6.1 Stability of the solution
In this study, the horizontal model plane has been set at hypocenter at 5 km depth, even though an actual fault rupture propagates not only horizontal but also in the depth direction. The results of the numerical experiment show that we can estimate the complex rupture processes of the two fault planes by assuming a horizontal model plane at the potency centroid depth. In order to evaluate the modeling sensitivity to the assumption of model domain depth, we tested alternative assumptions of the model plane depth at 4 km and 6 km. The moment rate functions show different peaks among the alternative solutions. The timing of the dominant peak of the moment rate is shifted from 4 to 3 s from shallower to deeper hypocentral models (Additional file 1: Fig. S11). The spatiotemporal distribution of the potency-rate density distributions also shows the time shift of the largest potency-rate release at middle of the EWTA from 3.0 to 2.5 s from shallower to deeper models. These time differences can be explained by the change in the Green’s function, which is mainly caused by the difference of model domain depths (e.g., Shimizu et al. 2020). However, the potency density tensor distributions remain the same among the alternative solutions. They show the strike orientations at NNE-SSW and ENE-WSW in the middle of the NSTA and EWTA, respectively (Additional file 1: Fig. S11), which are the same features as seen in our potency density tensor solution. The alternative solutions also show that the rupturing paths remain the same as our preferred solution; the first rupture propagates toward south along the NSTA, and then the secondary rupture initiates at the eastern edge of the EWTA and propagates toward southwest along the EWTA. The sensitivity tests suggest that, although the rupture timing can be uncertain within ~ 1 s due to the model domain depth, the overall pattern of the rupture episodes is robustly resolved by our modeling approach. We note that estimates of rupture velocity from the potency-rate density tensor solution can inherently be difficult primarily due to smoothing effects applied in both space and time, especially for the smaller-scale earthquake like the 2014 Thailand earthquake, which might be challenging to rigorously resolve the exact timing and location of rupture front.
To further evaluate a reproducibility of the results, we performed the reproduction test by using the solution from our potency density tensor inversion. We generated the synthetic waveforms from our solution and newly performed the inversion (Additional file 1: Fig. S12). The input synthetic waveforms for the reproduction test are generated using the Green’s function incorporating Gaussian noise and the background Gaussian noise. Then, we inverted the synthetic waveforms with the same model setting as for our preferred potency density tensor inversion for the 2014 Thailand earthquake. The result shows that the moment rate function has the major peak at about 3–4 s (Additional file 1: Fig. S12b), which is the same feature as we resolved for our solution (Additional file 1: Fig. S12a). The distribution of the potency density tensor shows that the strike orientations at NNE-SSW and ENE-WSW in the middle of the NSTA and EWTA, respectively, which are the same features as seen in our solution. In addition, the spatiotemporal distribution of the potency-rate density tensor (Additional file 1: Fig. S12d) exhibits two distinct rupture propagation: (1) southward rupture propagation during 0–1.5 s along the NSTA and (2) southwestern rupture propagation during 1.5–4.5 s along the EWTA, which are the main rupture features resolved in our solution (Additional file 1: Fig. S12c), and thus we will focus on these rupture processes in the Discussion section and will avoid discussing detailed features of rupture processes that are not reproduced in the reproduction test.
6.2 Two rupture episodes
Our source model of the 2014 Thailand earthquake distinguished two rupture episodes that show a dominant strike-slip faulting consisting of different rupture lineation along the NSTA and EWTA (Fig. 8), which are consistent with the nodal plane distribution (Fig. 6c) and thus facilitate identification of the possible fault geometry for the 2014 Thailand earthquake. The nodal plane distribution along the NSTA shows nodal strikes in the NNE-SSW direction and the auxiliary plane in the ESE-WNW direction (Fig. 6). The nodal plane distribution along the EWTA shows nodal strikes in the ENE-WSW direction and the auxiliary plane in the NNW-SSE direction (Fig. 6). The consistency between the nodal plane distribution (Fig. 6c) and the rupture directions of the spatiotemporal potency-rate density distribution (Fig. 8) helps facilitate identification of the possible fault geometry. The striking plane along the NSTA is determined to be in the NNE-SSW direction and is associated with the rupture propagating toward the south. The striking plane along the EWTA is determined to be in the ENE-WSW direction and is associated with the rupture propagating toward the southwest. The obtained two dominant fault planes along the NSTA and EWTA are consistent with the two distinct trends of the relocated aftershock distribution (Pananont et al. 2017). The first is the N-S trend (~ 180° from north) along the NSTA located near the epicenter, and the second is the ENE-WSW trend (~ 60° from north) along the EWTA located northwest from the epicenter. Although the geometry of our model, designed to cover the aftershock distribution area, is non-rectangular, the potency density and the potency-rate density of each sub-fault are estimated independently from the assumed model geometry.
