Notebook: Simulation of a 1D Magnetotelluric Problem

[lheagy]

Nice work @sgkang, I like the overall layout!

General comments

• after the Purpose section, I would consider adding a Resources that includes a link to the SimPEG Mesh documentation and the MT section on EM geosci (and any other resources you think are particularly relevant). Phil's tutorials might be a good place to go as well (https://github.com/jokulhaup/directed_studies)
• in terms of print statements, I think using format is better practice, eg.

print("Smallest cell size = {min_cs}".format(min_cs = 500*np.sqrt(100/fmax) / 4. ))

Specific comments

Physics

• within the "Physics" section, the statement of the FDEM and TDEM equations is different, could we make them consistent?
  

Discretization

• In the Discretization section - we may want to provide a bit more detail in terms of showing the matrix structure of the discrete gradient (up to you on gauging the expected background of the audience).
  • We are free to use content from https://github.com/jokulhaup/directed_studies/blob/master/Final%20Drafts/Module%201%2C%20%20Setting%20up%20the%20problem%2C%20April.ipynb, provided we acknowledge Phil (doesn't show grad, but does show averaging, so that might be enough of a linear algebra primer) . Or within the question section, including a pointer to this notebook could be sufficient for now.
• In terms of the code, step 2 is very well commented, but step 1 would benefit from a few comments (eg. cs is cell size)
• for step 2, there is a lot that happens in that cell. I have included a screen shot below where I would consider breaking up the pieces (and at each step outputting a plot or statement).
  • for the physical properties, having a plot will be helpful for when you suggest going back and changing the conductivity structure
  • when you create the differential operators, using an imshow plot to show the structure would be valuable
    

What to Solve

• to simplify things a bit in the construction of the A matrix, instead of creating tempUp, tempDown,
  
  I would do it in one go and use spacing / indentation to have it look like the math

A = sp.vstack([
    sp.hstack([Grad, 1j*omega*Mmu]),
    sp.hstack([Msighat, Div])
])

Explore

• for the plotting, I would suggest using different axes (eg plt.subplots(1,2)) for the apparent resistivity and phase (and include y-axis labels :) )

[lheagy]

I am happy to help get this launched whenever you are happy with it (there is some cleanup in the doc-structure that needs to be done to get this moving!)