Tsunami Propagation Research Articles

Probabilistic Tsunami Hazard Assessment from Manila Trench to Shantou City in China

Manila Trench is an ocean trench that lies to the west of Luzon Island in the Philippines, which has the potential to generate a significant tsunami that could affect the coastal areas around it. This paper analyzes the tsunami hazard at the southern coastline of China, and more specifically at the city of Shantou. A Monte Carlo-type probabilistic tsunami hazard assessment (PTHA) with 5000 simulation runs was conducted using the tsunami propagation model COMCOT. A wide range of earthquake magnitudes were stochastically simulated in these zones, ranging from 7.0 to 9.0 in magnitude, and the peak nearshore tsunami amplitude (PNTA), for return periods of 100, 1,000 and 10,000 years, was determined by propagation simulations to be 0.15 m, 0.65 m and 1.75 m, respectively. Inundation simulations for the case study area, which considered various scenarios of sea level rise between the present day and the year 2100, were also conducted. The results indicate the severe influence that sea level rise could have on tsunami risks, which can provide valuable information for disaster risk managers and planners on how to develop adaptation pathways not only for this city but also for other points in the southeast coastline of China.

Low power computation of transoceanic wave propagation for tsunami hazard mitigation

This paper proposes the use of specialized hardware accelerator based on the Field Programmable Gates Array (FPGA) microchip to compute tsunami wave propagation to assess and manage risks of marine natural disasters, namely, tsunami waves caused by underwater earthquakes. After a sufficiently strong seismic event, many countries and research centres launch extensive computations to estimate the tsunami wave parameters in certain parts of the coast to determine if a declaration of a tsunami alarm is warranted. This requires high computating powers which leads to higher energy costs. The paper demonstrates how an FPGA–based special Calculator (architecture of which has been earlier proposed by the authors), installed on a Personal Computer (PC) could be used to calculate the propagation of a tsunami wave over the entire Pacific Ocean, from the subduction zone offshore Kamchatka Peninsula and Kuril Islands to the coast of Chile. Such calculations offer reliable results within a few minutes and make it possible to obtain the distribution of expected tsunami wave heights along the coast. If the obtained results indicate a danger to the population or possible distruction of infrastructure, it becomes paramount to carry out more detailed calculations to accurately estimate the wave parameters at specific locations along the coast where negative consequences are expected. This requires cluster and/or supercomputer systems, which consume significant energy and hence are expensive. In case the modelling results indicate small values of maximum wave heights at populated coastal areas, population of the near–shore regions can be immediately informed about low amplitude tsunami wave; more detailed studies are not needed. This hence leads to noticeable savings in energy consumption. The paper presents a calculation of the propagation of a tsunami wave across the Pacific Ocean on a personal computer using a FPGA–based hardware acceleration of a computer code execution.

The effect of earthquake fault rupture kinematics on tsunami generation: a numerical study of real events

Summary The study is devoted to the effect of the fault rupture kinematics in the earthquake source on tsunami generation. Sixteen events of 1992–2021 years are investigated. For each event, the kinematic tsunami source (bottom motion during the earthquake) and the static tsunami source (permanent bottom deformation) were calculated using the Finite Fault Models provided by the U.S. Geological Survey. For both sources, numerical tsunami simulations were carried out within the framework of linear long-wave theory. Comparison of the simulation results showed that in ten out of sixteen events, the energy of tsunami excited by the kinematic source is greater than that excited by the static source. The maximum energy amplification (9.1 per cent) is observed at the minimum ratio of average rupture velocity to long-wave velocity. The Illapel 2015 event has been investigated more thoroughly using dispersive tsunami models jagurs and cptm. This investigation showed that the kinematic source causes a spatial redistribution of tsunami amplitudes and a noticeable amplification of the high-frequency component in the time series of tsunami height. At some points along the Chilean coast, the difference between the kinematic and static calculations is more than 2 m.

