Source Fault Model of the 1771 Yaeyama Tsunami, Southern Ryukyu Islands, Japan, Inferred from Numerical Simulation

The 1771 Yaeyama tsunami is successfully reproduced using a simple faulting model without submarine landslide. The Yaeyama tsunami (M 7.4), which struck the southern Ryukyu Islands of Japan, produced unusually high tsunami amplitudes on the southeastern coast of Ishigaki Island and caused significant damage, including 12,000 casualties. Previous tsunami source models for this event have included both seismological faults and submarine landslides. However, no evidence of landslides in the source has been obtained, despite marine surveying of the area. The seismological fault model proposed in this study, describing a fault to the east of Ishigaki Island, successfully reproduces the distribution of tsunami runup on the southern coast of the Ryukyu Islands. The unusual runup heights are found through the numerical simulation attributable to a concentration of tsunami energy toward the southeastern coast of Ishigaki Island by the effect of the shelf to the east. Thus, the unusual runup heights observed on the southeastern coast of Ishigaki Island can be adequately explained by a seismological fault model with wave-ray bending on the adjacent shelf.     

Some Aspects of Energy Balance and Tsunami Generation by Earthquakes and Landslides

— Tsunamis are generated by displacement or motion of large volumes of water. While there are several documented cases of tsunami generation by volcanic eruptions and landslides, most observed tsunamis are attributed to earthquakes. Kinematic models of tsunami generation by earthquakes — where specified fault size and slip determine seafloor and sea-surface vertical motion — quantitatively explain far-field tsunami wave records. On the other hand, submarine landslides in subduction zones and other tectonic settings can generate large tsunamis that are hazardous along near-source coasts. Furthermore, the ongoing exploration of the oceans has found evidence for large paleo-landslides in many places, not just subduction zones. Thus, we want to know the relative contribution of faulting and landslides to tsunami generation. For earthquakes, only a small fraction of the minimum earthquake energy (less than 1% for typical parameter choices for shallow underthrusting earthquakes) can be converted into tsunami wave energy; yet, this is enough energy to generate terrible tsunamis. For submarine landslides, tsunami wave generation and landslide motion interact in a dynamic coupling. The dynamic problem of a 2-D translational slider block on a constant-angle slope can be solved using a Green's function approach for the wave transients. The key result is that the largest waves are generated when the ratio of initial water depth above the block to downslope vertical drop of the block H ₀ /W sin δ is less than 1. The conversion factor of gravitational energy into tsunami wave energy varies from 0% for a slow-velocity slide in deep water, to about 50% for a fast-velocity slide in shallow water and a motion abruptly truncated. To compare maximum tsunami wave amplitudes in the source region, great earthquakes produce amplitudes of a few meters at a wavelength fixed by the fault width of 100 km or so. For submarine landslides, tsunami wave heights — as measured by b, block height — are small for most of the parameter regime. However, for low initial dynamic friction and values of H ₀ /W sin δ less than 1, tsunami wave heights in the downslope and upslope directions reach b and b/4, respectively.Wavelengths of these large waves scale with block width. For significant submarine slides, the value of b can range from meters up to the kilometer scale. Thus, the extreme case of efficient tsunami generation by landslides produces dramatic hazards scenarios.     

Finite element modeling of the July 12, 1993 Hokkaido Nansei-Oki tsunami

A fault plane model and a finite element hydrodynamic model are applied to the simulation of the Hokkaido Nansei-Oki tsunami of July 12, 1993. The joint performance of the models is assessed based on the overall ability to reproduce observed tsunami waveforms and to preserve mass and energy during tsunami propagation. While a number of observed characteristics of the waveforms are satisfactorily reproduced (in particular, amplitudes and arrival times at tidal gauges relatively close to the source, and general patterns of energy concentration), others are only marginally so (notably, wave periods at the same gauges, and wave heights along Okushiri); differences between observations and simulations are traceable to both the fault plane and the hydrodynamic models. Nonnegligible losses of energy occur throughout the simulated tsunami propagation. These losses seem to be due to a combination of factors, including numerical damping and possible deficiencies of the shallow water equations in preserving energy.     

