Complementing regional moment magnitudes to GCMT: a perspective from the rebuilt International Seismological Centre Bulletin

Abstract. Seismologists and geoscientists often need earthquake catalogues for various types of research.
This input usually contains basic earthquake parameters such as location (longitude, latitude, depth, and origin time), as well as
magnitude information. For the latter, the moment magnitude Mw has become the most sought after magnitude scale in the
seismological community to characterize the size of an earthquake. In this contribution we provide an informative account of
the Mw content for the newly rebuilt Bulletin of the International Seismological Centre (ISC, http://www.isc.ac.uk, last access: May 2021),
which is regarded as the most comprehensive record of the Earth's seismicity.
From this data, we extracted a list of hypocentres with Mw from a multitude of agencies reporting data to the ISC.
We first summarize the main temporal and spatial features of the Mw provided by
global (i.e. providing results for moderate to great earthquakes worldwide)
and regional agencies (i.e. also providing results for small earthquakes in a specific area).
Following this, we discuss their comparisons, by considering not only Mw
but also the surface wave magnitude MS and short-period body wave magnitude mb.
By using the Global Centroid Moment Tensor solutions as an authoritative global agency, we identify regional agencies
that best complement it and show examples of frequency–magnitude distributions in different areas obtained both
from the Global Centroid Moment Tensor alone and complemented by Mw from regional agencies.
The work done by the regional agencies in terms of Mw is fundamental to improve our understanding of the seismicity of an area, and we call for
the implementation of procedures to compute Mw in a systematic way in areas currently not well covered in this respect, such as vast parts of
continental Asia and Africa. In addition, more studies are needed to clarify the causes of the apparent overestimation of global Mw estimations
compared to regional Mw. Such difference is also observed in the comparisons of Mw with MS and mb.
The results presented here are obtained from the dataset (Di Giacomo and Harris, 2020, https://doi.org/10.31905/J2W2M64S)
stored at the ISC Dataset Repository (http://www.isc.ac.uk/dataset_repository/, last access: May 2021).


1975), initially applied to earthquakes with M w above 5-5.5, now expanded to smaller earthquakes recorded at regional distances (Dreger and Helmberger, 1993). Other techniques instead use spectral analysis (Andrews, 1986) to obtain M 0 and other source parameters (e.g. stress drop, corner frequency; Brune, 1970). Such techniques are useful for earthquakes recorded in the local distance range as they allow M 0 computation for small earthquakes.
Since the introduction of M w , many research groups developed techniques to routinely compute it for monitoring and/or research purposes. Some seismological agencies systematically compute M w on a global scale and also in recent years at regional scale (i.e. magnitude 5 and below in a specific area). As part of the mission of the International Seismological Centre (ISC, http://www.isc.ac.uk, last access: May 2021) to collect, integrate, review, and reprocess seismic bulletins from seismological agencies around the world, the ISC Bulletin (International Seismological Centre, 2020) is, to our knowledge, the most comprehensive resource where researchers interested in M w can combine the information from global agencies and regional ones over several decades (details in the following sections).
With the completion in early 2020 of the Rebuild project (Storchak et al., 2017(Storchak et al., , 2020 of the ISC Bulletin, here we provide an overview of the M w content in the rebuilt ISC Bulletin and discuss some of its features. In particular, we outline the spatial and temporal properties of M w from global and regional agencies (Sect. 2) and then discuss their comparisons (Sect. 3) and characteristics of M w with the ISC re-computed surface wave magnitude M S and short-period body-wave magnitude m b (Sect. 4). Finally, we discuss the feasibility of complementing regional M w to global ones by showing the Gutenberg-Richter distribution in some areas where regional M w is available for a long period of time (Sect. 5).