An Analytical Study of Tsunamis Generated by Submarine Landslides

In this work, the problem of tsunamis generated by underwater landslides is addressed. Two new solutions are derived in the framework of the linear shallow water equations and linear potential wave theory, respectively. Those solutions are analytical (1 + 1D) and another is semi-analytical (2 + 1D). The 1 + 1D model considers a solid body sliding over a sloping beach at a constant speed, and the 2 + 1D model considers a solid landslide that moves at a constant velocity on a flat bottom. The solution 1 + 1D is checked numerically using a different finite scheme. The 2 + 1D model examines the kinematic and geometric features of the landslide at a constant ocean depth and its influence on the generation of tsunamis. Landslide geometry significantly influences run-up height. Our results reveal a power law relationship between normalized run-up and landslide velocity within a realistic range and a negative power law for the landslide length–thickness. Additionally, a critical aspect ratio between the length and width of the sliding body is identified, which enhances the tsunamigenic process. Finally, the results show that the landslide shape does not have a decisive influence on the pattern of tsunami wave generation and propagation.

Physical experiments of waves generated by submerged steam eruptions with applications to volcanic tsunamis.

The tsunamigenic potential of underwater volcanic eruptions is not well understood, even though eruption-generated tsunamis can be devastating. To address how erupted steam bursts from underwater volcanoes generate tsunamis, we present the experiments, using pressurized steam injected vertically into a water tank. Results over various eruption conditions identify three eruption regimes, namely, shallow-, intermediate-, and deep-water eruptions, according to the combined effects of water depths, source strengths, and source durations. The transition between shallow and intermediate eruptions is characterized by critical depths maximizing tsunami wave heights, while the transition between intermediate and deep eruptions is characterized by containment depths inhibiting surface disturbances. Water depth and source intensity are the dominant factors controlling maximum wave amplitudes, more so than aspects of jet duration and condensation. These experiments and supporting dimensional analysis improve our understanding of how underwater volcanic eruptions form tsunamis, while also providing a complete dataset for advancing tsunami generation models.

Cascading hazards in volcanic environments: monitoring, modelling and impact analysis of tsunamigenic flows for risk reduction

Volcanic environments present complex multi-hazard scenarios where primary volcanic activity can trigger cascading hazards or where multiple hazards can occur simultaneously, leading to cascading and compounding impacts on communities and ecosystems. Stromboli, one of the most active volcanoes globally, exemplifies these challenges with its frequent eruptions, pyroclastic density currents, landslides, and tsunamis. In the present study, the mechanisms behind tsunamigenic flows at Stromboli are investigated by using extensive monitoring data from previous studies and numerical modelling. Key findings from simulations and parametric analysis are presented, showing the relationships between mass flow dynamics, morphological factors, and tsunami generation. A more comprehensive context is then considered by drawing the impact chain related to tsunamigenic flows during a volcanic eruption. This includes a broad evaluation of the exposure, vulnerability and possible mitigation measures. Starting from the study of the hazard and then following up with the evaluation of the impacts, this study emphasizes the necessity of a holistic approach in multi-hazards environment, where accurate hazards modelling and monitoring, interdisciplinary collaboration, and community engagement need to be considered to reduce risk.

The Multi‐Segment Complexity of the 2024 MW ${M}_{W}$ 7.5 Noto Peninsula Earthquake Governs Tsunami Generation

AbstractThe 1 January 2024, moment magnitude 7.5 Noto Peninsula earthquake ruptured in complex ways, challenging analysis of its tsunami generation. We present tsunami models informed by a 6‐subevent centroid moment tensor (CMT) model obtained through Bayesian inversion of teleseismic and strong motion data. We identify two distinct bilateral rupture episodes. Initial, onshore rupture toward the southwest is followed by delayed re‐nucleation at the hypocenter, likely aided by fault weakening, causing significant seafloor uplift to the northeast. We construct a complex multi‐fault uplift model, validated against geodetic observations, that aligns with known fault system geometries and is critical in modeling the observed tsunami. The simulations can explain tsunami wave amplitude, timing, and polarity of the leading wave, which are crucial for tsunami early warning. Upon comparison with alternative source models and analysis of 2000 multi‐CMT ensemble solutions, we highlight the importance of incorporating complex source effects for realistic tsunami simulations.

