ML19323H717

Investigation of Max Possible Earthquakes, Annual Rept

ML19323H717
Person / Time
Site:	Seabrook
Issue date:	08/15/1978
From:	Chinnery M MASSACHUSETTS INSTITUTE OF TECHNOLOGY, CAMBRIDGE
To:
Shared Package
ML19323H715	List: ML19323H714 ML19323H717
References
CON-NRC-04-77-019, CON-NRC-4-77-19 NUDOCS 8006160093
Download: ML19323H717 (90)

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Massachusetts Institute of Technology Lincoln Laboratory

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AN INVESTIGATION OF MAXLIUM POSSIBLE EARTHQUAKES Annual Report

Project

Title:

Investigations of the Seismological!nput to the Safety Design of Nuclear Power Reactors in New England.

NRC Contract: NRC-04-7 -019 Principal !nvestigator: Michael A. Chinnery. Group Leader Applied Seismology Group Lincoln Laboratory, ',11T

. 42 Carleton Street Canbridge. '.1A 12142 Period of Centract: 1 January 1977 - 31 December 1977 13 Aegust 1973 A

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. k' Abstrac-This re;cr. iescribes research :arriei :u under l20 Ocn rac l Oh-77-019 iuring the peried 1 January 1977 :: 31 Cecesber 1977. A detailed study of avai'.able scientific literature concerni:5 the esti=ati:n of maximus ;cssible earthquakes shows that all available =e:heds are ~

4 empirical and lack e. scuni physical basis. Evidence that even the enpirical methods are valid is very weak, pri=arily because :f the sher len6th of the earthquake record in most areas. An attemp: :: use global earthquake catalogs to eynine the regional variati:n of maxinus ;cssible earthquakes is unsuccessful.

o It is iemenstrated that saturation Of the sa6nitude scale and biases introduced by instrumental : lipping : sbine to make g values for large earthquakes very urceliable, and to :bscure i

the presence :r absence Of =axist:2 possible ea.~.hquakes. A pregress

, report :n a study of :Tev In61and crust and upper mantle structure is included.

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Table of Contents Abstract 111 Introduction 1

1. Maximum ?cssible Earthquakes: Current Status 2 1.1 Introduction 2 .

1.2 Definitions 3 1.3 Approaches to the Probles 5 1.h Physical Argusents 7 1.5 Arguments Using Earthquake statistics 10 1.6 Use of the Level of Seismic Activity 12 1.7 Pattern Recognition Approaches 16 1.8 Other Studies 18 19 Discussion and Conclusicas 19

2. Analysis of Global Catalogs 23 r -

2.1 Characteristics of Global Catalegs 23 2.2 Earthquake Statistics 2h 2.3 Saturation of the Magnitude scale 28 2.h The ISC Catalog 32 2.5 Events in the Aleutians-Iuriles Region ho 2.6 :sterpretation h9 2.7 Discussion ..

57 2.3 Oonclusions 60 References 61 Appendix:  ? regress Report: .Tev I: gland Crus and *;;per Mantle Structure 33 i'.-

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l In:reducti:n This re;cr descrites resear:h carried :u: under ::?.0 lentrae liRC-2 ch_?~ 019 during the peri d * .*anuary, 19~7 to 31 le enber, 19~~. The najor eff:r during this ;eri:d :ensisted of two studies aimed at evalua ing the possibility of esti=ating the ntxinun pcssible earthquake that sight a

be expected within a given regi:n.

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- The first study consisted Of a review and assess =en: Of available scientific literature on this tcpic. Since such of the resear:h in this area has been carried out in the Soviet Union, this reviev provides a g

reascnably ::mprehensive se: Of references, and a discussion of the a

a vari:us approaches which have been tried.

1 The second study was an attemp: to leek for evidence of upper j bounds to earthquake si:e within global tedy wave =agnitude :a:alogs, j

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, , and in particular in the 150 :stalog. This study seen turned into an '

atte=p to understand the sources :f bias in tne =agnitudes *isted in this :atales, since until these are understood it is i=possible to a

search for naximum possible events. It transpires tha: these biases, l l

together vith saturation of -he =b'#* ** ** * "' o :stal:gs essentially '

, useless fer this type of study.

I l

A third area of resear:h, into the crus and upper santle structure of ' lev Ingland, got u::de-vay i'.: ring the ; cried ::vered by this report, and a pr:gress re;cr: is included in the .2.;;endix.

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• 4e vouli like to k cv vhether or nc there is a lisi Or " upper bound" to the size of earthquakes for a varie y of reasons. First, earthquake size is usually intended to be a seasure cf ener y release.

