The　Inst．of　Natural　Sciences　Nihon　Univ．Proc．of　The　Inst．of　Natural　Sciences

Vol．24（1989）pp。53－62

Earthquake　Prediction　an（i　Seismic　Hazard

Analysis　in　Japan

Tsuneji　RIKITAKE（Received　October　31，　1988）

　　Probabilities　of　earthquake　generation　from　active　faults　in　Japan　are　evaluated　basing　on

crustal　strain　geodetically　obtained　over　fault　areas，From　the　data　of　earthquakes　that　oc・

curred　on　or　very　close　to　an　active　fault，the　relation　between　the　strain　rate（7）and　time

interval　between　a　speci丘ed　epoch，say　the　year2000，and　the　last　earth（luake　occ皿rence（T）

isstudied，s・thatthedistributi・ns・fTf・rthreeranges・fr，i．e．7＜2×10－7／yr，2×10－7／yr

≦7＜4×10－7／yr　and4x10－7／yr≦プrespectivelyシare　obtained．　The　distributions　are　approxi－

mated　wlth　Weibull　distribution．With　the　aid　of　the　parameters　of　Weibull　distribution　thus

determined，strain　accumulation　over　an　active　fault　is　estimated　on　the　assumption　that　the

strain　rate　is　constant．Probability　of　crustal　break　or　earthquake　occurring　in　a　time　interva1，

10yr　say，at　the　year2000is　then　evaluated　by　comparing　the　accumulated　strain　to　the　ul－

timate　strain。Such　an　evaluation　is　made　for　all　the　active　faults　amounting　to348in　num・

ber。

　　As　earthquake　magnitude　can　be　approximately　assessed　from　the　length　of　a　fault，

ground　motion　at　a　site　in　terms　of　acceleration　is　readily　calculated　by　making　use　of　an

exisiting　empirical　relation　between　maximum　mean　horizontal　acceleration，epicentral　dis－

tance　and　magnitude。

　　Summing　up　the　effects　from　all　faults，it　is　then　possible　to　evaluate　probability　of　ground

motion　at　a　site　exceeding　a　certain　acceleration　level・100and300gals　say・In　this　way

probability　distribution　of　seismic　hazard　can　be　obtained　all　over　the　Japanese　Islands，

　　The　present　zonation　is　different　from　existing　ones，which　are　liable　only　to　the　average

of　seismic　hazard　throughout　historical　and／or　geological　times，in　the　fact　that　the　present

state　of　crustal　strain　accumulation　is　taken　into　account．In　other　words　the　estimated

seismic　hazard　is　based　on　long－term　earthquake　prediction、

　　In　addition　to　the　probabilities　due　to　inland　active　faults，probabilities　of　major　earth－

quakes　Qccurring　in亡he　sea　suτrounding　Japan　are　also　evaluated　in　some　way　although　no

accurate　evaluation　is　possible．Combining　on－and　of〔一shore　seismic　activities，overa1玉zonation

of　seismic　hazard　is　put　forward．　It　tums　out　that　the　probability　representing　seismic　hazard

is　highest　in　the　Chubu　and　Kinki　districts，Central　Japan，and　next　highest　in　some　parts　of

Tohoku，Shikoku　and　Kyushu　districts．

　　The　probabihty　distribution　maps　brought　out　in　this　paper　may　be　useful　for　having

some　idea　about　future　seismic　hazard　in　terms　of　ground　acceleration　although　the　absolute

value　of　probabi1呈ty　may　not　be　quite　accurate．

Department　of　Earth　Sclences，College　of　Humanitles　and　Sciences，

Setagaya－ku，Tokyo，156，Japan

一53一

Nihon　University，25－40，Sakurajosui3－chome，

（1）

T．RIKITAKE

Intro“uction

　　Seismic　hazard　analyses　in　terms　of　maximum

seismic　intensity，acceleration，velocity　and　the　hke

have　been　made　in　Japan　in　the　hope　of　bringing

out　possible　earthquake　hazar（1s　throughout　the

country．Kawasumi（1951），　who　relied　on　the

earthquake　record　in　history，　obtained　expectancies

of　maximum　seismic　acceleration　in　gal　for　periods

of75，100and200yr，The　distribution　of　expec－

tancy　thus　obtained　is　called　the“Kawasumi　map”

