SimPEG.electromagnetics.frequency_domain.simulation.BaseFDEMSimulation#

class SimPEG.electromagnetics.frequency_domain.simulation.BaseFDEMSimulation(mesh, survey=None, forward_only=False, permittivity=None, storeJ=False, **kwargs)[source]#

Bases: BaseEMSimulation

We start by looking at Maxwell’s equations in the electric field (\(\mathbf{e}\)) and the magnetic flux density (\(\mathbf{b}\))

\[\mathbf{C} \mathbf{e} + i \omega \mathbf{b} = \mathbf{s_m} {\mathbf{C}^{\top} \mathbf{M_{\mu^{-1}}^f} \mathbf{b} - \mathbf{M_{\sigma}^e} \mathbf{e} = \mathbf{s_e}}\]

if using the E-B formulation (Simulation3DElectricField or Simulation3DMagneticFluxDensity). Note that in this case, \(\mathbf{s_e}\) is an integrated quantity.

If we write Maxwell’s equations in terms of \(\mathbf{h}\) and current density \(\mathbf{j}\).

\[\mathbf{C}^{\top} \mathbf{M_{\rho}^f} \mathbf{j} + i \omega \mathbf{M_{\mu}^e} \mathbf{h} = \mathbf{s_m} \mathbf{C} \mathbf{h} - \mathbf{j} = \mathbf{s_e}\]

if using the H-J formulation (Simulation3DCurrentDensity or Simulation3DMagneticField). Note that here, \(\mathbf{s_m}\) is an integrated quantity.

The problem performs the elimination so that we are solving the system for \(mathbf{e}\), \(mathbf{b}\), \(mathbf{j}\) or \(mathbf{h}\).

Attributes

`Mcc`	Cell center inner product matrix.
`MccMu`	Cell center property inner product matrix.
`MccMuI`	Cell center property inner product inverse matrix.
`MccMui`	Cell center property inner product matrix.
`MccMuiI`	Cell center property inner product inverse matrix.
`MccRho`	Cell center property inner product matrix.
`MccRhoI`	Cell center property inner product inverse matrix.
`MccSigma`	Cell center property inner product matrix.
`MccSigmaI`	Cell center property inner product inverse matrix.
`Me`	Edge inner product matrix.
`MeI`	Edge inner product inverse matrix.
`MeMu`	Edge property inner product matrix.
`MeMuI`	Edge property inner product inverse matrix.
`MeMui`	Edge property inner product matrix.
`MeMuiI`	Edge property inner product inverse matrix.
`MeRho`	Edge property inner product matrix.
`MeRhoI`	Edge property inner product inverse matrix.
`MeSigma`	Edge property inner product matrix.
`MeSigmaI`	Edge property inner product inverse matrix.
`Mf`	Face inner product matrix.
`MfI`	Face inner product inverse matrix.
`MfMu`	Face property inner product matrix.
`MfMuI`	Face property inner product inverse matrix.
`MfMui`	Face property inner product matrix.
`MfMuiI`	Face property inner product inverse matrix.
`MfRho`	Face property inner product matrix.
`MfRhoI`	Face property inner product inverse matrix.
`MfSigma`	Face property inner product matrix.
`MfSigmaI`	Face property inner product inverse matrix.
`Mn`	Node inner product matrix.
`MnI`	Node inner product inverse matrix.
`MnMu`	Node property inner product matrix.
`MnMuI`	Node property inner product inverse matrix.
`MnMui`	Node property inner product matrix.
`MnMuiI`	Node property inner product inverse matrix.
`MnRho`	Node property inner product matrix.
`MnRhoI`	Node property inner product inverse matrix.
`MnSigma`	Node property inner product matrix.
`MnSigmaI`	Node property inner product inverse matrix.
`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`	matrices to be deleted if the model for conductivity/resistivity is updated
`forward_only`	If True, A-inverse not stored at each frequency in forward simulation.
`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).
`solver`	Numerical solver used in the forward simulation.
`solver_opts`	Solver-specific parameters.
`storeInnerProduct`	Whether to store inner product matrices
`storeJ`	Whether to store the sensitivity matrix
`survey`	The simulations survey.
`verbose`	Verbose progress printout.

