Potency-magnitude scaling relations for southern California earthquakes with 1.0 < ML < 7.0

Abstract

Linear and quadratic scaling relations between potency P 0 and local magnitude M L for southern California earthquakes are derived using observed data of small events (1.0 < M L < 3.5) recorded in the Cajon Pass boreholeand moderate events (3.5 < M L < 6.0) recorded by the broad-band TERRAscope/TriNet network. The derived relations are extended to M L = 7.0 and compared with observed potency-magnitude values of four earthquakes in the extended range. The results indicate that a linear scaling relation can describe accurately data extending only over 2-3 orders of magnitudes. The best-fitting slope of a linear log P 0 vs M L scaling for the small Cajon Pass events is about 1.0, while the slope for the 3.5 < M L < 6.0 events is about 1.34. A quadratic relation can fit the data well over the entire 1.0 < M L < 7.0 magnitude range. The results may be explained in terms of a continuous transition from a limiting scaling P 0 ∼ (rupture area) for highly disordered small events, to a limiting scaling P 0 ∼ (rupture area times slip) for crack-like large events. Such a transition is expected to characterize evolving seismicity on heterogeneous faults, where small events propagate in (and are arrested by) a rough fluctuating stress field, while large events propagate across a relatively smooth correlated field.