However, energy usually varies strongly vith si:c. yor example, the standard relation betwee: =a6nitude M and energy I (in ergs) is ics E = oa +bM o (1.1)

Bath (1966) reviews several estimates for the :: stants aoand b o, and shows that b, appears to lie in the range 1.h to 2.0. Since the susber N of ea:-thquakes is usually described by the relation log N = a - bM (1.2) where b is about 1.(see, for example, Richter 1958), the Octal seissi energy release is dcminated by the largest events. We shall have reason to question both equatiens 1.1 and 1.2 later in this re;crt, but -he conclusion appears to remain valid. Analysis of the energy budge: Of the earth requires knowledge of the rate of Occurrence and energy release in the largest events that occur.

Second, 3ruce (1968) has shewn hev the re'.ative slip of ecteni:

plates can be esti=ated from ea-thquake si:e, and sheved tha: the :::a1 slip is dominated by the largest events ha :ce r. -'he fund =-=--2' questien of hev =uch ectenic =cti:n is released in seis=1: sli; :avies and 3 rune, 1971) can nly be ansvered clear'y ::ce ve understani -hese large events.

And, thiri'y, -he estimati:n Of maxin'.: ear-hquake si:e is in;cr-tan: in the esti=a-i: Of seissi: risk. te ;cssibility tha: Lar e erents say Oc: , eren infreque::17, in a: trea :an lesi te a seisri:

i I.

hazard that is unacceptable 'Or :ertain :ritical facilities such as nuclear ;cver plants. The i3C Rules and Reguia-ices, par *00, Appendix A, set cut the seissi: safety standards "Or these s:::ctures, and define the Safe Shutdevn Earthquake to be based n an evaluation of the ""a-r#'un earthquake potential" Of an aree.IZofmann, 197k). "he purpose " the -

present study is to assess our ability to est sate this quantity. #

We can usefully divide the overall probles into two parts. First, what is the evidence tha; earthquakes :ensidered as a global phencmenon have a naximus possible size? And second, hev dces this maxi =us possitie

si:e vary frcs regica to region? The first question ought to be such j ,

i simpler t,o answer than the second, and it is legi:al to exanine it I

i first. Ecvever, as ve shall see, # t is dif"icul: to give convincing ansvers to either of these questions.

1.2 Definitions e

There are two important definitions that we must exp;;re before ve continue. The "irst is the definiti:n of "saxim'.:s", and the second is the definition of " size".

The ters "saXimu=" is not, unf:rtunately, aivays used vi;h the 3ame seaning. One definitica is the obvious one, vhich refers c the largest possible event that can occur given the physi:11 Ocndi icns of the l scurce area. A second definiti:n, sese:ises used, includes the ::ccep

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=ax for the "true" raxi='.=1 possitie =agnitude 'I=ax fer the saxist:m o

ossible energy, ste), and T_ax for the =agnitude tha Occurs with probability ?, which defines the a

c?;;ed probability of "negligibilit~".

As ve shall see in the next section, very differen =etheds must be used u

in the esti mtion of M max and Ymax . . l The definition of earthquake "si::e" is eve :o-a d ' * *

• a ult . There are a large number of quantities which atte=;; te =casure this size. A i

partial list includes

a) Body vave =agnitude (g) b) Surface vuve =a6nitude (M,)

c) 100 second period sa6nitude ,

d) seissie =ccent (Mg )

e) radiated seismic energy

, f) ela.:, tic potential energy release g) mav4 m epicentral intensity (:)

h) maxi::nns epicentral acceleratice

1) localsagnitude('()

The basic problems here are not only A decide which of these =casures of size are the most appropriate for a given situation, but to recogni:e that the relationships between these seasures are in general ;corly understood and in se e cases demonstrably ver/ :: -linear. In parti-cular, scme of these quantities have buil:-i upper bounds whi:h :a obscure the search for a fundamental upper 1_:i: :o earthquake size. ~4e shan e'xamine this problem in sore detail in section 2.

An addi:ic al :c ;11:atics, whi:h arises i: the litera: r e very frequently, is that -he :ers =agnitude is s: :f;en.used vi:heu pr:per lefici;i . All prae:i:s; sessu es Of rag:itude a. e es;ri::ed ::  ::e

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5 limited portion Of the seismic spec r.:n, sr.d are closely tie:i to the

=ethod of seasure=en e=pl:yed. 2.ere is so much variability in to:h of

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these fac crs tha: he tem magnitude al: e is almos: seaningless ,

particularly when the characteristics f large earthquakes are :occer:ed.

