Title: Automatic amplitude and period measurements for ISC magnitudes estimations

The magnitude of seismic events is a fundamental seismological measure that provides information about the size and amount of energy released. Among the variety of the standard magnitude scales, teleseismic body- and surface-wave magnitudes are the two most common and (historically) important. Seismic network operators and observatories routinely estimate these magnitudes and report their results to the ISC. However, different processing setups (e.g., Havskov et al., 2024) may result in heterogeneous datasets that could bias the magnitude computation. To increase the consistency in the ISC recomputed magnitudes, we introduced an automatic procedure for measuring the body- and surface-wave amplitudes and periods for standard body- and surface-wave magnitudes estimation (mb, mB and MS), using globally available (through FDSN services) broadband waveform data. The procedure is based on the guidelines of the International Association of Seismology and Physics of the Earth’s Interior (IASPEI) Working Group on Magnitude measurements (Magnitude WG; IASPEI 2013; Bormann and Dewey 2012) and is currently in place for the event of magnitude ≥4.5. Its main goal is to provide uniform characterization of the earthquake size by estimating its magnitude in a consistent, reliable and reproducible manner.

Definitions and formulations:


1. Teleseismic body-wave magnitudes mb and mB:
  • Short-period body-wave magnitude - mb
    • Figure: Eq1.png                   (1)
    with epicentral distances (Δ) and periods (Ͳ) in the following intervals:
    20°≤Δ≤100° and Ͳ<3.0s
    where A is a P-wave ground displacement in nm, measured from the maximum trace-amplitude in the
    P-wave train window before the PP-phase, on a vertical component of the waveform filtered in such a way that the filter replicates the response of the WWSSN short-period seismograph (WWSSN-SP, Fig. 1).

  • Broad-band body-wave magnitude - mB
    Figure: Eq2.png                   (2)

    with epicentral distances (Δ) and periods (Ͳ) in the following intervals:
    20°≤Δ≤100° and 0.2s<Ͳ<3.0s
    where A is a P-wave ground displacement in nm, measured from the maximum trace-amplitude in the
    P-phase train window before the PP-phase, at the time around Vmax value of the equivalent velocity seismogram (Vmax/2π=⟮A/T⟯max ).



    Q(Δ,h), in both equations represents attenuation function for P-waves recorded on the vertical component seismogram at an epicentral distance Δ (°) from an earthquake with a focal-depth h (km) established by Gutenberg and Richter (1956). The digital form of the corresponding attenuation table is available from the summary of the IASPEI Magnitude WG recommendation (IASPEI, 2013).



    2. Surface-wave magnitude - Ms
    Estimated for earthquakes with depth ≤ 95 km, as the analyzed events are pre-review and their depth can change after the review by the ISC analysts and the following relocation procedure.
    The adapted formulation represents a relaxed version of the IASPEI MS_20 surface-wave magnitude allowing measurements for an extended epicentral distance range and a broader periods’ interval.
    Figure: Eq3.png                   (3)

    with epicentral distances ( ∆ ) and periods T in the following intervals:
    5°≤Δ≤160° and 10.0s < T < 60.0s
    where A is vertical component ground displacement in nm measured as the maximum of the surface- wave amplitude, having the period of 10 – 60 s, on a waveform that has been filtered with the filter that replicates the response of the WWSSN long-period seismograph (WWSSN-LP).

    The Rayleigh (LR) surface-wave time windows, within which the maximum amplitude is measured, are defined based on empirically derived relations of arrival times versus epicentral distances. These relations were obtained from LR amplitude timings reported in the ISC Bulletin by the NEIC (Fig. 2) specifying the start and the end of the expected LR window for amplitude measurements (Fig. 3). Our analysis shows that this approach to defining the LR arrival time window accounts better for regional variations in surface-wave propagation compared to the time intervals suggested in Willmore (1979).



    Figure: Fig1.png


    Fig. 1. Displacement amplitude-frequency responses of the standard WWSSN short-period (SP) and long- period (LP) instruments used for teleseimic body wave (mb ) and surface-wave (MS ) amplitude measurements.     		Figure: Fig2.png Fig. 2. LR wave amplitude arrival times (green dots) reported by NEIC as the function of epicentral distance. Red lines mar the beginning and end of the empirically-defined surface-wave time window.



    The standard procedures defined by the IASPEI Magnitude WG guidelines imply that, the amplitudes (A) are measured as half the maximum deflection of the trace, either peak-to-adjacent-trough or trough- to-adjacent-peak, with the peak and trough separated by one zero-crossing. This is also known as "half peak-to-peak amplitude." For the band-limited magnitudes mb and MS , magnitude should be calculated using the true ground motion amplitude A, obtained by converting the measured maximum trace amplitude by the magnification of the simulated WWSSN-(LP, SP) instrument response at period T. This is a crucial step that ensures the accuracy of the ground motion measurements, which will be subsequently used for magnitude estimation. Periods (T) are measured as twice the time interval between the peak and adjacent trough. All the amplitude measurements have to provide the timing information. This “amplitude-phase arrival times” are measured at the zero-crossing between the peak and trough.