Analysis of seismological and tsunami data from the 1993 Guam earthquake

The fault parameters of the Guam earthquake of August 8, 1993 are estimated from seismological analyses, and the possibility of identifying the actual fault plane from tsunami waveforms is tested. The Centroid Moment Tensor solution of long-period surface waves shows one nodal plane shallowly dipping to the north and the other nodal plane steeply dipping to the south. The seismic moment is 3.5×10²⁰ Nm and the corresponding moment magnitude is 7.7. The Moment Tensor Rate Function inversion ofP waves also yields a similar focal mechanism and seismic moment. The point source depth is estimated as 40–50 km.This earthquake generated tsunamis that propagated toward the Japanese coast along the Izu-Bonin-Mariana ridge system. The tsunamis are recorded on ocean bottom pressure gauges and tide gauges. Numerical computation of tsunamis shows that the computed waveforms from the two possible fault planes match well with the observed tsunami waveforms. The numerical computation also shows that the tsunami waveforms at Guam Island, just above the fault, should contain useful information regarding the identification of the actual fault plane. However, the current sampling rate of the tide gauges is so small that the records cannot help the identification.     

A note on tsunami amplitudes above submarine slides and slumps

Tsunami generated by submarine slumps and slides are investigated in the near-field, using simple source models, which consider the effects of source finiteness and directivity. Five simple two-dimensional kinematic models of submarine slumps and slides are described mathematically as combinations of spreading constant or slopping uplift functions. Tsunami waveforms for these models are computed using linearized shallow water theory for constant water depth and transform method of solution (Laplace in time and Fourier in space). Results for tsunami waveforms and tsunami peak amplitudes are presented for selected model parameters, for a time window of the order of the source duration.The results show that, at the time when the source process is completed, for slides that spread rapidly (c_R/c_T≥20, where c_R is the velocity of predominant spreading), the displacement of the free water surface above the source resembles the displacement of the ocean floor. As the velocity of spreading approaches the long wavelength tsunami velocity the tsunami waveform has progressively larger amplitude, and higher frequency content, in the direction of slide spreading. These large amplitudes are caused by wave focusing. For velocities of spreading smaller than the tsunami long wavelength velocity, the tsunami amplitudes in the direction of source propagation become small, but the high frequency (short) waves continue to be present. The large amplification for c_R/c_T1 is a near-field phenomenon, and at distances greater than several times the source dimension, the large amplitude and short wavelength pulse becomes dispersed.A comparison of peak tsunami amplitudes for five models plotted versus L/h (where L is characteristic length of the slide and h is the water depth) shows that for similar slide dimensions the peak tsunami amplitude is essentially model independent.     

Tsunami Assessment for Risk Management at Nuclear Power Facilities in Japan

The present study focuses on evaluation of the maximum and minimum water levels caused by tsunamis as risk factors for operation and management at nuclear power facilities along the coastal area of Japan. Tsunamis generated by submarine earthquakes are examined, basing literature reviews and databases of information on historical tsunami events and run-up heights. For simulation of water level along the coast, a numerical calculation system should be designed with computational regions covering a particular site. Also the calculation system should be verified by comparison of historical and calculated tsunami heights. At the beginning of the tsunami assessment, the standard faults, their locations, mechanisms and maximum magnitudes should be carefully estimated by considering historical earthquake-induced tsunamis and seismo-tectonics at each area. Secondly, the range of errors in the model parameters should be considered since earthquakes and tsunamis are natural phenomena that involve natural variability as well as errors in estimating parameters. For these reasons, uncertainty-induced errors should be taken into account in the process of tsunami assessment with parametric study of the tsunami source model. The element tsunamis calculated by the standard fault models with the errors would be given for the design. Then, the design tsunami can be selected among the element tsunamis with the most significant impact, maximum and minimum water levels, on the site, bearing in mind the possible errors in the numerical calculation system. Finally, the design tsunami is verified by comparison with the run-up heights of historical tsunamis, ensuring that the design tsunami is selected as the highest of all historical and possible future tsunamis at the site.     

