## INTRODUCTION

In contrast to seismic zoning or earthquake hazard analysis,very few analyses of future tsunami hazard have been conducted in Japan.Probably,the work by Takahashi （1951） is the only quantitative estimate of future tsunami damage on the Pacific coast of the Japanese Islands.The degree of future hazard is defined by the sum of squares of tsunami wave amplitude expected at a site on the coast during a 100−yr period.Assuming that the period of tsunami wave is approxi−mately constant,the aforementioned quantity is proportional to tsunami wave energy that reaches the site concerned.Since the estimate relies on the historical record,it can be applied to the future only on the condition that the tsunami activity in the past can be extended to the coming 100−yr period.

Aida （1969） conducted a numerical experiment on tsunami wave generation and propagation based on the sea−bottom deformation caused by an earthquake.By now,such computer simulation of tsunami waves has developed so markedly that highly plausible wave height and form on a 200 m depth contour can be obtained based on an earthquake fault model determined seismometrically.

Meanwhile,it has in recent years become possible to evaluate probability of a major offshore earthquake occurring in seismic areas adjacent to the Japanese Islands on the basis of recurrence time of earthquakes and/or accumulation of near−shore crustal strain （Wesnousky et al.,1984）.Although the accuracy of such evaluation is not always high,it is important that something can be said about future occurrence of major offshore earthquakes in terms of probability.

Combining numerical tsunami experiment and probability evaluation of off−shore earthquake occurrence,it is possible to evaluate the probability of having a tsunami,of which the maximum water elevation exceeds a certain value,at a site on the coast provided various parameters of the earthquake fault model are given.As there are a number of potential tsunami sources,probabilities for all the sources are to be synthesized.The overall probability of tsunami hazard at any site on the coast will thus be evaluated.

The previously mentioned probability evaluation will here be applied to tsunami arising from sources off the Pacific coast of the Japanese Islands.Attention should be drawn to the fact,however,that a major tsunami sometimes occurs in the Japan Sea,although less frequently.Even a tsunami from very distant sources,such as from South America,Aleutian Islands,Kamchatka,and so on,sometimes hits Japan.A crude evaluation of hazard probability for tsunamis of these kinds will also be made in this paper.

## TSUNAMI WAVES ARISING FROM A TYPICAL FAULT MODEL

Imminence of a great earthquake of magnitude 8 or so occurring in the Tokai （literally east sea） area off the Pacific coast of central Japan has become widely accepted not only by seismologists but also by the public at large in recent years.

One of the most likely fault models of the anticipated earthquake,which is cer−tainly associated with the subduction of the Philippine Sea plate,would be the one shown in Figure 1.The fault plane having a length of 130 km and a width of 60 km dips down to the west with an angle of 34° from the horizontal plane.The upward slip of the western side of the fault at the time of earthquake occurrence would amount to 3.8 m along the dipping plane,while a 1.3 m left−lateral slip would take place in the strike direction of the fault.The seismic moment would amount to 1.56×10^28 dyne−cm,which corresponds to a moment magnitude of 8.1.The model is a slightly modified version of the one proposed by Ishibashi （1981）.

Aida （1984） estimated the behavior of tsunami wave on the 200 m depth contour based on the previously mentioned fault model.The wave height,which is defined by the total amplitude of the first wave,is then converted into the wave height at the nearest shore,taking into account the amplification factor during wave propagation over the continental shelf （Aida,1977）.In such a way,tsunami wave heights,that are likely to hit the Pacific coast in association with the hypothetical Tokai earthquake,can be estimated.In Figure 2 are shown the wave heights thus estimated at various seashore sites.Very large wave heights exceeding 5 m are to be observed at sites close to the fault assumed.

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## TSUNAMI−GENERATING EARTHQUAKES

Figure 3 shows the seismic zones from which major tsunamis on the Pacific coast are originated.The tsunami associated with the hypothetical Tokai earthquake is generated at the easternmost portion of zone VII.According to the existing studies on earthquake origin （Iida,1983）,typical fault models can be assigned to zones I,III,VI,VII,and VIII,although the details of those models are put aside here for the sake of brevity （Aida,1984）.Probable tsunami wave heights from these sources can then be estimated on the Pacific coast in a fashion similar to the last section.For other zones,no representative models of tsunami source are known.However,wave height on the coast can be approximately inferred from the actual data of typical tsunamis in the past.It is therefore possible to estimate tsunami wave height at various sites on the Pacific coast on the condition that a tsunami is generated from one of the zones shown in Figure 3.

