simpeg.electromagnetics.time_domain.simulation.BaseTDEMSimulation#

class simpeg.electromagnetics.time_domain.simulation.BaseTDEMSimulation(mesh, survey=None, dt_threshold=1e-08, **kwargs)[source]#

Bases: BaseTimeSimulation, BaseEMSimulation

Base class for quasi-static TDEM simulation with finite volume.

This class is used to define properties and methods necessary for solving 3D time-domain EM problems. In the quasi-static regime, we ignore electric displacement, and Maxwell’s equations are expressed as:

\[\begin{split}\begin{align} \nabla \times \vec{e} + \frac{\partial \vec{b}}{\partial t} &= -\frac{\partial \vec{s}_m}{\partial t} \\ \nabla \times \vec{h} - \vec{j} &= \vec{s}_e \end{align}\end{split}\]

where the constitutive relations between fields and fluxes are given by:

\(\vec{j} = \sigma \vec{e}\)
\(\vec{b} = \mu \vec{h}\)

and:

\(\vec{s}_m\) represents a magnetic source term
\(\vec{s}_e\) represents a current source term

Child classes of BaseTDEMSimulation solve the above expression numerically for various cases using mimetic finite volume and backward Euler time discretization.

Parameters:

meshdiscretize.base.BaseMesh: The mesh.
surveytime_domain.survey.Survey: The time-domain EM survey.
dt_thresholdfloat: Threshold used when determining the unique time-step lengths.

Attributes

`Adcinv`	Inverse of the factored system matrix for the DC resistivity problem.
`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`	List of model-dependent attributes to clean upon model update.
`counter`	SimPEG `Counter` object to store iterations and run-times.
`deleteTheseOnModelUpdate`	matrices to be deleted if the model for conductivity/resistivity is updated
`dt_threshold`	Threshold used when determining the unique time-step lengths.
`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).
`nT`	Total number of time steps.
`needs_model`	True if a model is necessary
`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
`survey`	The TDEM survey object.
`t0`	Initial time, in seconds, for the time-dependent forward simulation.
`time_mesh`	Time mesh for easy interpolation to observation times.
`time_steps`	Time step lengths, in seconds, for the time domain simulation.
`times`	Evaluation times.
`verbose`	Verbose progress printout.

MccI
Vol

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])	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)	Compute and return the fields for the model provided.
`getInitialFields`()	Returns the fields for all sources at the initial time.
`getInitialFieldsDeriv`(src, v[, adjoint, f])	Derivative of the initial fields with respect to the model for a given source.
`getSourceTerm`(tInd)	Return the discrete source terms for the time index provided.
`make_synthetic_data`(m[, relative_error, ...])	Make synthetic data for the model and Gaussian noise provided.
`residual`(m, dobs[, f])	The data residual.