[CIG-SEISMO] Mineos problem

[Matthew Knepley]

We have a problem with the eigenfunctions calculated by Mineos at near
degenerate eigenvalues.

Mineos works fine to calculate the eigenfrequencies of normal modes, but
there is a problem for the eigenfunctions. For those different modes with
very close eigenfrequencies in the mathematical point of view(see Figure
f-l), Mineos regards them as degeneracy in the numerical point of view, and
therefore it gets a linear combination of pure R mode's and pure Stoneley
mode's eigenfunctions, i.e. the eigenfunctions are not orthogonalized. For
example, based on Okal's classification [1], 2S25  and 3S25 should be
Stoneley mode and R mode, respectively. But the eigenfunctions from Mineos
have both surface oscillations (the feature of R modes) and exponentially
decaying along CMB (the feature of Stoneley modes).(see Figure 2S25 and
3S25)

Since the eigenfunction is not calculated properly, the group velocity is
also not reliable. According to Okal's paper [1], for each branch of R
modes or Stoneley modes, the group velocity should be continuous. And we
notice that there are some "bad points" in the group velocity picture,
which are exactly the modes we mention before. (see Figure groupV_R2)

What eigensolver is being used inside Mineos? The standard symmetric
eigensolvers in LAPACK handle this problem I believe.

  Thanks,

    Jingchen and Matt

References:

[1] Okal, Emile A. "A physical classification of the earth's spheroidal
modes." Journal of Physics of the Earth 26.1 (1978): 75-103.
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