Total magnetic fields: Dipole and Pole sources

Seogi KangRowan Cockett

August 19, 2018

In this example, we plot anomalous total magnetic field from a magnetic dipole and pole targets. These targets are excited by Earth magnetic fields. We can vary the direction of the Earth magnetic field, and magnetic moment of the target.

import micropip
await micropip.install('ipywidgets')
await micropip.install('https://cdn.curvenote.com/pypi/geoana-0.5.0-py3-none-any.whl')

import numpy as np
import matplotlib.pyplot as plt
from matplotlib.colors import LogNorm
from scipy.constants import mu_0, epsilon_0
from ipywidgets import interactive

from geoana import utils, spatial
from geoana.em import static

Setup¶

define the location, orientation, and source, physical properties of the wholespace and source parameters.

mu = mu_0  # permeability of free space (this is the default)
location = np.r_[0., 0., -10.]  # location of the dipole or pole

# dipole parameters
moment = 1

Magnetostatic Dipole and Loop¶

Here, we build the geoana magnetic dipole and poie in a wholespace using the parameters defined above.

def id_to_cartesian(inclination, declination):
    ux = np.cos(inclination/180.*np.pi)*np.sin(declination/180.*np.pi)
    uy = np.cos(inclination/180.*np.pi)*np.cos(declination/180.*np.pi)
    uz = -np.sin(inclination/180.*np.pi)
    return np.r_[ux, uy, uz]

def plot_amplitude(ax, x, y, v):
    plt.colorbar(
        ax.pcolormesh(
            x, y, v.reshape(len(x), len(y), order='F')
        ), ax=ax
    )
    ax.axis('square')
    ax.set_xlabel('y (east,  m)')
    ax.set_ylabel('x (north,  m)')

def plot_fields(inclination, declination):
    orientation = id_to_cartesian(inclination, declination)
    
    dipole = static.MagneticDipoleWholeSpace(
        location=location,
        orientation=orientation,
        moment=moment
    )
    
    pole = static.MagneticPoleWholeSpace(
        location=location,
        orientation=orientation,
        moment=moment
    )
    x = np.linspace(-36, 36, 100)
    y = np.linspace(-36, 36, 100)
    xyz = utils.ndgrid([x, y, np.r_[1.]])
    
    # evaluate the magnetic field
    b_vec_dipole = dipole.magnetic_flux_density(xyz)
    b_vec_pole = pole.magnetic_flux_density(xyz)
    b_total_dipole = dipole.dot_orientation(b_vec_dipole)
    b_total_pole = pole.dot_orientation(b_vec_pole)

    fig, ax = plt.subplots(1, 2, figsize=(12, 5))
    # plot dipole vector potential
    plot_amplitude(ax[0], x, y, b_total_dipole)
    # plot loop vector potential
    plot_amplitude(ax[1], x, y, b_total_pole)

    plt.show()

# inclination and declination (e.g. Vancouver)
interactive(plot_fields, inclination=(0.,67.,1.), declination=(0., 90.))

Geoana in JupyterLite

Magnetostatic Vector Potentials: Dipole and Loop Sources