simpeg.electromagnetics.natural_source.Simulation1DPrimarySecondary

class simpeg.electromagnetics.natural_source.Simulation1DPrimarySecondary(mesh, survey=None, sigmaPrimary=None, **kwargs)

Bases: Simulation1DElectricField

A NSEM problem solving a e formulation and primary/secondary fields decomposition.

By eliminating the magnetic flux density using

\[\mathbf{b} = \frac{1}{i \omega} \left(-\mathbf{C} \mathbf{e} \right)\]

we can write Maxwell’s equations as a second order system in \(\mathbf{e}\) only:

\[\left[ \mathbf{C}^{\top} \mathbf{M_{\mu^{-1}}^e } \mathbf{C} + i \omega \mathbf{M_{\sigma}^f} \right] \mathbf{e}_{s} = i \omega \mathbf{M_{\sigma_{s}}^f } \mathbf{e}_{p}\]

which we solve for \(\mathbf{e_s}\). The total field \(\mathbf{e} = \mathbf{e_p} + \mathbf{e_s}\).

The primary field is estimated from a background model (commonly half space ).

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.
MccRho	Get cell center property inner product matrix.
MccRhoI	Get cell center property inner product inverse matrix.
MccSigma	Get cell center property inner product matrix.
MccSigmaI	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.
MeRho	Get edge property inner product matrix.
MeRhoI	Get edge property inner product inverse matrix.
MeSigma	Get edge property inner product matrix.
MeSigmaI	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.
MfRho	Get face property inner product matrix.
MfRhoI	Get face property inner product inverse matrix.
MfSigma	Get face property inner product matrix.
MfSigmaI	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.
MnRho	Get node property inner product matrix.
MnRhoI	Get node property inner product inverse matrix.
MnSigma	Get node property inner product matrix.
MnSigmaI	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.
forward_only	Whether to store the factorizations of the inverses of the system matrices.
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
permittivity	Dielectric permittivity (F/m)
rho	Electrical resistivity (ohm m) physical property model.
rhoDeriv	Derivative of Electrical resistivity (Ohm m) wrt the model.
rhoMap	Mapping of the inversion model to Electrical resistivity (Ohm m).
sensitivity_path	Path to directory where sensitivity file is stored.
sigma	Electrical conductivity (s/m) physical property model.
sigmaDeriv	Derivative of Electrical conductivity (S/m) wrt the model.
sigmaMap	Mapping of the inversion model to Electrical conductivity (S/m).
sigmaPrimary	A background model, use for the calculation of the primary fields.
solver	Numerical solver used in the forward simulation.
solver_opts	Set solver-specific parameters.
storeInnerProduct	Whether to store inner product matrices
storeJ	Whether to compute and store the sensitivity matrix.
survey	The FDEM survey object.
verbose	Verbose progress printout.

Methods

Jtvec(m, v[, f])	Compute the adjoint sensitivity matrix times a vector.
Jtvec_approx(m, v[, f])	Approximation of the Jacobian transpose times a vector for the model provided.
Jvec(m, v[, f])	Compute the sensitivity matrix times a vector.
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.
MccRhoDeriv(u[, v, adjoint])	Get derivative of MccProperty with respect to the model.
MccRhoIDeriv(u[, v, adjoint])	Get derivative of MccPropertyI with respect to the model.
MccSigmaDeriv(u[, v, adjoint])	Get derivative of MccProperty with respect to the model.
MccSigmaIDeriv(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.
MeRhoDeriv(u[, v, adjoint])	Get derivative of MeProperty with respect to the model.
MeRhoIDeriv(u[, v, adjoint])	Get derivative of MePropertyI with respect to the model.
MeSigmaDeriv(u[, v, adjoint])	Get derivative of MeProperty with respect to the model.
MeSigmaIDeriv(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.
MfRhoDeriv(u[, v, adjoint])	Get derivative of MfProperty with respect to the model.
MfRhoIDeriv(u[, v, adjoint])	Get derivative of MfPropertyI with respect to the model.
MfSigmaDeriv(u[, v, adjoint])	Get derivative of MfProperty with respect to the model.
MfSigmaIDeriv(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.
MnRhoDeriv(u[, v, adjoint])	Get derivative of MnProperty with respect to the model.
MnRhoIDeriv(u[, v, adjoint])	Get derivative of MnPropertyI with respect to the model.
MnSigmaDeriv(u[, v, adjoint])	Get derivative of MnProperty with respect to the model.
MnSigmaIDeriv(u[, v, adjoint])	Get derivative of MnPropertyI with respect to the model.
dpred([m, f])	Predicted data for the model provided.
fields([m])	Compute and return the fields for the model provided.
fieldsPair
getA(freq)	System matrix
getADeriv(freq, u, v[, adjoint])	The derivative of A wrt sigma
getJ(m[, f])	Generate the full sensitivity matrix.
getJtJdiag(m[, W, f])	Return the diagonal of \(\mathbf{J^T J}\).
getRHS(freq)	Function to return the right hand side for the system.
getRHSDeriv(freq, src, v[, adjoint])	The derivative of the RHS wrt sigma
getSourceTerm(freq)	Return the discrete source terms for the frequency provided.
make_synthetic_data(m[, relative_error, ...])	Make synthetic data for the model and Gaussian noise provided.
residual(m, dobs[, f])	The data residual.

getADeriv_mui
getADeriv_sigma