[magnitudes] Add Mwpd duration-amplitude moment magnitude plugin

[comoglu]

Summary

Adds Mwpd — a per-station duration–amplitude moment magnitude for large earthquakes from teleseismic P waveforms, after Lomax & Michelini (2009) (a port of the Mwpd implementation in Early-est). Unlike Mwp, which uses the peak of the displacement integral, Mwpd integrates the P-displacement over the apparent source duration T0, so it does not saturate for great events.

The change is purely additive: a new plugin directory plugins/magnitudes/mwpd/ plus one SUBDIRS(mwpd) line in plugins/magnitudes/CMakeLists.txt. No existing behaviour changes. The plugin registers an amplitude processor and a magnitude processor, both of type Mwpd (vertical broad-band, amplitude unit nm*s).

Method

• Restitute counts → ground velocity, high-pass at 0.005 Hz (Butterworth, order 2 — the Early-est BRB-HP), single-integrate to displacement.
• Accumulate the running double integral into positive/negative displacement lobes; the larger lobe is the amplitude (eq. 3 of the paper).
• Estimate the apparent source duration T0 from the high-frequency (1–5 Hz) envelope via its 90/80/50/20 %-of-peak last-crossing times.
• Integrate over min(T0, S−P, MAX_MWPD_DUR) — the S−P cap (travel-time table) keeps the integral free of S/surface-wave energy.
• M0 = C_M · ∫u dt · Δ (Tsuboi constant), Mwpd = ⅔(log10 M0 − 9.1) minus the INGV/Early-est distance correction, plus the PREM step depth correction and the duration-gated moment-scaling ramp (T0 > 90 s) for great/slow events (eq. 5a).
• Computation is progressive (setUpdateEnabled): the value updates as data stream in and finalises once T0 resolves.

Validation

Calibrated against GCMT moment magnitudes for 972 events (Mw 6.0–8.8, 2015–2026): Mwpd tracks Mw(GCMT) along the 1:1 line with slope ≈ 1.02, mean difference +0.05, σ ≈ 0.15, no saturation and no significant depth dependence — consistent with operational Early-est and with the paper (±0.2). Per-magnitude and per-depth tables and the scatter figure are in descriptions/global_mwpd.rst.

Documentation

• descriptions/global_mwpd.rst — method, processing, calibration (figure + tables), configuration, references.
• descriptions/global_mwpd.xml — per-parameter binding descriptions for scconfig.

References

• Lomax, A. & Michelini, A. (2009), Geophys. J. Int. 176, 200–214, doi:10.1111/j.1365-246X.2008.03974.x
• Tsuboi, S. et al. (1995), Bull. Seismol. Soc. Am. 85, 606–613.

[gempa-jabe]

Interesting addition, thank you. From the technical side I prefer to implement as much as possible in private namespace to not expose symbol which won't be used outside the plugin and which are cluttering the symbol table. I still have no final recipe to do that with multiple object files, but visibility(hidden) and some compiler flags could help in that regard.

[comoglu]

Thanks! Addressed in 5fd3a1b: the plugin's classes and helpers used across object files now get hidden visibility via a small MWPD_LOCAL

[jsaul]

This looks pretty good. I haven't tried it but I trust you. 👍 Certainly a very valuable addition, thanks a lot!

In your comparison with Mw(GCMT) it would seem to me that Mw is slightly but systematically overestimated for Mw around 6 - 6.5 - is this just a visual impression? Generally speaking, even small trends can be corrected for by defining a mapping Mwpd -> Mw(Mwpd) just like we have it for other Mw proxies. Please evaluate if that would make sense. Can also be added later, of course.

Technically there are some minor code formatting suggestions especially avoid one-liners like

if ( ...) { ... }

but write them as

if ( ... ) {
        ...
}