and　w1dely　used　for　designing　earthquake－proof

construction　in　Japan，A　similar　analysis　for　max－

imum　velocity　was　put　forward　by　Kanai　and　Su－

zuki（1968）。

　　It　apPears　that　the　period　covered　by　the

history　of2，000yr　or　so　is　oftell　too　short　for

evaluating　seismic圭ty　because　retum　period　of　large

earthquakes　is　longer　than　1，000yr　in　some　parts

of　Japan．Wesnousky（1982）and　Wesnousky　et　aL

（1984）evaluated　inland　seismicity　averaged　over　a

much　longer　period　on　the　condition　that　the　past

activity　of　an　active　fault　can　be　inferred　from　its

slip　rate　and　length、　The　fault　activity　thus

brought　out　is　converted　into　the　rate　of　earthquake

generation　on　a　few　assumptiolls．　Taking　the　con－

tributions　of　all　faults　in　an　area　of　interest　into

consideration，it　is　possible　to　estimate　the　average

time　interval　between　seismic　shakings　of　a　given

strength　for　a　site　in　the　area．From　such　a　time

interval，we　can　readily　evaluate　probab呈1ity　of　ground

shaking　exceeding　a　certain　level　in　a　speci后ed　time

interval　provided　earth（luake　occurrence　is　stationary

alld　random，and　so　occurrence　frequency　obeys　the

Poisson　distribution．

　　The　zonation　maps　by　Wesnousky（1982）and

W▼esnousky　et　al．　（1984）　are　interesting　in　that　the

earthquake　hazards　averaged　over　a　period　much

longer　than　that　obtained　by　Kawasumi　are　present－

ed，It　should　be　pointed　out，however，that　these

maps　are　good　only　for　the　average　during　the

period　probably　since　recent　geological　era．As　no

account　of　crustal　strain　accumulating　in　the　area

covering　all　fault　at　present　is　taken　into　considera・

（2）

tion，　the　probability　of　ground　　shaking　　for　a

prescribed　time　interval　from　a　speci丘ed　epoch　can・

not　be　evaluated　by　the　above　method。

　　As　the　earthquake　prediction　program　made

progress　in　Japan，the　writer　feels　that　something

more　de丘nite　can　be　said　about　probability　of＆n

earthquake　occurring　from　an　active　fault　basing

on　the　data　taken　by　the　program，For　instance，

accumulation　of　crustal　strain　over　a　fault　can　in

many　cases　be　monitored　by　repetition　of　geodetic

surveys，　and　so　probability　of　crustal　break　related

to　earthquake　occurrence　may　in　some　cases　be

evaluated　by　comparing　accumulated　stra1n　to

ultimatestrainthatleadstothecatastrophe．Amethod　of　evaluating　probability　of　a　fault　genera・

ting　an　earthquake　as　a　function　of　time　will　be

presentedinthispaperbased・nthecrustalstrain

data（Rikitake，1983，1984）．Summing　up　contribu－

tions　of　all　active　faults　in　Japan，probability　of

ground　shaking　exceeding　a　certain　level　during　a

prescribed　time　interval　from　a　speci丘ed　epoch　can

then　be　calculated　for　any　site．It　thus　becomes

possible　to　present　a　sort　of　zonation　map　of

ground　shaking　on　the　basis　of　long－term　prediction

of　earthquakes　originating　frっm　active　faults　in

Japan．

　　The　approach　is　different　from　those　by　Kawa・

sumi，Wesnousky　and　Wesnousky　et　aL　in　that　the

probability　is　speci6ca11y　obtained　　at　a　　certain

epoch．The　former　studies　are　concerned　only　with

the　average　probability　during　historical　and／or

geological　t1mes．

　　This　paper飯st　of　all　describes　how　to　evaluate

pr・babilities・faccelerati・n・fgr・undshakingex・

ceeding　a　certain　value　due　to　earthquakes　origi・

nating　from　active　faults　on　land，Zonations　basing

on　such　probabilities　will　be　shown　in　a　form　of

distribution　map．

　　In　the　next　place，the　writer　will　try　to　evaluate

thepr・babilitiesduet・earthquakesintheseaareas

surrounding　　the　　Japanese　　Islands　　in　　order　　to

elucidate　overall　earthquake　hazard　in　Japan・As

Wesnousky（1982）and　Wesnousky　et　aL（1984）did，

there　are　some　means　of　evaluating　future　seismic

一54一

Earthquake Prediction and Seismic Hazard Analysis in Japan

~¥'

