Toward automated directivity estimates in earthquake moment tensor inversion

Abstract

S U M M A R YRapid 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.

Near‐Real‐Time Estimates on Earthquake Rupture Directivity Using Near‐Field Ground Motion Data From a Dense Low‐Cost Seismic Network

“…To further examine this basis, we apply the method to 11 March 2013 M W 4.7 San Jacinto fault trifurcation, southern California earthquake that is a purely strike-slip event with strong spatial radiation pattern and in a different tectonic setting (i.e., different site conditions). As shown in Figure S5 and Movie S2, a northwestward directivity can stably be derived within 11 s and shows a good agreement with previous studies (H.-H. Huang et al, 2017;Ross & Ben-Zion, 2016) and the nodal plane of the focal mechanism. The consistency of our directivity estimates with previous studies and the best performance of using shortest 25-km profile length therefore sustain the basis made in the method (Table S1).…”

“…As shown in Figure S5 and Movie S2, a northwestward directivity can stably be derived within 11 s and shows a good agreement with previous studies (H.‐H. Huang et al, ; Ross & Ben‐Zion, ) and the nodal plane of the focal mechanism. The consistency of our directivity estimates with previous studies and the best performance of using shortest 25‐km profile length therefore sustain the basis made in the method (Table S1).…”

“…• Movie S2 Huang et al, 2017) for small to moderate earthquakes. However, these methods are not ideal for early warning purposes as they often require several tens of minutes or longer to issue the directivity results.…”

“…Rupture directivity information can be obtained with various means, such as finite fault inversion (Kikuchi & Kanamori, ) and backprojection technique (Ishii et al, ) for large earthquakes, and source duration analysis (Tan & Helmberger, ), spectral ratio method (Ross & Ben‐Zion, ), second moment method (McGuire et al, ), and directivity moment tensor inversion (H.‐H. Huang et al, ) for small to moderate earthquakes. However, these methods are not ideal for early warning purposes as they often require several tens of minutes or longer to issue the directivity results.…”

Earthquake Directivity, Orientation, and Stress Drop Within the Subducting Plate at the Hikurangi Margin, New Zealand

“…Huang et al () also noted that the stretching methods work better for complex ruptures than does the second‐order moment approach (McGuire, ). In the case of complex ruptures, with multiple subevents, rupture velocities calculated using a line source will represent a lower bound, as discussed by Park and Ishii ().…”