M w in the ISC Bulletin
The ISC Bulletin (International Seismological Centre, 2020) contains the M w from a multitude of seismological agencies around the world. Each agency contributing data to the ISC Bulletin is identified with a code, and their details can be found at http://www.isc.ac.uk/iscbulletin/agencies (last access: May 2021). The aim of this work is not to outline the different techniques adopted by each agency to compute M w . Such techniques have been extensively documented in scientific literature, and readers should refer to the citations (if available) for more information on the technique of a specific agency.
Without repeating the whole process behind the production of the ISC Bulletin (see, e.g. Sect. 3 of International Seismological Centre, 2013, for a detailed overview), here we recall that the ISC, to begin with, groups the reported hypocentres and related data (e.g. arrival times, amplitudes, nodal planes, moment tensors) by physical event. Then, usually 24 to 30 months behind real-time, the ISC analysts review the Bulletin by assessing the location and magnitude (Bondár and Storchak, 2011) of selected events (usually with magnitude above 3.5) and running a series of checks, some of which include the unreviewed events (e.g. events too small and often reported by a single agency). During the review process, among other changes, events may be banished, merged or split, hypocentres (and possibly related data) may be re-associated or, in exceptional cases, deprecated. The final product is a bulletin containing the ISC relocations (if the event has been relocated) in addition to the results (e.g. hypocentres, centroid locations, magnitudes) of contributing agencies.
The ISC Bulletin 1964-2017 contains over 7 million events, and about 1.9 million of those have been reviewed. As we focus on M w in this work, we extracted from the ISC Bulletin (1964Bulletin ( -2017 a list of hypocentres with M w from reporting agencies (the ISC does not currently compute M w ). This dataset is freely available at the ISC Dataset Repository at https://doi.org/10.31905/J2W2M64S (Di Giacomo and Harris, 2020) and is the input for most of the results shown in the following sections. For simplicity, hereafter we refer to this dataset as the "DH M w List". Details on how we created the list of M w entries from the ISC Bulletin, as well as the explanation of the parameters included, can be found in Sect. 6. The DH M w List starts in 1964 (the official starting year of the ISC) and stops in 2017 (coinciding with the last complete calendar year of the reviewed ISC Bulletin at the time of writing). M w is obviously available in the ISC Bulletin from 2018 to present and also before 1964, but they are not considered here.
The DH M w List contains 210 929 entries belonging to 179 112 earthquakes. Of those earthquakes, 42 478 have M w ≥ 5.0. The ISC Bulletin 1964-2017 contains about 66 000 earthquakes with ISC m b ≥ 5.0 and about 545 000 with ISC m b < 5. Hence, M w , despite being the preferred magnitude scale by the seismological community, is not available for a significant fraction of the Earth's seismicity (see also Di Giacomo and Storchak, 2016). In total, 89 different M w authors (hereafter, we use agency and magnitude author interchangeably) are included in DH M w List. Table 1 lists the M w agency details, along with the methodology used (to the best of our knowledge), whereas their timeline is shown in Fig. 1. Only a few agencies report M w systematically or with few gaps over several years. Those include the solutions at global scale of the Global Centroid Moment Tensors project (GCMT, http://www.globalcmt.org, last access: May 2021, Dziewonski et al., 1981;Ekström et al., 2012), the National Earthquake Information Center of the US Geological Survey (NEIC, https://earthquake.usgs.gov/earthquakes/ search/, last access: May 2021, e.g. Benz and Herrmann, 2014), and, at regional scale, the National Research Institute for Earth Science and Disaster Prevention (NIED, Fukuyama et al., 1998, https://www.fnet.bosai.go.jp/top.php, D. Di Giacomo et al.: M w in the ISC Bulletin Table 1. Details of the agencies contributing with M w to the ISC Bulletin. Country refers to where the agency is based. The column M w procedure is to characterize agencies using waveform inversion techniques to obtain moment tensors (Lentas et al., 2019) or spectral fitting techniques (Havskov and Ottemöller, 1999;Havskov et al., 2020) to obtain M 0 . For several agencies to procedure is not known to us. The "×" symbol in the last column (Analysed) is to identify agencies that will be discussed in the magnitude comparison sections. Full agency details can be found by typing the agency code at http://www.isc.ac.uk/iscbulletin//agencies/ (last access: May 2021).  Kao et al., 1998;Kao and Jian, 1999). In addition, in the last ∼ 20 years there has been an increase in the agencies reporting M w to the ISC, particularly in the Americas. In the following sections, we look in more detail at the agencies reporting M w to the ISC first at global scale and then the ones operating at regional scale.

