Update skindepth.rst #563
Update skindepth.rst #563
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add minus to beta in A(z)
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| .. math:: | ||
| A(z) = A_0 e^{\beta z} | ||
| A(z) = A_0 e^{-\beta z} |
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must be minus in order to attenuate the amplitude.
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If it is positive, the "z" values must be negative. I think we can clarify this in some sentences. For example "z subsurface is between zero and -infinity". That is because, in several books, the "z" is positive, thus, the beta value in the amplitude equation must be with a minus.
thast
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thast
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Hi @PAULGOYES,
Thank you for your contribution.
EM geosci is defined with a "Z positive is up" convention. See for example the harmonic planes derivation page (and especially figure 44): https://em.geosci.xyz/content/maxwell1_fundamentals/harmonic_planewaves_homogeneous/derivation.html
I thus believe the equation is correct as it is, with a positive sign. The negative is included in the z-value.
I can leave this PR open for now if you wish to propose some changes in the wording to make things more clear. I can also close the PR and let you create a new one. Let me know what you prefer.
Thanks again.
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please, maybe it will be more clear if we add some comment like "in this derivation is used the "z positive is up" convention". Something like this: For a downgoing planewave, where is used the "z positive is up" convention, the attenuation formula is given by: ... |
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Hello @thast, I spoke with my students and I found why they are confused. This is because in Fig. 44 the convention is "depth is negative in the subsurface" so, it does not need the minus in the attenuation equation. However, if you check the first experiment in "Response of a layered Earth to a plane wave" you can see this: In the subsurface the depth is positive, and "in the air media" has depth-negative. In addition, the attenuation equation on the same page (see eq 422) has the minus. |
update equation 422
update de eq 144 and some typo changes
Update MT_N_layered_Earth.rst
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add minus to beta in A(z)