_error, ...])	Make synthetic data for the model and Gaussian noise provided.
residual(m, dobs[, f])	The data residual.

getJ

Notes

This simulation solves for the magnetostatic PDE:

\[\nabla \cdot \mathbf{B} = 0\]

where the constitutive relation is specified as:

\[\mathbf{B} = \mu\mathbf{H} + \mu_0\mathbf{M_r}\]

where \(\mathbf{M_r}\) is a fixed magnetization unaffected by the inducing field and \(\mu\mathbf{H}\) is the induced magnetization.