M w from global agencies
The two long-running agencies reporting M w systematically to the ISC for earthquakes occurring anywhere in the world are GCMT and NEIC. In addition, after the great Sumatra earthquake of 26 December 2004, many agencies developed fast procedures to compute M w soon after earthquake occurrence. Hence, other agencies also started computing M w for global earthquakes. Among such agencies, the Institut de Physique du Globe de Paris (IPGP, http://www.ipgp.fr/, last access: April 2021, Vallée et al., 2010;Vallée, 2013) started to report to the ISC. In the following, we give a brief summary of the M w contribution to the ISC Bulletin of these agencies. Our aim is not to assess the magnitude of completeness of the M w reporters but simply to highlight their main features.
Seismologists are very familiar with the M w provided by GCMT, and its use is quite common in scientific literature (see, e.g. Yoder et al., 2012, for an assessment of GCMT completeness). Its formal start is in 1976, and it was initiated by Harvard University, USA (Dziewonski et al., 1981). Since summer 2006 the GCMT project has been operated at the Lamont-Doherty Earth Observatory of Columbia University (Ekström et al., 2012). Figure 2 is a summary plot showing the GCMT centroid locations, along with the timeline, magnitude histograms, and the number of events per year. We will show such a plot for different agencies to summarize the time and spatial coverage of an agency and the M w range. The GCMT solutions pre-1976 are only for deep Figure 1. Timelines of the agencies contributing with M w to the ISC Bulletin. Details about each agency's code can be found by typing the agency code at http://www.isc.ac.uk/iscbulletin//agencies/ (last access: May 2021). Each symbol represents the origin time of an earthquake, and in brackets is the total number of M w for an agency. For better visibility, grey and black text and symbols refer to the agencies listed on the left and on the right, respectively. Note that 25 M w authors with fewer than 10 entries have been skipped from the DH M w List. (Huang et al., 1997) and intermediate-depth (Chen et al., 2001) earthquakes, and from 1977 to 2004 they contain mostly earthquakes with M w 5.0 and above. From 2004-2005 GCMT also computed moment tensors and M w for earthquakes down to 4.5 or even lower, as obtained from special studies (see Nettles and Hjörleifsdóttir, 2010, and further references at https://www.globalcmt.org/Events/, last access: April 2021). Due to its long-term and highly homogenous solutions, GCMT is considered the most authoritative M w agency for earthquakes worldwide and used as the reference magnitude in many seismological studies.
Soon after the earthquake occurrence and before the final GCMT solution is available, however, the M w solution of the NEIC, IPGP, and others are often used as the reference estimation of an earthquake magnitude. Figure 3 shows the summary of the NEIC M w available in the ISC Bulletin up to 2017. It has to be pointed out that currently the NEIC may obtain M w using different approaches: the M ww (Hayes et al., 2009) from W-phase (Kanamori, 1993) inversion; the M wb from body-wave inversion (based on Ammon et al., 1998, and expanded for teleseismic distances); the M wc from longperiod surface wave inversion (see Polet and Thio, 2011, and references therein). In addition, NEIC bulletins may also include the M wr from different contributors as obtained from the inversion of regional recordings (see the M wr section at https://earthquake.usgs.gov/data/comcat/#prods, last access: May 2021). The M w from NEIC does not specify the type for earthquake data prior to August 2013 in the ISC Bulletin. Appendix A contains the summary plots from August 2013 for M ww ( Figure 3 shows that the NEIC M w solutions increase in number over the years, particularly over the last 10 years. This is mostly due to the inclusion of M wr (Fig. A4) from different contributors, with M wr available even for earthquakes down to magnitude 3. Differently from the regional contributors that we consider in Sect. 2.2, M wr NEIC is not restricted to a well-defined region, as it is available for earthquakes in the Americas, Euro-Mediterranean area, parts of Asia, and the Pacific ocean. Figure A5 in Appendix A shows the summary plots for IPGP, which reports earthquakes with magnitude 5.8 and above, predominantly from subduction zones. The comparison between M w from GMCT, NEIC, and IPGP will be discussed in Sect. 3.
2.2 M w from regional agencies At regional scale several agencies report M w during different periods ( Fig. 1) and in different parts of the world (Fig. 4).  (Huang et al., 1997) and intermediate-depth (Chen et al., 2001) earthquakes are available before 1976. The map was drawn using the Generic Mapping Tools (GMT) (Wessel et al., 2013) software.
The bounding boxes of Fig. 4 are drawn from the hypocentres included in the DH M w List and are not meant as limits of the area investigated by an individual agency. For the sake of brevity we do not include summary plots for each agency here (as shown in Fig. 2), but we give priority to major regional contributors that are currently active. However, readers interested in reproducing the summary plot for a specific agency or magnitude author can use the DH M w List and the script available in Di Giacomo and Harris (2020). More details to this end are given in Sect. 6.
In North America, the major regional reporters to the ISC include the Canadian Hazards Information Service, Natural Resources Canada (agencies PGC and OTT, http://www.earthquakescanada.nrcan.gc.ca/index-eng. php, last access: April 2021, Fig. A6), the University of Alaska (UAF, http://www.uaf.edu/geology/research/ seismology-geodesy/, last access: April 2021), and, via NEIC reports, Saint Louis University (SLM, http:// www.eas.slu.edu/Department/department.html, last access: April 2021, Herrmann et al., 2011), Berkeley Seismologi-  Overview of the agencies reporting M w to the ISC at regional scale. For simplicity, only agencies with at leat 100 M w entries are shown (including agencies not reporting; see Fig. 1). Furthermore, JMA is not shown here as it covers the same region of NIED but only starting from 2016. The bounding boxes are retrieved from the hypocentres included in the DH M w List and are not meant as limits of the area monitored by an agency. The boxes are drawn to highlight the regions where M w is available from one or more agencies and areas where M w is available in the ISC Bulletin only from global agencies (e.g. vast parts of Asia, Australia, and Africa). The map was drawn using the Generic Mapping Tools (GMT) (Wessel et al., 2013) Scognamiglio et al., 2006) and other agencies currently not reporting to the ISC (e.g. ZUR_RMT, IPRG and GII, ATA, NIC). The M w from the Instituto Andaluz de Geofisica (IAG, http://www.ugr.es/ iag/, last access: April 2021, Stich et al., 2003Stich et al., , 2006Stich et al., , 2010Martín et al., 2015) and GEOMAR (GEOMR, https://www. geomar.de/, last access: April 2021, Grevemeyer et al., 2015) have been included after the Rebuild project of the ISC Bulletin (Storchak et al., 2017(Storchak et al., , 2020 from results in journal publications. With the exception of North African earthquakes reported by MED_RCMT, no active regional agency is reporting M w to the ISC for most of Africa. Past contributions come from the work of Hofstetter and Beyth (2003, and references therein, in the ISC Bulletin under agency AFAR) and the Council for Geoscience in South Africa (PRE, https://www. geoscience.org.za/, last access: April 2021) for 2003-2005. In Asia, the two largest and continuous M w contributors are NIED (Fig. 6) for the Japanese archipelago and ASIES ( Fig. 7) for the Taiwan island region. Smaller contributions in terms of M w come from the National Centre for Seismology (NDI, https://seismo.gov.in/, last access: April 2021) for the Indian subcontinent (Fig. A14) and the Badan Meteorologi, Klimatologi dan Geofisika (DJA, https://www.bmkg.go.id/ gempabumi/gempabumi-terkini.bmkg?lang=EN, last access: April 2021, for the Indonesian archipelago (Fig. A15). These last two agencies started to contribute more systematically in August 2017 and January 2017, respectively.
In Oceania, the only regional contributor is the Institute of Geological and Nuclear Sciences (WEL, http://www.gns.cri. nz/, last access: April 2021), mostly for the area surrounding New Zealand's North and South islands (Fig. A16).
Overall, the contribution of regional agencies to the ISC is important for expanding the M w data for earthquakes not usually considered by global agencies (i.e. about magnitude 5 and below). We have seen that regional agencies can cover anything from relatively small areas (e.g. BRK/NCEDC, PAS, UAF) to larger ones (e.g. NIED, SLM, SJA, MED_RCMT) and that from a temporal point of view Figure 6. The same as Fig. 2 but for NIED. The map was drawn using the Generic Mapping Tools (GMT) (Wessel et al., 2013) software. many more regional agencies started computing M w in the last 10-20 years, although gaps are present and some agencies stopped reporting or are no longer active.
In the context just described, we give special attention in the following sections to NIED and ASIES in Asia, MED_RCMT in the Euro-Mediterranean region, and the above-mentioned agencies in the Americas that currently report M w to the ISC.

