simpeg.electromagnetics.frequency_domain.sources.MagDipole#
- class simpeg.electromagnetics.frequency_domain.sources.MagDipole(receiver_list, frequency, location=None, moment=1.0, orientation='z', mu=1.25663706212e-06, **kwargs)[source]#
Bases:
BaseFDEMSrc
Point magnetic dipole source calculated by taking the curl of a magnetic vector potential. By taking the discrete curl, we ensure that the magnetic flux density is divergence free (no magnetic monopoles!).
This approach uses a primary-secondary in frequency. Here we show the derivation for E-B formulation noting that similar steps are followed for the H-J formulation.
\[\begin{split}\mathbf{C} \mathbf{e} + i \omega \mathbf{b} = \mathbf{s_m} \\ {\mathbf{C}^T \mathbf{M_{\mu^{-1}}^f} \mathbf{b} - \mathbf{M_{\sigma}^e} \mathbf{e} = \mathbf{s_e}}\end{split}\]We split up the fields and \(\mu^{-1}\) into primary (\(\mathbf{P}\)) and secondary (\(\mathbf{S}\)) components
\(\mathbf{e} = \mathbf{e^P} + \mathbf{e^S}\)
\(\mathbf{b} = \mathbf{b^P} + \mathbf{b^S}\)
\(\boldsymbol{\mu}^{\mathbf{-1}} = \boldsymbol{\mu}^{\mathbf{-1}^\mathbf{P}} + \boldsymbol{\mu}^{\mathbf{-1}^\mathbf{S}}\)
and define a zero-frequency primary simulation, noting that the source is generated by a divergence free electric current
\[\begin{split}\mathbf{C} \mathbf{e^P} = \mathbf{s_m^P} = 0 \\ {\mathbf{C}^T \mathbf{{M_{\mu^{-1}}^f}^P} \mathbf{b^P} - \mathbf{M_{\sigma}^e} \mathbf{e^P} = \mathbf{M^e} \mathbf{s_e^P}}\end{split}\]Since \(\mathbf{e^P}\) is curl-free, divergence-free, we assume that there is no constant field background, the \(\mathbf{e^P} = 0\), so our primary problem is
\[\begin{split}\mathbf{e^P} = 0 \\ {\mathbf{C}^T \mathbf{{M_{\mu^{-1}}^f}^P} \mathbf{b^P} = \mathbf{s_e^P}}\end{split}\]Our secondary problem is then
\[\begin{split}\mathbf{C} \mathbf{e^S} + i \omega \mathbf{b^S} = - i \omega \mathbf{b^P} \\ {\mathbf{C}^T \mathbf{M_{\mu^{-1}}^f} \mathbf{b^S} - \mathbf{M_{\sigma}^e} \mathbf{e^S} = -\mathbf{C}^T \mathbf{{M_{\mu^{-1}}^f}^S} \mathbf{b^P}}\end{split}\]- Parameters:
- receiver_list
list
of
simpeg.electromagnetics.frequency_domain.receivers.BaseRx
A list of FDEM receivers
- frequency
float
Source frequency
- location(
dim
)numpy.ndarray
, default:numpy.r_
[0., 0., 0.] Source location.
- moment
float
Magnetic dipole moment amplitude
- orientation{‘z’, x’, ‘y’}
or
(dim
)numpy.ndarray
Orientation of the dipole.
- mu
float
Background magnetic permeability
- receiver_list
Attributes
Source frequency
Integrated source term
Location of the dipole
Amplitude of the dipole moment of the magnetic dipole (\(A/m^2\))
Magnetic permeability in H/m
Number of data associated with the source.
Orientation of the dipole as a normalized vector
List of receivers associated with the source
Universal unique identifier
Vector number of data.
Methods
bPrimary
(simulation)Compute primary magnetic flux density.
bPrimaryDeriv
(simulation, v[, adjoint])Compute derivative of primary magnetic flux density times a vector
ePrimary
(simulation)Compute primary electric field
ePrimaryDeriv
(simulation, v[, adjoint])Compute derivative of primary electric field times a vector
eval
(simulation)Return magnetic and electric source terms
evalDeriv
(simulation[, v, adjoint])Return derivative of the magnetic and electric source terms with respect to the model.
get_receiver_indices
(receivers)Get indices for a subset of receivers within the source's receivers list.
hPrimary
(simulation)Compute primary magnetic field.
hPrimaryDeriv
(simulation, v[, adjoint])Compute derivative of primary magnetic field times a vector
jPrimary
(simulation)Compute primary current density
jPrimaryDeriv
(simulation, v[, adjoint])Compute derivative of primary current density times a vector
s_e
(simulation)Electric source term (s_e)
s_eDeriv
(simulation, v[, adjoint])Derivative of electric source term with respect to the inversion model
s_m
(simulation)Magnetic source term (s_m)
s_mDeriv
(simulation, v[, adjoint])Derivative of magnetic source term with respect to the inversion model
Galleries and Tutorials using simpeg.electromagnetics.frequency_domain.sources.MagDipole
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Heagy et al., 2017 1D RESOLVE and SkyTEM Bookpurnong Inversions

Heagy et al., 2017 1D RESOLVE Bookpurnong Inversion

1D Forward Simulation for a Susceptible and Chargeable Earth