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

Ranjit DAS Das, Arindam DAS

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.