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.