_1 r'4 400hm -~~iF~:~~ 'L 'bO _ ~/ ' ' ;~; f~~~ ~ ~' I~;P~ J/' /~ ~ ? i // ~~ 1

'/F~ /

[ ; i'~'¥ J' _ L:~ l /" " - " '_'_;l (3 _ -_1-_' - _=_i":L _ ' Jr'_~~~:1Fl/J/f i~ :;':~ .~i~;_7~~ ~' ':P' 'J: J J~4/~~~'~'-{'1'._; - c:~ * r- ~~1 -- '-~~~ '~ t /~_~: : t /_ ~i:~:~~- ? -:_ _ ~tr'~C//~ _ ' ~ ~ f--,(~~i~~~ -::~1"~_l; rl 1':':1'~~ - ~f ~~ *~ ~~' ~~;"df~,~:r~~;;~' :j~:;r :~~_--'r'!~~T~::IJ/:~~ ¥ ~~ ~ ~;~~~¥*~¥ '~;1 ~ ;1 ~ " ')/' / ~:~~>~~~~~~~~~¥t¥~t~ ~ ¥

~~~~~~'~~~~-- 1;¥~~~¥~~~t¥~~ /'~~;.' y ¥~~.~.*~;~~~E.¥~~ = ' ';;(,./ ; / ¥~- ': ~i ' ' '/" ~~' ~/ ~/ '-/ /~~~ ~~ ~i ' ~ i-'~ -¥~~~:~¥~i:)~~ ~ ~- "" '/' ' ')/;~:~'~/ ~~ ~i /7:::~. ~ 1;** . r' ,I ~~~~.; / ~ t¥~~b 1)¥f / ' /=7~l;;~:z:~~/1/i:~1~;/~~;~~~~v/~:._;:.T/;~:'~';.;~i~d~///~(;//~P:~/._;: ~~/~4e.//;_･･~//~4/e

___'¥ _ - o~ ' .)1' ~ ti~~~~Jl¥ ; '

' _ _ If;~~; ~/a r ;( ¥~L~ ~ ' / 's¥ ~ ~ ~'-/ ~t¥!~ 4 ¥r;~

Fig' I Active faults in JTapan (Research Group for Active Faults' 1980)'

activity in the sea area surrounding Japan even

though monitoring of crustal strain by means of

geodetic survey cannot be used.

The writer will evaluate probabilities of earth-

quake occurrence in a number of seismically active

areas in the seas adjacent to the Japanese Islands

in some way or other, so that the probabilities of

ground shaking due to these off-shore activities ex-

ceeding a certain level can be evaluated.

Finally, effects 0L inland and off-shore seismic

activities will be synthesized reaching zonations of

overall earthquake hazard in terms of probability

of ground acceleration exceeding certain levels for a

prescribed time interval from a specified epoch.

Strain Accumulation over Active Faults

An extensive catalog of active Laults in Japan

was put forward by Research Group for Active

Faults (1980), the distribution of active faults

having been shown by the group as can be seen in

Fig. 1.

Meanwhile, Geographical Survey Institute has

been conducting triangulation and trilateration sur-

veys of the precise geodetic networks composed of

the Ist- and 2nd-order triangulation stations a-

mounting to some 6,000 in number. As the survey

made progress, it becomes possible to see the

accumulation of crustal strain over most portions

of the Japanese Islands, if not all. Dividing the

accumulated strain by the number of years between

two surveys, which usually amounts to scores of

years, the crustal strain rate per year can be obtain-

ed. The rate of maximum horizontal shear strain

for an active fault is estimated as an average of

d

i

,~

1?o

~

,2

~ 3 / 1817

_ 9 5 12~ 10 1¥ I .~ 4 11 6 '-

o 4eO km

'c' g

Fig. 2

- 55 -

The 14 faults associated with a large earth-

quake in the past. I : West of Aomori, 2 : Senya. 3 : Shiroishi-Fukushima, 4 : Sagami trough S : Tanna, 6 : Suruga trough, 7 : Zenkoji-Iiyama, 8 : Atotsugawa, 9 : Neodani,

10: Yanagase. 11 : West of Suzuka, 12: Hi-ra, 13 : Yamasaki, 14: Shikano.

(3)

T。RIKITAKE

such　rates　for　a　number　of　triangles　covering　the

fault．Strain　rates　for348active　faults　can　thus　be

estimated．

　　For　the14faults　shown　in　Fig．2，we　know

thatalargeearthquake・ccurfedinthepastinassociation　with　their　movements，As　the　exact

dates　of　occurrence　are　infeπed　from　the　history

for　these　earthquakes，we　have　the　relation　between

the　strain　rateプand　the　time　interval　T　between　a

speci丘edep・ch，theyear2000say，andtheyear・f

thelastearthquake・ccurrencef・rthefaults・In

addition　to　these　faults，there　are15examples　of

earthquakesthat・ccurredinthepastveryc1・set・

a　fault　although　no　detail　of　fault　movement　is

available．

　　Examining　theプーT　relationship　for　these　faults，

we　see　that　there　is　a　tendency　that　the　retum

peri・d・fearthquake・ccurrencef・rahighstrain

丁

　0　　　49

50　　　99

100　　149150　　199200　　249250　　299500　　349550　　399

0

FREαUεNCY

r（2

T

■■■■■■■1　2

－　　1■■■■■■■■　　2

－　　1　0　0　0

FREOUENCY

2≦k4　0　－　49

50　　　99

100　　14915α　　1ワ9

200　　2奪9

250　　299500　　549350　　399

T

　〇　一

50

100150200250300350

脳■■■　　1

　0　0口■■顧　　1

■■■圏■團■■　　2

7