We are in a position to see how often a tsunami−generating earthquake occurs from the cited zones.Probability of a major earthquake of M ＝ 7 or over occurring in respective zones is evaluated primarily on the basis of historical records.When the number of historical earthquakes is sufficiently large,we make use of a Weibull distribution analysis for estimating mean recurrence period and thus occurrence probability.Meanwhile,we have to rely on a Poisson distribution in the cases of scarce data on the assumption that earthquake occurrence is stationary and random.Weibull distribution analysis is widely used in quality control engineering and was first introduced into the earthquake prediction study by Hagiwara （1974）.The analysis is different from the Poisson distribution analysis because the probability increase after a particular earthquake can be evaluated.

Zone I,or the seismic area off Hokkaido−Kurile,can be divided into six subareas,each of which having been a seat of major earthquakes in the past.A Weibull distribution analysis of recurrence period is made for the data set as a whole,while a fault model that represents that of the 1952 Tokachi−Oki earthquake （M ＝ 8.1） is chosen as the typical tsunami source.As major earthquakes have already occurred in the 1950’s,1960’s,and 1970’s in all of these subareas,the probabilities of having a major earthquake off Hokkaido−Kurile during a period from 2000 to 2010 are not high as can be seen in Table 1.

For zone III,from where the great 1896 Meiji Sanriku and 1933 Showa Sanriku tsunamis were originated,a fault model equivalent to that of the 1896 one is assumed,although the source location is somewhat shifted to the south because a conspicuous seismic gap exists there.

No historical data for evaluating occurrence probability of a major earthquake are available for zone VI.However,the crustal strain monitoring over the Sagami Bay area to the southwest of Tokyo is useful for probability evaluation.As for the fault model,the one for the 1923 Kanto earthquake （M ＝ 7.9） is adopted.

For the easternmost portion of zone VII,both historical data and crustal strain are available.The fault model assumed is already shown in Figure 1.The probability of having a great earthquake there exceeds 40 per cent for the 10−yr period in question.As for the middle and southern parts of zone VII,the probabilities are small because the 1944 Tonankai （M ＝ 7.9） and 1946 Nankai （M ＝ 8.1） earthquakes have already occurred there,respectively.In view of the small probabilities,the height of the tsunami wave from these parts of the zone is estimated by means of interpolation of the 1944 and 1946 tsunami data.

Zone VIII is known for frequent occurrences of earthquakes having a magnitude around 7,so that a fairly high probability is obtained （Table 1）.As for the fault model,the one for the 1968 Hyuganada earthquake （M ＝ 7.5） is adopted.

No fault models are specified for zones II,IV,and V,but tsunami wave heights from these sources are estimated based on tsunami data in the past.Only a tsunami of 1 m or so in wave height is expected from these source areas.

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## OVERALL TSUNAMI HAZARD PROBABILITY

The information presented in the previous two sections makes it possible to evaluate the probability of tsunami wave height exceeding a certain level at a seashore site during a period from 2000 to 2010,as will be shown in the following.

As an example,let us evaluate the tsunami probability at Shimoda near the extremity of Izu Peninsula （see Figure 2）.According to Figure 2,the wave height due to the coming Tokai earthquake at Shimoda amounts to 5.6 m.On the other hand,the probability of the said earthquake occurring during the period in question is evaluated as 0.41 （Table 1）.The probabilities for Shimoda being hit by a tsunami wave caused by the hypothetical Tokai earthquake are then evaluated for wave heights equal to or larger than 0.5,1,2,5,7,and 10 m as 0.41,0.41,0.41,0.41,0,and 0,respectively.

The respective probabilities at the same site due to the Kanto earthquake or the earthquake arising from zone VI are obtained as 0.22,0.22,0,0,0,and 0.Similarly,the respective probabilities for the middle portion earthquake of zone VII are evaluated as 0.05,0.05,0.05,0,0,and 0.Meanwhile,those for the southernmost portion earthquake of zone VII amount to 0.04,0.04,0.04,0,0,and 0.No tsunami wave height exceeding 0.5 m is expected at Shimoda from other tsunami−generating areas shown in Figure 3.

Denoting the probability of tsunami wave height exceeding a certain level due to a tsunami from the ith area by pi,the synthetic probability p is estimated by

【式】:（1）

where n is the total number of tsunami−generating areas.Applying equation （1）to the probabilities for Shimoda,the synthetic probabilities of tsunami wave exceeding respective heights are evaluated （Table 2）.

Similar probability evaluations are made for key sites along the Pacific coast of the Japanese Islands as shown in Figures 4,5,6,and 7 for Hokkaido,Tohoku,Kanto−Chubu−Kinki−Shikoku,and Shikoku−Kyushu coasts,respectively.

