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.

Galleries and Tutorials using simpeg.electromagnetics.time_domain.simulation.BaseTDEMSimulation#

Time-domain CSEM for a resistive cube in a deep marine setting

Time-domain CSEM for a resistive cube in a deep marine setting

EM: TDEM: Permeable Target, Inductive Source

EM: TDEM: Permeable Target, Inductive Source

EM: TDEM: 1D: Inversion

EM: TDEM: 1D: Inversion

EM: TDEM: 1D: Inversion with VTEM waveform

EM: TDEM: 1D: Inversion with VTEM waveform

Heagy et al., 2017 1D RESOLVE and SkyTEM Bookpurnong Inversions

Heagy et al., 2017 1D RESOLVE and SkyTEM Bookpurnong Inversions

Heagy et al., 2017 1D FDEM and TDEM inversions

Heagy et al., 2017 1D FDEM and TDEM inversions

3D Forward Simulation for Transient Response on a Cylindrical Mesh

3D Forward Simulation for Transient Response on a Cylindrical Mesh

3D Forward Simulation with User-Defined Waveforms

3D Forward Simulation with User-Defined Waveforms

Forward Simulation Including Inductive Response

Forward Simulation Including Inductive Response