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The 2016 Kaikoura earthquake, New Zealand, ruptured more than a dozen faults, making it difficult to prescribe a model fault for analysing the event by inversion. To model this earthquake from teleseismic records, we used a potency density tensor inversion, which projects multiple fault slips onto a single model fault plane, which reduced the non-uniqueness due to the uncertainty in selecting the faults’ orientations. The resulting distribution of potency-rate density tensors is consistent with observed surface ruptures. In its initial stage, the rupture propagated northeastward primarily at shallow depths, and the rupture propagated northeastward at deep depths beneath a gap in reported surface ruptures. The main rupture phase started in the northeastern part of the Kekerengu fault after 50 s and propagated bilaterally to the northeast and southwest. The non-double-couple component grew to a large fraction of the source elements as the rupture went through the junction of the Jordan Thrust and the Papatea fault, which suggests that the rupture branched into both faults as it back-propagated toward the southwest. The potency density tensor inversion sheds new light on the irregular evolution of this earthquake, which produced a fault rupture pattern of unprecedented complexity. Our source model should provide new insights into source process of the 2016 Kaikoura earthquake (e.g., back-rupture propagation), which should prompt research to determine a more realistic model with segmented faults using near-field data.

On September 5, 2022, a strike-slip earthquake with a moment magnitude (Mw) 6.7 occurred along the Moxi segment of the Xianshuihe fault zone in Luding, Sichuan province, China. To estimate the rupture evolution of the 2022 Luding earthquake, we inverted teleseismic P-waves by applying the Potency Density Tensor Inversion, a novel method that can estimate fault geometry and source process. We found the rupture process can be divided into two episodes. In the first episode, the initial deep rupture continues for 2 second on a westward tilting fault plane. In the next episode (3 to 7 s), the main rupture propagated along the Xianshuihe fault zone toward the south-southeast and halts ~15 km south-southeast from the epicentre. An isolated rupture also occurred ~10 km west from the Xianshuihe fault zone. The main rupture propagated in a south-southeast direction where strain have been accumulating, and our resolved strike direction rotated counterclockwise as it propagated from the epicentre to south-southeast. The along-strike migration of the main rupture stopped in a region with a complex fault network, and the along-dip migration did not go through the shallow-most region to the surface. Our seismic source model suggests that the 2022 Luding earthquake has failed to cascade up to a lager event, contrary to the last largest 1786 Kangding-Luding earthquake in this region, due to the fault geometry and shallow sedimentary layers inhibiting rupture propagation.

Additional file 1: Text S1. Uncertainty and sensitivity analyses of the potency density tensor inversion. Figure S1. The summary of the relative weight smoothness constraint for each basis moment tensor component from M1 to M5 (Kikuchi and Kanamori 1991). Figure S2. The comparison of the results adopting the different weight smoothness constraints of 5%, 10% and 20% of the maximum relative standard deviation. Figure S3. The waveform fitting between the observed waveform and the synthetic waveform of the 2014 Thailand earthquake. Figure S4. The summary of the sensitivity test of the near-source structure models using the CRUST1.0 model (Laske et al. 2013) (Additional file 1: Table S2) and the regional velocity model (Wongwai et al. 2013) (Additional file 1: Table S1). Figure S5. An impulse response function of the effect of inelastic attenuation of the Earth. Figure S6. The summary of the sensitivity test of the total rupture duration assumption at 6 s, 8 s, 10 s, and 12 s. Figure S7. The summary of the sensitivity test of the maximum rupture velocity assumption at 3.2 km/s, 3.6 km/s, and 4.0 km/s. Figure S8. The waveform fitting between the input and output waveforms from the numerical test (Figs. 4 and 5). Figure S9. Summary of the numerical test of the input of rupture propagating toward NE along Fault 2. Figure S10. Summary of the numerical test of one input rupture fault of the Fault 1. Figure S11. The summary of the sensitivity test of the different model plane depth at 4 km, 5 km, and 6 km. Figure S12. The summary of the reproduction test. Figure S13. The summary of a single vertical fault plane analysis. Figure S14. The waveform fit between the observed waveform and the synthetic waveform of our study, an assumed horizontal plane covering only on the N-S analysis in Additional file 1: Fig. S15, and a single vertical mode plane analysis in Additional file 1: Fig. S13. Figure S15. The summary of the analysis assuming a horizontal model plane covering only the N-S segment. Table S1. Velocity structure (Wongwai et al. 2013) used for calculating Green’s function. Table S2. Velocity structure used for calculating Green’s function made from CRUST1.0 model (Laske et al. 2013).