M w comparisons
In this section we show the comparisons between M w GCMT (as the most homogenous and long-running agency for global earthquakes) with NEIC and selected regional agencies. The aim of such comparisons is to show the variability in M w estimates for global and regional events. The figures shown in the following also include the orthogonal regression (e.g. Bormann et al., 2007, and references therein). The regression results from this work are not meant to be used as authorita- tive formulas for magnitude conversions but are only shown for guidance to highlight similarities and/or the most significant differences in the magnitude comparisons shown here.

M w GCMT and M w NEIC
As shown in Sect. 2, NEIC can report different types of M w : M ww , M wb , M wc , and M wr . However, only from August 2013 onwards do reports from NEIC specify the procedure used to obtain M w . For this reason, we compare M w GCMT and NEIC before August 2013 (generic M w ) and from August 2013 for NEIC M ww , M wc and M wb (Fig. 8). The comparison with M wr will be included in Sect. 3.3.6. Overall, the agreement between GCMT and NEIC M w is very good, both in the period 1980-2013/07 and 2013/08-2017, as the average difference is within 0.1 magnitude units (m.u.), with 0.1 standard deviation. However, some features can still be seen, as already pointed out by Gasperini et al. (2012). Indeed, Fig. 8 shows how GCMT and NEIC agree well particularly in the magnitude range 5 to 7, whereas GCMT, with a few exceptions, is marginally larger than NEIC for earthquakes below 5 and above 7. In recent years, however, Fig. 8 shows how NEIC and GCMT M w fit each other very well, particularly with NEIC's M ww , M wc , and M wb . Figure A17 shows the comparison between M w from GCMT and IPGP. The M w from IPGP shows slightly larger values than GCMT, sometimes by up to 0.4 m.u. However, IPGP in general follows GCMT well along the 1 : 1 line and is confirmed to be an important asset for the community when it comes to rapidly assessing M w .

M w GCMT and M w from regional agencies
Since the M w from global agencies shows very good agreement at global level, here we use the authoritative M w from GCMT for the comparisons with M w from regional agen-cies. We consider M w from active agencies in the Americas (North America, Central America, and South America), the Euro-Mediterranean area, and the areas around Japan (agency NIED) and Taiwan island (agency ASIES). Finally, we give a quick overview for other agencies, excluding the Caribbean (SDD, JSN, SSNC) that have insufficient data to create comparisons with GCMT and m b and M S from the ISC.
As GCMT provides M w mostly for earthquakes with magnitude 5.0 and above (see Fig. 2), the M w shown in the following comparisons are mostly for moderate (i.e. M w between 5 and 6) and larger earthquakes. The comparisons shown here also serve to establish a hierarchy in the preference of regional agencies when there are spatial overlaps, such as in Central America (see Fig. 4). We will make use of such preferences in Sect. 5.

North America
Among the regional agencies reporting M w to the ISC in North America (Fig. 4), we show the comparisons with M w GCMT for agencies PGC/OTT, BRK/NCEDC, PAS, and SLM. All of those agencies use regional waveform inversion methodologies (Table 1). We do not consider UAF and MEX in this section as we have only a few events in common with GCMT in the DH M w List. Figure 9 shows that M w GCMT is overall marginally (about 0.1 m.u.) larger than M w given by North American agencies. Agencies PAS and BRK/NCEDC show a good agreement with GCMT as the orthogonal regression closely follows the 1 : 1 line, albeit with an average difference of about 0.1 m.u., whereas for PGC/OTT the scatter is larger, particularly for moderate earthquakes and below, and SLM seems offset by −0.1 m.u. from GCMT. For North America the regional M w preference is therefore PAS with BRK/NCEDC, followed by PGC/OTT.

Central America
Among the regional agencies reporting M w to the ISC in Central America (Fig. 4), we show the comparisons with M w GCMT for agencies INET/CATAC, UCR, and UPA. We are not aware of the procedures used by those agencies to obtain M w (Table 1). Figure 10 shows large differences between M w GCMT and M w from INET/CATAC and UCR. Agency UPA shows a better agreement with GCMT (∼ 14 % of the GCMT; UPA M w values differ by more than ±0.5 m.u.), although large differences of about 1 m.u. can occur. Agency INET/CATAC has a significant average difference with GCMT of about 0.4 m.u., whereas UCR shows a distribution similar to PGC/OTT but with larger scatter and variability (average difference = 0.2 m.u.). For this area, we will use the results from agency UPA in the following sections.

