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
#
2D inversion of Loop-Loop EM Data
Heagy et al., 2017 1D RESOLVE and SkyTEM Bookpurnong Inversions
Heagy et al., 2017 1D RESOLVE Bookpurnong Inversion
Heagy et al., 2017 1D FDEM and TDEM inversions
1D Forward Simulation for a Single Sounding
1D Forward Simulation for a Susceptible and Chargeable Earth
3D Forward Simulation on a Cylindrical Mesh
3D Forward Simulation on a Tree Mesh
1D Inversion of for a Single Sounding