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Abstract We explored nonlinear effects within the context of tsunami waveform inversion, wherein Green's functions were linearly superimposed to estimate earthquake slips. We focused on these effects while developing a source model for the 2003 Tokachi–Oki earthquake off Hokkaido, Japan. A source model for this earthquake was developed based on linear tsunami waveform inversion using Green’s functions and tsunami waveforms observed at tide gauge stations. Subsequently, tsunami waveforms from the source were simulated at the stations using nonlinear long-wave theory and compared with those estimated by inversion. The comparisons demonstrated that the waveforms had a non-negligible discrepancy that was attributed to advection effects, even for the primary wave used in the inversion at the two stations. This result strongly suggests that advection effects should be considered in the source modeling of the 2003 earthquake based on tsunami waveforms observed by tide gauges. Based on these results, a new tsunami waveform inversion technique that incorporates linearly approximated advection effects and maintain the framework of linear tsunami waveform inversion using Green’s functions is proposed and applied. The proposed method successfully mimicked the advection effects during the 2003 tsunami, reproduced better tsunami waveforms, and developed a source model for the 2003 earthquake using these effects. The peak slip amount and seismic moment were greater in the source model with advection effects than those without the effects. This finding suggests that the values in the source models developed for other earthquake events without considering these effects may have been underestimated. Graphical abstract

Abstract This paper provides an overview of inverse studies that estimate earthquake source processes using tsunami-related data. Methods and techniques developed with those data associated with the 2004 Sumatra and 2011 Tohoku-oki earthquakes were reviewed. These events significantly impacted subsequent studies that focused on great historical earthquakes. Thus, recent advancements from studies on great historical earthquakes (M > 8) using old tsunami data, including documents and non-digital tsunami waveforms, have been reviewed. Another key earthquake was the 1700 Cascadia earthquake, and its source process was revealed using geological tsunami deposit data, which have led to a recent surge in prehistorical earthquake studies using tsunami deposit data. Considering this, the advancements in prehistorical earthquake studies have been reviewed. Finally, expected advancements in earthquake source process studies using tsunami-related data in the near future have been discussed.

Abstract A tsunami generated by an earthquake that occurred off the east coast of Japan in 1611 was predominantly concentrated along the Sanriku Coast. The 1611 event produced its greatest observed tsunami height at Koyadori, 28.8 m, higher than that produced by other representative tsunamis at the same location such as the 2011 Tohoku and 1896 Meiji Sanriku tsunamis. The characteristics of the source that resulted in the remarkable tsunami height at Koyadori have been widely debated. In this study, we simulated the local intensification mechanism of the 1611 tsunami and derived some key characteristics of the earthquake that produced the intensification at Koyadori based on these results. First, we investigated the topographical inundation characteristics in representative areas on the Sanriku Coast, including Koyadori, by numerical means. By comparing the numerical results with the observed heights for the 1611 tsunami, we found that a simulated tsunami that was dominated by short-wave components yielded a promising reproduction of the observed heights. The development of a local resonance seemed a more likely cause for the observed local intensification at Koyadori than a single-pulse wave. These results suggested that the 1611 earthquake produced a tsunami dominated by short-wave components. Furthermore, the source must have been located far off the Tohoku coast near the Japan Trench axis to have had substantial short-wave components along the Sanriku Coast. Based on these findings, we constructed a source scenario for local intensification by investigating the characteristics of Green’s functions from single-point sources. The scenario involves two separate earthquake sources in shallow crustal areas at the plate interface of the subduction zone, resulting in a moment magnitude of 8.5. The tsunami produced by this source model, which reflected the characteristics of a tsunami earthquake, effectively reproduced the local intensification observed on the Sanriku Coast.

Abstract A large eruption of the Hunga Tonga-Hunga Haʻapai volcano in Tonga on January 15, 2022 generated air–sea coupled tsunamis observed at the ocean-bottom pressure sensor network along the Japan Trench (S-net) in Japan. Initial tsunamis from the 2022 Tonga eruption, detected by 106 ocean-bottom pressure sensors, were well modeled by an air–sea coupled tsunami simulation, with a simple atmospheric pressure pulse as sine function, having a half-wavelength of 300 km and a peak amplitude of 2 hPa. A one-dimensional air–sea coupled tsunami simulation having a simple bathymetry shows that an input atmospheric pressure pulse with a short half-wavelength of 50 km, which is shorter than the length of the ocean bottom slopes, caused an amplitude increase via the Proudman resonance effect near the deep trench. The wavefront distortion due to the separation of the air–sea coupled wave propagating with a speed of 312 m/s and tsunami propagating with that of $$\sqrt{gd}$$ gd , where g is gravity acceleration and d is the ocean depth, is also significant near the shore. In contrast, these effects are not significant for the half-wavelength of the input atmospheric pressure pulse of 300 km. These results indicate that the air–sea coupled tsunami propagating through the trench is sensitive to the wavelength of an atmospheric pressure pulse. Graphical Abstract