MccI
Vol

Methods

`Jtvec`(m, v[, f])	Sensitivity transpose times a vector
`Jtvec_approx`(m, v[, f])	Approximation of the Jacobian transpose times a vector for the model provided.
`Jvec`(m, v[, f])	Sensitivity times a vector.
`Jvec_approx`(m, v[, f])	Approximation of the Jacobian times a vector for the model provided.
`MccMuDeriv`(u[, v, adjoint])	Derivative of MccProperty with respect to the model.
`MccMuIDeriv`(u[, v, adjoint])	Derivative of MccPropertyI with respect to the model.
`MccMuiDeriv`(u[, v, adjoint])	Derivative of MccProperty with respect to the model.
`MccMuiIDeriv`(u[, v, adjoint])	Derivative of MccPropertyI with respect to the model.
`MccRhoDeriv`(u[, v, adjoint])	Derivative of MccProperty with respect to the model.
`MccRhoIDeriv`(u[, v, adjoint])	Derivative of MccPropertyI with respect to the model.
`MccSigmaDeriv`(u[, v, adjoint])	Derivative of MccProperty with respect to the model.
`MccSigmaIDeriv`(u[, v, adjoint])	Derivative of MccPropertyI with respect to the model.
`MeMuDeriv`(u[, v, adjoint])	Derivative of MeProperty with respect to the model.
`MeMuIDeriv`(u[, v, adjoint])	Derivative of MePropertyI with respect to the model.
`MeMuiDeriv`(u[, v, adjoint])	Derivative of MeProperty with respect to the model.
`MeMuiIDeriv`(u[, v, adjoint])	Derivative of MePropertyI with respect to the model.
`MeRhoDeriv`(u[, v, adjoint])	Derivative of MeProperty with respect to the model.
`MeRhoIDeriv`(u[, v, adjoint])	Derivative of MePropertyI with respect to the model.
`MeSigmaDeriv`(u[, v, adjoint])	Derivative of MeProperty with respect to the model.
`MeSigmaIDeriv`(u[, v, adjoint])	Derivative of MePropertyI with respect to the model.
`MfMuDeriv`(u[, v, adjoint])	Derivative of MfProperty with respect to the model.
`MfMuIDeriv`(u[, v, adjoint])	I Derivative of MfPropertyI with respect to the model.
`MfMuiDeriv`(u[, v, adjoint])	Derivative of MfProperty with respect to the model.
`MfMuiIDeriv`(u[, v, adjoint])	I Derivative of MfPropertyI with respect to the model.
`MfRhoDeriv`(u[, v, adjoint])	Derivative of MfProperty with respect to the model.
`MfRhoIDeriv`(u[, v, adjoint])	I Derivative of MfPropertyI with respect to the model.
`MfSigmaDeriv`(u[, v, adjoint])	Derivative of MfProperty with respect to the model.
`MfSigmaIDeriv`(u[, v, adjoint])	I Derivative of MfPropertyI with respect to the model.
`MnMuDeriv`(u[, v, adjoint])	Derivative of MnProperty with respect to the model.
`MnMuIDeriv`(u[, v, adjoint])	Derivative of MnPropertyI with respect to the model.
`MnMuiDeriv`(u[, v, adjoint])	Derivative of MnProperty with respect to the model.
`MnMuiIDeriv`(u[, v, adjoint])	Derivative of MnPropertyI with respect to the model.
`MnRhoDeriv`(u[, v, adjoint])	Derivative of MnProperty with respect to the model.
`MnRhoIDeriv`(u[, v, adjoint])	Derivative of MnPropertyI with respect to the model.
`MnSigmaDeriv`(u[, v, adjoint])	Derivative of MnProperty with respect to the model.
`MnSigmaIDeriv`(u[, v, adjoint])	Derivative of MnPropertyI with respect to the model.
`dpred`([m, f])	Predicted data for the model provided.
`fields`([m])	Solve the forward problem for the fields.
`fieldsPair`	alias of `FieldsFDEM`
`getJ`(m[, f])	Method to form full J given a model m
`getJtJdiag`(m[, W, f])	Return the diagonal of JtJ
`getSourceTerm`(freq)	Evaluates the sources for a given frequency and puts them in matrix form
`make_synthetic_data`(m[, relative_error, ...])	Make synthetic data for the model and Gaussian noise provided.
`residual`(m, dobs[, f])	The data residual.