Toward automated directivity estimates in earthquake moment tensor inversion

Abstract

Rapid estimates of earthquake rupture properties are useful for both scientific characterization of earthquakes and emergency response to earthquake hazards. Rupture directivity is a particularly important property to constrain since seismic waves radiated in the direction of rupture can be greatly amplified, and even moderate magnitude earthquakes can sometimes cause serious damage. Knowing the directivity of earthquakes is important for ground shaking prediction and hazard mitigation, and is also useful for discriminating which nodal plane corresponds to the actual fault plane particularly when the event lacks aftershocks or outcropped fault traces. Here, we propose a 3-D multiple-time-window directivity inversion method through direct waveform fitting, with source time functions stretched for each station according to a given directivity. By grid searching for the directivity vector in 3-D space, this method determines not only horizontal but vertical directivity components, provides uncertainty estimates, and has the potential to be automated in real time. Synthetic tests show that the method is stable with respect to noise, picking errors, and site amplification, and is less sensitive to station coverage than other methods. Horizontal directivity can be properly recovered with a minimum azimuthal station coverage of 180°, whereas vertical directivity requires better coverage to resolve. We apply the new method to the M_w 6.0 Nantou, Taiwan earthquake, M_w 7.0 Kumamoto, Japan earthquake, and M_w 4.7 San Jacinto fault trifurcation (SJFT) earthquake in southern California. For the Nantou earthquake, we corroborate previous findings that the earthquake occurred on a shallow east-dipping fault plane rather than a west-dipping one. For the Kumamoto and SJFT earthquakes, the directivity results show good agreement with previous studies and demonstrate that the method captures the general rupture characteristics of large earthquakes involving multiple fault ruptures and applies to earthquakes with magnitudes as small as M_w 4.7.