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e Quite often, in reference to the 1: cal seismicity of area, the term magnitude refers to local magnitude 1.. Of all measures of =agnitude a

• his is one of the hardest to quantify. It vas introduce:i Originally by l Richter, and designed for local shocks is California. Its :lerist:ica is very arbitrary, and refers to the icgariths of the ,ar%us re:Orded L

ii ' trace amplitude f a. specific instru=ent ,"Jood-Andersen seis=cs a.ph) at ii *

]! a specific distance (100 *cn). .

3ecause the instrument 4111 receri a vide i i I

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range of frequen:les in the short pericd band, and because there is no

{ seismic phase identification, the significance of the maximum trace

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r amplitude is =ct : lear. For small earthquakes, the maximu:n trace amplitude i

vill often refer to body wave arrivals at shcrt distances. For large 4

earthquakes, the = v' um trace amplitude vill usually be assceinted with

, fundamental sede or higher mode (L ;hase) surface vaves.

The princ1;al usefulness of ld is, Of ecurse, that it is a = essure i

of ground motion in the near field at a range Of frequencies tha are relevant to engineering ecusiderations. -=provements in the es,isa-ion

! of 4 w(Ka:ameri and Jennings,1975) =ay .ead o a scre :c= sis:en: scale, '

l.

,.but its relatic :c far field magnitude de:e=inati:ns is stil'. une'. ear.

1.3 Atoreaches o the ?-obles 4

The nu=ter :f papers in the literatu e ia: 1 Sempt o ge: o the .  !

l hesr: of the ;r:blen Of the esti=ati:n :f -he =aximus possit'.e earth-quake is 1:1 e Wa. "he =aj:ri y :f -hese are :he verk :f s:te -is:s in -he 'JSSR, where there.has bee: a .': s er: i: eres; in his :;i:.

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( ( s 1*nt:rtuna:eiy seme Of these ; aper: are hard to obtain and difficult to read.

A number Of approaches to the proble: have been ;r:pesed 'see, for exa= pie , Shenkova and T.arnik,197'4 ) . 71rst, there are a number Of broad arguments that attempt to lisit the' upper si:e of earthquakes on the

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basis of physical principles, including fault gecce:ry and slip, and the strength of earth caterials.  :-enerally speaking, these arguments make a convincing case in favor of a global upper tcund, bu give little indicati:n where -his might be. A secced approach uses earthquake statistics, either in the form of frequency-=agnitude data er =cdelled by the theory of extremes. These two analytical techniques generally lead to sL=ilar resulta, but both turn out to be severely limited by -he definitions of 9agnitude used. A third apprcach, which see=s very icgical yet which lacks any ccavincin6 physical basis, attempts to relate the size of the maxisun possible earthquake to the level of seismic activity in a region.

It vould be very nice if such a relationship were to exist, but there is no : lear evidence that it does. More recent apprcaches have tended to focus en information frca nec-seismic sources, such as sec10gical and gec=orphological data. Sc=e of these approaches are statistical, using pattern recognition techniques. Others are =cre deterninistic, and atta=p: to link 1cng ter= geci:gical fault seve=ent :: shcr ters earthquake siip.

In virtually all of these apprcaches one problas ;reic=inates. The receri :f earthquakes is relatively shcr- in =cs: par s :f the verld.

Ca:a ief:re abcut 19C0 are generally qualitative and c.ari to interpre .

Adequa:e seis=ic netveris have :nly been available sin:e -he early 1960's , and ' as ve shall see in secti:n 2,' there are ::111 pr:b;e=s in

, , , .I . .

5 defining the si:e of large earthquakes. It therefore bece=es very difficult to establish esp 4 *~a' 'a:a f r =axi=us ;cssitie earthquakes

! in specific regicns, since these larges: even s =ay have retur: peri:ds of 1C00 years or = ore. *41thout these espirical estimates, i is vir ually impossible to exasine the validity of =any propose; approaches. *

! 1.h Physical Arguments There seems to be universal argreesent that any =easure f si:e of i

an earthquake must have an upper bound. This argument is often intuitive, l but it can be refined to seme extent. Certainly equations 1.1 and 1.2 I

I cannot both be valid for indefinitely large M, since this veuld imply an I

l infinite release of seismic energy per unit time (Nev= ark and Ecse blue:h, t

,! 1971). However, both of these equations are ;ccrly defined at large ma6nitudes, so the argn=ent is not too helpful, Intuition is often carried into the discussion of regi::a1 upper f

bounds. Newmark and Rosenblueth (1971) remark that earthquakes vith M > 9 in the continents and M > T under the deep oceans are :=likely, though they admit there is ro real basis f:r -hese esti=ates.  : fact, if M is surface vave magnitude M,, ve shall see that M pr bably ices ct exceed about 3.o anywhere, but this is an artifact of the =agni ude scale and act a true upper beund (se :ict 2.3). Earthquakes of M >7 s

have been Observed several ti=es aa -ha ~'i-ccean ridges, where the

. ae:ivity is 10v.