A Theoretical Comparison of Tsunamis from Dislocations and Landslides

— We use simple physical models to evaluate and compare the orders of magnitude of the energy generated into a tsunami wave by seismic dislocations and underwater slumps. We conclude that the two sources can generate tsunamis of comparable total energy. However, the slumping source is shown to be fundamentally dipolar in nature, which results in a low-frequency deficiency in the far-field. These simple conclusions corroborate the interpretation of the 1998 Papua New Guinea tsunami as being generated by an underwater slump.     

Tsunami Source of the 2010 Mentawai, Indonesia Earthquake Inferred from Tsunami Field Survey and Waveform Modeling

The 2010 Mentawai earthquake (magnitude 7.7) generated a destructive tsunami that caused more than 500 casualties in the Mentawai Islands, west of Sumatra, Indonesia. Seismological analyses indicate that this earthquake was an unusual “tsunami earthquake,” which produces much larger tsunamis than expected from the seismic magnitude. We carried out a field survey to measure tsunami heights and inundation distances, an inversion of tsunami waveforms to estimate the slip distribution on the fault, and inundation modeling to compare the measured and simulated tsunami heights. The measured tsunami heights at eight locations on the west coasts of North and South Pagai Island ranged from 2.5 to 9.3 m, but were mostly in the 4–7 m range. At three villages, the tsunami inundation extended more than 300 m. Interviews of local residents indicated that the earthquake ground shaking was less intense than during previous large earthquakes and did not cause any damage. Inversion of tsunami waveforms recorded at nine coastal tide gauges, a nearby GPS buoy, and a DART station indicated a large slip (maximum 6.1 m) on a shallower part of the fault near the trench axis, a distribution similar to other tsunami earthquakes. The total seismic moment estimated from tsunami waveform inversion was 1.0 × 10²¹ Nm, which corresponded to M_w 7.9. Computed coastal tsunami heights from this tsunami source model using linear equations are similar to the measured tsunami heights. The inundation heights computed by using detailed bathymetry and topography data and nonlinear equations including inundation were smaller than the measured ones. This may have been partly due to the limited resolution and accuracy of publically available bathymetry and topography data. One-dimensional run-up computations using our surveyed topography profiles showed that the computed heights were roughly similar to the measured ones.     

A note on the effects of nonuniform spreading velocity of submarine slumps and slides on the near-field tsunami amplitudes

The effects of variable speeds of spreading of submarine slides and slumps on near-field tsunami amplitudes are illustrated. It is shown that kinematic models of submarine slides and slumps must consider time variations in the spreading velocities, when these velocities are less than about 2c_T, where is the long period tsunami velocity in ocean of constant depth h. For average spreading velocities greater than 2c_T, kinematic models with assumed constant spreading velocities provide good approximation for the tsunami amplitudes above the source.     

Sources and depositional processes of tsunami deposits: Analysis using foraminiferal tests and hydrodynamic verification

Foraminiferal tests are commonly found in tsunami deposits and provide evidence of transport of sea floor sediments, sometimes from source areas more than 100 m deep and several kilometers away. These data contribute to estimates of the physical properties of tsunami waves, such as their amplitude and period. The tractive force of tsunami waves is inversely proportional to the water depth at sediment source areas, whereas the horizontal sediment transport distance by tsunami waves is proportional to the wave period and amplitude. We derived formulas for the amplitudes and periods of tsunami waves as functions of water depth at the sediment source area and sediment transport distance based on foraminiferal assemblages in tsunami deposits. We applied these formulas to derive wave amplitudes and periods from data on tsunami deposits in previous studies. For some examples, estimated wave parameters were reasonable matches for the actual tsunamis, although other cases had improbably large values. Such inconsistencies probably reflect: (i) local amplification of tsunami waves by submarine topography, such as submarine canyons; and (ii) errors in estimated water depth at the sediment source area and sediment transport distance, which mainly derive from insufficient identification of foraminiferal tests.     

