Visualization of tsunami waves with Amira package

In recent years numerical investigations of tsunami wave propagation have been spurred by the magnitude 9.3 earthquake along the Andaman–Sumatra fault in December, 2004. Visualization of tsunami waves being modeled can yield a much better physical understanding about the manner of wave propagation over realistic seafloor bathymetries. In this paper we will review the basic physics of tsunami wave propagation and illustrate how these waves can be visualized with the Amira visualization package. We have employed both the linear and nonlinear versions of the shallow-water wave equation. We will give various examples illustrating how the files can be loaded by Amira, how the wave-heights of the tsunami waves can be portrayed and viewed with illumination from light sources and how movies can be used to facilitate physical understanding and give important information in the initial stages of wave generation from interaction with the ambient geological surroundings. We will show examples of tsunami waves being modeled in the South China Sea, Yellow Sea and southwest Pacific Ocean near the Solomon Islands. Visualization should be a part of any training program for teaching the public about the potential danger arising from tsunami waves. We propose that interactive visualization with a web-portal would be useful for understanding more complex tsunami wave behavior from solving the 3-D Navier–Stokes equation in the near field.     

Tsunami simulation due to seaquake at Manila Trench and Sulu Trench

Seaquake is a phenomenon where there are water disturbance at the sea, caused by earthquake or submarine eruption. The scope of this study focuses on tsunami simulation due to Manila Trench and Sulu Trench seaquake which is prone to harm Malaysia offshore areas. Manila Trench is a highly potential earthquake source that can generate tsunami in South China Sea. Meanwhile, Sulu Trench could be a threat to east of Sabah offshore areas. In this study, TUNA-M2 model was utilized to perform tsunami simulation at South China Sea and Sulu Sea. TUNA-M2 model applied Okada source model to create tsunami generation due to earthquake. It utilized linear shallow water equation during tsunami propagation with its radiant boundary condition. Five simulations performed at each study region. Forecast points at South China Sea areas were divided into three separate locations which are at the Peninsular Malaysia, west of Sabah and Sarawak offshore areas. Forecast points at Sulu Sea were focused at the east of Sabah offshore areas. This paper will present the simulation results of tsunami wave height and arrival time at various forecast points. The findings of this study show that the range of tsunami wave height at Sulu Sea is higher than that of South China Sea. The tsunami arrival time at Sulu Sea is less than South China Sea. It can be concluded that Sulu Sea poses worse tsunami threat than South China Sea to the Malaysian offshore areas.     

Numerical Simulation of the 1969 Portuguese Tsunami by a Finite Element Method

On 28 February 1969, the coasts of Portugal, Spain and Morocco were affected by sea waves generated by a submarine earthquake (Ms = 7.3) with its epicenter located off Portugal. The propagation of this tsunami has been simulated by a finite element numerical model solving the Boussinesq equations. These equations have been discretized using the finite element Galerkin method and a Crank–Nicholson scheme in time. The model is validated by investigating the propagation of a solitary wave over a flat bottom. The grid sizes for the 1969 event have been determined by one-dimensional tests offshore and in shallow water regions. The two-dimensional simulation of the 1969 tsunami is carried out using the hydraulic source calculated from the geophysical model of Okada and seismic parameters of Fukao. The modeled waves are compared with the recorded ones with respect to travel times, maximum amplitudes and periods of the signal. The comparison between Boussinesq and shallow-water models shows that the effects of frequency dispersion are minor. Good agreement is found for most of the studied gauges.     

Estimates of Tsunami Risk Zones on the Coasts Adjacent to the East (Japan) Sea based on the Synthetic Catalogue