South America
Among the regional agencies reporting M w to the ISC in South America (Fig. 4), we show the comparisons with M w GCMT for agencies RSNC, GUC, FUNV, and SJA. The latter two use spectral analysis to obtain M w , whereas we have no record of the procedures used by RSNC and GUC (Table 1). The M w comparisons shown in Fig. 11 highlights  a good fit between GCMT and agency GUC for the whole magnitude range. Agency SJA shows significant deviations from GCMT in the whole magnitude range. It is more difficult to assess agency RSNC and FUNV due to the paucity of data (total number of points is 60 and 56, respectively). However, we note that RSNC shows a scatter similar to PGC/OTT for moderate earthquakes and agrees well with GCMT for strong (M w between 6 and 7) to major (M w between 7 and 8) earthquakes, whereas FUNV shows a larger scatter. Since the areas considered by GUC and SJA as well as RSCN and FUNV overlap to some extent, we give preference to GUC over SJA and to RSNC over FUNV.

Euro-Mediterranean area
This area is one of the best-monitored in the world, as several agencies report or have reported M w to the ISC (see Fig. 4). Features of the M w computed by MED_RCMT, ZUR_RMT and ROM have already been discussed in recent literature (e.g. Konstantinou and Rontogianni, 2011;Gasperini et al., 2012). For the sake of simplicity, here we focus on the M w from MED_RCMT as it is the most long-running and consistent active reporter to the ISC in this area. The left subplot in Fig. 12 shows its M w comparison with GCMT. Over about 20 years of data, we notice the good fit between GCMT and MED_RCMT over the whole magnitude range, and generally we confirm the findings of Gasperini et al. (2012). Indeed, also for MED_RCMT, as for regional M w cases discussed earlier, we notice the tendency of M w to be smaller than GCMT for earthquakes at lower magnitudes.
We checked the comparisons of the other agencies actively reporting in this area (Fig. 4) and found that IAG (M w from publications; see text for details) is in very good agreement with GCMT, whereas M w from AFAD and ROM also show the usual feature of having M w progressively smaller than GCMT going from strong (M w between 6 and 7) to light (M w between 4 and 5) earthquakes. Finally, large differences are present for agency NIC (not actively reporting M w ), whereas not enough points are available for GEOMR, ATA, BER, or IPRG/GII. In this context we give preference to M w from MED_RCMT for the entire Euro-Mediterranean area.

Japanese islands (NIED) and Taiwan island (ASIES) areas
NIED and ASIES are authoritative agencies for the Japanese archipelago and the region around Taiwan island, respectively. Both agencies show an excellent agreement with GCMT (Fig. 12). We note that among the biggest regional contributors, NIED does not show the common trend of regional M w to be smaller than GCMT for lower magnitudes. ASIES shows such a trend but it appears less prominent compared to other regional agencies.

Other agencies
Among the other agencies reporting M w , we show in Fig. A18 the comparison of GCMT with DJA, WEL, and M wr NEIC. WEL reports to the ISC in terms of M w are somewhat discontinuous, but they fit well with GCMT. For DJA the reports are also discontinuous and characterized by a subset of events with M w smaller than GCMT and another subset of events with M w larger than GCMT. Further investigations in this respect are beyond the scope of this work. Similar to other regional agencies, the M wr included in NEIC reports appears to be progressively smaller than M w GCMT as the earthquake magnitude decreases. Due to the discontinuous nature of the DJA and WEL reports and the overlap of M wr included in NEIC reports with other regional agencies, in the following sections we focus our attention to agencies in the Americas, MED_RCMT, NIED, and ASIES.