rate　fault　is　shorter　than　that　for　a　low　rate　one，

InFig．3aresh・wnthefrequencydistributi・ns・f

Tinyrf。rthethreeranges・fプ，Le・r＜2×10－7／

yr，2x10－7ノシr≦7〈4×10－7yrand4x10－7／yr≦rin

regardt。thご27faults・nland。Weinfact・bserve

thatthepeak・ffrequencyshiftst・asmallervalue

。fT－rangeastheプーrangetakes・nalargervalue・

　　Letusden。tethepr・bability・fanearthquake

。ccurringbetweenTandT＋∠Tbyμ（孟）whichis

assumed　to　be　expressed　by　a　Weibull　distribution

such　as

　　μ（T）＝KT鵬　　　　　　　　（1）in　which　parameters　K　and形are　constants　and　K

＞O　and窺＞一1。

　　　When　the　probability　of　an　earthquake　occurr－

ingbetweenOandTisden・tedbyF（T）・wehave

　　F（T）＝1－R（T）

where

　　R（T）一expHlμ（T）dT］

　　　　　　一exp［一KT　・／（翻）］　　（2）

　　Thepr・babilitydensity∫（T）isthengivenby

　　∫（T）＝一dR／dT

　　　　　　＝KT皿exp［一KT酬／（”3＋1）］　　（3）

　　　Parameters　K　and形can　be　determined　from

ther－Trelati。nsandtake・nthevaluesgiveninTable　l　for　respective　r－ranges．　The　probability

densities　are　also　obtained　with　the　aid　of　these

parametersassh・wninFig・4f・rrespectiveプー「anges・

4999

1491992492993存9

399

0

o

FREOUENCY

45r

Fig．3

（4）

■■■■■■■■■■■　　5

■■■■■■■■　　2

　0　0　0　0　0

The　frequency　distributions　of　time　interval

（T）betw－een　the　year200Q　and　the　year　for

the　last　earthquake　occurrence　for　threeranges　of　strain　rate（プ），T　andプare　mea－

sured　in　units　of　year　and　10 7／yr，　respec’

tively．

＞　．012ト

罰Z，01田

o　．008

＞卜

一

ロ雛．004

く自コ

0002配’

匹

YR

3

2

o

Fig．4

一56一

　50　1D巳　150　200　250　300　350　　　　　　　　T　l　N　YR

Probability　densities　of　earthquake　occur－

rence　as　a　function　of　T　at　the　year2000・

Curves，1，2and3correspond　for　the　tbree

ranges・fstrainrate，i・e・1f・げ＜2・2f・r2

≦7＜4and3for4≦7。プis　measured　inunitsoflO－7／yr．

Earthquake　Prediction　and　Seismic　Hazard　Analysis　in　Japan

ζ．012

5Z．01国

o　，008

＞←

一

ロ．o園

くoユ

0、002

配

ら

Y罠13

N

＼

　　　　　　　　　　　　Table　l

Parameters　K　and”3for　the　two　epochs2000and2010when　T　is　measured　in　units　of　year．Strain

rateプis嫌easured　in　units　of　lo『7／yr．

Epochプ＜2 2≦プ＜4 4≦7

2K　　　解　　　K　　　”z　　K　　　”3

20005，14×10田51．101．78x10－40。9482，47×10－70。991

2010　　7．03x10－5　1．01　4。12x10－5　1．26　　8．97×10－7　2．27

　　0　50　鵬　150　200　250　300　350　　　　　　　　　　　T　IN　YR

Fig。5　Probabilit1y　densities　of　earthquake　occur－

　　　　rence　as　a　function　of　T　at　the　year2010．

　　　　Strain　rate　ranges　are　the　same　as　those　for

　　　　Fig．4．

　　　　Tab互e2τ’s　for　the　two　epochs．

Epoch プく2　　2≦プ＜4　　4≦72000

2010

140

146

105

111

81．2

91．6

　　On　the　assumption　that　no　earthquake　occurs

until2010，similar　probabilities　are　estimated，The

parameters　are　also　given　in　Table1，while　the

probability　densities　become　as　shown　in　Fig．5．It

seems　likely，however，that　some　earthquakes　occur

during2001－2010，　so　that　the　peaks　of　probability

density　curve　would　in　actuality　shift　to　sma11er

valUes　of　T。

　　According　to　Geographical　Survey　Institute

（1981），it　is　reported　that　a42，5km　base－line　con・

necting　two　triangulation　stations　across　Suruga　Bay

has　shortened　by90and42cm　during　the　periods

1884－1973and　1931－1973シrespectively．　The　base－

1ine　crosses　Suruga　trough　which　is　a　typical　active

fault．　It　appears，t｝lerefore，that　the　strain　rate　圭n

the　direction　of　base－line　has　b㏄n　almost　constant

over　the90－year　period，As　such　steady　develop・

ment　of　crustal　strain　is　known　for　a　number　of

active∫aults，it　is　assumed　in　this　paper　that　the

strain　rate　is　constant。Although　the　strain　rate

may　considerably　vary　immediately　before　and　after

an　earthquake，the　assumption　of　constant　rate　for

a　period　of亡he　order　of100yr　may　not　be　unrea－

sonable．

　　The　strain　accumulated　during　a　period　from

the　last　earthquake　and　the　epoch　at　which　data

analysis　is　conductedン　say　the　years　2000and　2010

in　the　present　case，is　given　by

・一∫r∫（T）dT∫『プ（孟）dオ　　（4）

When7＝const．is　assumed，we　obtain

　　　ε一∫rT∫（T）dT一τ　　　（5）

where

　　τ＝［K／（勉＋1）］一1伽＋1）r［（解＋2）／（窺＋1）］（6）

in　wh三ch　r　denotes　a　Gamma　function。

　　On　the　basis　of　K　and解given　in　Table1，τ

is　calculated　as　given　in　Table2for　the　respective

strain　ranges，　Puttingτthus　estimated　into　equa・