Normal Mode Energetics for Far-field Tsunamis Generated by Dislocations and Landslides

— We apply the normal mode representation of tsunami waves, as introduced by Ward (1980) to the systematic study of the excitation of far-field tsunamis by both dislocation sources (represented by double-couples of moment M ₀), and landslides (represented by single forces). Using asymptotic representations of the continuation of the tsunami eigenfunction into the solid Earth, we derive analytical expressions of the spectral amplitude generated by both systems. We show that the quadrupolar corrections defined by Dahlen (1993) in the case of landslides can result in an increase of 1 to 2 orders of magnitude of the effective force. Even so, the spectrum of tsunami waves generated by landslides is found to be offset significantly to relatively high frequencies (10 mHz), where dispersion becomes important and eventually diminishes time-domain amplitudes. We proceed to calculate the total energy delivered into the tsunami modes by integrating the energy of multiplets for an average source geometry. In the case of dislocation sources, and taking into account the corner frequency of the source, we reproduce the scaling with M ₀ ^4/3 which was derived from purely static arguments by Kajiura (1981). We compare the directivity patterns of far-field tsunami waves by dislocations and landslides, and conclude that the latter cannot give rise to pronounced lobes of directivity for physically acceptable values of the velocity of the slide. Directivity thus constitutes a robust discriminant of the nature of the source which, when applied to the 1946 Aleutian tsunami in the far-field, requires generation by a dislocative source.     

Tsunami and mechanism of great earthquakes

The relation between tsunamis and sea-bottom deformations associated with the Kurile Islands earthquake of 1969 and the Tokachi-Oki earthquake of 1968 is studied on the basis of a fairly complete set of seismological and tsunami data. The seismic results are included in the calculation of static crustal deformations. The calculated deformations are compared with the tsunami source area as obtained by the inverse refraction diagram, the first motion of tsunami waves, and the height of the sea-level disturbance at the source. It is found that such deformations as predicted by the seismic results can quantitatively explain the source parameters of tsunamis. These findings strongly favor the idea that tsunamis are generated by tectonic deformations rather than by large submarine landslides and slumps. This conclusion is supported by additional analyses for the 1964 Niigata, 1944 Tonankai, 1933 Sanriku earthquakes. For the 1946 Nankaido earthquake, the source deformation responsible for the tsunami generation is of much greater magnitude than that for seismic waves.     

A note on tsunami caused by submarine slides and slumps spreading in one dimension with nonuniform displacement amplitudes

Tsunami created by spreading submarine slides and slumps with spatially variable final uplift are investigated in the near-field using a kinematic model. It is shown that for velocities of spreading comparable to and smaller than the long period tsunami velocity (g is the acceleration due to gravity and h is the ocean depth), the models with spatially uniform final uplift of the accumulation and depletion zones provide good approximation for the tsunami amplitudes in the near-field. For spreading velocities 2–5 times greater than c_T, and for applications that use wavelengths of the order of the source dimensions, the spatial variability of the final uplift has to be considered in estimation of the high-frequency tsunami amplitudes in the near-field.     

海底地震有限断层破裂模型对近场海啸数值预报的影响

快速准确的海啸源模型是近场海啸精确预警的关键.尽管目前还没有办法直接对其进行正演定量计算,但是可以通过多源地震、海啸观测数据进行反演或联合反演推算.不同的海啸源可能导致不同的预警结论,了解不同类型海啸源适用性、评估海啸源特征差异对近场海啸的影响,无论对于海啸预警还是海啸模拟研究尤为重要.本文评估分析了6种不同同震断层模型对2011年3月11日日本东北地震海啸近场数值预报的影响,重点对比分析了有限断层模型与均一滑动场模型对近场海啸产生、传播、淹没特征的影响及各自的误差.研究表明:近场海啸波能量分布主要取决于海啸源分布特征,特别是走向角的差异对海啸能量分布影响较大;有限断层模型对海啸灾害最为严重的39°N以南沿岸地区的最大海啸爬坡高度明显优于均一滑动场模型结果;综合对比DART浮标、GPS浮标及近岸潮位站共32个站次的海啸波幅序列结果发现有限断层模型整体平均绝对/相对误差比均一滑动场模型平均误差要低,其中Fujii海啸源的平均绝对/相对误差最小,分别是0.56m和26.71%.UCSB海啸源的平均绝对/相对误差次之.3个均一滑动场模型中USGSCMT海啸源模拟精度最高.相对于深海、浅海观测站,有限断层模型比均一滑动场模型对近岸观测站计算精度更高.海啸源误差具有显著的方向性,可能与反演所采用的波形数据的代表性有关;谱分析结果表明Fujii海啸源对在12至60min主频波谱的模拟要优于UCSB海啸源.海啸源中很难真实反映海底地震破裂过程,然而通过联合反演海啸波形数据推算海啸源的方法可以快速确定海啸源,并且最大限度的降低地震破裂过程与海啸产生的不确定性带来的误差.     

