Bilinearity in the Gutenberg‐Richter Relation Based on ML for Magnitudes Above and Below 2, From Systematic Magnitude Assessments in Parkfield (California). Issue 14 (20th July 2018) - Staudenmaier, Nadine
Abstract: Several studies have shown that local magnitude, M L, and moment magnitude, M, scale differently for small earthquakes (M < ~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 ≈ 1.5 M is observed, while for events M L > 3, M L ≈ 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. Key Points: Scaling break is present between local magnitude and moment magnitude Different slopes of the earthquake frequency‐magnitude distribution for local magnitudes below and above 2.0 is the consequence of the break in magnitude scaling Seismic hazard studies need to carefully consider these scaling breaks