Prognostic characteristics of tsunamis in the East (Japan) Sea based on numerical simulations are investigated by using linear long wave theory. Due to the lack of observed data, the concept of the synthetic catalogue is applied to generate possible tsunami scenarios. It includes four real events that occurred in the East (Japan) Sea during the 20th century, 24 hypothetical tsunamigenic earthquakes located in the gap zones of the seismic map, and 76 idealized model ‘hydrodynamic’ sources covering the eastern part of the East (Japan) Sea uniformly. The tsunami wave height distributions along the East (Japan) Sea coastline due to these hypothetical events are computed. From the geographical distributions of tsunami wave height for all possible events, it is found that there exist several coastal locations where the tsunami risk is relatively lower than in other zones. The relation between the maximal value of the tsunami height and its average value is analyzed. It is found that the maximal tsunami height does not exceed the mean wave height times a constant. The uniform bounded curve for all areas can be obtained if the mean wave height is replaced by the modified mean wave height (1/3 of largest waves). The problem of quantitative definition of the prognostic tsunami wave height for each location based on the data from the synthetic catalogue is discussed. The results of tsunami wave height analysis based on the synthetic catalogue can be used as a tool for coastal disaster mitigation planning.     

Potential Tsunami Hazard Associated with the Kerepehi Fault,Firth of Thames,New Zealand

Geophysical data have identified four submarine segments of the Kerepehi Fault, roughly bisecting a back-arc rift (Hauraki Rift). These segments have been traced through the shallow waters of the Firth of Thames, which lies at the southern end of the Hauraki Gulf, New Zealand. No historical or paleotsunami data are available to assess the tsunami hazard of these fault segments.Analysis of the fault geometry, combined with paleoseismic data for three further terrestrial segments of the Fault, suggest Most Credible Earthquake (MCE) moment magnitudes of 6.5–7.1. Due to the presence of thick deposits of soft sediment, and thesemi-confined nature of the Firth, the MCE events are considered capable of generating tsunami or tsunami-like waves. Two numerical models (finite element and finite difference), and an empirical method proposed by Abe (1995), were used to predict maximum tsunami wave heights. The numerical models also modelled the tsunami propagation.The MCE events were found not to represent a major threat to the large metropolitan centre of Auckland City (New Zealand's largest population centre). However, the waves were a threat to small coastal communities around the Firth, including the township of Thames, and 35,000 ha of low-lying land along the southern shores of the Firth of Thames.The Abe method was found to provide a quick and useful method of assessing the regional tsunami height. However, for sources in water depths < 25 m the Abe method predicted heights 2–4 times larger than the numerical models. Since the numerical models were not intended for simulating tsunami generation in such shallow water, the Abe results are probably a good guide to the maximum wave heights.     

A non-hydrostatic model for the numerical study of landslide-generated waves

This paper proposes and demonstrates a two-layer depth-averaged model with non-hydrostatic pressure correction to simulate landslide-generated waves. Landslide (lower layer) and water (upper layer) motions are governed by the general shallow water equations derived from mass and momentum conservation laws. The landslide motion and wave generation/propagation are separately formulated, but they form a coupled system. Our model combines some features of the landslide analysis model DAN3D and the tsunami analysis model COMCOT and adds a non-hydrostatic pressure correction. We use the new model to simulate a 2007 rock avalanche-generated wave event at Chehalis Lake, British Columbia, Canada. The model results match both the observed distribution of the rock avalanche deposit in the lake and the wave run-up trimline along the shoreline. Sensitivity analyses demonstrate the importance of accounting for the non-hydrostatic dynamic pressure at the landslide-water interface, as well as the influence of the internal strength of the landslide on the size of the generated waves. Finally, we compare the numerical results of landslide-generated waves simulated with frictional and Voellmy rheologies. Similar maximum wave run-ups can be obtained using the two different rheologies, but the frictional model better reproduces the known limit of the rock avalanche deposit and is thus considered to yield the best overall results in this particular case.     

Characteristics of Tsunamis Propagating over Oceanic Ridges: Numerical Simulation of the 1996 Irian Jaya Earthquake Tsunami

The 1996 Irian Jaya earthquake tsunami was simulated by using the numerical model based on the linear long wave theory including Coriolis force in the spherical coordinate system. The numerical modeling result at Chichijima is in good agreement with the observed tide gauge data. The distinctive oscillation at Chichijima can be interpreted as the formation of boundary waves, so called ridge waves that are excited on the South-Honshu ridge. The mechanism of tsunami propagation trapped on an oceanic ridge is analyzed with the simple ridge model. The result explains the characteristics of ridge waves excited on theSouth-Honshu ridge.     