tion　（5），the　strain　accumulation　is　obtained　for　a

fault　for　whichプis　known。

Probability　of　Earthquake　Generation

　　　　　fromanActiveFault

　　Let　us　assume　that　the　crustal　strain　so　far

accumulated　around　an　active　fault　was　released　at

the　time　o｛the　last　earthquake　originating　from

that　fault　and　that　the　strain　has　been　accumulat・

ing　again　since　then　with　the　rate　inferred　from

geodetic　surveys．In　that　case，strain　accumulation

for　any　epoch　can　be　estimated　in　a　manner

mentioned　in　the　last　section．Comparing　the

accumulated　strain　to　the　ultimate　strain，which

was　estimated　by　Rikitake（1975），it三s　possible　to

evaluate　probability　of　a　crustal　break　or　an　earth一

（luake　taking　place　within　a　prescribed　time　interval

from　a　speciGed　epoch，As　such　probability　evalua－

tion　of　active　faults　has　already　been　presented　by

Rikitake　（1984），no　detailed　account　of　evaluation

method　is　given　here。

　　As　we　can　estimate　strain　accumulation　by　the

一57一 （5）

T．RIKITAKE

years　2000　and　2010　based　on　7　and　　τ　already

obtained，the　cumulative　probabilities　F2000and　F2010

0f　an　earthquake　occurring　by　the　years　2000and

2010can　be　calculated．The　probability　of　an　earth・

quake　occurring　during2001－2010　is　then　obtained

as

　　　F3＝（F2。、。ぞ2。。。）／（1－F2。。。）　　　　（7）

on　the　con（1ition　that　no　earthquake　occurs　by　the

year　2000．

　　　The　probabilities　of　earthquake　occurrence

within　the10・yr　period　from　the　year2001are　thus

evaluated　for　the　348　active　faults　distributed　al呈

over　the　Japanese　Islands．

Grouna　Motion　aue　to　Earth“uakes

　Relatea　to　hlanαActive　Faults

　Matsuda　（1977）proposed　an　empirical　relation

between　the　magnitude　M　of　an　earthquake　caused

by　a　fault　movement　and　the　fault　Iength　L　such　as

　　　Mニ（1・gL＋2。9）／0．6　　　　　　（8）

where　L　is　measured　in　units　of　kilometer．Equation

（8）is　useful　for　estimating　the　earthquake　magni－

tude　when　a　fault　moves。

　　　On　the　other　hand，Katayama（1974）obtained

a　statistical　relation　between　maximum　mean　hori、

zontal　acceleration　J　in　gal　and　epicentral　distance

D　in　km　which　is　given　as

　　　I・9ク＝0，982－1．2901・9．D＋0．466M　　　（9）

in　whichハ4is　the　earthquake　magnitude．

　　　Combining（9）with（8），maximum　mean　hori－

zontal　acceleration　碗ゴ　at　the∫一th　site　due　to　the

movement　of　the．ノーth　fault　can　readily　be　calculat・

ed．As　the　probability　for　each　fault　giving　rise　to

an　earthquake　has　been　obtained　as　mentioned　pre－

vi・usly，itispossiblet・evaluatepr・babilityP却of

maximum　mean　horizontal　acceleration　at　theゼーth

site　exceeding　a　certain　leve1．

　　　When　there　areηfaults，the　synthetic　proba－

bility　is　given　by

acceleration，In　practice，distributions　of　maximum

mean　horizontal　acceleration　exceeding100and300

gals　for10－yr　time　interval　from　the　year2001are

obtained　as　can　be　seen　in　Figs．6and7．

　　　In　the　actual　calculation　of　probab丑ities，faults

of　which　the　length　is　shorter　than5km　are　dis－

regarded，When　a　number　of　faults　are　located

very　closely，　they　are　sometimes　represented　by　a

single　fault。When　a　site，for　which　the　proba・

bility　is　to　be　evaluated，is　within　a　distance　of5

km　from　a　fault，σ＝400gals　is　assumed．

　　　Looking　at　Figs．6and7，it　is　apparent　that

the　probability　is　highest　in　the　Chubu　and　Kinki

districts　in　Central　Japan．　This　certainly　reHects

the　fact　that　many　active　faults　are　densely　distri・

buted　in　the　districts．　There　are　a　few　areas　of

relatively　high　probability　hl　the　Shikoku，Kyushu

and　Tohoku　districts．　The　low　probability　in　the

Kanto　district，which　includes　the　Tokyo　area，is

certainly　due　to　the　fact　that　no　active　faults　can

be　recognized　because　of　thick　sediments　covering

the　Kanto　plain　and　also　that　crustal　strain　moni．

tQring　is　di伍cult　to　conduct　because　many　triangu・

lation　stationS　have　been　destroyed　by　human

aCtiVity　in　reCent　yearS．

　　　It　is　interesting　to　compare　the　probability　dis－

tributions　as　shown　in　Figs，6and7to　those　given

by　Wesnousky（1982）and　Wesnousky　et　a1。（1984）．

Apart　from　the　absolute　values　of　probability，dis－

