# geoana.em.tdem.vertical_magnetic_flux_time_deriv_horizontal_loop#

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

Time-derivative of the vertical transient magnetic flux density at the center of a horizontal loop over a halfspace.

Compute the time-derivative of the vertical component of the transient magnetic flux density 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

radius of the horizontal loop

currentfloat, optional

current of the horizontal loop

turnsint, optional

number of turns in the horizontal loop

Returns
dbz_dtfloat, or numpy.ndarray

The vertical magnetic flux time derivative at the center of the loop. The shape will match the t input.

Examples

Reproducing part of Figure 4.8, scaled by magnetic suscpetibility, from Ward and Hohmann 1988.

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


Calculate the field at the time given

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


Match the vertical magnetic field plot

>>> plt.loglog(times*1E3, -dbz_dt, '--')
>>> plt.xlabel('time (ms)')
>>> plt.ylabel(r'$\frac{\partial b_z}{ \partial t}$ (T/s)')
>>> plt.show()