It is observed from these figures that the highest probability of tsunami wave having a height of 5 m or larger is expected for the Pacific coast of central Japan.Most seashore sites in Shizuoka Prefecture are characterized by a probability higher than 40 per cent during the 10−yr period in question.Such a high probability is certainly brought about by the anticipated Tokai earthquake that is feared to occur in the near future.There are also a few sites,where a wave height exceeding 5 m is expected on the southernmost coast of Hokkaido and the Sanriku area in Tohoku of North Japan,although the probabilities are smaller than 10 per cent.

As for tsunami waves having a height of 1 m or thereabout,a high probability amounting to 69 per cent is assigned to the Pacific coast of Shikoku and Kyushu because of frequent Hyuganada earthquakes in zone VIII.It is therefore said that the worst sites for a highly dangerous tsunami are located on the Pacific coast of central Japan and that such sites for a moderately dangerous tsunami are found on the Shikoku and Kyushu coasts.

We also see that probabilities of being hit by a tsunami having a wave height of 0.5 to 1 m exceed 50 per cent at most seashore sites except Hokkaido.This means that the possibility of moderate tsunami hazard cannot be ignored along the whole Pacific coast of the Japanese Islands.

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## TSUNAMI HAZARD ON THE JAPAN SEA COAST

The tsunami associated with the 1983 Nihonkai Chubu earthquake （M ＝ 7.7） that occurred underneath the Japan Sea off Akita Prefecture killed 100 people.Maximum water height locally exceeded 10 m at some beaches.In view of this and a few violent tsunamis found in Japan’s history,hazard analysis is also important for tsunamis occurring in the Japan Sea.

In contrast to offshore earthquakes on the Pacific side of the Japanese Islands,

it is no easy matter to evaluate occurrence probability of tsunami−generating earthquakes located in the Japan Sea because occurrence frequency is extremely small.The available history is too short for discussing the recurrence period. Nevertheless,Shimazaki （1984） attempted to estimate recurrence periods based on the size of epicentral areas and historical records for the past 400 yr and concluded that an earthquake equivalent to the 1983 event probably recurs every 600 to 1200 yr.

Kanamori and Astiz （1985）,who relied on the relation between age of subducting plate and aseismic slip,estimated a recurrence period of the 1983 earthquake as 600 to 1370 yr.

Let us assume that the mean recurrence period is 1000 yr.When a Poisson distribution is assumed,the probability of this class of earthquake occurring in the Japan Sea amounts to about 1 per cent for a 10−yr period.As the area occupied by the northern half of the Japan Sea may accommodate approximately four earthquakes of this class,the probability amounts to 4 per cent for the northern half of the Japan Sea.No great earthquakes occur in the southern half of the sea.

Wave height of the tsunami excited by an earthquake of the previously mentioned class exceeding several meters,the probability of a 100 to 200 km segment of Japan Sea coast being hit by a tsunami having a wave height of several meters,is evaluated as 1 per cent or so for a 10−yr period.

Tsunamis of somewhat smaller scale,which are characterized by a wave height of about 1 m or thereabout,occur approximately every 10 yr or so in the Japan Sea as inferred from the historical record.Assuming a Poisson distribution,the probability of having at least one tsunami of this class occurring in the Japan Sea amounts to 50 per cent for a 10−yr period,so that the probability of such a tsunami hitting a coastal segment of 100 km in length is about 3 per cent.

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## TSUNAMIS FROM DISTANT SOURCES

A tsunami caused by a great earthquake （M ＝ 8.5,1960） that occurred off Chile gave rise to much damage to Japan.The maximum tsunami height along the coast of Japan was reported as large as 4 m.The numbers of dead and missing people were 119 and 20,respectively.It is therefore important to estimate possible tsunami hazard due to an earthquake that occurs at an extremely distant locality.

According to an evaluation based on a Poisson distribution,great earthquakes that generate tsunamis that affect Japan occur off Peru and Chile,with a probability of 27 per cent for a 10−yr period.On the basis of such probability value,it is evaluated that the probabilities of a tsunami with a wave height that exceeds 0.5,1,and 3 m,hitting the Pacific coast of Japan,amount to 26,14,and 4 per cent,respectively.

Similar probabilities for a tsunami from Kamchatka and Aleutian−Alaska are evaluated as 15,6,and 3 per cent,respectively.Combining the effects of the two sources,probabilities of tsunami wave height exceeding 0.5,1,and 3 m are,respectively,evaluated as 37,19,and 15 per cent on the Pacific coast of Japan for a 10−yr period.It should be stressed that the tsunami probabilities from distant earthquakes thus evaluated are not quite smaller than those from near offshore earthquakes as shown in Figures 4 to 7.

