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_listlist of simpeg.electromagnetics.frequency_domain.receivers.BaseRx

A list of FDEM receivers

frequencyfloat

Source frequency

location(dim) numpy.ndarray, default: numpy.r_[0., 0., 0.]

Source location.

momentfloat

Magnetic dipole moment amplitude

orientation{‘z’, x’, ‘y’} or (dim) numpy.ndarray

Orientation of the dipole.

mufloat

Background magnetic permeability

Attributes

frequency

Source frequency

integrate

Integrated source term

location

Location of the dipole

moment

Amplitude of the dipole moment of the magnetic dipole (\(A/m^2\))

mu

Magnetic permeability in H/m

nD

Number of data associated with the source.

orientation

Orientation of the dipole as a normalized vector

receiver_list

List of receivers associated with the source

uid

Universal unique identifier

vnD

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

2D inversion of Loop-Loop EM Data

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 Bookpurnong Inversion

Heagy et al., 2017 1D RESOLVE Bookpurnong Inversion

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

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

1D Forward Simulation for a Single Sounding

1D Forward Simulation for a Single Sounding

1D Forward Simulation for a Susceptible and Chargeable Earth

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3D Forward Simulation on a Cylindrical Mesh

3D Forward Simulation on a Cylindrical Mesh

3D Forward Simulation on a Tree Mesh

3D Forward Simulation on a Tree Mesh

1D Inversion of for a Single Sounding

1D Inversion of for a Single Sounding