The Relationship between M and ML: A Review and Application to Induced Seismicity in the Groningen Gas Field, The Netherlands

The use of local magnitude (M-L) in seismic hazard analyses is a topic of recent debate. In regions of weak or moderate seismicity, small earthquakes (characterized by M-L) are commonly used to determine frequency-magnitude distributions (FMDs) for probabilistic seismic hazard calculations. However, empirical and theoretical studies on the relation between moment magnitude (M) and M-L for small earthquakes show a systematic difference between the two below a region-dependent magnitude threshold. This difference may introduce bias in the estimation of the frequency of larger events with given M, and consequently seismic hazard. For induced seismicity related to the Groningen gas field, this magnitude threshold is determined to be M similar to 2, with equality between M and M-L at higher magnitudes. A quadratic relation between M and M-L is derived for 0: 5 < M-L < 2, in correspondence to recent theoretical studies. Although the seismic hazard analysis for Groningen is internally consistent when expressed in terms of M-L (with the implicit assumption of equivalence between the two scales), a more physical interpretation of the seismicity model requires transformation of the earthquake catalog from local to moment magnitude, especially because the dataset currently used in estimating time-dependent hazard consists mainly of M-L < 2:5 events. We show that measured station effects, derived from M calculations, correspond to predicted model calculations used to determine a ground-motion model for the region.