During the first 1.5 s, the rupture propagates from the hypocenter to the southern edges of the NSTA (Fig. 8b). Then, at around 1.5 s as the rupture migrates from the NSTA to the EWTA, the fault strike direction changes from NNE-SSW at the northern edge of the NSTA to ENE-WSW at the eastern edge of the EWTA, which implies that the fault planes in the NSTA and EWTA can be considered as a conjugate fault, where the planes inclined at angles on either side of the maximum principal stress (Scholz 2002). Next, between 2.0 and 3.5 s the second rupture propagates along EWTA from its eastern edge toward the southwest and terminates at around 5.0 s at its western edge. It is associated with the second rupture arising at the eastern edge of the EWTA, propagating west during the period between the 2.0 and 3.5 s and having the highest potency-rate of around 0.9 m/s (Fig. 8b). Our result of the major slip along the EWTA is robustly resolved even if we change the near-source structure model, the assumptions of the total duration, and the maximum rupture velocity (Additional file 1: Figs. S4, S6, and S7). According to the surface fault lines (DMR 2016; Noisagool et al. 2016), the orientation of the known active conjugated strike-slip faults of the PF and MLF shows striking at N5°E–N13°E and N30°E–N50°E; this is consistent with our findings that at the northern edge of the NSTA, the striking is in the NNE-SSW direction and at the eastern edge of the EWTA, in the ENE–WSW direction. The multiple subevents at the conjugated strike-slip fault system are possibly due to the complex rupture evolution among the geometrically complex fault system (e.g., Meng et al. 2012; Yamashita et al. 2021). Therefore, our solution suggests that the rupture evolution of the 2014 Thailand earthquake is characterized by multiple subevents in the conjugated strike-slip fault system of the PF and MLF.
Our results indicate that the conjugate fault ruptured during the mainshock, but Pananont et al. (2017) suggests that primary rupture on the N-S trending fault plane during the mainshock may host the aftershock activity triggered on the conjugate structure of the ENE-WSW trending fault plane. Therefore, we examined whether the observed waveforms could be explained if the rupture occurred only on the N-S trending fault. We first set up a single fault plane with reference to the north–south-striking nodal plane of the focal mechanism obtained in Pananont et al. (2017) and inverted the observed waveforms on that plane using the finite-fault inversion method (Yagi and Fukahata 2011), assuming a two-component basis slip vector (Additional file 1: Fig. S13). As a result, the variance reduction (Shimizu et al. 2021) decreases significantly from 73% to 54% (Additional file 1: Fig. S14), indicating that the model with no variation in fault geometry cannot explain the complex teleseismic waves of the present earthquake. We next performed the potency density tensor inversion (the adopted method in this study), placing the horizontal model plane only on the NSTA (Additional file 1: Fig. S15). The potency density tensor inversion projects the slips on multiple faults onto the assumed model plane. Therefore, if a large seismic potency is released on the ENE-WSW trending fault, it is expected that subevents corresponding to the ENE-WSW trending fault slip will be detected near the model plane boundaries and that the waveforms will be poorly fitted due to the improper model plane. As expected, the obtained results of the spatial distribution and the spatiotemporal distribution (Additional file 1: Fig. S15) show that subevents with focal mechanisms corresponding to slip on the ENE-WSW trending fault are projected on the northwest boundary of the assumed model plane and with a variance reduction of 66% (Additional file 1: Fig. S14). These two results indicate that a model in which two faults rupture during the mainshock is necessary to explain the complex teleseismic body waves.
6.3 P-axis distribution
The spatial distribution of the P-axis azimuth, extracted from the potency density tensor for each sub-fault, exhibits two major orientations at ENE-WSW in the NSTA and NNE-SSW in the EWTA (Fig. 7). The histogram of the P-axis azimuth distribution displays two peaks, one at 20°–30° and the other at 50°–60° (Fig. 7b), which should reflect the dominant orientations within the EWTA and NSTA, respectively. Our P-axis orientations at 20°–30° within the EWTA are consistent with the one obtained by Noisagool et al. (2016), which is estimated based on the mainshock and aftershocks focal mechanisms, mostly located within the EWTA (Pananont et al. 2017), while the direction of our P-axis azimuth along the NSTA obtained in this study (~ 50°, Fig. 7) is not consistent with the one (~ 18°) obtained by Noisagool et al. (2016). However, if Coulomb's friction factor is a typical value of 0.6, the two peaks of our P-axis histogram (Fig. 7) can be naturally explained as a shift of the P-axis of the conjugate fault plane (Iio 1997), which leads to ~ 35°. We should mention, however, the focal mechanism solutions obtained in this study are affected by dynamic changes in the stress field due to seismic waves or localized fault structures, and estimation of the principal stress axis is beyond the scope of this study. Our results suggest that further investigation of the stress field in this region is needed, taking into account the spatial bias of aftershock distribution, which affects the estimates of the principal stresses for the conjugate fault earthquake.