Comparisons of M S and m b from the ISC with M w
We have seen in previous sections that M w GCMT and several regional M w providers fit well for strong and major earthquakes, whereas for moderate and smaller earthquakes the variability of the differences between GCMT and regional M w values is higher, with GCMT nearly always larger than regional M w values. This observation is not new as, for example, Patton (1998) and Patton and Randall (2002) showed the tendency of GCMT to overestimate seismic moments (hence of M w ) in central Asia, particularly for lowermagnitude earthquakes. It is not the scope of this work to further investigate the reasons for such differences (Hjörleifsdóttir and Ekström, 2010), as our main aim is to highlight some features of the M w from the ISC Bulletin as an instrumental resource for further research into M w . Figure 2 shows how GCMT, although it is the authoritative agency for global earthquakes, is not systematically computing M w for earthquakes below 5. Therefore, to further assess the variability of the regional M w providers at lower magnitudes, we use the ISC re-computed M S and m b (Bondár and Storchak, 2011). The main reasons to use ISC re-computed M S and m b here are that (1) they provide many more data points below magnitude 5 than the GCMT dataset and that (2) they are often used as basis for deriving proxy M w (e.g. Scordilis, 2006;Lolli et al., 2014;Di Giacomo et al., 2015).
In Figs. 13 and 14 we show, for each regional agency discussed in previous sections, the comparisons between ISC re-computed M S and m b , respectively, with GCMT and each regional agency (the only difference here is that we grouped PAS with BRK/NCEDC). The global comparisons between GCMT M w and ISC re-computed M S and m b have been extensively discussed in literature. Therefore, Figs. 13 and 14 only include GCMT M w values for earthquakes that occurred in the same area of the corresponding regional agency (see Fig. 4 for the spatial limits of each agency). Figures 13 and 14 also show the non-linear regressions between ISC magnitudes and GCMT and regional M w agencies. The non-linear regressions have been computed similarly to Di Giacomo et al. (2015), with the difference being that in this work we did not use a global dataset split in training and validation subsets. Other non-linear models have been proposed by Lolli et al. (2014) but, as we do not aim to create new conversion relationships, we only use our nonlinear regressions to discuss features of the ISC re-computed M S and m b with GCMT and regional agencies.
The non-linear models for regional agencies shown in Figs. 13 and 14, obtained with the same regression technique, serve us as a sort of guideline for earthquakes below magnitude 6 in particular, as for large earthquakes the M S and m b relations with M w have been studied by several authors (e.g. Bormann et al., 2013, for a comprehensive overview on the subject).
Several papers have shown that M S scales with M w better than m b for strong and larger earthquakes (e.g. Scordilis, 2006). This is also confirmed by inspecting Fig. 13. Indeed, the M S ISC and M w GCMT distribution show how the nonlinear model closely follows the 1 : 1 line in the magnitude range between ∼ 5.6 and ∼ 7.7, whereas for great earthquakes M S tends to underestimate M w (Kanamori, 1983) and deviates even more significantly from the 1 : 1 line going down in magnitude for moderate and smaller earthquakes (see also Bormann et al., 2009). Similar trends can be seen for agencies MED_RCMT, NIED, ASIES, PGC/OTT, BRK/NCEDC and PAS, UPA, and GUC, although the nonlinear models below 6 are much closer to the 1 : 1 line than the GCMT model. This is not surprising considering the M w comparisons that showed how M w GCMT is generally larger than those agencies for moderate earthquakes and below. Larger deviations are observed for the other agencies. Overall, the regional M S -M w distributions appear to complement the global M S -M w distribution well, although regional variations are present (compare, e.g. MED_RCMT and ASIES), as already pointed out by Ekström and Dziewonski (1988). The difference between M S ISC and M w GCMT and all other agencies is also shown as box-and-whisker plot for bins of 0.2 m.u. of M S ISC (last subplot in Fig. 13). Despite the large scatter of M w shown by regional agencies, such differences become progressively larger as the magnitude decreases.
The comparison between m b ISC and M w GCMT is characterized by a large scatter in the whole magnitude range and shows stronger features compared to M S . Indeed, due to the early saturation of m b already for strong to major earthquakes (Kanamori, 1983), M w is, in general, significantly larger than m b . This feature is well documented in the literature; hence, we focus on the significant difference between GCMT and the other agencies for lower-magnitude earthquakes. Indeed, whilst the GCMT distribution with m b is strongly non-linear, for all other agencies the non-linear models are much closer to the 1 : 1 line than the GCMT curve. In particular, agencies MED_RCMT and ASIES appear to extend nearly linearly the m b -M w global distribution from the GCMT. Similar trends can be noticed for NIED and PGC/OTT, although with a larger scatter, whereas for other agencies the number of data points are significantly smaller and the regional m b -M w distribution appears to complement the global m b -M w distribution less clearly. As for M S , we observe a significant difference between m b -M w from GCMT and all other agencies for smaller earthquakes (last subplot in Fig. 14).

