Total magnetic fields: Dipole and Pole sources#

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.

author

Seogi Kang (@sgkang)

date

Aug 19, 2018

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

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
# inclination and declination (e.g. Vancouver)
inclination, declination = 67., 0.

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]

orientation = id_to_cartesian(inclination, declination)

dipole = static.MagneticDipoleWholeSpace(
    location=location,
    orientation=orientation,
    moment=moment
)

pole = static.MagneticPoleWholeSpace(
    location=location,
    orientation=orientation,
    moment=moment
)

Evaluate magnetic fields#

Next, we construct a grid where we want to plot the magentic fields and evaluate

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)

and define plotting code to plot an image of the amplitude of the vector field / flux as well as the streamlines

def plot_amplitude(ax, 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)')

Create subplots for plotting the results. Loop over frequencies and plot the electric and magnetic fields along a slice through the center of the dipole.

fig, ax = plt.subplots(1, 2, figsize=(12, 5))

# plot dipole vector potential
plot_amplitude(ax[0], b_total_dipole)

# plot loop vector potential
plot_amplitude(ax[1], b_total_pole)


# set the titles
ax[0].set_title("Total field: dipole")
ax[1].set_title("Total field: pole")

# format so text doesn't overlap
plt.tight_layout()
plt.show()
Total field: dipole, Total field: pole

Total running time of the script: ( 0 minutes 0.245 seconds)

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