from geoscilabs.em.PlanewaveWidgetTD import PlanewaveWidget, InteractivePlaneProfile
from geoscilabs.em.VolumeWidgetPlane import InteractivePlanes, plotObj3D
We visualizae downward propagating planewave in the homogeneous earth medium with impulse excitation. With the two apps: a) Plane wave app and b) Profile app, we understand fundamental concepts of planewave propagation in time-domain.
Planewave EM solutions for homogeneous earth with impulse exictation can be expressed as
$$\mathbf{e}(t) = -E_0 \frac{(\mu\sigma)^{1/2}z}{2 \pi^{1/2} t^{3/2}} e^{-\mu\sigma z^2 / (4t)} \mathbf{u_x}$$$$ \mathbf{h}(t) = E_0 \sqrt{\dfrac{\sigma}{\pi\mu t}}\, e^{-\mu\sigma z^2/4t} \, \mathbf{u_y} $$Note that this dervation based upon quasi-static approximation, which ignores displacement currents. For detailed derivation see EM geosci.
ax = plotObj3D()
dwidget = PlanewaveWidget()
dwidget.InteractivePlaneWave()
InteractivePlaneProfile()