Resolving Earthquake Directivity with Relative Centroid Location : A Case Study for the 18 April 2008 Illinois Earthquake

Earthquake rupture directivity is essential for studying seismic hazard and understanding seismogenic processes by resolving the ruptured fault. Point source approximation with centroid moment tensor (CMT) or fault plane solution only provides two nodal planes instead of specifying the physical rupture plane, thus leading to fault plane ambiguity. For mega-earthquakes (M7+), slip distribution can be resolved through finite fault modeling (Ji et al., 2002). For moderate earthquakes (M4~6), relative source time function (RSTF) can be obtained from deconvolving the empirical green's functions or forward modeling, and the rupture directivity can be determined from fitting RSTF of stations with small azimuth gap in a dense seismic network(Luo et al., 2010). But for sparse network, station azimuthal coverage is not sufficient for such studies.

We propose a technique to determine the rupture plane via measuring the spatial difference between centroid location and hypocenter. The technique involves of waveform time shift difference of mainshock and refer events (smaller events with similar focal mechanism), which calibrates errors due to velocity heterogeneity and absolute location error. Relative hypocenter locations and relative centroid locations are resolved by relative location method of onset travel times and waveform cross-correlation respectively. The difference between onset travel times and waveform-derived centroid times against the azimuthal variations is then used to infer the mainshock rupture directivity.

We apply the method to the 2008 Illinois Mw5.2 earthquake. Four M3.4+ aftershocks are chosen as refer events, we generate synthetics using focal mechanism from SLU earthquake center, and measure the time shift difference for stations. The resolved rupture plane strikes northwest-southeast, consistent with spatial distribution of relocated aftershocks using hypoDD (Hongfeng Yang et al., 2009). The method works for earthquakes of unilateral rupture, which consist of 80% of all earthquake as demonstrated by previous studies.