    Implementation details:

    The IASPEI Magnitude WG guidelines are transformed into an automated procedure for systematic measurement of the amplitudes and periods for ISC body- and surface-wave magnitudes.


    The procedure can be in summarised as follows:
    • Waveform data (BHZ components) selection, given the origin time and coordinates of an event (M≷4.5) in the ISC-Bulletin. Data are available through the ISC waveform-download system and selected for the globally-distributed stations satisfying the epicentral distance conditions and appearing in the ISC Bulletin with P- and/or S-phase arrival readings.
    • Data processing: data integrity checks and pre-processing (demeaning, detrending and resampling); estimation of the broadband traces proportional to the ground velocity and displacement; conversion to the short- and long-period traces by removing the instrumental sensitivity and applying the WWSSN instrumental responses (IASPEI 2013; Fig. 1).
    • Amplitude (A) and period (T) measurements for stations corresponding to the epicentral distance conditions of each magnitude type after the signal-to-noise ratio (SNR) checks (waveform-based and spectral-based SNR).
    A preliminary pre-processing step of the duplicate removal, addressing the issue of potential overlapping phase arrivals from event-pairs at globally distributed stations, was implemented to address the issue of the space and time complexity of the global earthquake occurrence and provide a cleaner dataset for the ISC Bulletin before the review. The ISC automated amplitude and period measurements scheme provides event station-specific measurements that are further included into the ISC Bulletin prior to review as input data with ISC as the reporter (Fig. 4) and are integrated into the standard ISC Bulletin review procedure, including the ISC magnitude estimations.

    Figure: Fig3.png

    Fig. 3. Outline of the automated amplitude and period measurement procedure workflow on an example of a selected event and station waveforms. The time windows in which the body- and surface-wave amplitude and period measurements are performed are outlined by green rectangle.

    Current status:

    The automatically measured (on monthly bases) amplitudes and periods from the ISC reporter are included into the ISC-Bulletin and reviewed by the analysts on 22 month behind the real-time time schedule. We are currently analysing the data from the events with magnitude ≥4.5 (as reported in the ISC Bulletin by at least one of the reporters) and including only the measurements corresponding to the 3teleseismic body-wave magnitude mb and surface-wave magnitude MS . Broadband teleseismic body- wave magnitude mB will be integrated into the ISC Bulletin at the late stages. The procedure was implemented from April 2024, starting with data month May 2022. An example of the ISC Bulletin call displaying the automatic ISC amplitude and period measurements is provided in Fig. 4. Figure 5 presents an example summary output figure for a selected event.

    Figure: Fig4.png

    Fig. 4. Example of an ISC Bulletin query for a selected event (evid 622516905) highlighting (in red) the automated amplitude and period measurements reported by the ISC. The station magnitudes are calculated by the using the standard procedure of the ISCloc (Bondár and Storchak 2011; Di Giacomo and Storchak 2022).




    Figure: Fig5_v2.png

    Fig. 5. Example of the automatic amplitude and period measurements for the 2022/10/05, 08:26:19.68, Mw 5.9 (GCMT) event in Peru-Ecuador border region (evid 624850030).


    Outlook:

    We are grateful to all reporters that provide data that allow us to recompute m b and M S . We aim to create a dataset of ISC own measurements for a few years before assessing the best way forward to complement the data by ISC data contributors and our own processing.

    References: 

         Bondar, I. and D. Storchak, 2011. Improved location procedures at the
International Seismological Centre, Geophys. J. Int., 186, 1220-1244, 
doi: 10.1111/j.1365-246X.2011.05107.x.
     Bormann, P. and Dewey, J.W., 2012. The new IASPEI standards for determining
magnitudes from digital data and their relation to classical magnitudes. 
In: New manual of seismological observatory practice 2 (NMSOP-2), Deutsches 
GeoForschungsZentrum GFZ, pp. 1-44.
     Di Giacomo, D. and Storchak, D. A. (2022). One hundred plus years of 
recomputed surface wave magnitude of shallow global earthquakes,
Earth Syst. Sci. Data, 14, pp. 393–409.
Gutenberg, B., and C. F. Richter (1956). Magnitude and energy of earthquakes.
Annali di Geofisica, 9, 1-15.
     Havskov, J., Ottemöller, L. and Gkika, F., 2024. Magnitude mb: Reducing
Processing‐Related Variability. Seismological Research Letters, 95(4), pp.2118-2123.
     IASPEI, 2013. Summary of Magnitude Working Group recommendations on standard
procedures for determining earthquake magnitudes from digital data, (available 
online at http://www.iaspei.org/commissions/commission-on-seismological-observation
-and-interpretation/Summary_WG_recommendations_20130327.pdf
     Willmore, P.L. (1979). Manual of Seismological Observatory Practice. World Data
Center A for Solid Earth Geophysics, Report SE-20, September 1979, Boulder, Colorado,
165 pp.; http://www.seismo.com/msop/msop79/inst/inst1.html