## CONCLUSIONS

Combining occurrence probability of offshore earthquakes with tsunami wave height estimated at seashore sites,the probability of tsunami wave height exceeding a certain level is evaluated on the Pacific coast of the Japanese Islands.It seems that probability of a violent tsunami,of which the wave height exceeds 5 m,hitting the coast of the Tokai area in central Japan,amounts to about 40 per cent for a 10−yr period from 2000 to 2010.Such a high hazard probability is due to the earthquake that is expected to occur off the Tokai area sooner or later.The probability of the earthquake occurring within the 10−yr period from 1988 is evaluated as 30 to 35 per cent.As for the probability of a moderately large tsunami having a wave height of 1 m or so,the highest value around 70 per cent is found at some sites on the Shikoku and Kyushu coasts because of fairly frequent occurrence of moderately large earthquakes in the Hyuganada Sea.

It also should be borne in mind that a tsunami originated by a great earthquake that occurs in the north Pacific and off South America sometimes affects the Japanese Islands.According to a crude evaluation,probabilities of a tsunami from such a source hitting the Pacific coast of the Japanese Islands amount to 19 and 15 per cent for a 10−yr period,respectively,for wave heights exceeding 1 and 3 m.Such probabilities are not quite negligible in comparison with those for tsunamis from offshore earthquakes in the vicinity of Japan.It is therefore necessary to modify the graphs in Figures 4 to 7 in such a manner as to make all of the probability columns a little taller.

Tsunami probabilities on the Japan Sea coast are considerably lower than those on the Pacific coast because of low seismicity in the Japan Sea area.A tsunami having a wave height of several meters hits a seashore site on the northern half of Japan Sea coast with a probability of 1 per cent or so for a 10−yr period.For a moderately large tsunami,of which the wave height amounts to about 1 m,the probability is evaluated as 3 per cent.Tsunami probability is almost zero for the southern half of the Japan Sea coast.

The tsunami hazard probability evaluated in this paper may be used for planning public evacuation from a tsunami area,selecting coastal sites for construction purposes or estimating rates for tsunami insurance.

## REFERENCES

Aida,I.（1969）.Numerical experiments for the tsunami propagation−The 1964 Niigata tsunami and the 1968 Tokachi−oki tsunami,Bull.Earthquake Res.Inst.,Tokyo Univ.47,673−700.

Aida,I.（1977）.Relation between tsunami inundation heights and water surface profiles on a 200 m depth contour,Zisin （J.Seism.Soc.Japan） 30,11−23 （in Japanese）.

Aida,I.（1984）.Study on tsunamis （2）:case study of tsunami hazard （1）,Association for the Development of Earthquake Prediction,20−126 （in Japanese）.

Hagiwara,Y.（1974）.Probability of earthquake occurrence as obtained from a Weibull distribution analysis of crustal strain,Tectonophysics 23,313−318.

Iida,K.（1983）.Some remarks on the occurrence of tsunamigenic earthquakes around the Pacific,in Tsunamis:Their Science and Engineering,K. Iida and T.Iwasaki,Editors,Terra Scientific Publishing Co.,Tokyo,Japan,61−76.

Ishibashi,K.（1981）.Specification of a soon−to−occur seismic faulting in the Tokai district,central Japan,based upon seismotectonics,in Earthquake Prediction−An International Review,D.W.Simpson and P.G.Richards,Editors,American Geophysical Union,Washington,D.C.,297−332.

Kanamori,H.and L.Astiz （1985）.The 1983 Akita−oki earthquake （Mω＝7.8） and its implications for systematics of subduction earthquakes,Earthquake Pred.Res.3,305−317.

Shimazaki,K.（1984）.Great earthquakes in the Japan Sea−Estimation of recurrence period,Study on Safe Shutdown Earthquake [S2] （3）,Association for the Development of Earthquake Prediction,87−102 （in Japanese）.

Takahashi,R.（1951）.An estimate of future tsunami damage along the Pacific coast of Japan,Bull.Earthquake Res.Inst.,Tokyo Univ.29,71−95.

Wesnousky,S.G.,C.H.Scholz,K.Shimazaki,and T.Matsuda （1984）.Integration of geological and seismological data for the analysis of seismic hazard:a case study of Japan,Bull.Seism.Soc.Am.74,687−708.

ASSOCIATION FOR THE DEVELOPMENT OF EARTHQUAKE PREDICTION 3,KANDA MITOSHIRO−CHO CHIYODA−KU,TOKYO,JAPAN

Manuscript received 23 November 1987