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.

$$\begin{array}{r}\mathbf{C}\mathbf{e}+i\omega \mathbf{b}={\mathbf{s}}_{\mathbf{m}}\\ {\mathbf{C}}^T{\mathbf{M}}_{{\mu }^{\mathbf{-}\mathbf{1}}}^{\mathbf{f}}\mathbf{b}-{\mathbf{M}}_{\sigma }^{\mathbf{e}}\mathbf{e}={\mathbf{s}}_{\mathbf{e}}\end{array}$$

We split up the fields and ${\mu }^{-1}$ into primary ($\mathbf{P}$) and secondary ($\mathbf{S}$) components

• $\mathbf{e}={\mathbf{e}}^{\mathbf{P}}+{\mathbf{e}}^{\mathbf{S}}$

• $\mathbf{b}={\mathbf{b}}^{\mathbf{P}}+{\mathbf{b}}^{\mathbf{S}}$

• ${\mathit{\mu }}^{\mathbf{-}\mathbf{1}}={\mathit{\mu }}^{{\mathbf{-}\mathbf{1}}^{\mathbf{P}}}+{\mathit{\mu }}^{{\mathbf{-}\mathbf{1}}^{\mathbf{S}}}$

and define a zero-frequency primary simulation, noting that the source is generated by a divergence free electric current

$$\begin{array}{r}\mathbf{C}{\mathbf{e}}^{\mathbf{P}}={\mathbf{s}}_{\mathbf{m}}^{\mathbf{P}}=0\\ {\mathbf{C}}^T{{\mathbf{M}}_{{\mu }^{\mathbf{-}\mathbf{1}}}^{\mathbf{f}}}^{\mathbf{P}}{\mathbf{b}}^{\mathbf{P}}-{\mathbf{M}}_{\sigma }^{\mathbf{e}}{\mathbf{e}}^{\mathbf{P}}={\mathbf{M}}^{\mathbf{e}}{\mathbf{s}}_{\mathbf{e}}^{\mathbf{P}}\end{array}$$

Since ${\mathbf{e}}^{\mathbf{P}}$ is curl-free, divergence-free, we assume that there is no constant field background, the ${\mathbf{e}}^{\mathbf{P}}=0$, so our primary problem is

$$\begin{array}{r}{\mathbf{e}}^{\mathbf{P}}=0\\ {\mathbf{C}}^T{{\mathbf{M}}_{{\mu }^{\mathbf{-}\mathbf{1}}}^{\mathbf{f}}}^{\mathbf{P}}{\mathbf{b}}^{\mathbf{P}}={\mathbf{s}}_{\mathbf{e}}^{\mathbf{P}}\end{array}$$

Our secondary problem is then

$$\begin{array}{r}\mathbf{C}{\mathbf{e}}^{\mathbf{S}}+i\omega {\mathbf{b}}^{\mathbf{S}}=-i\omega {\mathbf{b}}^{\mathbf{P}}\\ {\mathbf{C}}^T{\mathbf{M}}_{{\mu }^{\mathbf{-}\mathbf{1}}}^{\mathbf{f}}{\mathbf{b}}^{\mathbf{S}}-{\mathbf{M}}_{\sigma }^{\mathbf{e}}{\mathbf{e}}^{\mathbf{S}}=-{\mathbf{C}}^T{{\mathbf{M}}_{{\mu }^{\mathbf{-}\mathbf{1}}}^{\mathbf{f}}}^{\mathbf{S}}{\mathbf{b}}^{\mathbf{P}}\end{array}$$

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#

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

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3D Forward Simulation on a Cylindrical Mesh

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3D Forward Simulation on a Tree Mesh

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1D Inversion of for a Single Sounding

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