tr二butions　of　earth（1uake　hazard　in　terms　of　proba・

bility　obtained　in　this　study　generally　agree　with

those　by　Wesnousky　and　his　colleagues．There　are

of　course　some　differences　between　the　two　distri・

butions．　For　instance，the　high　probability　area　in

Central　Japan　in　the　Wesnousky　map　is　somewhat

shifted　to　the　east　comparing　to　those　in　Figs，6

and　7，　Such　points　are　caused　by　the　di鉦erence　in

the　basic　assumption　for　evaluating　hazard　proba・

bility　between　the　two　studies，

　　　　　　ルP¢＝1一π　（1－P乞ゴ）　　　　　ゴ＝1

（10）

　　　On　the　basis　of　equation　（10），　P〆s　can　be　ca1－

culated　for　any　site　and　for　any　Ievel　of　ground

（6）

　　OccurrenceProbabilityofO」f一曲ore

Earthquakes　an｛l　Gro覗nd　Motion　on　Land

　　　Major　earth（1uakes　ofエM＝7－80ccur　in　the　sea

surrounding　Japan，so　that　it　is　important　to

58一

Earthquake　Prediction　and　Seismic　Hazard　Analysis　in　Japan

’

ρo’

9

ら〃

◎

　　　　6

　　　　　ア　　　　　1　　　　『　1　　　　P　　一　『　1　　　　　』　　　　　　　　コ　　　ロ　　　　ドコ　　　コ　　　　ド　　　ア　　

⑳蓑綴鷲Vll

　VIll

多

戯㈱朋1

⑱v

Vl

Fig，8　Seismic　belts　and　clusters　from　where　major

　　　off－shore　earthquakes　around　Japan　are　ori・

　　　ginated．

estimate　seismic　hazard　caused　by　off－shore　earth－

quakes．The　seismic　belts　or　cfusters，from　which

major　interplate　earthquakes　are　originated，are

shown　in　Fig8，　Monitoring　of　crustal　strain　is

possible　only　for　near－shore　areas　such　as　VI　and

V旺a，　so　that　evaluation　of　earth（王uake　occurrence

probability　is　forced　to　rely　on　historical　records　of

seismicity　in　respective　earthquake　areas。

　　No　detailed　account　of　probability　evaluation

is　given　here　for　the　sake　of　simplicity。Only　the

probabilities　of　a　large　earth（1uake　ofハ4＝70r　over

occurring　in　the　respective　areas　are　evaluated　and

given　in　Table3along　with　the　Iocations　of　earth・

quake　area，mean　magnitudes，years　of　the　Iast

earthquake　and　mean　return　periods．When　the

number　of　data　is　su伍ciently　large，we　make　use

of　Weibull　distribution　for　estimating　mean　retum

period　and　probability．Meanwhile，we　have　to　rely

on　Poisson　distribution　in　the　cases　of　scarce　data

on　the　assumption　that　earthquake　occurrence　is

stationary　and　random。In　the　table，the　last

column　indicates　which　distribution　is　used　by

notationsW（Weibu11）andP（Poisson），Earthquake

areas　Nos．　I　and　V旺　are　divided　into6　and　3

subareas，　respectively，　although　the　statistics　for

evaluating　Probabilities　are　conducted　bas玉ng　on　the

data　sets　for　the　whole　areas．

　　The　probabilities　of　earthquake　occurrence　be－

ing　thus　evaluated，we　can　readily　estimate　probabi1－

ities　at　an　on－shore　site　exceeding　a　specif三ed　level　of

　　　　　　　　　Table3Probabilities　of　a　large　earth（1uake　occurring　from

off－shore　earthquake　areas（Iuring2001－2010。

No． Earthquake　areaMean　　Mean

latitude　　Iongitude

（。N）　　　（。E）

Mean　Year　of　　Mean　　　　　last　　　　　returnmagn1冒　earth－　　　period　tude　　　quake　　　　（yr）

Probability

　　for　　　　　Remark

　2001－2010

IaIbIcIdIeIfH皿

wVwVEa

WbV匪c

皿

Off　Hokkaido－Kurile

Off　Aomori　Pref。

Off　Sanriku

Off　Miyagi　Pref．

Off　Fukushima　Pref．

Sagami　trough

Nankai　trough

Hyuganada　Sea

44．5

44，0

43。3

42．6

42．2

40．7

40．7

39．4

38．2

37．2

34．7

34、7

33。9

32．9

32．1

151．2「

149，0

147．6

146．2

144．6

143．6－

142．4

144．4

142．0

141．6

139．8

138．3－

136。8

134．4－

132．1

7，9

7，3

7．7

7．4

7，5

8，0

8．0

7。0

1963

1958

1969

1973

1952

1968

1945

1933

1978

1938

1923

1854－1944

1946－

1984

85．3

69

107

34．9146

156

117

7。2

0．037－　　　0．050i　　　lO．021

　　　　wO。017

0．070

0．026一

0．14

0．089

0．33

0．066

0．20

PPWPw

0．41－

0．044　　　WO．041－

0．66　　　W

一59一 （7）

T。RIKITAKE

ground　acceleration　on　the　condition　that　the　Ka－

tayama　formula（9）can　be　applied　even　to　o旺・shore

shocks．Such　probabilities　can　then　be　combined

with　those　from　earthquakes　due　to　inland　active

faults　　obtained　　previously　　reaching　　synthetic

probabilities　that　represent　overa11seismic　hazard　in

Japan　for　the10－yr　period　between　the　years2001

and2010，The　probability　distributions　of　maximum

mean　horizontal　acceleration　exceeding　100and　300