On wave–current interaction by the Green–Naghdi equations in shallow water

This work is on the use of the Green–Naghdi (GN) nonlinear wave equations for simulating wave–current interaction in shallow water. The stream-function wave theory is used at the wave-maker boundary to generate nonlinear incident waves to consider the wave–current interaction. The nonlinear GN equations are solved in the time domain by use of the finite-difference method. The model is evaluated with data from three experimental studies. A strong opposing current over a submerged bar is investigated in the first test case. In the second test case, the interaction of waves with a uniform current over flat bottom is considered. In the third case, wave–current interaction over a variable bathymetry with the following and opposing currents is studied. The numerical results obtained by the GN equations are compared with the experimental data and results based on the Boussinesq equations. A good agreement is obtained for the three experimental studies considered for a wide range of wave and current conditions.     

The 1987–88 Alaskan Bight tsunamis: Deep ocean data and model comparisons

Excellent deep ocean records have been obtained of two tsunamis recently generated in the Alaskan Bight on 30 November 1987 and 6 March 1988, providing the best available data set to date for comparison with tsunami generation/propagation models. Simulations have been performed with SWAN, a nonlinear shallow water numerical model, using source terms estimated by a seafloor deformation model based on the rectangular fault plane formalism. The tsunami waveform obtained from the model is quite sensitive to the specific source assumed. Significant differences were found between the computations and observations of the 30 November 1987 tsunami, suggesting inadequate knowledge of the source characteristics. Fair agreement was found between the data and the model for the first few waves of the 6 March 1988 tsunami. Model estimates of the seismic moment and total slip along the fault plane are also in fair agreement with those derived from the published Harvard centroid solution for the 6 March 1988 event, implying that the computed seafloor deformation does bear some similarity to the actual source.     

Numerical modeling of a landslide-generated tsunami following a potential explosion of the Montserrat volcano

The explosion of the Montserrat volcano (Caribbean Sea) could trigger a major landslide and lead to the generation of a tsunami in the Caribbean Sea. In the worst case scenario, the volume of material reaching the sea has been estimated at 80 millions of cubic meters. The sliding of this mass and the generation of the associated tsunami have been simulated numerically, assuming that the debris behave like a heavy fluid flowing into the sea. The numerical model solves the 3D Navier-Stokes equations for a mixture composed of rocks and water. The generated water waves is then propagated around the coast of Montserrat by means of a shallow water model. The numerical results show that the water heights above sea level are higher than 5 meters within a radius of 5 km of the source.     

滑移流对浅水湖泊风浪传播特性影响试验研究

浅水湖泊等有限风吹程及水深水域的风浪多处于发展阶段，风拖曳表层水体产生的滑移流会对风浪传播特性产生影响，风浪的波速、波长等参数难以通过线性波的理论频散关系获取。为准确预测湖泊风浪参数，在考虑浅水湖泊的有限吹程和水深特征的基础上，利用风洞水槽模拟研究了滑移流对风浪传播特性的影响。结果表明：滑移流、斯托克斯流及表面流均与风速正相关，滑移流与表面流比值随着风速的增加逐渐降低并稳定于75%；滑移流对波速和波长有促进作用，对小尺度波浪的促进作用尤其显著；波浪非线性会抑制滑移流对波速及波长的促进作用；建立了考虑滑移流影响的风浪经验频散关系式以及风浪主频波速经验关系式。     

滑移流对浅水湖泊风浪传播特性影响试验研究

浅水湖泊等有限风吹程及水深水域的风浪多处于发展阶段，风拖曳表层水体产生的滑移流会对风浪传播特性产生影响，风浪的波速、波长等参数难以通过线性波的理论频散关系获取。为准确预测湖泊风浪参数，在考虑浅水湖泊的有限吹程和水深特征的基础上，利用风洞水槽模拟研究了滑移流对风浪传播特性的影响。结果表明:滑移流、斯托克斯流及表面流均与风速正相关，滑移流与表面流比值随着风速的增加逐渐降低并稳定于75%；滑移流对波速和波长有促进作用，对小尺度波浪的促进作用尤其显著；波浪非线性会抑制滑移流对波速及波长的促进作用；建立了考虑滑移流影响的风浪经验频散关系式以及风浪主频波速经验关系式。     