Global tsunami modelling on a spherical multiple-cell grid

A model of shallow water equations (SWEs) on a spherical multiple-cell (SMC) grid of 4-level (2.5–5–10–20 km) spatial resolutions is used to simulate tsunami propagation on global ocean surfaces. The unstructured SMC grid retains rectangular cells of the longitude-latitude grid so that efficient finite-difference schemes could be used. It also supports multi-resolutions like mesh refinement to resolve small islands and coastline details while keeping models compact enough to fit into available computers. Two earthquake-induced tsunami cases are simulated and compared with available observations. Results indicate that the modelled tsunami arrival times agree well with observations while tsunami wave heights are underestimated, particularly the observed runups on remote coastal lands. Possible reasons for this underestimation include the smoothing scheme used to suppress numerical oscillations and the missing of initial kinetic energy input from the earthquakes. Another reason is the limitation of the SWEs to describe coastal bores and breaking waves in coastal waters. A possible tsunami scenario induced by a landslide in the Canary Islands is also simulated to assess its potential impact on Atlantic coastal regions. Model results indicate that this kind of tsunami may cause severe damage to local areas but its effects on far fields, like the UK and American coastal regions are small. As the initial landslide disturbance is overly simplified, this study does not give a true representation of a real landslide tsunami but rather a qualitative assessment of its impact on the Atlantic Ocean. More realistic initial condition and improved model representation of coastal processes are needed for further studies of this possible landslide hazard.

Numerical modelling of pump-driven tsunami generation and fluid-structure-interaction in idealized urbanized coastal areas during run-up

Tsunami wave inundations are still one of the most devastating natural disasters worldwide. Tsunamis striking a settlement frequently devastate much of its infrastructure. In instances where infrastructure withstands the tsunami’s actions, it acts as a flow resistance for the wave’s run-up, altering inundation dynamics and flow depth. Accurately predicting the complex dynamics of tsunami wave run-up in densely populated urban areas is paramount for informing effective evacuation protocols and conducting comprehensive hazard and risk assessments. In pursuit of improving wave run-up prediction capabilities, this study delves into the three-dimensional numerical modelling of wave run-up of non-breaking, long tsunami waves in urbanized areas. Leveraging insights from a physical experiment with pump-driven wave generation and idealized infrastructure, a novel pressure-based wave generation boundary condition is developed. The boundary condition achieves an average of 4.9% accuracy in replicating the water surface elevation from experiments. Additionally, it attains an average 1.5% precision in reproducing flow velocities, furthermore reproducing the spatial flow dynamics accurately. Physical experiment wave run-up is modelled with an average 6.9% deviation for both simulations with and without idealized infrastructure. 63.0% higher non-linearity waves than in the physical experiments are additionally investigated to highlight the boundary conditions capabilities of high non-linearity wave generation, change in run-up reduction for higher non-linearity waves for infrastructure interaction and furthermore in-depth flow field characteristics during tsunami inundation. Finally, the study highlights deviations from analytically calculated wave run-up, emphasizing the necessity for numerical and physical experimental evaluation for both high non-linearity waves and tsunami infrastructure interaction, ultimately fostering both resilience and preparedness against tsunami hazards.