Someti=es intuition is quantified by -he use of 3ayesian statisti:s Ocnnell and Mer: (* ??i,1975) pre;cse an u;;er Scund to ear-hquake epicentral intensi-ies is -he 3cs : ares :: :he basis :f a ;resu ;;i:n tha such an upper beurd exists , *- A ---versati::s with seis=:1: gists'.

The resul-ing seir=i:17 curve is used :c es isate seis=i: risk in this

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area (see also Is eva, 1969; Veneziano, 1975'.  :: seems '_ikely that this study reflects a general telief tha; areas :f 1:v seis=icity shculd have icv upper bounds to earthquake si:e (see see:ics 1.6).

It is possible to go secevhat teyend intuition. Tsuboi (195o) has proposed an upper bound to earthquake energy. He first relates earthquake -

! energy to the volu=e 7 the strained egica around the scurce, then assu=es that the strain is uniform throughcut this volume, and then uses field evidence for the maximun strain which the earth's crus: :an withstand i

(aoout 10_4). Then, if V is limited by the thickness of the crust, an 2h upper bound to energy of about 5 x 10 ergs is obtained. It is hard to assess the validity of the assumptions used in obtaining this result.

A very similar approach has been given by Shebalin (1970), though it is less convincing. He quotes linear relations be:veen earthquake

, magnitude and both mean length of focus and vertical extent of focus, from an earlier paper (Shebalin, 1971). He then uses limitaticas on both length and depth to set an upper bound to magnitude. The validity of his starting relations is very such Open to question.

Sisilar procedures have been Outlined by Hofnenn (197h), vio describes hov sagnitude fault-length relationships (e.g. 3cnilla and and 3uchanan, 1970) may be used to assign =axista magnitudes. Obvious'.y this type of apcreach ,cresur.reses that we can :lesrly define the icca--

. . =-*'a-h 3 of all active faults in an area, -ha treakage bey:ni the ;rasen: fault length is i=possible, and that the =agnitude-fa e- 'a s h re*sti:n is

. sin 16 e valded l:his is equivalent to preposing -ha all earthquakes have the sane stress irep). Each of hese assu=pti:ss is diffi:ul: :: 'ustify.

.a_e__,..,

__ _a v. ar...-< ,. ? ~ ,h ,\ -,s..

,_y, ---o. . _- ,. .c o. . s . _< < ../ . _,. .-,. .,_., >

strain accanu' a i:n say se: lisits :n the axi=u= energy released in in

~

. '. i*

(

. i

( 9 earthquake. They indicate, for exsspie, tha if upper and icver bcunds can be placed on a 3enioff strnin release graph, the naxi=un pcssible earthquake vill be specified. This approach is neaningless unless the record of earthquakes already :entains at leas; One naxi=um possible event.

These studies are typical of these atte=pting to use physical arguments. The strength of rock, under various physical conditions, is not vell known. F.ovever, ve know even less abcut,the lisitations on the size of the zone of slip, and it is this variable which probably limits the usefulness of physical arg'ments. The largest known fault area is probably the 1960 Chile earthquake, which vas about 1000 km long and i

perhaps 200 kn vide on a shallev dipping fault place (Kana=ori and Cipar,197h). There do not seem to be any convincing arguments why fault breaks could not te larger than this On occasion. Could the entire Aleutian are systes break at cace, for exa ple?

The effect of strength of rock is related to stress drop. The basic problem can then be formulated as fo novs: Seismic moment M is o

defined by M = u1*JD (1.3) o where u is the rigidity, 1 .s the length (long heri:enta' ** ~ si:n),

W is the vidth (shorter vertical Or deva di; "ension), and 3 is the average fault offse:.

"'he stress dr:p le can be vritten

• 3D 10 2 'l --

4

,1.a.l Where 7 is a geene rical fac cr which ypically ra.ges fr:n 0.25 'f:r 1:ng strike slip faul s} :: 2.~5 (for 1:ng 11; s'.ip f aul s ) , as is sicvn b ,r .~- ' .. . .* . .r f. * ,:4.

. i,.

. , . ,1 10 So ve say generally vrite

~

2 M

o

' 2LW t.o (1.5)

If stress drops are rcughly the same 'abcu; 50 bars) for all earthquakes, as has been suggested (Kanascri and Andersen,1975), then '.imita: Lens to seismic =c=ent M o depend only on limitatiens to the dimensicas c. the w

fault area.

