The rupture extent of low frequency earthquakes near Parkfield, CA

The low frequency earthquakes (LFEs) that constitute tectonic tremor are often inferred to be slow: to have durations of 0.2 to 0.5 s, a factor of 10 to 100 longer than those of typical Mw 1-2 earthquakes. Here we examine LFEs near Parkfield, CA in order to assess several proposed explanations for LFEs long durations. We determine LFE rupture areas and location distributions using a new approach, similar to directivity analysis, where we examine how signals coming from various locations within LFEs finite rupture extents create differences in the apparent source time functions recorded at various stations. We use synthetic ruptures to determine how much the LFE signals recorded at each station would be modified by spatial variations of the source-station travel time within the rupture area given various possible rupture diameters, and then compare those synthetics with the data. Our synthetics show that the methodology can identify inter-station variations created by heterogeneous slip distributions or complex rupture edges, and thus lets us estimate LFE rupture extents for unilateral or bilateral ruptures. To obtain robust estimates of the sources similarity across stations, we stack signals from thousands of LFEs, using an empirical Greens function approach to isolate the LFEs apparent source time functions from the path effects. Our analysis of LFEs in Parkfield implies that LFEs apparent source time functions are similar across stations at frequencies up to 8 to 16 Hz, depending on the family.The inter-station coherence observed at these relatively high frequencies, or short wavelengths (down to 0.2 to 0.5 km), suggest that LFEs in each of the 7 families examined occur on asperities. They are clustered in patches with sub-1-km diameters. The individual LFEs rupture diameters are estimated to be smaller than 1.1 km for all families, and smaller than 0.5 km and 1 km for the two shallowest families, which were previously found to have 0.2-s durations. Coupling the diameters with the durations suggests that it is possible to model these Mw 1-2 LFEs with earthquake-like rupture speeds: around 70% of the shear wave speed. However, that rupture speed matches the data only at the edge of our uncertainty estimates for the family with highest coherence. The data for that family are better matched if LFEs have rupture velocities smaller than 40% of the shear wave speed, or if LFEs have different rupture dynamics. They could have long rise times, contain composite sub-ruptures, or have slip distributions that persist from event to event.