This is the Jupyter Notebook, an interactive coding and computation environment. For this lab, you do not have to write any code, you will only be running it.
To use the notebook:
%matplotlib inline
from IPython.display import display
from em_examples.PlanewaveWidgetTD import PlanewaveWidget, InteractivePlaneProfile
from em_examples.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()
Q = dwidget.InteractivePlaneWave()
display(Q)
display(InteractivePlaneProfile())