Seismic moment and local magnitude scales in Ridgecrest, CA from the SCEC/USGS Community Stress Drop Validation Study

We illustrate the systematic difference between moment magnitude and local magnitude caused by underlying earthquake source physics, using seismic moments submitted to the Statewide California Earthquake Center/United States Geological Survey Community Stress Drop Validation Study 2019 Ridgecrest data set. While the relationship between seismic moment and moment magnitude (M or Mw) of log₁₀(M₀) ~ 1.5* M is uniformly valid for all earthquake sizes by definition (Hanks and Kanamori, 1979), the relationship between local magnitude M_L and moment is itself magnitude dependent. For moderate events, ~3< M < ~6, M and M_L are coincident; for earthquakes smaller than ~3, M_L ~ 1.0 log₁₀ M₀ (Hanks and Boore, 1984). This is a physical consequence of the corner frequency fc becoming larger than the upper frequency of observation and implies that M_L and M differ systematically by a factor of 1.5 for these small events. While this idea is not new, we propose a new, continuous relationship between local magnitude and moment, for magnitudes 2 to 6 which extrapolates to smaller and larger magnitudes, applicable to southern California specific to the Ridgecrest region. We make use of the plethora of seismic moments as submitted by many participants of the Community Stress Drop study, compared to the Southern California Seismic Network (SCSN) catalog magnitudes. Overall, the seismic moments in the Community Study recover moment magnitude well, so we use our new M_L-M₀ to convert M_L to M, refining the SCSN operational M_Lr scale. This systematic difference of 50% in slope between local and moment magnitude at small magnitudes has implications for spectral stress drop estimates, earthquake ground motion modeling, as well as other magnitude scales and earthquake occurrence statistics.