A Seismic Moment Magnitude Scale

Abstract

The goal of harmonizing earthquake magnitude scales has led researchers either to correlate existing scales or devise a new composite scale covering a wide magnitude range. While the moment magnitude (M_W) scale is widely regarded as optimal—particularly matching observed surface-wave magnitudes (M_S ≥ 7.5)—its formulation and validation have mostly focused on southern California for small to moderate earthquakes. This study extends the applicability of the M_w scale to low- and medium-magnitude earthquakes globally by placing emphasis on abundant body-wave (especially P-wave) data.Analyzing 25,708 global earthquakes (magnitude ≥ 4.5) from 1976 to 2006 using ISC and Global CMT databases, the authors developed a generalized seismic moment magnitude scale (denoted M_wg), defined as:M_wg = (log M₀ / 1.36) – 12.68 This scale is valid for M_B ≥ 3.5 and aligns the relationships among seismic moment (M₀), and body- and surface-wave magnitudes (M_B, M_S, M_W). Statistical tests reveal that M_wg offers significantly improved accuracy over Mw for small to intermediate events. Testing against 394 global radiated seismic energy values, they found that 76 % of M_wg estimates more closely matched observed energy than M_w. Since M_wg is derived from both low- and high-frequency spectra and maintains consistency across small to large events, the authors propose it as a robust magnitude estimator suitable for diverse seismic research applications.