Relationship of Tsunami Intensity to Source Earthquake Magnitude as Retrieved from Historical Data

Operational prediction of near-field tsunamis in all existing Tsunami Warning Systems (TWSs) is based on fast determination of the position and size of submarine earthquakes. Exceedance of earthquake magnitude above some established threshold value, which can vary over different tsunamigenic zones, results in issuing a warning signal. Usually, a warning message has several (from 2 to 5) grades reflecting the degree of tsunami danger and sometimes contains expected wave heights at the coast. Current operational methodology is based on two main assumptions: (1) submarine earthquakes above some threshold magnitude can generate dangerous tsunamis and (2) the height of a resultant tsunami is, in general, proportional to the earthquake magnitude. While both assumptions are physically reasonable and generally correct, statistics of issued warnings are far from being satisfactory. For the last 55 years, up to 75% of warnings for regional tsunamis have turned out to be false, while each TWS has had at least a few cases of missing dangerous tsunamis. This paper presents the results of investigating the actual dependence of tsunami intensity on earthquake magnitude as it can be retrieved from historical observations and discusses the degree of correspondence of the above assumptions to real observations. Tsunami intensity, based on the Soloviev-Imamura scale is used as a measure of tsunami “size”. Its correlation with the M _s and M _w magnitudes is investigated based on historical data available for the instrumental period of observations (from 1900 to present).     

Was Grand Banks event of 1929 a slump spreading in two directions?

This paper describes a kinematic model of tsunami generated by submarine slides and slumps spreading in two orthogonal directions. This model is a generalization of our previously studied models spreading in one direction. We show that focusing and amplification of tsunami amplitudes can occur in an arbitrary direction, determined by the velocities of spreading. This kinematic model is used to interpret the asymmetric distribution of observed tsunami amplitudes following the Grand Banks earthquake—slump of 1929.     

Re-examination of the Source Mechanism of the 1998 Papua New Guinea Earthquake and Tsunami

— Simulation of tsunami propagation and runup of the 1998 Papua New Guinea (PNG) earthquake tsunami using the detailed bathymetry measured by JAMSTEC and adding bathymetric data at depths less than 60 m is carried out, reproducing the tsunami energy focus into Warapu and Arop along the Sissano Lagoon. However, the computed runup heights in the lagoon are still lower than those measured. Even if the error in estimating the fault parameters is taken into consideration, computational results are similar. Analysis by the wave ray method using several scenarios of the source size of the tsunami and location by the wave ray method suggests that a source characterized by small size in water 1,000-m deep approximately 25 km offshore the lagoon, best fits the arrival determined from the interviews with eyewitnesses. A two-layer numerical model simulating the interaction of the tsunami with a landslide is employed to study the behavior of a landslide-generated tsunami with different size sand depths of the initial slide just outside the lagoon. A landslide model with a volume of 4–8 × 10⁹ m³ is selected as the best in order to reproduce the distribution of the measured tsunami runup in the lagoon. The simulation of a tsunami generated in two stages, fault and landslide, could show good agreement with the runup heights and distribution of the arrival time, but a time gap of around 10 minutes remains, suggesting that a tsunami generated by the mainshock at 6:49 PM local time is too small for people to notice, and the following tsunami triggered by landslide or mass movement near the lagoon about ten minutes after the mainshock attacked the coast and caused the huge damage.     

Linear and nonlinear computations of the 1992 Nicaragua earthquake tsunami

Numerical computations of tsunamis are made for the 1992 Nicaragua earthquake using different governing equations, bottom frictional values and bathymetry data. The results are compared with each other as well as with the observations, both tide gauge records and runup heights. Comparison of the observed and computed tsunami waveforms indicates that the use of detailed bathymetry data with a small grid size is more effective than to include nonlinear terms in tsunami computation. Linear computation overestimates the amplitude for the later phase than the first arrival, particularly when the amplitude becomes large. The computed amplitudes along the coast from nonlinear computation are much smaller than the observed tsunami runup heights; the average ratio, or the amplification factor, is estimated to be 3 in the present case when the grid size of 1 minute is used. The factor however may depend on the grid size for the computation.     

