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We explore the potential of the adjoint-state full waveform tsunami inversion method for tsunami warning and source imaging using S-net, an array of ocean bottom pressure gauges. Compared to finite-fault tsunami source inversions, the method we use does not require as densely gridded Green’s functions to obtain a high resolution result, thus reducing computation time. What is required is a dense instrument network with good azimuthal coverage. The S-net pressure gauges fulfill this requirement and reduce the data collection time, thus making it possible to invert the recordings for the tsunami source and issue a timely tsunami warning. We apply our method to synthetic waveforms of the 2011 Mw 9.0 Tohoku earthquake and tsunami as well as data from the 2016 Mw 6.9 Fukushima earthquake. The results of the synthetic tests show that using the first 5 minutes of the waveforms, the adjoint-state inversion method achieves good performance with an average accuracy score of 93%, with the error of predicted wave amplitudes ranging between -5.6 to 1.9 m. Our application to the 2016 Fukushima earthquake shows the required waveform duration to achieve accurate inversions for smaller events is longer than that of a larger event. However, using the first 25 minutes of the waveforms, the inversion yields a tsunami source that is sufficient for making accurate predictions of arrival times and amplitudes. Assuming a uniformly distributed fault slip, we estimated a stress drop for the latter event to be 4.6 MPa, which is in line with estimations from recent studies.

We re-examined the slip distribution on faults of the 2004 Sumatra–Andaman (M 9.1 according to USGS) earthquake by the inversion of tsunami data with phase-corrected Green’s functions applied to linear long waves. The correction accounts for the effects of compressibility of seawater, elasticity of solid earth, and gravitational potential variation associated with the motion of mass to reproduce the delayed arrivals and the reversed phase of the first tsunami waves. We used sea surface height (SSH) data from satellite altimetry (SA) measurements along five tracks, and the tsunami waveforms recorded at tide gauges (TGs) and ocean bottom pressure gauges (OBPGs) in and around the Indian Ocean. The inversion results for both data sets for different rupture velocities (Vr) show that the reproducibility of the spatiotemporal SSHs and tsunami waveforms is improved by the phase corrections, although the effects are not so significant within the Indian Ocean. The best slip distribution model from joint inversion of SA, TG and OBPG data with Vr of 1.3 km/s shows the largest slips of 16–25 m off Sumatra Island, large slips of 2–11 m off the Nicobar Islands, and moderate slips of 2–6 m in the Andaman Islands. The inversion results reproduce the far-field tsunami waveforms well at distant stations even more than 13,000–25,000 km from the epicenter. The total source length is about 1400 km and the seismic moment is Mw 9.2, longer and larger than that of our previous estimates based on TG records.

The 2022 eruption of the Hunga Tonga-Hunga Ha'apai volcano excited an atmospheric Lamb wave, which induced a fast-traveling tsunami. This tsunami was driven by the pressure-forced wave traveling at the speed of the Lamb wave, and thus, was much faster than conventional tsunamis. This was the first case in which ocean bottom monitoring systems widely observed an air pressure-induced tsunami. The observation showed that the pressure-forced wave split after passing the Japan trench. Our simulations show that changes in water depth can amplify or decrease the pressure-forced wave. Simultaneously, an ocean gravity wave is generated due to the conservation of water volume. Because the ocean gravity wave was slower than the pressure-forced wave near Japan, it was separated from, and traveled behind, the pressure-forced wave. We reproduced the waveforms of different splitting stages observed by the stations near the Japan Trench.

The 2022 volcanic eruption in Tonga caused an unusually large tsunami around the Pacific. It travels with a faster apparent velocity and has larger amplitudes at long distances than what would be expected from a conventional tsunami from the volcanic source. This tsunami was generated by the moving atmospheric Lamb wave and traveled at the speed of the Lamb wave (0.31 km/s). Japanese data showed the amplitude of this first tsunami becomes small when approaching the coast, due to the weaker air-sea coupling at the shallow depth. This wave split when passing the continental slope, and traveled at the speed of the ocean gravity wave. Therefore, the tsunami observed at the coast is delayed by thousands of seconds from the passage of the Lamb wave. Tsunamis generated by this atmospheric mechanism have not been previously observed by modern digital recording systems and should be considered in the tsunami warning systems.

