Limitations of Mw and M Scales: Compelling Evidence Advocating for the Das Magnitude Scale (Mwg)—A Critical Review and Analysis

Abstract Precise determination of earthquake size is cru cial for various geoscientific and engineering applications. The Moment Magnitude (Mw) scale, introduced by Kan amori in 1977, was a significant advancement. Kanamori (1977) advocated use of Mw for large earthquakes (≥ 7.5). (Hanks and Kanamori in J. Geophys. Res. 84:2348–2350) later extended the Mw scale named as M scale by considering close coincidence of three equations. The use of the moment magnitude scale M scale for magnitudes below 7.5 is not appropriate, as Eq. (1) from Purcaru and Berckhemer (Pur caru and Berckhemer in Tectonophysics 49:189–198, 1978) was specifically derived for Ms values in the range of Ms ≲ 7.0. Furthermore, the M scale has not been validated globally for magnitudes below 7.5; its validation is limited to South ern California. Additionally, the M or Mw scale is based on surface waves and may not be applicable for all earthquake depths. Furthermore, Gutenberg and Richter (Gutenberg and Richter in Bull Seismol Soc Am 46:105–145, 1956) recom mended using body waves, rather than surface waves, for the development of a magnitude scale as surface waves do not represent the earthquake source. To address these short comings, the Das Magnitude scale (Mwg) has been intro duced in recent literature (Bulletin of Seismological Society of America, Das et al. (Das et al. in Bull Seism Soc Am 109:1542–1555, 2019); Natural Hazard, 2023), incorporat ing global data during 1976–2006 with 25,708 events with observed seismic moments (Mo) and body wave magnitudes (mb), in line with the recommendations of Gutenberg and Richter (Gutenberg and Richter in Bull Seismol Soc Am 46:105–145, 1956). Recent seismological literature (Gasp erini and Lolli, (Gasperini and Lolli in Bull Seismol Soc Am, 2024)) has inaccurately critiqued Das et al. (Das et al. in Bull Seism Soc Am 109:1542–1555, 2019), stating that the M scale is adequate and suggesting that certain foun dational assumptions of the Mwg scale are inappropriate. However, our detailed analysis demonstrates that the Mwg scale is firmly grounded in robust scientific evidence and constructed on sound principles. It is important to note that all magnitude scales, including Mw, M, and Me, are devel oped using linear least squares methods. Therefore, if the fundamental assumptions underlying the Mw, M, and Me scales are considered valid, there is no justifiable reason to challenge the foundational assumptions of the Mwg scale. Mwg uses body-wave magnitude instead of surface waves and is applicable to all depths, making it more suitable for a wider range of earthquakes. Mwg is a better measure of energy release compared to Mw, providing a more accurate representation of earthquake strength. The Mwg scale dem onstrates a closer correspondence with observed mb and Ms values at a global level compared to the M scale. The aver age difference between observed mb and M is − 0.31 ± 0.30, whereas the difference between observed mb and Mwg is sig nificantly smaller at 0.008 ± 0.33 (Das et al. (Das et al. in Bull Seism Soc Am 109:1542–1555, 2019)). The uncertainty associated with the development of Mwg is limited due to its simplicity, while Mw or M involve a constant term and multiple substitutions, potentially introducing additional uncertainty. Mwg was developed and validated using global datasets, ensuring its applicability to a diverse range of seis mic events. The Mwg scale significantly reduces the statistical differences with mb and Ms compared to the larger discrepan cies observed with M, offering a more reliable framework for understanding regional energy budgets. In this manuscript, we critically compare Mw, M, and Mwg scales. We revalidated the M scale using a comprehensive global dataset, finding that it significantly deviates from observed mb (< 5.5) and Ms (6–8) within their respective applicable ranges. Furthermore, revalidation of the M scale concludes that it is not appropriate to be below 7.5.