Abstract For Japanese coastal communities along the Japan Sea, where the risk of earthquake-induced tsunamis is deemed lower than that along the Pacific Ocean, tsunami disaster mitigation strategies have not been sufficiently developed. This study estimated the tsunami inundation characteristics for three major Japanese coastal cities along the Japan Sea. Based on tsunami simulations for representative coastal areas, we aimed to identify common vulnerabilities, which included those suggested by previous studies and local governments, to develop disaster mitigation strategies. Comprehensive simulations for tsunami propagation and inundation were performed for coastal areas in Akita City, Sakata City, and Niigata City based on earthquake and tsunami source scenarios developed by the Japanese Government for the Japan Sea area. To demonstrate the effectiveness of the estimated inundation characteristics, tsunami inundation was simulated for each coastal area under varying tsunami source conditions (including excessive tsunami magnitude) with a high resolution of the topography and infrastructure. Natural sand dunes, ports with man-made breakwaters, and rivers with levees are typical topographical features found in urbanized and densely populated areas along the Japan Sea coastline. According to the simulated results, the dunes and port breakwaters contribute significantly to decreasing the total amount of tsunami inundation for the areas behind them. However, the presence of the breakwaters also increases the tsunami heights in the areas immediately beyond the ports. Additionally, even the areas protected by the dunes might be exposed to an inundation risk in which the tsunamis invade a river channel, causing it to overflow. These findings were common to the coastal areas, and could be generally applicable to tsunami inundation for all coastal areas along the Japan Sea. Based on these results, the enhancement of existing infrastructure such as breakwaters and river levees should be the priority measure within tsunami risk-mitigation strategies; these, combined with natural resources such as dunes, can effectively mitigate tsunami disasters. Graphical Abstract

Abstract In the present study, the local tsunami amplification observed in Ryori Bay, located on the Sanriku coast of Japan, was investigated using numerical simulations. Large-scale tsunami propagation simulations and tsunami inundation simulations for the bay were systematically conducted to estimate and model the 2011, 1933, and 1896 tsunamis that occurred off the Sanriku coast and which resulted in large run-ups. The simulation results, which are moderately consistent with observations, presented larger run-up heights and inundations for the 1933 and 1896 tsunamis (which followed relatively small earthquakes) compared to those of the 2011 tsunami (which followed a larger earthquake). Furthermore, the frequency analysis indicated that the former two tsunamis comprised higher predominant components. A tsunami inundation simulation using parametrized synthetic waveforms was conducted to identify the contributing factors associated with the large amplification and run-ups. The results indicated that the predominant components are significantly amplified in the bay and the initial decrease in the water surface elevation prior to the primary waves of the two tsunamis leads to an increase in their run-up heights. Furthermore, the simulated waveforms of the tsunamis revealed that the 1933 and 1896 tsunamis had their wavefronts changed into a steep wavefront, i.e., a bore-like wave, during their wave developments in the bay, attributed to shoaling, narrowing bay width, and the nonlinear effect of the wave. These results, therefore, indicate that bores which are known to generate large run-up heights were generated in the bay during the two tsunamis.

Abstract The 2011 Tohoku-oki earthquake generated a large tsunami that caused catastrophic damage along the Pacific coast of Japan. The major portion of the damage along the Pacific coast of Tohoku in Japan was mainly caused by the first few cycles of tsunami waves. However, the largest phase of the tsunami arriving surprisingly late in Hakodate in Hokkaido, Japan; that is, approximately 9 h after the origin time of the earthquake. It is important to understand the generation mechanism of this large later phase. The tsunami was numerically computed by solving both linear shallow water equations and non-linear shallow water equations with moving boundary conditions throughout the computational area. The later tsunami phases observed on southern Hokkaido can be much better explained by tsunami waveforms computed by solving the non-linear equations than by those computed by solving the linear equations. This suggests that the later tsunami waves arrived at the Hokkaido coast after propagating along the Pacific coast of the Tohoku region with repeated inundations far inland or reflecting from the coast of Tohoku after the inundation. The spectral analysis of the observed waveform at Hakodate tide gauge shows that the later tsunami that arrived between 7.5 and 9.5 h after the earthquake mainly contains a period of 45–50 min. The normal modes of Hakodate Bay were also computed to obtain the eigen periods, eigenfunctions, and spatial distribution of water heights. The computed tsunami height distributions near Hakodate and the fundamental mode of Hakodate Bay indicate that the large later phases are mainly caused by the resonance of the bay, which has a period of approximately 50 min. The results also indicate that the tsunami wave heights near the Hakodate port area, the most populated area in Hakodate, are the largest in the bay because of the resonance of the fundamental mode of the bay. The results of this study suggest that large future tsunamis might excite the fundamental mode of Hakodate Bay and cause large later phases near the Hakodate port.

Abstract The 1906 Colombia–Ecuador earthquake induced both strong seismic motions and a tsunami, the most destructive earthquake in the history of the Colombia–Ecuador subduction zone. The tsunami propagated across the Pacific Ocean, and its waveforms were observed at tide gauge stations in countries including Panama, Japan, and the USA. This study conducted slip inverse analysis for the 1906 earthquake using these waveforms. A digital dataset of observed tsunami waveforms at the Naos Island (Panama) and Honolulu (USA) tide gauge stations, where the tsunami was clearly observed, was first produced by consulting documents. Next, the two waveforms were applied in an inverse analysis as the target waveform. The results of this analysis indicated that the moment magnitude of the 1906 earthquake ranged from 8.3 to 8.6. Moreover, the dominant slip occurred in the northern part of the assumed source region near the coast of Colombia, where little significant seismicity has occurred, rather than in the southern part. The results also indicated that the source area, with significant slip, covered a long distance, including the southern, central, and northern parts of the region.