Use of tsunami waveforms for earthquake source study

Tsunami waveforms recorded on tide gauges, like seismic waves recorded on seismograms, can be used to study earthquake source processes. The tsunami propagation can be accurately evaluated, since bathymetry is much better known than seismic velocity structure in the Earth. Using waveform inversion techniques, we can estimate the spatial distribution of coseismic slip on the fault plane from tsunami waveforms. This method has been applied to several earthquakes around Japan. Two recent earthquakes, the 1968 Tokachi-oki and 1983 Japan Sea earthquakes, are examined for calibration purposes. Both events show nonuniform slip distributions very similar to those obtained from seismic wave analyses. The use of tsunami waveforms is more useful for the study of unusual or old earthquakes. The 1984 Torishima earthquake caused unusually large tsunamis for its earthquake size. Waveform modeling of this event shows that part of the abnormal size of this tsunami is due to the propagation effect along the shallow ridge system. For old earthquakes, many tide gauge records exist with quality comparable to modern records, while there are only a few good quality seismic records. The 1944 Tonankai and 1946 Nankaido earthquakes are examined as examples of old events, and slip distributions are obtained. Such estimates are possible only using tsunami records. Since tide-gauge records are available as far back as the 1850s, use of them will provide unique and important information on long-term global seismicity.     

Simulation of the Arabian Sea Tsunami propagation generated due to 1945 Makran Earthquake and its effect on western parts of Gujarat (India)

The 1945 Tsunami generated due to Makran Earthquake in the Arabian Sea was the most devastating tsunami in the history of the Arabian Sea and caused severe damage to property and loss of life. It occurred on 28th November 1945, 21:56 UTC (03:26 IST) with a magnitude of 8.0 (M _w), originating off the Makran Coast of Pakistan in the Arabian Sea. It has impacted as far as Mumbai in India and was noticed up to Karvar Coast, Karnataka. More than 4,000 people were killed as a result of the earthquake and the tsunami. In this paper an attempt is made for a numerical simulation of the tsunami generation from the source, its propagation into the Arabian Sea and its effect on the western coast of India through the use of a numerical model, referred to as Tunami-N2. The present simulation is carried out for a duration of 300 min. It is observed from the results that the simulated arrival time of tsunami waves at the western coast of India is in good agreement with the available data sources. The paper also presents run-up elevation maps prepared using Shuttle Radar Topographic Mission (SRTM) data, showing the possible area of inundation due to various wave heights along different parts of the Gujarat Coast. Thus, these results will be useful in planning the protection measures against inundation due to tsunami and in the implementation of a warning system.     

Rogue events in spatiotemporal numerical simulations of unidirectional waves in basins of different depth

The evolution of unidirectional nonlinear sea surface waves is calculated numerically by means of solution of the Euler equations. The wave dynamics corresponds to quasi-equilibrium states characterized by JONSWAP spectra. The spatiotemporal data are collected and processed providing information about the wave height probability and typical appearance of abnormally high waves (rogue waves). The waves are considered at different water depths ranging from deep to relatively shallow cases (k _p h > 0.8, where k _p is the peak wavenumber, and h is the local depth). The asymmetry between front and rear rogue wave slopes is identified; it becomes apparent for sufficiently high waves in rough sea states at all considered depths k _p h ≥ 1.2. The lifetimes of rogue events may reach up to 30–60 wave periods depending on the water depth. The maximum observed wave has a height of about three significant wave heights. A few randomly chosen in situ time series from the Baltic Sea are in agreement with the general picture of the numerical simulations.     

Finite-element simulations of the 28 december 1908 Messina Straits (Southern Italy) tsunami

The earthquake we are dealing with occurred on December 28, 1908: because of the number of victims (about 60,000) and the extension of the destroyed area (6,000 km²), this earthquake with the epicentral MCS intensity XI may be considered the strongest event ever reported for Italy along with the 1693 eastern Sicily earthquake. The shock produced a large tsunami that caused severe damage and many victims. In all places the first sea movement was a withdrawal for a few minutes, followed by a flooding of the coast with at least three big waves. A post-event survey allowed to estimate flooding and run-up heights (more than 10 m in some places). In this work we perform some numerical simulations of the tsunami generation and propagation, taking into account different source faults: the model is based on the shallow water equations, solved numerically by means of a finiteelement method. The computational domain, covered by a mesh consisting of triangular elements, includes the Messina Straits and the sea facing the northeastern coast of Sicily and southern Calabria.     

