In [ ]:
from geoscilabs.em.PlanewaveWidgetTD import PlanewaveWidget, InteractivePlaneProfile
from geoscilabs.em.VolumeWidgetPlane import InteractivePlanes, plotObj3D

Planewave propagation in a Whole-space (time-domain)

Purpose

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.

Set up

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.

In [ ]:
ax = plotObj3D()

Planewave app

Parameters:

  • Field: Type of EM fields ("Ex": electric field, "Hy": magnetic field)
  • Time: Time (s)
  • Sigma: Conductivity of homogeneous earth (S/m)
  • Scale: Choose "log" or "linear" scale
In [ ]:
dwidget = PlanewaveWidget()
dwidget.InteractivePlaneWave()

Profile app

We visualize EM fields at vertical profile

Parameters:

  • Field: Ex, Hy, and Impedance
  • $\sigma$ : Conductivity (S/m)
  • Scale: Log10 or Linear scale
  • $t$: Time
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InteractivePlaneProfile()
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