SimPEG.electromagnetics.time_domain.Simulation3DElectricField#

class SimPEG.electromagnetics.time_domain.Simulation3DElectricField(mesh, survey=None, dt_threshold=1e-08, **kwargs)[source]#

Bases: SimPEG.electromagnetics.time_domain.simulation.BaseTDEMSimulation

Solve the EB-formulation of Maxwell’s equations for the electric field, e.

Starting with

\[\nabla \times \mathbf{e} + \frac{\partial \mathbf{b}}{\partial t} = \mathbf{s_m} \ \nabla \times \mu^{-1} \mathbf{b} - \sigma \mathbf{e} = \mathbf{s_e}\]

we eliminate \(\frac{\partial b}{\partial t}\) using

\[\frac{\partial \mathbf{b}}{\partial t} = - \nabla \times \mathbf{e} + \mathbf{s_m}\]

taking the time-derivative of Ampere’s law, we see

\[\frac{\partial}{\partial t}\left( \nabla \times \mu^{-1} \mathbf{b} - \sigma \mathbf{e} \right) = \frac{\partial \mathbf{s_e}}{\partial t} \ \nabla \times \mu^{-1} \frac{\partial \mathbf{b}}{\partial t} - \sigma \frac{\partial\mathbf{e}}{\partial t} = \frac{\partial \mathbf{s_e}}{\partial t}\]

which gives us

\[\nabla \times \mu^{-1} \nabla \times \mathbf{e} + \sigma \frac{\partial\mathbf{e}}{\partial t} = \nabla \times \mu^{-1} \mathbf{s_m} + \frac{\partial \mathbf{s_e}}{\partial t}\]

Methods

Fields_Derivs

alias of SimPEG.electromagnetics.time_domain.fields.FieldsDerivativesEB

Jtvec(m, v[, f])

Jvec computes the adjoint of the sensitivity times a vector

fieldsPair

alias of SimPEG.electromagnetics.time_domain.fields.Fields3DElectricField

getAdiag(tInd)

Diagonal of the system matrix at a given time index

getAdiagDeriv(tInd, u, v[, adjoint])

Deriv of ADiag with respect to electrical conductivity

getAsubdiag(tInd)

Matrix below the diagonal

getAsubdiagDeriv(tInd, u, v[, adjoint])

Derivative of the matrix below the diagonal with respect to electrical conductivity

getRHS(tInd)

right hand side

getAdc

getAdcDeriv

getRHSDeriv

Galleries and Tutorials using SimPEG.electromagnetics.time_domain.Simulation3DElectricField#

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

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: 1D: Inversion

EM: TDEM: 1D: Inversion

EM: TDEM: 1D: Inversion
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 RESOLVE and SkyTEM Bookpurnong Inversions