# 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:

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

 location Location of the dipole moment Amplitude of the dipole moment of the magnetic dipole ($$A/m^2$$) mu Magnetic permeability in H/m orientation Orientation of the dipole as a normalized vector

Methods

 bPrimary(simulation) Compute primary magnetic flux density. hPrimary(simulation) Compute primary magnetic field. 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)

## 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

1D Forward Simulation for a Susceptible and Chargeable Earth 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