Dynamic Rupture Modeling of Large Earthquake Scenarios at the Hellenic Arc Toward Physics‐Based Seismic and Tsunami Hazard Assessment

AbstractThe Mediterranean Hellenic Arc subduction zone (HASZ) has generated several 8 earthquakes and tsunamis. Seismic‐probabilistic tsunami hazard assessment typically utilizes uniform or stochastic earthquake models, which may not represent dynamic rupture and tsunami generation complexity. We present an ensemble of ten 3D dynamic rupture earthquake scenarios for the HASZ, utilizing a realistic slab geometry. Our simplest models use uniform along‐arc pre‐stresses or a single circular initial stress asperity. We then introduce progressively more complex models varying initial shear stress along‐arc, multiple asperities based on scale‐dependent critical slip weakening distance, and a most complex model blending all aforementioned heterogeneities. Thereby, regional initial conditions are constrained without relying on detailed geodetic locking models. Varying epicentral locations in the simplest, homogeneous model leads to different rupture speeds and moment magnitudes. We observe dynamic fault slip penetrating the shallow slip‐strengthening region and affecting seafloor uplift. Off‐fault plastic deformation can double vertical seafloor uplift. A single‐asperity model generates a 8 scenario resembling the 1303 Crete earthquake. Using along‐strike varying initial stresses results in 8.0–8.5 dynamic rupture scenarios with diverse slip rates and uplift patterns. The model with the most heterogeneous initial conditions yields a 7.5 scenario. Dynamic rupture complexity in prestress and fracture energy tends to lower earthquake magnitude but enhances tsunamigenic displacements. Our results offer insights into the dynamics of potential large Hellenic Arc megathrust earthquakes and may inform future physics‐based joint seismic and tsunami hazard assessments.

Well-posedness and potential-based formulation for the propagation of hydro-acoustic waves and tsunamis

Abstract We study a linear model for the propagation of acoustic and surface gravity waves in a stratified free-surface ocean. A formulation was previously obtained by linearizing the compressible Euler equations. In this paper, we introduce a new formulation written with a generalized potential. The new formulation is obtained by studying the functional spaces and operators associated to the model. The mathematical study of this new formulation is easier and the discretization is also more efficient than for the previous formulation. We prove that both formulations are well posed and show that the solution to the first formulation can be obtained from the solution to the second. Finally, the formulations are discretized using a spectral element method, and we simulate waves generation from submarine earthquakes and landslides. Résumé Nous étudions un modèle linéaire pour la propagation des ondes acoustiques et des vagues dans un océan stratifié à surface libre. Une première formulation, déduite des équations d’Euler compressible linéarisées, a été proposée dans un précédent article. Dans cet article, nous développons une nouvelle formulation écrite avec un potentiel généralisé. Cette nouvelle formulation est obtenue en étudiant les espaces fonctionnels et les opérateurs associés au modèle. L’étude mathématique et la discrétisation de cette nouvelle formulation sont plus simples que celles de la précédente formulation. Nous montrons que les deux formulations sont bien posées, et que la solution de la première formulation peut être calculée avec la solution de la seconde. Les deux formulations sont ensuite discrétisées avec une méthode d’éléments finis spectraux. Nous présentons des simulations d'ondes générés par des tremblement de terre et des glissements de terrain sous-marins.

Adjusting Manning coefficients to simulate tsunami propagation over porous coral reef

This study investigates the effect of porous coral reef on the tsunami propagation in terms of experimental and numerical modelling. It aims at quantifying the influence of several input parameters on the wave attenuation and at adjusting Manning coefficients to reproduce experimental results. The density and the surface of individual reefs are fixed as well as the width and length of the coral barrier. Results show that the reef height is the most sensitive parameter. This latter affects the tsunami propagation with an attenuation of the first wave reaching 15 % compared to the case with a smooth reef. Wave breaking occurs on the reef flat for each test but, as expected, its location depends greatly on the reservoir depths difference. Numerical simulations show that the Manning coefficient must be adjusted both by considering the coral reef height and the spatial grid resolution. It varies from 0.01 (for lowest reef with highest grid resolution) to 0.058 (for higher reefs with coarsest grid resolution).