Examples of frequency-magnitude distributions
As one of the possible uses of the ISC Bulletin as a source of M w , Fig. 15 shows the frequency-magnitude distributions (FMD) for GCMT alone and GCMT complemented by regional agencies discussed above. The FMDs are used in many hazard studies and are fundamental in catalogue-based assessments of the magnitude of completeness M c for an area in a given time period. The FMDs have been obtained for the time period covered both by GCMT and the corresponding regional agency, as also outlined in the magnitude timelines of Fig. 15. The choice of the agency that best complements GCMT in a specific area has been discussed in previous sections. Figure 15 also shows M c estimations by two different methods, the median-based analysis of the segment slope by Amorese (2007) and the goodness-of-fit test by Wiemer and Wyss (2000). Other methods for estimating M c are available (see, e.g. Mignan and Woessner, 2012), but here we only use these two methods to provide two independent estimations of M c for GCMT and GCMT complemented by a regional agency. Overall, the effect of complementing the M w from a regional agency with GCMT is to improve the M c for an area, with the exception of Chile, where the recent contribution by the regional agency GUC does not yet significantly expand the GCMT contribution.
We note significant fluctuations in the FMDs for all agencies shown for the Americas, as, for example, in California and neighbouring regions (agencies PAS/BRK-NCEDC), as also shown by the large discrepancy between the M c from the goodness-of-fit test and median-based analysis of Figure 13. Comparisons between M S ISC and M w GCMT (orange dots) for regional agencies (blue circles) considered in previous sections (the only difference here is that we grouped PAS with BRK/NCEDC). The nonlinear regressions between M S ISC and M w GCMT (black solid curves) and between M S ISC with the regional agencies (solid purple curves) are also shown, along with the 1 : 1 lines (dashed dark grey). The second subplot from the left at the bottom shows the box-and-whisker plot for 0.2 M S ISC bins of the difference between M S ISC and M w GCMT (black, transparent) and M w from all other agencies (cyan). The box represents the 25 %-75 % quantile, the band inside the box represents the median, and the ends of the whiskers represent the minimum and maximum of all data. the segment slope methods. Agencies NIED, ASIES, and MED_RCMT extend the GCMT's FMDs to lower magnitudes better than other agencies. Such FMD examples further emphasize the important role of regional agencies in complementing global solutions (e.g. from GCMT).
The database identifiers (isc_evid, hypid, and magid) are included for facilitating identification of entries from users. Note that for the same event (i.e. one isc_evid) there can be from 1 to N hypid and magid entries. For some entries the n.author is different from the h.author as some reporters (e.g. NEIC) often provide magnitude values from third parties.
The entries included in the DH M w List, as extracted from the ISC Bulletin, include only the following mtype (case in- Figure 15. Magnitude timelines and frequency-magnitude distributions (FMD) for GCMT only (orange symbols) and GCMT complemented by some regional agency discussed above (blue in the timelines and black in the FMDs, with agency name reported in each subplot). The date range in the FMD panels (coinciding with the shaded grey areas in the timeline panels) in every subplot identifies the time period over which the FMD have been obtained both for GCMT alone and by complementing it with the corresponding regional agency. The filled and empty circles are cumulative and single frequencies, respectively. The dashed-dotted vertical lines (orange for GCMT only, black for GCMT and regional agency) depict the magnitude of completeness (M c ) obtained with the median-based analysis of the segment slope by Amorese (2007), whereas the dotted vertical lines depict the M c as obtained from the goodness-of-fit test by Wiemer and Wyss (2000). Note that M c values for Chile (as covered by agency GUC) are identical for GCMT and GCMT + GUC, as from the timeline the GUC contribution started only in recent years. All the M c values shown here have been obtained by using the rseismNet R package by Arnaud Mignan, available at https://github.com/amignan/rseismNet, last accessed in September 2020. Details about the M c estimation methods can be found in Mignan and Woessner (2012). sensitive): M w , M wb , M wc , M wr , M ww . This means that M w computed for rapid response purposes, such as Mwp (Tsuboi et al., 1995(Tsuboi et al., , 1999Tsuboi, 2000), MwMwp (Whitmore et al., 2002), Mwpd (Lomax et al., 2007), or proxy values such as Mw(mB) (Bormann and Saul, 2008) have been skipped.
Other M w entries in the ISC Bulletin not included in the DH M w List are those with associated uncertainty larger than 0.5 (note that unc = 0 means no formal uncertainty is associated to the magnitude value). Finally, with the exception of M w from GCMT, we skipped M w entries where dist is larger than 300 km and Hdiff > 150 km.
Below are the Perl lines used to write out the DH M w List:  (2020) we also include the Generic Mapping Tools (GMT4.5, Wessel et al., 2013) script to create the summary plots (as in Fig. 2 or 5 for any magnitude author the user may wish to visualize, as mentioned in Sect. 2.2).
Finally, users can find (see README file in Di Giacomo and Harris, 2020) the files used to create the magnitude comparisons shown in this work in dedicated subfolders.

