I guess I'm glad I'm not in seismology; it looks like a whole separate culture of jargon and object definitions. Makes me wonder how its development may've been held back from the benefit of related developments in radio or DSP; and vice versa, how much is lost to signal analysis, buried in obscure geophysical journals, or just trade-specific knowledge.
The reference is here:
https://archive.org/details/bstj14-2-211/All BSTJ is public and free; it used to be hosted on the former Bell site (which was, uh, Alcatel-Lucent I think?), then they dropped it, then archive.org picked it up (good guys that they are!).
That seems to be just a note or preface for the meat of the subject here,
https://archive.org/details/bstj14-2-215/which is a little dated with regards to modern analysis and notation, but still just as foundational as ever.
The minimum phase condition seems to be violated trivially with a transmission line, or an all-pass filter like,
https://en.wikipedia.org/wiki/Bridged_T_delay_equaliserso I'm not sure where you're going with that? An all-pole filter is minimal-phase, but nothing prohibits RHP zeroes in a passive network.
It sounds like you're talking about triangle waves like this,
This is a square wave approximated with I think 15 harmonics, with the phase of all the harmonics (same phase for all harmonics in each frame) going around the circle in the animation. The Hilbert transformed version (90°) looks roughly triangular, so I wonder if that's what you are referring to? But it's clearly not a triangle wave, because a triangle wave has harmonics that go as 1/N^2, while the square goes as 1/N. Obviously, the Hilbert Square (as it were) will be much more peaky, maybe closer to a tan(theta) segment rather than a triangular segment? Or maybe it's actually triangular, with Gibbs phenomenon isolated to the peaks only (hm, infinitesimal nipples?...nevermind), but no, that wouldn't make sense, the peaks have to have nonzero power to keep the same harmonic amplitudes.
Unfortunately, no matter how experienced you are, if you aren't communicating clearly, your point will simply be missed: this is one cost of domain-specific jargon.
I've never heard "zero phase" applied to a signal (a "symmetric triangular waveform") before, admittedly I'm not terribly deep into signal processing myself but from an electronics background it just sounds like... word soup?
I assume it means something on the geophysical side -- but to show that meaning, you'll have to provide your definitions as well (in turn defined in terms of other definitions, as far down as necessary to find definitions that agree). Which inevitably means some definitions that are so natural in your field that they feel intuitively obvious.
It's, well, learning a new language, to a modest extent. It's going to be frustrating, yes.
Tim