Physical Modeling of Tsunamis Generated by Submarine Volcanic Eruptions

AbstractSubmarine volcanic eruptions can induce major local and regional tsunami hazards through varied source mechanisms. Large‐scale experiments of tsunamis generated by submarine volcanic eruptions are conducted to study the cylindrical wave generation and propagation in a three‐dimensional wave basin. A unique volcanic tsunami generator (VTG) was deployed at the bottom of the wave basin to generate volcanic tsunamis with repeatable and controlled source parameters. The physical modeling is based on the generalized Froude number defined with the VTG velocity and the near source water depth. The pneumatically driven vertical stroke motion generates leading elevation waves in the wave basin. The tsunami waves generated by the VTG are measured with a wave gauge array. The wave maker performance is characterized by the dimensionless leading wave amplitudes and periods. The experimental data show the variations of the leading wave amplitude, period, and celerity along the radial propagation distance. The generated cylindrical waves belong to the weakly nonlinear wave regime in the near field with decaying wave amplitude along radial propagation. The attenuation rate of the leading wave exceeds the range from the linear wave theory in runs with higher Froude numbers. The dimensionless leading wave period increases with the dimensionless propagation distance due to the dispersion relation. Empirical equations for the characteristic wave parameters such as amplitudes and periods are derived. The experimental results contribute to the understanding of volcanic tsunami generation processes and may serve rapid volcanic tsunami hazard assessments as well as the advancement and validation of numerical models.

Compressible ocean waves generated by sudden seabed rise near a step-type topography

A typical tsunami generation occurs through submarine earthquakes leading to large volume displacement. The corresponding mathematical problem involves modeling surface water waves generated by an arbitrary temporal motion of the ocean floor. The propagation of tsunami wave and the subsequent scattering from a sudden drop in bathymetry away from the ground motion is studied following linearized water wave theory and a weakly compressible ocean, including static oceanic background compression. The Fourier transformation and eigenfunction expansion techniques are employed to find the surface displacement and pressure profiles by leveraging appropriate matching conditions between regions of different depths. A novel energy balance relationship is derived by considering both the pure-gravity and acoustic-gravity modes. The model is validated in the limit that the depth difference approaches zero, showing a vanishing reflection contribution from the depth change. An efficient numerical code is developed that accurately captures the contribution of the cutoff frequencies of acoustic-gravity modes. Apart from the time-domain propagation of tsunami waves away from the origin, standing wave formations are observed within the shallow region, supported by significantly large pressure fluctuations in time. These standing waves or, equivalently, the pressure fluctuations sustain longer for larger ocean depth. The increase in tsunami speed in the deeper region is readily visible in the time-domain simulations. A three-dimensional axisymmetric solution is also developed, and results show a more gradual sloping tsunami wavefront compared to the equivalent two-dimensional solution for shallower depths. Animation movies corresponding to the two- and three-dimensional surface profiles are provided for better visualization.

A Typical of Tsunami Generation Caused by Volcano Flank Collapse in Banda Neira, Maluku, Indonesia

Abstract The history eruption of the Banda volcanoes was recorded in 1632, 1816, and 1988 and was preceded by significant earthquakes. In the eruption in 2017, there were 28 volcanic earthquakes, indicating a rock cracking process due to the movement of magma in the form of gas, liquid, and rock solids. We suspect that when the earthquake occurs, the rock-cracking process upon the eruption will potentially trigger the volcano flank to collapse into the sea and generate a tsunami in the Banda Naira and surrounding area. We contribute to modeling the travel time and tsunami inundation resulting from the flank collapse of Banda Volcano. BATNAS bathymetry data is used to run tsunami simulations. We use aerial photography from field survey data to interpret Banda Volcano failure parameters, including diameter, direction of sliding of the collapse, and slope of the collapse of the side of the Banda Volcano. Based on the tsunami simulation, the volcano flank collapse source on Banda Volcano produced a maximum tsunami in Banda Naira as high as 6.2 meters, and the tsunami will arrive around 6 – 8 minutes. While in AI Island, tsunami inundation reached 55.87 m and arrived in 4 minutes. Meanwhile, the maximum elevation of Banda Naira Island is 3.5 meters, with a population of 21,000 people in March 2024. Tsunami inundation has the potential to submerge entire residential areas in Banda Neira.

