geoana.em.static.MagneticPoleWholeSpace.magnetic_field

MagneticPoleWholeSpace.magnetic_field(xyz, coordinates='cartesian')

Compute the magnetic field produced by the static magnetic pole.

This method computes the magnetic field produced by the static magnetic pole at the set of gridded xyz locations provided. Where \(\mu\) is the magnetic permeability of the wholespace, \(m\) is the moment amplitude, \(\mathbf{r_0}\) the pole’s location and \(\mathbf{r}\) is the location at which we want to evaluate the magnetic field \(\mathbf{H}\):

\[\mathbf{G}(\mathbf{r}) = \frac{m}{4\pi} \frac{\Delta \mathbf{r}}{| \Delta \mathbf{r}|^3}\]

where

\[\mathbf{\Delta r} = \mathbf{r} - \mathbf{r_0}\]

For reference, see equation Griffiths (1999).

Parameters:

xyz(n, 3) numpy.ndarray xyz

gridded locations at which we calculate the magnetic field

coordinates: str {‘cartesian’, ‘cylindrical’}

coordinate system that the location (xyz) are provided. The solution is also returned in this coordinate system. Default: “cartesian”

Returns:

(n, 3) numpy.ndarray

The magnetic field at each observation location in the coordinate system specified in units A/m.