Peculiarities of tsunamis generated by Asteroid impact or nuclear explosions in the northwest of Black Sea

Different models are used to evaluate the seashore effects of the tsunami generated by an asteroid impacting the shallow-water plateau in the northwest basin of the Black Sea. The shortest distance between the impact location and the coast is about 185 km. The tsunami’s effects on the coastal regions depend on many factors among which the most important is asteroid size. The tsunami generated by a 250-m asteroid reaches the nearest dry land location in 35 min and needs about 2 h to arrive all over the Black Sea coast. The run-up value is about 2 m high on Turkish and Crimean coasts. In the western Black Sea regions, the wave height is about 3 m. The run-up values strongly depend on bathymetry and topography peculiarities. The run-up values in case of the tsunami generated by a 1,000-m-sized asteroid are up to five to six times larger than in case of the 250-m impactor, depending on location. Differences between the tsunami’s dynamics on coastal regions situated in the proximity of deep water and shallow water, respectively, are outlined. Aspects concerning accidental or deliberate nuclear explosions are briefly referred. Possible social consequences and prevention are shortly discussed.     

Historical tsunami records and potential tsunami scenarios near Haikou coastal region

Historical tsunami records in the South China Sea are collected and analyzed in this paper. There have been about 54 tsunamis in the South China Sea since 1076. The impacts of the transoceanic tsunamis on the southeast coast of China are weak. However, the regional tsunamis in the South China Sea bring varying degrees of influence to the south coast of China, which occurred about 18 times. By the analysis of the potential tsunami sources in the South China Sea, numerical simulations of tsunami induced in the Manila Trench are carried out. It is found that the tsunami wave height is small near Haikou if the general earthquake tsunami occurred. But the tsunami wave height is large when a giant earthquake of M9.3 occurred. If this extreme situation arises, the impacts to the coast of Haikou will be serious.     

海底滑坡海啸的颗粒流耦合模型

海底滑坡的运动可能引发海啸,破坏离岸设施,威胁海岸带安全。国内外关于海底滑坡引发海啸的研究方兴未艾。采用Mih颗粒流模型控制具弱黏聚力的砂土滑坡运动,利用两相流模型计算岩土体-水体相互作用及RNG湍流模型控制水体运动,构建了基于颗粒流模型的海底滑坡海啸全耦合数值分析方法。通过简单水槽水下滑坡案例进行了海底滑坡海啸全过程研究。数值分析再现了变形滑体的不均一运动、密度分异流动、水滑机制和以波谷为典型特征的涌浪波等典型海底滑坡及海啸现象,这表明数值模型具有有效性。许多海域（包括中国南海北部）都存在弱黏聚力和无黏聚力的水下滑坡,该数值方法值得推广和进一步研究完善。     

Preliminary investigations of the tsunami hazard of Kick'em Jenny submarine volcano

Kick'em Jenny is a submarine volcano situated 9 kilometres north of Grenada in the Lesser Antilles. A preliminary study suggests that the volcano is a prime candidate for tsunamigenic eruptions on a potentially hazardous scale, possibly affecting the whole of the Eastern Caribbean region. The uniqueness of individual volcanic eruptions means that attempts to generalise tsunamigenic mechanisms are extremely tentative. However, the theory of underwater explosion generated water waves is applicable to submarine volcanoes to model explosive eruptions. Using this theory, initial maximum ocean surface displacements are calculated for Kick'em Jenny hydroeruptions, corresponding to various event magnitudes (up to a worst-case scenario eruption on the scale of Krakatau, 1883). Wave propagation theories are then applied to the resulting tsunami wave dispersion, before beach shoaling equations are used to estimate the maximum tsunami run-up at adjacent coastal areas. Maps of the region have been prepared showing the paths of the wave-fronts (ray-tracing), travel times and maximum wave run-up amplitudes along coastlines. Finally, an attempt is made to assess how great a hazard the volcano represents, by considering the probability of each magnitude event occurring.