However, questiens about the :enstancy of .la re=ain. Scme studies appear to indicate local stress d ops as high as seve-a' ' cbars ( A chas-beau,1978). In the eastern US, the occurrence of medera e sized earthquakes in the lover crust with no surface expressi:n of movement vould appear to require rather small fault di=ensions and :orrespondingly large stress drops. To take an example, if a fault area 20 x 20 k:: vere possible in an area of stress concentratien in the Faster: '.S, vi h a stress drop of one kilobar, equation 1.5 gives a seismic secenn of ever 28 10 dyne-en (equivalent to an M S of over 7 5, see Figure '4) . This is prcbably larger than any earthquakes so far observed is this a ea.

We cenclude, then, that while physical arg.:=ents supper; the idea that there sust be an upper bound to earthquake size, and suggest that there :ny te a. substantial regional variation of this upper bcund, ve *-

'/

cannet yet constrain the appropris,te pare =eters enough to esti= ate the '

r sicos of these upper bounds.

1.5 A r.:=ents 'Jsinz Earthcuake Statistics A variety of authers have attempted to use the statisti:a' :har-ac eristics of the earthquake record c estimate naximus ; css'v - ==--h-quakes. It is not a- = 'aa- '

--a- axis-ing earthquake 2e.:a'.:ss ar=

goed enough f:r this ;ype Of study, :ertai.'.7, in -he exan,le discussed

ie: ail in secti:n 2 :f -his reper:, it is :;ea- :'..a: prcble=s :f

~,

saturation of the =agnitude scale and individual station detection-ecmpletely obscure the presence or absence :f upper bounds. -

There are , o possible apprcaches to -he analysiz of eerthquake catalogs. The first involves the use of the frequency-sagnitude cu: re, which is discussed extensively in section 2. *he other is based on Gumbel's (1958) Theory of 2rtremes. Gumbel described three asymptotic distributions which =ay be used to model the iistribution of largest events cccurring in a sequence of cqual time periods through the earthquake record. The ?ype I asymptotic distribution Of largest values corresponds to a linear frequency-magnitude relation, vi:h no upper bound. The ?/pe II asymptotic distribution includes the case where large events are less frequent than would be expected on the basis cf smaller events, i.e. a non-linear frequency-sasnitude curve. "'he ?ne :2! asymptotic distribution

, specifically includes an upper bound. Algebraic details can be f:und, for example, in Yegulalp and Kuo (197k).

Applications of the S fpe distributice generally accesplish ne more than the use of linear frequency sagnitude statistics, and nc upper beund is included. Papers using this distribution include I;ste " =~d L:mnitn (1966), Gayshiy and Katok (1965), Mi'_ne and Caven;cr (1965 ,

Ccnnell (1968), .t=_rnik and Zubnerova (19ed,19~0), Ye5ulalp and uc l197h), Shenkova and 7=-

'> (19?h) and O'~ h ' =-' *<sc: ( ~_9?? ) . hcugh

, sete of these papers sensica =aximus zagni uie earthquakes, it is :les-o that what is discussed is the qualit-/Ycax, he magnitude which has a probability of occurrence (during sc=e fixed geried? tha; is less tha:

Studies that attemp to use the ?/pe ::: 1s;. :p;c-ic dis;ributi:n 1 e ;ctentially =cre in:eres:ing. ~~nese incluie p'e_-chan 1 d lin

, , . /.

I -

( ( 12 (1973), and *_*egulalp and Kuo (197h). Se first of ,hese studies ices not define the magnitude usd, while the second. is based :: Sutenberg ar.d Richter's (195h) data. n ey can both be shev: Oc be f:= ally equivalen to trying to fit the frequency-sagnitude curve with a ;runcated distributien (Cosentino el al., 1976, 1977). ~4e cte that Knopoff and Xagan (1977) have argued that frequency-sagnitude statistics ~are to be preferred Over extre=al statistics since the first uses all of the available data.

To anticipate section 2, there is no doubt that saturatica of the M scale begins in the range 7-7.5 It is interesting to note that most s

of the estimates of M frem these studies are greater than M = 7.5, max s and the vast majority are greater than M, = 8.0. As long as saturation of the magnitude scale is not censidered, there is no vay that the results can be unambiguously interpreted as indicating the presence of an upper beund vith regional variations.