A coupled atmosphere-ocean source mechanism was a predictor of the 2022 Tonga volcanic tsunami

Volcanic tsunamis pose significant threats to nearby coastal communities. Despite extensive research, the mechanism behind tsunami generation remains unclear, and the ability to forecast a destructive tsunami has proven elusive. Here we present findings from the 2022 Tonga volcanic incident, showing that the leading air-pressure wave holds promise as a key predictor of tsunami behavior. We constructed an integrated atmosphere-ocean model to explain the underlying mechanism and validated it with various data, including satellite altimetry measurements. Contrary to prior hypotheses, our results reveal that: (1) the eruption process governs both the air-pressure and tsunami dynamics; and (2) the resulting crater volume controls the volcanic ejecta that produces the air-pressure waves, while the corresponding mass loss in the ocean triggers influxes of water into the crater, generating the tsunami. This study unveils a coupled atmosphere-ocean source mechanism in generating volcanic tsunamis and advocates for incorporating air-pressure sensors into early warning systems.

Forearc crustal faults as tsunami sources in the upper plate of the Lesser Antilles subduction zone: the case study of the Morne Piton fault system

Abstract. In this study, alternatively to the megathrust, we identify upper-plate normal faults orthogonal to the trench as a possible tsunami source along the Lesser Antilles subduction zone. The Morne Piton fault system is such a trench-perpendicular upper crustal fault at the latitude of Guadeloupe. By means of seismic reflection, high-resolution bathymetry, remotely operated vehicle (ROV) imaging and dating, we reassess the slip rate of the Morne Piton fault since 7 Ma, i.e., its inception, and quantify an average rate of 0.25 mm yr−1 since ca. 1.2 Ma. This result divides by two previous estimations, increases the earthquake time recurrence and lowers the associated hazard. The ROV dive revealed a metric scarp with striae at the toe of the Morne Piton fault system, suggesting a recent fault rupture. We estimate a fault rupture area of ∼ 450–675 km2 and then a magnitude range for a maximum seismic event around Mw 6.5 ± 0.5, making this fault potentially tsunamigenic as the nearby Les Saintes fault responsible for a tsunami following the 2004 Mw 6.3 earthquake. Consequently, we simulate a multi-segment tsunami model representative of a worst-case scenario if all the identified Morne Piton fault segments ruptured together. Our model provides clues for the potential impact of local tsunamis on the surrounding coastal area as well as for local bathymetric controls on tsunami propagation. We illustrate that (i) shallow-water plateaus act as secondary sources and are responsible for a wrapping of the tsunami waves around the island of Marie-Galante; (ii) canyons indenting the shallow-water plateau slope break focus and enhance the wave height in front of the most touristic and populated town of the island; and (iii) the resonance phenomenon is observed within the Les Saintes archipelago, showing that the waves' frequency content is able to perturb the sea level for many hours after the seismic rupture.

Tsunami propagation and flooding maps: An application for the Island of Lampedusa, Sicily Channel, Italy