The prediction errors that originate from the uncertainty of underground structure is often a major contributor of the errors between the data and the model predictions in fault slip estimation using geodetic or seismic waveform data. However, most studies on slip inversions either neglect the model prediction errors or do not distinguish them from observation errors. Several methods that explicitly incorporated the model prediction errors in slip estimation, which has been proposed in the past decade, commonly assumed a Gaussian distribution for the stochastic property of the prediction errors to simplify the formulation. Moreover, the information on slip distribution and the underground structure is expected to be successfully extracted from the data by accurately incorporating the stochastic property of the prediction errors. In this study, we develop a novel flexible Bayesian inference method for estimating fault slips that can accurately incorporate non-Gaussian prediction errors. This method considers the uncertainty of the underground structure, including fault geometry based on the ensemble modeling of the uncertainty of Greens function. Furthermore, the framework allows the estimation of the posterior probability density function (PDF) of the parameters of the underground structure, by calculating the likelihood of each sample in the ensemble. To validate the advantage of the proposed method, we performed simple numerical experiments for estimating the slip deficit rate (SDR) distribution on a 2D thrust fault using synthetic data of surface displacement rates. In the experiments, the dip angle of the fault plane was the parameter used to characterize the underground structure. The proposed method succeeded in estimating a posterior PDF of SDR that is consistent with the true one, despite the uncertain and inaccurate information of the dip angle. In addition, the method could estimate a posterior PDF of the dip angle that has a strong peak near the true angle. In contrast, the estimation results obtained using a conventional approach, which introduces regularization based on smoothing constraints and does not explicitly distinguish the prediction and observation errors, included a significant amount of bias, which was not noticed in the results obtained using the proposed method. The experiments with different settings of the parameters suggested that inaccurate prior information of the underground structure with a small variance possibly results in significant bias in the estimation results, particularly the posterior PDFs for SDR, those for the underground structure, and the posterior predicted PDF of the displacement rates. The distribution shapes of the prediction errors for the representative model parameters in certain observation points are significantly asymmetric with large absolute values of the sample skewness, for which Gaussian approximation is not usually applied.

The last earthquake that affected the city of Coquimbo took place in September 2015 and had a magnitude of Mw = 8.3, resulting in localized damage in low-lying areas of the city. In addition, another seismic gap north of the 2015 earthquake rupture area has been identified; therefore, a significant earthquake (Mw = 8.2 to 8.5) and tsunami could occur in the near future. The present paper develops a tsunami fragility curve for the city of Coquimbo based on field survey data and tsunami numerical simulations. The inundation depth of the 2015 Chile tsunami in Coquimbo was estimated by means of numerical simulation with the Non-hydrostatic Evolution of Ocean WAVEs (NEOWAVE) model and five nested grids with a maximum grid resolution of 10m. The fragility curve exhibited behavior similar to that of other curves in flat areas in Japan, where little damage was observed at relatively high inundation depths. In addition, it was observed that Coquimbo experienced less damage than Dichato (Chile); in fact, at an inundation depth of 2m, Dichato had a ∼ 75% probability of damage, while Coquimbo proved to have only a 20% probability. The new fragility curve was used to estimate the damage by possible future tsunamis in the area. The damage assessment showed that ∼ 50% of the structures in the low-lying area of Coquimbo have a high probability of damage in the case of a tsunami generated off the coast of the study area if the city is rebuilt with the same types of structures.

Previous research revealed a dynamically triggered earthquake front propagating along Southwest Japan, in correlation with the arrival of surface waves from the 2011 M9.0 Tohoku-oki earthquake. However, some characteristics of the dynamically initiated seismic activation have not been investigated in detail. We analyse first the dynamic triggering process, using NIED waveform data. Our results suggest that at several triggering sites in SW Japan, including volcanic areas in Kyushu, the arrival of larger amplitude Love waves may correlate better with the occurrence of first locally triggered events compared to the Rayleigh wave arrivals. We also observe that triggering takes place during relatively long-period surface waves. We search for other cases of dynamic triggering in SW Japan by remote large earthquakes and show that the distinctive phase arrivals of both Love and Rayleigh waves from the 2008 M7.9 Wenchuan earthquake triggered local events in Kyushu. These observations suggest that sharing motion on well-lubricated local faults may have started failure in these areas. Based on the analysis of an extended earthquake catalogue, we find that the stacked seismicity for the dynamically triggered regions in SW Japan after the 2011 Tohoku-oki earthquake has a significant, albeit weak increase after the megathrust event, followed by a relatively slow decay towards the background level for the next several days. The relatively slow decay may reflect the temporal pattern of stacked, swarm-like clustered seismicity, which has been mainly activated at volcanic/geothermal areas in Kyushu. The decay of seismicity within a single, activated earthquake cluster may have, however, different characteristics. The analysis of the aftershocks initiated dynamically at the Yufuin-Beppu geothermal area (Kyushu), by the 2016 M7.3 Kumamoto earthquake, shows a fast decay that may reflect quick stress recovery near higher-temperature volcanic or geothermal regions.