Slip Distribution and Seismic Moment of the 2010 and 1960 Chilean Earthquakes Inferred from Tsunami Waveforms and Coastal Geodetic Data

The slip distribution and seismic moment of the 2010 and 1960 Chilean earthquakes were estimated from tsunami and coastal geodetic data. These two earthquakes generated transoceanic tsunamis, and the waveforms were recorded around the Pacific Ocean. In addition, coseismic coastal uplift and subsidence were measured around the source areas. For the 27 February 2010 Maule earthquake, inversion of the tsunami waveforms recorded at nearby coastal tide gauge and Deep Ocean Assessment and Reporting of Tsunamis (DART) stations combined with coastal geodetic data suggest two asperities: a northern one beneath the coast of Constitucion and a southern one around the Arauco Peninsula. The total fault length is approximately 400 km with seismic moment of 1.7 × 10²² Nm (Mw 8.8). The offshore DART tsunami waveforms require fault slips beneath the coasts, but the exact locations are better estimated by coastal geodetic data. The 22 May 1960 earthquake produced very large, ~30 m, slip off Valdivia. Joint inversion of tsunami waveforms, at tide gauge stations in South America, with coastal geodetic and leveling data shows total fault length of ~800 km and seismic moment of 7.2 × 10²² Nm (Mw 9.2). The seismic moment estimated from tsunami or joint inversion is similar to previous estimates from geodetic data, but much smaller than the results from seismic data analysis.     

The landslides and tsunamis of the 30th of December 2002 in Stromboli analysed through numerical simulations

On the 30th of December 2002 two tsunamis were generated only 7 min apart in Stromboli, southern Tyrrhenian Sea, Italy. They represented the peak of a volcanic crisis that started 2 days before with a large emission of lava flows from a lateral vent that opened some hundreds of meters below the summit craters. Both tsunamis were produced by landslides that detached from the Sciara del Fuoco. This is a morphological scar and is the result of the last collapse of the northwestern flank of the volcanic edifice, that occurred less than 5 ka b.p. The first tsunami was due to a submarine mass movement that started very close to the coastline and that involved about 20×10⁶ m³ of material. The second tsunami was engendered by a subaerial landslide that detached at about 500 m above sea level and that involved a volume estimated at 4–9×10⁶ m³. The latter landslide can be seen as the retrogressive continuation of the first failure. The tsunamis were not perceived as distinct events by most people. They attacked all the coasts of Stromboli within a few minutes and arrived at the neighbouring island of Panarea, 20 km SSW of Stromboli, in less than 5 min. The tsunamis caused severe damage at Stromboli.In this work, the two tsunamis are studied by means of numerical simulations that use two distinct models, one for the landslides and one for the water waves. The motion of the sliding bodies is computed by means of a Lagrangian approach that partitions the mass into a set of blocks: we use both one-dimensional and two-dimensional schemes. The landslide model calculates the instantaneous rate of the vertical displacement of the sea surface caused by the motion of the underwater slide. This is included in the governing equations of the tsunami, which are solved by means of a finite-element (FE) technique. The tsunami is computed on two different grids formed by triangular elements, one covering the near-field around Stromboli and the other also including the island of Panarea.The simulations show that the main tsunamigenic potential of the slides is restricted to the first tens of seconds of their motion when they interact with the shallow-water coastal area, and that it diminishes drastically in deep water. The simulations explain how the tsunamis that are generated in the Sciara del Fuoco area, are able to attack the entire coastline of Stromboli with larger effects on the northern coast than on the southern. Strong refraction and bending of the tsunami fronts is due to the large near-shore bathymetric gradient, which is also responsible for the trapping of the waves and for the persistence of the oscillations. Further, the first tsunami produces large waves and runup heights comparable with the observations. The simulated second tsunami is only slightly smaller, though it was induced by a mass that is approximately one third of the first. The arrival of the first tsunami is negative, in accordance with most eyewitness reports. Conversely, the leading wave of the second tsunami is positive.