AbstractThe Mediterranean coastlines are densely populated zones which host key socio‐economic and commercial activities. For this reason, coastal areas are vulnerable sites in case of natural disasters as tsunamis that can strike coasts causing widespread damage to the population and facilities. For these reasons, several studies were performed over the last decade to study the impact of tsunami waves on the coasts. This research assessed the inundation risk due to a tsunami wave which can hit the southeastern coast of Lampedusa Island. The coastal low‐lying geomorphological setting of the southeastern part of the island led to significant socio‐economic growth, but Lampedusa falls within the Mediterranean Sea, a high‐tsunamigenic area, therefore, the need to investigate tsunami propagation and coastal flooding of this sensitive site emerged. For this scope, a calculation chain model was implemented incorporating three steps: the DELFT‐3D software for earthquake effects modelling, MIKE 21 Flow Model FM for nearshore propagation and HEC‐RAS for onshore tsunami inundation modelling. The simulations illustrate the impact of three tsunami scenarios with different magnitudes (Mw 8.5, 7.5, 6.5) generated by hypothetical earthquakes in the Hellenic Arc. In the Mw 8.5 magnitude scenario, significant flooding occurs in the harbour region, with maximum water depths reaching approximately 3.5 m. The maximum water velocity in this scenario reaches about 15 m/s in the eastern portion, adjacent to cliffs impacted by the tsunami wave. In contrast, the Mw 7.5 magnitude scenario demonstrates reduced flooded areas, with the cliffs containing the waves and preventing further flooding. Water depths and velocities in the Mw 7.5 scenario remain minimal. Changes in both propagation and flooding are not significant between scenarios Mw 7.5 and Mw 6.5. This methodology can be employed for more accurate tsunami wave simulations not only in the Mediterranean region but also in various case studies.

Volcano tsunamis and their effects on moored vessel safety: the 2022 Tonga event

Abstract. The explosion of the Hunga Tonga–Hunga Ha'apai volcano on 15 January 2022 (Tonga 2022) was the origin of a volcano-meteorological tsunami (VMT) recorded worldwide. At a distance exceeding 10 000 km from the volcano and 15 h after its eruption, the moorings of a ship in the port of La Pampilla, Callao (Peru), failed, releasing over 11 000 barrels of crude oil. This study delves into the profound implications of the Tonga 2022 event, investigating whether it could have led to the breaking of the mooring system. We conducted a comprehensive analysis of this significant event, examining the frequency content of the time series recorded at tide gauges, DART (Deep-ocean Assessment and Reporting of Tsunamis) buoys, and barometers in the southern Pacific Ocean. Our findings revealed that the maximum energy of the spectra corresponds to the 120 min wave period off the coast of Peru, with the arrival time of these waves coinciding with the time of the accident in the port. We used a Boussinesq model to simulate the propagation of the volcano-meteorological tsunami from the source to the port in Peru to study the impact of those waves on the mooring system. We used the synthetic tsunami recorded in the port as input for the model that simulates mooring line loads based on the ship's degrees of freedom. The results suggest that the 120 min wave triggered by the VMT could significantly increase mooring stresses due to the resulting hydrodynamic effects, exceeding the minimum breaking load (MBL). We conclude that the propagation of the long wave period generated by the VMT caused overstresses in moored lines that triggered accidents in port environments. This event showed the need to prepare tsunami early warning systems and port authorities for detecting and managing VMTs induced by atmospheric acoustic waves. The work provides new insights into the far-reaching impacts of the Tonga 2022 tsunami.

Influence of Bed Variations on Linear Wave Propagation beyond the Mild Slope Condition

As water waves travel from deep to shallow waters, they experience increased nonlinearity and decreased dispersion due to the reduced water depth. While the impact of bed slope on wave propagation celerity is documented, it is often overlooked in commonly used depth-integrated wave models. This study uses the WKB approximation and solves higher-order slope-related terms to analyze the influence of varying depth, including the gradient and laplacian of water depth. One result is an extended longwave for linear wave reflection and transmission on a ramp to deeper waters. The main outcome and focus of this work, however, is a new, simple analytical expression for linear dispersion that includes bed variations. The results are applied to two cases: wind-generated water wave propagation in the nearshore, emphasizing corrections to bathymetry inversion methods, and tsunami propagation over the continental slope, highlighting the limitations of neglecting slope on dispersion and the significant role of the Laplacian of water depth.