John A. Chulick, Robert B. Herrmann; The Relation Between mLg And ML, for California Earthquakes: Observations and Modeling. Seismological Research Letters ; 57 (3): 95–102. doi: https://doi.org/10.1785/gssrl.57.3.95
An extension of the study of Herrmann and Nuttli (1982) on the relation between the mLg and ML magnitude scales is made using the California strong motion data base. The technique of Kanamori and Jennings (1978) for synthesizing Wood-Anderson seismograms from acceleration time histories was easily extended to synthesize equivalent WWSSN short period seismograms. The mLg and ML magnitudes so obtained are highly correlated, with the mLg value being at least 0.30 magnitude units larger than the corresponding ML value. Using the parameters available in random vibration theory simulation, observed magnitudes and peak velocities and accelerations can be easily modeled as a function of distance.