gals　are　shown　in　Figs，9and10，respectively．

　　　It　is　noticeable　in　these　且gures　that　the　high

probabihty　in　the　Chubu　and　Kinki　districts　predo－

minates　even　though　the　contribution　of　o狂一shore

earthquakes　is　taken　into　account．That　the　future

off－shore　seismic　activity　expected　in　the　Hyugana－

da　Sea　near　Kyushu　and　off　the　Tokai　area　in　the

middle　Honshu　results　in　relatively　high　probabil－

ities　can　also　be　clearly　observed　in　the丘gures。As

major　earth（1uakes　in　　the　Hokkaido－Kurile　area

have　already　occurred　in　the　later　half　of　1900’s，

theearthquakehazardduet・sh・cks・riginatingfrom　the　area　is　not　high　for　the　period　in　question．

　　　It　is　no　easy　matter　to　evaluate　probability　of

a　major　earthquake　occurring　in　Japan　Sea　because

oflackofdata，Averyroughestimate，however，1eads　to　a　very　low　value　amounting　to　a　few　per－

cent　for　a　10－yr　period．　It　is　therefore　surmised

that　the　probability　distributions　shown　in　Figs．9

and　10are　affected　very　little　by　Iarge　earth（luakes

originating　from　the　Japan　Sea　area．

Seismic　HazarαWhen　Low　Strain　Rate

　　　　　Fa腿lts　are　Disregar－e盛

　　　The　above　probabilities　of　earth（luake　genera－

tion　from　active　faults　are　evaluated　on　the

assumption　that　all　the　faults　treated　are　capable　of

generating　an　earthquake　although　many　of　them

are　characterized　by　a　low　strain　rate．Among　the348

faults　studied，strain　rate　for105faults　is　lower　than

the　average　rate　of　maximum　horizontal　shear

strain　of　Japanese　Islands　as　a　whole　as　revealed

by　the　repetitioτl　of　the　lst－order　triangulation／

trilateration　surveys．A　Weibull　distribution　anal－

ysis　of　geodetic　data　for　the　lst－order　surveys

（8）

Ieads　to　a　mean　rate　amounting　to　1、3×10－7／yr

（Rikitake，1983）。

　　　When　there　are　many　faults　which　are　assumed

to　be　independellt　o｛each　other，we　see　that　the

synthetic　probability　as　calculated　by　formula（10）

becomes　extremely　high　even　though　the　probability

for　each　fault　is　not　very　high．Let　us　for　instance

assume　that　there　are10independent　faults　each

having　a　probability　amounting　to　O．10，we　see

that　the　synthetic　probability　is　estimated　as　O．65。

When　there　are20faults，the　probability　becomes　as

high　as　O。88．

　　　In　view　of　such　a　consideration，we　suspect　that

high　probabilities　of　seismic　hazard　in　some　areas

as　presented　in　Figs。6シ7，9，and10may　be

brought　about　by　the　fact　that　there　are　many

壬aults　even　though　the　probability　of　earth（1uake

generation　from　each　fau玉t　is　not　quite　high，At

the　moment，there　is　no　clue　to　judge　whether　a

fault　is　capable　or　not　capable　of　generating　an

earthquake、　But　it　would　not　be　u皿easonable　to

presume　that　a　fault　of　which　the　strain　rate　is

substantially　smaller　than　the　average　may　not　gene－

rate　an　earthquake　after　alL　In　other　words　such

a　fault　is　totally　dead　in　the　sense　of　earthquake

generation。

　　　Let　us　assume　that　a　fault，of　which　the　rate

is　smaller　than　the　average　rate　of　general　defor・

mation　of　the　Japanese　Islands　or1。3x10－7／yr　as

cited　in　the　above　has　nothing　to　do　with　crustal

break　or　earthquake　generation．The　probability　of

maximum　mean　horizontal　acceleration　at　a　site

exceeding　respectively　100and300gals　is　then　re－

evaluated．In　spite　of　such　elimination　of　low－rate

faults，　it　turns　out　that　the　general　pattern　of

probability　distribution　　is　not　greatly　　altered，

especially　in　the　Chubu－Kinki　area　w五ere　the

probability　is　high　although　probabilities　at　sites

very　close　to　an　ignored　fault　become　considerably

Iower．　In　view　of　this，no　probability　distribution

map　for　which　the　Iow－rate　faults　are　disregarded

is　presented　for　the　sake　of　simplicity．

一60一

Earthquake　Prediction　and　Seismic　Hazard　Analysis　in　Japan

Conclusion

　Seismic　hazard　in　terms　of　probabihty　of　ground

shaking　exceeding　a　specified　level　is　estimated　in

Japan・nthebasis・factivefaultdistributi・nand

crustal　strain　accumulation．Unlike　the　existing

studies，that　deal　with　only　the　average　over　his・

torical　and／or　geological　times，the　probability　for

