Bilinearity in the Gutenberg-Richter Relation Based on ML for Magnitudes Above and Below 2, From Systematic Magnitude Assessments in Parkfield (California)

Several studies have shown that local magnitude, M-L,M- and moment magnitude, M, scale differently for small earthquakes (M< similar to 2) than for moderate to large earthquakes. Consequently, frequency-magnitude relations based on one or the other magnitude type cannot obey a power law with a single exponent over the entire magnitude range. Since this has serious consequences for seismic hazard assessments, it is important to establish for which magnitude type the assumption of a constant exponent is valid and for which it is not. Based on independently determined M, M-L and duration magnitude, M-d, estimates for 5,304 events near Parkfield, we confirm the theoretically expected difference in scaling between the magnitude types, and we show that the frequency-magnitude distribution based on M and M-d follows a Gutenberg-Richter relation with a constant slope, whereas for M-L it is bilinear. Thus, seismic hazard estimates based on M-L of small earthquakes are likely to overestimate the occurrence probability of large earthquakes. Plain Language Summary It is a fundamental requirement for many seismological studies and a prerequisite for seismic hazard assessment to have uniform magnitude definition. Increasingly, native estimates of moment magnitudes, M, are available for earthquakes with magnitude below 3.0 and have revealed a break in scaling between M and M-L. This break implies that the commonly observed 1:1 scaling of earthquake magnitude for moderate events must break down below 3.0 for at least one of the magnitude types. However, this predicted break has so far not been convincingly observed in earthquake catalogs. To address this unresolved question, we derive independent moment, local, and duration magnitudes for 5,304 events on the San Andreas Fault near Parkfield. By focusing on events with the same focal mechanism and recorded on a single instrument, our analysis avoids the typical issues affecting such calculations, in particular site effects. Consistent with theoretical studies, we show empirically that for small events (M-L<2) a scaling of M-L approximate to 1.5 M is observed, while for events M-L>3, M-L approximate to 1.0 M is observed. As a consequence of this break between M-L and M, the frequency-magnitude distribution with respect to M-L has a different slope for small and large events, which has significant implications for seismic hazard assessments.