I 1.6 Use of the Level of Seismic Actirity Ferhaps the sost persistent attempts to study the nature of earth-quake upper bounds have teen made in the USSR by Ri:nichenko and his ec-verkers, teginning with R1:nichenko (1962, 196ha, 196hb). Many associated references are listed by Ri: niche:ko and 3agdasa-cva (1975).

Risnichenko's basic postulate is that there is a clear cut upper bound to the energy released in an earthquake. Setting the total energy 1 r' release 3 = 10 joules, he discusses the treblan in te=s :f ?

max K . He uses an implied relaticaship be:veen energy and the Observed sax quantity, sagnitude, of the f:rs log 3 = a

• bM (1.6) _

"he parti: d ar values Of a and b usa' ra o qu::ed 'ani a e still :pe:

questi::.', and the pa--ic'La- definition Of magni;uie M is sc - given. l l

l l

F  !

I l

( ( 13 He recogni:ed frem the beginning that it was iifficult er impossible to determine K sax iirectly fres the observed earthquake : stales cf an area. He has therefore focussed on the possibility of establishing a relationship between I nax and the level of seismic activity A in the frequency-energy relation log N7 e A - y(K - :% ) (1.7)

(A is therefore the activity at the reference energy level Ko ). He has discussed the forn of the relationshio A(Ksax) in several papers (Ri:ni-chenko 196ha, Rznichenko and 3agdasarova 1976 and others). -3riefly, his argn=ent is to relate the energy K of an earthquake to a volt =te radius R (for Central Asia he obtained R = 0 315 10I-10), t, ,y,rLge t3, ,c=Lygty A over a circular region of radius R to obtain I, and then_ determine an espirical relation between I and K . For Central Asia he determined

=ax t

(Riznichenko and Sagdasarova, 1976)-

log I = 2.8h + 0.21 (K nax-15) (1.3) vhile for Japan he found a better fit with ics I = 2.Sh + 0 39 (Inax-15) (1 9)

These equations are intended to te valid for 15<I<19, or 10 2,7,1g26 e s,,

The form of these equations was derived very artificially (Ri:-i-chenko, 196ha). K ax vas st= ply chosen as the largest event for a given region (often using a short time sample), and I determined-for the region. The plo: Of I against I had :ensiderable scatter, and a i

. rax 1 nax values (Riznicha->-

linear relation vas fitted to the larges: I 2-4 Zakhareva, 1971). :n 196h the :cestants estimated in equatica 1.3 vere 2.30 and 0.20, so there has been li::le change in the rela:ica in the l l

subsequen; 12 years. The difference in :he sl:;e f:und f:r Japan ':.39 instead of 0.21'. is listurbing.

. . * /*

• ( ( ,

t i

w

't 4

log N log N = A - yK I

r s

J

'.I i

K L , ,us- ,-

mex log 3 max w.

w.

. ~4 .,- e.x. o .,.c s.

-_ . . , . . s a . ..

. . .u.... ....,.

.y .. .s-._. 2. . , , , , . , . _ , . , .

ear-hquake energy 3, and assc.=es a linea- frequency-e:ery rela-10:

for energ values belev I .

max i

4 1

t t , . , . _

. . . ;*

( (-

15 Obviously, the probles in this ac.ercach is that I m needs to be determined in scue regi: s before the gene-=' 'av can be established.

~4e must allow, hcvever, the possibility that successive applica:icn of the equation in varicus regions (e.g. Gorbuncva, 1969: Dr.:mya and Stepanenko ,

1972) may improve the constants by an iterative er "bco:-strapping" '

methed. "he logical basis for the expressien 1.8 is not established.

Whether or not it works in practice is less clear. Se authors cc= pare 31 large earthquakes in Japan vith the predictions of equation 19 Brenty-one are found to be in agreement, 10 are found to be larger than the predicted Kmax, thou6h the authors note that uncertainties in many of the epicenters sake it hard to sa'<e a firs conclusion from this result.

The situation is far frem satisfactory. 'he existence of a relation between I m and A is not oroven, and ap.cears to be = ore of a ho.te than a scientific fact.

We should note, in passing, that if the =axi=us value is defined u

using a probability ? (5'=ax), then there is a very clear relation be:veen the maximun value and the rate of seismic activity. This has been described, in a most obscure way, by Housser (1970). His arg=ent =ay be restated as follows:

let us ass =e a linear unbounded frequency-

=agnitude law of the form (1.10) leg 3 = a - bM where N is the cumu~ ative nt:sber :f events, vith sagnitude > M, per =it area, during a =1; ;ise peried .';er year, say! . Suppose tha 2 is _

the =ber :f events / yea- tha: :an be ::nsidered negligible for risk purpcses.

