# geoana.em.tdem.vertical_magnetic_field_horizontal_loop#

geoana.em.tdem.vertical_magnetic_field_horizontal_loop(t, sigma=1.0, mu=1.25663706212e-06, radius=1.0, current=1.0, turns=1)#

Vertical transient magnetic field at the center of a horizontal loop over a halfspace.

Compute the vertical component of the transient magnetic field at the center of a circular loop on the surface of a conductive and magnetically permeable halfspace.

Parameters:
tfloat, or numpy.ndarray
sigmafloat, optional

conductivity

mufloat, optional

magnetic permeability

currentfloat, optional

current of the horizontal loop

turnsint, optional

number of turns in the horizontal loop

Returns:
hzfloat, or numpy.ndarray

The vertical magnetic field in H/m at the center of the loop. The shape will match the t input.

Notes

Equation 4.98 in Ward and Hohmann 1988

$h_z = \frac{I}{2a}\left[ \frac{3}{\sqrt{\pi} \theta a}e^{-\theta^2 a^2} + \left(1 - \frac{3}{2 \theta^2 a^2}\right)\mathrm{erf}(\theta a) \right]$

Examples

Reproducing part of Figure 4.8 from Ward and Hohmann 1988

>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> from geoana.em.tdem import vertical_magnetic_field_horizontal_loop


Calculate the field at the time given

>>> times = np.logspace(-7, -1)
>>> hz = vertical_magnetic_field_horizontal_loop(times, sigma=1E-2, radius=50)


Match the vertical magnetic field plot

>>> plt.loglog(times*1E3, hz)
>>> plt.xlabel('time (ms)')
>>> plt.ylabel('H$_z$ (A/m)')
>>> plt.show()