Back-projection rupture process imaging
To resolve its high frequency radiation and the rupture speed of the Maduo earthquake independent from FFM and MPS solutions, we perform a MUltiple SIgnal Classification (MUSIC) back-projection (BP) analysis[Meng et al. , 2011; Zeng et al. , 2020] using high-frequency (0.3-1.0 Hz) teleseismic P-waves recorded by the European array (EU) and Australian array (AU) (Supplement text - 4 ). To take into account the potential impact of the 3D source-side velocity structure on the travel time, we apply a path calibration algorithm using the arrival times of mainshock and other nearby events, which was proved to be necessary for more accurate BP analysis [Zeng et al. , 2022]. The effectiveness of the calibration is verified by applying it to the BP analysis of the M > 5 aftershocks. We compare the differences between the BP locations and the refined epicenter locations for these events [W Wang et al. , 2021]. Note that our calibration events include the earthquakes away from the mainshock rupture zone (Fig.S14), such selection was shown to be more accurate for travel time error interpolation [Zeng et al. , 2022]. After trying different groups of calibration events, it appears that we need to use different calibration event combinations to obtain high consistency between the calibrated BP locations and the refined epicenters for the events located to the east and west of the mainshock epicenter, respectively (Fig.S14-15). This calibration strategy works well for the EU and AU arrays, as they can only resolve the rupture directivity towards west and east, respectively, likely due to the Doppler effect from rupture directivity. We consider the average difference between the BP locations and epicenters as the location uncertainty of BP results, which is 7.5 km for AU array and 4.5 km for the EU array.
Using this path-calibrated BP method, we derive the spatial and temporal evolution of the mainshock rupture using EU and AU arrays. The results are presented as location of high-frequency radiators colored by their timing (Fig.2a). BP results from the EU array reveal only the rupture directivity towards the west, and the results from the AU array show only rupture directivity towards the east. The locations of the BP results are mostly less than 10 km away from the surface rupture, suggesting reliable solutions. The location of the large amplitude high-frequency radiators are highly correlated with the fault bends or step-overs (Fig.2a), which also mark the boundaries of fault segments (Fig.3c). This is because stress is usually concentrated at fault kinks and bends [King and Nábělek , 1985], where coseismic slip distribution shows larger gradients (e.g., Fig.3d). Such complementary feature between BP result and slip distribution also presents in the moment-rate vs BP power plot (Fig.3a), where the peaks of BP power always locate at the edges of moment-rate peaks.
With the timing and location of the high-frequency radiators, the rupture speed of the earthquake can be derived (Fig.5), which shows a speed of 2.4 km/s towards the west and of 2.5 km/s towards the east. These rupture speeds are quite stable throughout the rupture and highly consistent with the result from FFM and MPS inversions. Given that the shallow part (<6 km, where most of the slip took place) of the crust has a shear wave (Vs) velocity of 2.7 km/s [L Zhu and Helmberger , 1996], these rupture speeds are roughly 90% of Vs speed, that is, of the Rayleigh wave speed. Note, that to the west of the fault bifurcation, the BP results show a gap that almost overlaps with the gap in the aftershock seismicity (Fig.3). The coseismic rupture of this fault segment is deeper, as shown on fault segment S6 in the FFM, and smoother, as shown in the waveform decomposition (Fig.4), than the rupture on the other fault segments. Such a smoother rupture could be explained as more uniform stress distribution and/or smoother fault geometry [Z Shi and Day , 2013]. As the rupture propagated through the junction of bifurcation, high-frequency radiators started to appear on both fault branches, with their amplitudes increasing gradually as the rupture propagated on each of the fault branch (Fig.2a). Enhanced higher-frequency radiation from the bifurcated fault branches (segments S7-10) is consistent with the waveform decomposition analysis of the high-rate GPS data recorded at HSHX station (Fig.4 and Fig.S12). But note, that GPS velocity waveforms are dominated by the ~0.2 Hz energy, while the BP results are derived at ~1.0 Hz. It is interesting to see that the largest amplitude of high-frequency radiators on the bifurcated fault branches are located at the end of each fault branch (Fig.2a inset). The timings of these peaks are also consistent with the end of the rupture time, as shown in both the MPS source time function and FFM moment-rate function (Fig.3a). Therefore, we propose that the large amplitude high-frequency radiators on each fault branch were produced by the stopping phase of the rupture [Savage , 1965]. Rupture on the southern branch (S10) stopped ~5s earlier than the rupture on the northern branch (S8) (Fig.3a and Fig.5b). As shown in the surface deformation image (Fig.2a), the distance between the rupture tips on the two fault branches is ~15 km, which corresponds to ~5s for the S-wave of the stopping phase to travel between the two fault tips. It is therefore likely that the stopping phase on the southern branch (S10), which produced negative Coulomb stress change on the northern branch (S8), therefore stopped the rupture on S8. From the timing and location of the BP results, we show that the rupture propagated simultaneously on the two branches of the bifurcation.