Estimating finite source properties of small earthquake ruptures

Many of the most fundamental questions in earthquake science are currently limited by a lack of knowledge about small earthquake ruptures. Small earthquakes are difficult to study owing to the poor constraints placed on many of the interesting physical parameters by bandlimited, far-field, seismic data. Traditionally, dynamic models, such as an expanding circular crack, have been utilized to bridge the gap between the easily measurable quantities for small earthquakes and more interesting physical parameters such as stress drop and rupture velocity. Here I present a method for estimating the basic finite source properties of a rupture that is independent of any a priori model and utilizes the description of a finite source, the second moments, that far-field waves are inherently sensitive to. Application to two magnitude 5 events in southern California demonstrates the ability of an empirical Green's function approach to estimating the second moments to resolve the fault-plane ambiguity, rupture length, and overall directivity. Additional results are presented for two example M 2.7 events from the creeping section of the San Andreas fault to examine the likely lower bound on event size that can be studied with surface seismometers. The creeping section earthquakes have very similar rupture areas but would be improperly interpreted as significantly different using the traditional methodology. One of these events presents a relatively clear interpretation of the velocity of rupture front propagation, which is about 0.8 of the Rayleigh speed, suggesting little difference in rupture velocity between it and typical large earthquakes.