SUMMARY Tsunamis are often modelled as surface gravity waves of incompressible homogenous water propagating over a rigid seafloor. Previous studies have noted that when computing long-period tsunamis travelling at trans-oceanic distances with dominant periods of thousands of seconds, we need to consider four factors that are not included in the surface gravity wave theory: compressibility of seawater, density stratification of oceans, elasticity of the Earth and gravitational potential change associated with the tsunami motion. However, their effects on short-period tsunamis with dominant periods below 1000 s have not been examined. Here, we investigate how the four factors influence short-period tsunamis. Theoretical analyses and 1-D simulations using phase speeds of different tsunami models indicate that the resultant phase delay of short-period tsunamis becomes apparent after ∼1000 km propagation, mainly because of the first three factors. We then introduce a new phase correction method for dispersive short-period tsunamis with consideration of period-dependent ray paths and apply it to a 2-D simulation of a short-period tsunami from a submarine volcanic earthquake near Japan in 2015. The correction of the traveltime of a synthetic waveform by including the four factors amounts to ∼40 s at a distant station 1430 km away from the source, whereas the effects of the four factors on the waveforms are negligibly small at stations < ∼500km from the source. The observed traveltime at the ocean bottom pressure (OBP) gauge with a sampling interval at 15 s of the distant station can be explained only when these factors are incorporated into synthetic waveforms, indicating the effects due to the four factors are detectable by high-sampling OBP gauges that are deployed over broad oceanic regions.

SUMMARYWe estimated the slip distribution on the fault of the 2005 Nias earthquake (Mw 8.6) by inversions of local GPS and coastal uplift/subsidence data and tsunami waveform data. The 2005 Nias earthquake occurred approximately three months after the 2004 Sumatra–Andaman earthquake (Mw 9.1) at the southern extension off Sumatra Island, Indonesia. The tsunami from the 2005 earthquake caused significantly less damage than the 2004 tsunami, yet was recorded at tide gauges and ocean bottom pressure gauges around the Indian Ocean, including the coasts of Africa and Antarctica. The elastic and gravitational coupling between the solid earth and the ocean causes not only a traveltime delay but also the change of waveforms of far-field tsunamis relative to the prediction based on the long-wave theory. We corrected the computed tsunami Green's functions for the elastic and gravitational coupling effect in the tsunami waveform inversion. We found a diffused slip (∼2 m over an area of 400 km × 100 km) at deeper parts (20–54 km) of the fault with a large localized slip (7 m over 100 km × 100 km) slightly south of the epicentre. The large slips at deeper parts of the fault were responsible for the small tsunami generation. Inversion using far-field tsunami data yielded a slip distribution similar to that obtained using local geodetic data alone and that from the joint inversion of local geodetic and far-field tsunami data, which is also similar to slip distributions from previous studies based on local geodetic data. This demonstrates that far-field tsunami waveforms, once corrected for propagation effects, can be used to estimate the slip distribution of large submarine earthquakes leading to results that are similar to those obtained using sparse local geodetic data.

We estimated the origin time of the 1854 Ansei–Tokai tsunami from the tsunami waveforms recorded at three tide gauge stations (Astoria, San Francisco, and San Diego) on the west coast of North America. The tsunami signal is apparent in the San Francisco and San Diego records, and the arrival time was 0–1 p.m. Greenwich Mean Time (GMT) on 23 December 1854, whereas the tsunami signal of Astoria is ambiguous, and the arrival time could not be determined from the waveform. The simulated waveforms on the basis of nonlinear dispersive wave theory by assuming an origin time of 0 a.m. GMT on 23 December arrived earlier than the observations. Cross-correlation functions between the observed and simulated waveforms recorded at San Francisco and San Diego showed a time gap between them of approximately 30 min. Based on these results, we concluded that the origin time of the 1854 Ansei–Tokai tsunami was approximately 00:30 a.m. GMT or 09:46 local time on 23 December. Our result is roughly consistent with reports by a Russian frigate anchored in Shimoda Bay, ranging the earthquake between 09:00 and 09:45 and the tsunami between 09:30 and 10:00. The earthquake was also reported in historical Japanese documents ranging from 8 and 10 o’clock in local time.

