4.1 Implications for the active fault tsunami source
Comparing tsunami waveforms and inundation supported the scenario involving simultaneous ruptures of F42 and F43 (Case #2). In general, the GSI model (Case #3) generated the smallest tsunami among the three scenarios, underestimating both maximum amplitude and inundation substantially. While F43 (Case #1) caused a larger tsunami than that by the GSI model, the maximum amplitude at the Sado and Toyama stations and the inundation of Iida Port were underestimated. In contrast, the maximum amplitude and inundation were successfully reproduced in Case #2.
Case #2 utilized projected tsunami sources from MLIT (2014) designed for tsunami hazard assessments, which typically employ a larger magnitude to avoid underestimation. Assuming a crust rigidity at 34 GPa, the moment magnitude in Case #2 was calculated as Mw 7.66, exceeding the instrumental observation of Mw 7.5. Better tsunami rupture models that explain not only the observed tsunami waveforms and inundation but also the geodetic and seismic observations should be explored in future works. Estimating a sophisticated tsunami source model requires quantitative comparisons of tsunamis and other geophysical data with simulations; but this is beyond the scope of this study. However, we attempted to obtain the general characteristics of the tsunami source, such as the primary generation regions and their extents, based on the discrepancies between our simulation results and observations.
The waveform at the Kashiwazaki station was not accurately reproduced by any of the three models, failing to capture tsunami height, wavelength, or phase. In Case #3, the water level began to rise 3.5 min earlier than that observed (Fig. S2). In contrast, the timings of tsunami arrival in Cases #1 and #2 were consistent with the observed values (Figs. 2 and S1). Therefore, the distance between the tsunami source and Kashiwazaki station was better modeled by Cases #1 and #2 than by Case #3. This was probably because of the exclusion of a longer, straight-fault geometry extending offshore from the peninsula (GSI model; Fig. 2a). The amplitude discrepancy serves as an indicator for a sophisticated tsunami source model, but data processing may be necessary due to the well-type station’s potential inability to its response characteristics (Namegaya et al., 2009).
At Sado station, the tsunami in Case #2 arrived 5 min earlier than that observed (Fig. 1b). Although Case #1 (single rupture of F43) better explained the arrival time, the required amplitude indicated the necessity of the simultaneous rupture of F43 and F42 (Case #2), offering valuable insights for further source modeling. Additionally, a possible underestimation of the later time may occur because the diffracted wave from the outside of the computational domain was ignored.
The differences between Cases #1 and #2 in terms of the tsunami source were the rupture length to the northeast and the initial water level in the superposed areas of F43 and F42. Although the larger rupture length seems to have contributed to the improved reproducibility in Case #2, the difference in arrival time at the Sado station implies that the tsunami source did not extend to the northeastern tip of the F42 fault. If the tsunami heights at each tide station can be explained by the increasing fault slip of the eastern segment of F43, the rupture of F42 may be dispensable. However, existing tsunami waveform inversion, focusing on a slip of approximately 4 m in the eastern offshore area of the Noto Peninsula, fails to explain amplitudes at Toyama and Sado stations (Satake and Fujii, 2024). Further research is required to clarify the rupture extent explaining the tsunami, seismic, and geodetic observations. Also, GSI updated the GNSS-based fault model on January 15, 2024 with an increased slip 4.31 m for the east portion (GSI, 2024c). While a consensus existed that the eastern half of the source fault slipped by > 4 m, a more in-depth investigation of the northeastern limit of the rupture was warranted, relying on a multi-proxy analysis of the event.
4.2 Possible landslide-induced tsunami
One of the most important discrepancies between the observations and simulations was the waveform at the Toyama tide station during the early period (0–20 min). The numerical simulations indicated a delayed arrival of the seismic triggered tsunami compared to arrival of the observed first wave, implying the presence of an additional tsunami source near the Toyama station.
Southern Toyama Bay is characterized by complex coastal fan deltas developed at the mouths of several torrential rivers drained from the high mountains. The submerged portions of the delta form steep continental slopes prone to submarine landslides. Many past submarine landslides have been identified by analyzing bathymetric charts (Moriki et al., 2017; Inui and Shigihara, 2023). To address the arrival time of the negative wave at the Toyama tide station, we tested 11 hypothetical submarine landslides (L1 to L11; Fig. 4, Table S1) along the continental slope of southern Toyama Bay as additional tsunami sources. Each landslide was approximated using the motion of a normal fault. The dip and width of the approximated fault plane were determined based on bathymetric sloping; the upper side of the fault was set along the 100 m isobath, and the lower side was set along the knick line of the bathymetry. L9 and L10 were narrowed from L7 to a fixed lower end. The fault strike was adjusted to fit the general direction of the 100 m isobath. A fault slip of 100 m with a rise time of 10 min was used to simulate a submarine landslide. The resulting seafloor deformation was calculated using Okada’s (1985) elastic theory. Considering the geological and geomorphological settings of southern Toyama Bay and the absence of seismic activity within the bay, the study explored tsunami generation and propagation by submarine landslides.
Tsunamis triggered by landslide-mimicking normal faults vary in arrival time, amplitude, and wave period (Figs. 4 and S5). We found that the observed period of the first negative wave could be explained by landslide L5 (5.3 km northwest of Toyama station), but the resulting amplitude and arrival time were inconsistent. In contrast, L10 (in front of Toyama station) yielded a negative wave at a speed matching the observation; however, the period of the first negative wave was much shorter than that observed. Therefore, we deduced that the mass failure occurred simultaneously at L10 and L5. The location of L10 crudely corresponded to the possible slope failure interpreted by comparing bathymetric data acquired during January 15–17, 2024 with the data obtained in 2010 (Japan Coast Guard, 2024).