. t

( ( 16 o

Then log :!

n

=a-bY =ax (1.11)

For ivo differen: regicas, with different a and 'o values, ve have o o icg N n = a, b.T. max (1) = a b .T2 2 =ax(2) so, o b,^ 3 a,-a3

~ -

Ysax (2) = b-- T=ax (1) + .o - (1.12) 2 2 It is reasenable to set b : b: 1, and then 2

e o Y:nax(2) = Wmax(1) + 2(a - a,) .

or 2

e o 't Tmax(2) = T=ax(1) + ics 3 A . (1.13) o where N is the number of events with =a.gnitude 0, which =ay te taken as o

an indication of the level of activity. In a simple example, if area 2 t

o has a seissicity of one-hund edth of area 1, then the T value for

=ax o

area 2 vill be two units m'ler than the Y for area 1.

max The reasca that Housner's (1970) argument 's obscure is that he tries to asscelate the above with a true M value, as shown in Figure max

1. Clearly the analysis really refers to Our ;nbounded frequency-

=agnitude lav.

I In s -

• y, existing literature s:metimes attempts Oc ;csiulate a  !

1 1

relationship be veen seismic activity and the upper tcund :: ear-hquake i size, but success in establishing he nature and even the v Cidity of l l

this rela i:: ship has been essentia'ly ncn-existent.

1." Fatter: Ree:gnitien Anpreaches Reccgni:i:g the fundamental "' ' ' as involvei in ; ying re'a:e the si:e :f " r'-us ;casible ea-;hquakes to the level :f seisri:

= *

(

( 17 1

l activity alone there have been several atte= pts to include a variety of other geophysical and geol:gical info =ati:n.

Ri:nichecho and 2:hibladze (197k) have Oc= pared and correlated the estimation of I using the level of seismic activity, the gradient of max the Bouguer gravity ancmaly (suggested by Tsubci,19h0, and 3 erg el g_. ,

196k), and the velecity of vertical revements determined by secdetic and gectorpholeg***' - -heds. *he three estimates vere ec=bined tegether to obtain a single estimate using veights of 1.0 for the seissi data, and 0.5 for each of the other =ethods. ?e results are no sore eccvincing than those based en seismic activity alene. His paper is notable, e

however, for its ertensive collection of references.

Shenkova and Karnik (19Th) state frequency-energy data are not reliable enough for the estication of Imax, and rge the inclusien of data on " environmental properties and the rate of energy accumulation" t

(i.e. Senioff graphs). Ecvever they give litnle indice. tion how these pieces of informatica should 'ce tied together.

In view of the interest of several Russian geophysicists in pattern recognition problems (see, for example, Gelfand et al. ,1976), it is non surprising that attempts have been =ade to apply these sethods ;o ,he determination of M zax . "his tooic is addressed by Sune et a' . (1975),

and an application to the Carpathian regien is described by 3crisev and Reyster (1976). "he general ides is te 1 ck f:r these :cabinati:ns Of Obse.-table features that a:: ear to be indicative of the Obse.-ted M_,

values. The features selected include such iters as rates of recen.

ver-i:al =ction, nea-ty v *-+ *=n, presa--a '

'-=--"-=s and fra r e

~

intersecti ns, seissi: s. -ivi y, gravi y e.nently e :. he ia * '-*'ysis f:';:vs the usual pr:cedres.

. Mos: Of the fez r es :hesen vere f:u.i ::

.t a_ ,.... .. .. ...e._ .s. ...

., . ..v. .

nax

s

( ( 18 The basic proble: Of this analysis is, however, nc Ediressed by the authors. In order Oc deduce the appr0priate relati:nship, values Of hacvn M

=ax are needed in a substantial number of regions. Since :hese are not readily available, the authors used "es:L ates nade by expehts.

This introduces such a strongly subjective elenent into the analysis

~

that it must be regarded as meaningless.

1.8 Other Studies Tvo recent studies should be sectioned, the first for cc=pleteness and the second because it has an interesting approach to the probles.

Caputo (1977) has proposed s ccmplex model which pur;crts not only to account for the linearity of the frequency-nagnitude relatice, but to predict the max 1=um seismic ma6:itude and sc=ent. Se assu=ptiens on which the author bases his analysis appear to be ecmpletely unreasonable, and the paper is =eaningless.

Smith (1976), en the other hand, has proposed using geclogical data to obtain a mean rate of slip for a fault zone over the past 10's of thousands of years or icnger. Then, if the frequency-ncnent relation-ship for the area is linear, and can be defined (see Chinne y and Nc: :h, 1975; Enith's argument here is less riscrcus', then there nust be an upper bound mement that is consistent vith Observed slip (3 rune,1969) .