a　prescribed　time　interval　from　a　speci丘ed　epoch

can　be　evaluated，so　that　it　may　be　said　that　Iong－

term　earthquake　prediction　is　taken　into　account　in

the　evaluation．

　It　turns　out　that　the　highest　probability　apPears

in　the　Chubu　and　Kinki　districts，Central　Japan，

where　many　faults　are　concentrated，There　are

some　areas　of　next　highest　probability　in　the　Shi・

koku，Kyushu　and　Tohoku　districts。

　If　low　strain　rate　faults　are　disregarded，the

probability　lowers　to　some　extent　although　the

general　tendency　of　probability　distribution　is　much

the　same、

　　Probabilities　of　a　large　earthquake　occurring　in

theseasurroundingtheJapaneselslandscanbe

evaluated　in　some　way　or　other　though　the

evaluation　may　not　be　quite　accurate，The　contri－

bution　from　such　o鉦一shore　seismic　activities　to　on－

shore　ground　shaking　can　be　combined　with　that

from　inland　active　faults　providing　overall　hazard

estimation　in　terms　of　probability　of　gromd　acce1・

eration　exceeding　a　certain　leveL

　　The　hazard　maps　presented　here　are　di鉦erent

from　the　existing　ones，which　represent　seismic

hazard　averaged　over　a　long　Period，　in　the　fact

that　earthqake　prediction　in　terms　of　probability　of

earthquake　occurring　in　a　prescribed　time　interval

from　a　speci丘ed　epoch　is　taken　into　consideration．

It　is　the　writer’s　belief　that　the　seismic　hazard

maps　presented　in　this　paper　would　be　of　some

usef。ranti－earthquakepr・graminJapaninthe

future．

　　　　　　　Refere皿cesGeographical　Survey　Institute（1981）．Crustal　movement

in　the　Tokai　district，Rψ．Coo74．Co”z”z．Eαπhα。

Pプ84乞α．，25，213－222（in　Japanese），

Kanai，K．and　T，Suzuki（玉968）・Expectancy　of　the

maximum　velocity　of　earthquake　motions　at　bed

rock，B％ZZ．Eαπhg灘た6R85．1n5孟，，τo妙o　Uπ加，，46，

663－666．

Katayama，T．（1974）．Statistical　analysis　of　peak　accelera－

tions　of　recorded　earthquake　ground　motions，5E1－

S。41V－KE1〉Kyu，26，18－20、

Kawasumi，H．（1951）．Measures　of　earthquake　danger

and　expectancy　of　maximum　intensity　throughout

Japan　as　inferred　from　the　seismic　activity　in　histori－

　Cal　times，β％lJ．Eαπ物襯為6R85，1π5オ．，To妙o　U麗加・・

　29，469－482。

Matsuda，T．（1977）．Estimation　of　future　destructive

　earthquakes　from　active　faults　on　land　in　Japan，」．

　Phζy5．Eαπh，25，5麗汐ψ」，S251－S260，

Research　Group　for　Active　Faults（1980）・Active　faults

　in　Japan，sheet　maps　and　inventories，Uη幻8プ5⑳o／

　7b々yo　Pプε55，7b為ッo，」4♪‘zπ，363pp．（in　Japanese），

Rikitake，T，（1975）．Statistics　of　ultimate　strain　of　the

　earth・s　crust　and　probability　of　earthquake　occurren－

　ce，7セ6勲o頚ツ5f65，26，1－2L

Rikitake，T．（1983）．Active　fault　and　crustal　strain，

　E碗んα．Pプ84㍑．R65，，2，167－189・

Rikitake，T，（1984）．Strain　rate　of　active　fault　and

　earthquake　risk，Eαプ‘h（z・P764∫o筑・R65・・　2・277－303・

Wesnousky，S，G。（1982）、Crustal　defomation　and　earthquake　risk　in　Japan，Pゐ，五），Tんθ5∫5，Colπ甥6ガα

　Uπ掬67麟ツ，Nθτσyo矯．

Wesnousky，S．G。，C．H．Scholz，K　Shimazaki　and　T。

　Matsuda（1984）。Integration　of　geological　and　seismo・

　10gical　data　for　the　analysis　of　seismic　hazard：a　case

　study・fJapan，B祝」1。S召枷．5・・．肋・，74・687－708・

一61一（9）

/

g

/

l~

L/~_. J~'~'(

<)g

~;~~¥

A 100 - 81 o/o

B 11 80-61 60- 41

D 1 40- 21 E ~I 20-11 E'] 10-0

~~l'

e~ o

e

e

/

O p

o

f o

Og

ve o

~e

6O-41 9~0 C

D 1 40-21 20- 11 E

10- O E'

Fig. 6 Probability in percent of a exceeding 100 gals in a tlme interval

of 10 yr from the year 2001 due to earthquakes originating from

inland active faults. a denotes the maximum mean horizontal acce le rat ion .

Fig. 7 Probability of a exceeding 300 gals in a time interval of 10 yr

from the year 9-001 due to earthquakes originating from inland

active faults.

/

Og

/

,"~~~

~~~

A 11 Io0-81~~

B 1 80-61 60-41

DII 40-21 E~~] 20-11 E'] lo-o

･f

e~ o

,

,

o

/

/

o

dP

o

<)d

~~~

~)

B 1 80-61 ~6 C J 60-41 D 1 40-21 E 1 20-11 E'] IO-O

o

Fig. 9 Probability of a exceeding 100 gals in the 10-year period as specified

before. Both the on. and off-shore seismicities are taken into

account.

Fig. 10 Probability of a exceeding 300 gals.

as those in the legend of Fig. 9.

Other conditions are the same