A composite tsunami source model for the simultaneous rupture of F42, F43, L5, and L10 was also examined based on the above comparison. In this composite model, the amount of slip at L5 was doubled (200 m) to explain the amplitude of the negative waves. Consequently, the arrival time and amplitude of the first, maximum, and subsequent waves were well reproduced (Fig. 4c). The maximum amplitude was slightly overestimated owing to the additional tsunami generated by the landslides; however, the effect was limited in the following waves, probably owing to rapid attenuation.
While our testing was not exhaustive, other landslide combinations may be acceptable by adjusting their parameters; fast travel time could be explained by L7 or L9, and the long period may be attributed to other landslides relatively distant from the tide station. Our model is not conclusive; however, landslides located both in front of and some distance away from the tide station are indispensable for explaining the observed waveform. Although the fine-tuning of landslide tsunami sources will yield a more precise simulation, this is beyond our scope because further investigation requires sophisticated approaches, such as landslide kinematics and wave dispersion. In addition, the time difference between the initiation of the earthquake and landslide was not considered in this study. TYMH03 station (KiK-net facilitated by the National Research Institute for Earth Science and Disaster Resilience; Fig. 4a) recorded peak ground acceleration approximately 50 s after the origin time. The start of the landslides was likely delayed because of the seismic wave propagation. Therefore, the travel time of the first negative tsunami wave was shorter than that examined in this simulation. A closer landslide tsunami source may be required to explain the arrival times.
4.3 Relevant past events
The tsunami simulations showed that the inundation of Iida and Toyama Bays and the western coast of the Noto Peninsula was predominantly caused by the eastern segment of F43, and probably F42 (Fig. 2a and Movie S1). This region has been evaluated for tsunami hazards from active submarine faults based on paleoseismological studies both onshore and offshore (e.g., Inoue and Okamura, 2010; Shishikura et al., 2020; Takashimizu et al., 2020).
In 2007, an Mj 6.9 earthquake occurred on an active fault in the north-western offshore region of the Noto Peninsula (Monzen-oki segment; Inoue and Okamura, 2010). Bathymetric surveys have identified other shore-parallel offshore active faults on the northern coast of the peninsula (Inoue and Okamura, 2014). The 2024 earthquake could be explained by multiple-segment ruptures of known offshore active faults. The F43 fault (Case #1), which was projected for the governmental tsunami hazard assessment (MLIT, 2014), mimicked the Saruyama-oki, Wajima-oki, and Suzu-oki segments, as reported by Inoue and Okamura (2010). Shishikura et al. (2020) identified three marine terraces (L1–L3) on the northern coast of the peninsula formed in the last 6,000 years, suggesting past coseismic uplift; however, their formation ages are uncertain. Since the up-dip end of the fault is close to the present shoreline, a large coseismic uplift was observed after the 2024 event (Ishiyama et al., 2024; Shishikura et al., 2024). The post-event field survey reported that the coastal uplift formed a new terrace, “L4”, due to the 2024 earthquake (Shishikura et al., 2024). Therefore, paleoseismological findings imply the past recurrence of earthquakes similar to the 2024 event. Although tectonic geomorphology have identified past activity in the proximal portion of the F43 fault, the seismicity of the distant segments, which caused tsunami inundations at many locations, is difficult to understand from onshore records. Instead, tsunami deposits provide evidence of past tsunamigenic submarine faults (Takashimizu et al., 2020). Around the Noto Peninsula and Toyama Bay, earlier geological investigations have discovered four layers of tsunami deposits of different ages that can be traced along the coast (Yano and Takeuchi, 2014; Urabe et al., 2015, 2016; Tateishi and Kawamura, 2020). In the coastal lowlands of Iida Bay, Urabe et al. (2015) found two layers of possible tsunami deposits dated to approximately 2,500 and 3,500 years ago. The possible paleotsunami deposits are distributed far beyond the inundation limit of the 2024 tsunami (Fig. 3a). Further, at the southern coast of Sado Island where a high tsunami wave may have reached (Fig. 2), a tsunami deposit dated at 3,700–4000 years ago has been found (Iida et al., 2022). Iida et al. (2022) suggested that the tsunami deposit can be related to the past activity of F42 fault. The paleoseismological findings should be reviewed by analyzing the 2024 earthquake to reveal the relationship between the latest event and the causal events of the possible tsunami deposits. Paleotsunami records in the eastern margin of the Japan Sea are sparse compared to those on the Pacific coast of Japan (Takashimizu et al., 2020). Findings on the timing and size of past tsunamis derived from geological researches will improve our understanding of past rupture patterns of the active faults through numerical modeling of the paleotsunami source.
Submarine landslides in Toyama Bay could explain the tsunami arrival time at the Toyama station (Fig. 4c). A similar submarine landslide and subsequent tsunami were reported in Toyama Bay during the 2007 Noto earthquake (Abe et al., 2008). Previous investigations of bathymetric features clarified the distribution of past submarine landslides within the bay (Moriki et al., 2017; Inui and Shigihara, 2022). Although dozens of submarine landslides have occurred in Toyama Bay, no landslides were reported previously at L5 and L10 (Abe et al., 2007; Moriki et al., 2017; Inui and Shigihara, 2023). Therefore, a sufficient amount of sediment, ready to slide, may have accumulated at these locations, highlighting the importance of mapping past submarine landslides and slope susceptibility to ground motions in tsunami hazard assessments.