The direct simulation of inundation in developed urban areas presents a much greater challenge than the more common bare earth simulations that use roughness, which are used in many tsunam...

We propose a ray-tracing method to solve the two-point boundary value problem for tsunamis based on the long-wave theory. In the long-wave theory, the tsunami wave velocity is proportional to the square root of water depth, which is available from global bathymetric atlases. Our method computes the shortest travel times starting from each of the two given points and calculates the local ray direction to trace the ray path. We utilize an explicit, non-iterative tracing scheme that exhibits robust results and applies to any tsunami-accessible locations, and the global-shortest travel-time path is derived. In simple and real bathymetry cases, our method demonstrates stable results with neglectable low uncertainties. The ray-tracing method is then applied to analyze the path of tsunamis from different directions to four important bays in Japan. The result shows that tsunami ray paths are significantly influenced by local bathymetry, and some crucial structures, such as trench and trough, behave as the primary routes of this region. Deploying stations near these routes will be most beneficial for tsunami early warning. The existing tsunami-observing system off the Honshu area works well for tsunamis from the east side but slightly deficient for tsunamis from the west side. The far-field ray tracing shows that tsunamis traveling from Chile to Japan through two main routes—one via north Hawaii and the other via the south— depending on the location of the source.

Systemic travel time delays of up to 15 min relative to the linear long waves for transoceanic tsunamis have been reported. A phase correction method, which converts the linear long waves into dispersive waves, was previously proposed to consider seawater compressibility, the elasticity of the Earth, and gravitational potential change associated with tsunami motion. In the present study, we improved this method by incorporating the effects of ocean density stratification, actual tsunami raypath, and actual bathymetry. The previously considered effects amounted to approximately 74% for correction of the travel time delay, while the ocean density stratification, actual raypath, and actual bathymetry, contributed to approximately 13%, 4%, and 9% on average, respectively. The improved phase correction method accounted for almost all the travel time delay at far-field stations. We performed single and multiple time window inversions for the 2011 Tohoku tsunami using the far-field data (>3 h travel time) to investigate the initial sea surface displacement. The inversion result from only far-field data was similar to but smoother than that from near-field data and all stations, including a large sea surface rise increasing toward the trench followed by a migration northward along the trench. For the forward simulation, our results showed good agreement between the observed and computed waveforms at both near-field and far-field tsunami gauges, as well as with satellite altimeter data. The present study demonstrates that the improved method provides a more accurate estimate for the waveform inversion and forward prediction of far-field data.

We investigate the feasibility of inverting high-resolution vertical seafloor displacement from tsunami waveforms. An inversion method named "SUTIM" (small unit tsunami inversion method) is developed to meet this goal. In addition to utilizing the conventional least-square inversion, this paper also enhances the inversion resolution by Grid-Shifting method. A smooth constraint is adopted to gain stability. After a series of validation and performance tests, SUTIM is used to study the 2010 Chile earthquake. Based upon data quality and azimuthal distribution, we select tsunami waveforms from 6 GLOSS stations and 1 DART buoy record. In total, 157 sub-faults are utilized for the high-resolution inversion. The resolution reaches 10 sub-faults per wavelength. The result is compared with the distribution of the aftershocks and waveforms at each gauge location with very good agreement. The inversion result shows that the source profile features a non-uniform distribution of the seafloor displacement. The highly elevated vertical seafloor is mainly concentrated in two areas: one is located in the northern part of the epicentre, between 34° S and 36° S; the other is in the southern part, between 37° S and 38° S.