Conclusions
The ISC Bulletin, in its rebuilt shape after the work described in Storchak et al. (2017Storchak et al. ( , 2020, is a unique resource for seismological and multidisciplinary geoscience studies. In this work we focused on the content and features of the moment magnitude M w , as it is possibly the preferred magnitude scale in the seismological community. The earliest records of M w are for deep and intermediate-depth earthquakes in the 1960s obtained from special studies by the GCMT group (Huang et al., 1997;Chen et al., 2001). Following this, since 1976 GCMT has become the authoritative global agency providing M w for moderate to great earthquakes. In recent decades other agencies also implemented procedures to compute M w for global earthquakes (e.g. NEIC and IPGC), often due to the need for having a quick but reliable assessment of an earthquake's impact soon after its occurrence (e.g. Hayes et al., 2009;Vallée et al., 2010). We have summarized the main time and spatial features of the global M w providers, and by their comparisons we confirm the findings of previous works . In brief, there is a very good agreement between such agencies for strong to great earthquakes, although minor differences are present.
In recent years, the computation of M w has been expanded to smaller earthquakes by a multitude of agencies covering anything from small areas (i.e. country-wide) to whole continents. The contributions from regional agencies are fundamental for improving seismicity records of an area. To emphasize this point, Fig. 16 shows the summary of the contribution from regional agencies if we exclude earthquakes with M w from global agencies (the only exception is M wr from NEIC, which is included in the figure). As regional agencies make up about 72 % of the earthquakes in the DH M w List, we remark the need for continuous and systematic M w solutions to be provided over a long period of time, as such datasets will be fundamental tools for a better understanding of the seismicity of an area. It would also be desirable that agencies document the procedures used over time and whether automatic or revised solutions are obtained.
The time and spatial summaries of the regional agencies highlighted the recent increase in M w providers, although the agencies currently active and having few interruptions in their contributions are located mostly in North America, Euro-Mediterranean, Japanese archipelago, and Taiwan areas. Unfortunately, large parts of the world with significant seismicity (e.g. vast parts of continental Asia and Africa) lack regional agencies reporting M w (see Figs. 4 and 16).  Fig. 2 but for earthquakes with M w from regional agencies only (i.e. earthquakes with M w from global agencies, with the exception of M wr from NEIC, are excluded). The map was drawn using the Generic Mapping Tools (GMT) (Wessel et al., 2013) software.
The M w comparisons between GCMT and regional agencies showed a characteristic already discussed in literature, i.e. a growing deviation from the 1 : 1 line for moderate to smaller earthquakes. Such deviation is usually accompanied by a larger scatter in the data points compared to earthquakes in higher magnitude ranges (e.g. magnitude 6 and above). These observations are not limited to a specific area but appear to be common in different parts of the world. In addition, the GCMT M w comparisons with the ISC-recomputed magnitudes, M S and m b , confirm such discrepancies. Indeed, GCMT appears systematically larger than regional ones for earthquakes in the same area below about magnitude 5.5, as highlighted by the nonlinear regressions shown in this work. Nearly all deviate from the 1 : 1 line more significantly for GCMT than corresponding models for regional agencies.
When multiple agencies overlap in space and time, we used magnitude comparisons to select individual regional agencies that better complement GCMT in a given area. This way we discussed examples of frequency-magnitude distributions from GCMT alone and GCMT complemented by specific regional agencies in different parts of the world. It is not surprising that by complementing GCMT with the M w of a regional agency we have shown improvements in M c estimations. The best examples of extending the GCMT FMDs to smaller magnitudes are from agencies MED_RCMT, NIED and ASIES, whereas in other areas the GCMT and the GCMT complemented by regional agencies show marked fluctuations. Although we did not aim to investigate the frequency-magnitude distributions in detail, a possible source of such fluctuations, e.g. for California, may be due to the short time window considered. Hence, we encourage agencies to continue or implement procedures for systematically computing M w for the years to come so that future works may benefit from long-running and homogenous datasets.
Finally, we point out that further investigations on the difference between M w from GCMT and regional agencies are desirable, although several papers (e.g. Patton, 1998;Patton and Randall, 2002;Hjörleifsdóttir and Ekström, 2010;Konstantinou and Rontogianni, 2011) considered this aspect. Addressing such discrepancies may have significant impacts in different types of studies (e.g. magnitude conversion relationships, ground-motion prediction equations, hazard). In particular, we envisage studies that estimate the effects of possible data censoring in M w computations in different regions, which may even partially explain the growing deviations from the 1 : 1 lines between M w GCMT and m b |M S in the lower magnitude ranges. Figure A1. The same as in Fig. 2 but for NEIC and M ww . The map was drawn using the Generic Mapping Tools (GMT) (Wessel et al., 2013) software. Figure A2. The same as in Fig. 2 but for NEIC and M wb . The map was drawn using the Generic Mapping Tools (GMT) (Wessel et al., 2013) software. Figure A3. The same as in Fig. 2 but for NEIC and M wc . The map was drawn using the Generic Mapping Tools (GMT) (Wessel et al., 2013) software. Figure A4. The same as in Fig. 2 but for NEIC and M wr . The map was drawn using the Generic Mapping Tools (GMT) (Wessel et al., 2013) software. Figure A5. The same as in Fig. 2 but for IPGP. The map was drawn using the Generic Mapping Tools (GMT) (Wessel et al., 2013) software. Figure A6. The same as in Fig. 2 but for PGC and OTT. The procedures used by this reporter are described at http://www.isc.ac.uk/ iscbulletin/agencies/OTT-MW-mags.pdf (last access: April 2021) and Mulder (2015). The map was drawn using the Generic Mapping Tools (GMT) (Wessel et al., 2013) software. Figure A7. The same as in Fig. 2 but for INET and CATAC. The map was drawn using the Generic Mapping Tools (GMT) (Wessel et al., 2013) software. Figure A8. The same as in Fig. 2 but for UPA. The map was drawn using the Generic Mapping Tools (GMT) (Wessel et al., 2013) software. Figure A9. The same as in Fig. 2 but for UCR. The map was drawn using the Generic Mapping Tools (GMT) (Wessel et al., 2013) software. Figure A10. The same as in Fig. 2 but for RSNC. The map was drawn using the Generic Mapping Tools (GMT) (Wessel et al., 2013) software. Figure A11. The same as in Fig. 2 but for FUNV. Possible rounding effects in pre-2013 M w values are visible in the timeline and histograms. The map was drawn using the Generic Mapping Tools (GMT) (Wessel et al., 2013) software. Figure A12. The same as in Fig. 2 but for GUC. The map was drawn using the Generic Mapping Tools (GMT) (Wessel et al., 2013) software. Figure A13. The same as in Fig. 2 but for SJA. The map was drawn using the Generic Mapping Tools (GMT) (Wessel et al., 2013) software. Figure A14. The same as in Fig. 2 but for NDI. The map was drawn using the Generic Mapping Tools (GMT) (Wessel et al., 2013) software. Figure A15. The same as in Fig. 2 but for DJA. The map was drawn using the Generic Mapping Tools (GMT) (Wessel et al., 2013) software. Figure A16. The same as in Fig. 2 but for WEL. The map was drawn using the Generic Mapping Tools (GMT) (Wessel et al., 2013) software. Figure A17. The same as in Fig. 8 but for GCMT and IPGP. Figure A18. The same as in Fig. 8 but for GCMT and DJA (a), GCMT and WEL (b), and GCMT and M wr NEIC (c).