Esith uses gec1 sical data of Easilten (19~5) te obtain these upper bound nc=ents (which he :enverts bac% ;c upper beund nagnitudes) .

This approach is One of the nest rescenable that we have seen, bu-proble=s s.:ill re=ain. There are :Onsiderabia "'-"'-das in the

' - * '-'- - -=*. f- *--

-e'------~...'-.-=.~,~--cmc"---.~.=.~=--.-.s'-..--<--~--..='~~~*.

vy ,.-. .z ~ . <. 3

. . . . e . ...L:s . .,3. , -. .y,.....,

. . . . . . . , . -.2.

.. . a.

- -_ . , a s o a . . . .a a.. ..--... >- ,. -,. a., ..,,--..a..

--..-:...g---- .. s s --

..>- a..,

a--, --... .-.a.,

.. .., .a..-...a.-,...

(A 19 fault systes has clearly been distributed Over a rather vide :ene :n a geological ti=e scale. It is likely that individual faults could carry much of this slip for a pericd of time, and then it could be transferred to other neighboring faults. To put this another vay, S=ith's (1970}

approach requires that the earthquake process te stationary ever the -

period of the geological data on each faul: considered. This is a questionable assu=ption for the fault :ene as a vhole, and =ay be invalid for individual faults vithin the system. And, of course, there appears to be no vay to apply Smith's se hed to regions such as the Eastern L'S, where geological information en fault slip is not available.

1.9 Discussica and Ocnclusions The basic problem in atte=pting to deter =ine the =aximus ossible earthquake in a regica can be stated quite si= ply. If the earthquake record for the region has a length T years, then evidence is available that bears on the earthquakes that have rean return perieds of up to ?

years, or a probability of occurrence devn to 1/T per year. This evidence is not necessarily scod evidence, for the largest earthquakes in :he sample.

The occurrence of large earthquakes appears Oc be described 1li e well by a Poissen listribution (Tpstein and ;c= nit ,1966; ictnit:,

1966). The probability that at leas: :ne e. er.: vi'" a- =--ual pr:iability of 1/T vill Occur vithin a peried f years is

? = , - e-0/T

. . 2)

So, if t = T, the probability is 635. This suggests that in scre than

-l one third Of all regi:ns studied there is likely to be an appare..- I l

l deficiency Of iarst tvents.

4

20

( (

Co Ptrase this another way, a 100 year record of earthquakes vill Only give reliable infer =atic 'at the 905 level) fer these earthquakes with a sean retur peried of abcut 20 years or less, er an annual pre-bability of .025 er more. In practice, of course, the length of the earthqua%e record is often considerably less than 100 years, and this applies to most of the regions of the USSR studfed in the quoted literature, and to California and other active :cces. Clearly, then, a 100 year record of seismicity is only adequate for the determina:ica of maximum possible earthquakes if the mean return periods of these earthquakes are significantly less than 50 years. ""his implies tha the axisun possible earthquake must have occur ed several times during the period of observaticc.

In all of the literature that has been surveyed, there is no esse of a specific region where a maximus possible earthquake can be eles-ly defined. Even when all regicas are censiderei together in a global t.

earthquake record, the apparent upper bound to surface veve magnitude M s

can easily be acccunted for en the basis of saturatice of the magnitude r

l scale (Chinnery and " orth, 1975). Perhaps the = cst useful contributien to this area that could be made at the present time veuld be the clear I

i and unambiguous descastraticc Of the existence Of an upper Scund Oc earthquake size in just ene region, anywhere On the siche.

It is necessary to add, here, that ve have not atta=pted to define 1

l

. .,rs *_,.3.on".

,4 m.. w .< s.=. a . .. _. c .._s.

..o, p .s.. t. s e ,. , .,. . , ., , ,_.,

.. __ -_ , 4 2.,m_,y . _.. .. .a_

1 Cevine,197h) which has been a=;iasi:ed by the :ers " ec:ccic province" which appe,ars in the NRC ?.ules and 2e'ulatices, o Far: 1:C, A.rt.endix A.

, = _ _ , _ _ - ...

. . . . a..sg e n., .- s. o,-...,

. . . , ,x....

....f. .o 3_,.. , =g. ,

I

,_a.

.,..._. ..a_.s .o.,- . . e ....u....,a.,.s

. _ . . s . _ _ _, ,.z,s_s..

e

_r.. _a .= ,._.,s= ,c=s .

. ._n,.

,. ! 1

.~ se.'=..~~.a.-=._*.~~'.'-=_..'.-._*_'_=-.o_'_s_-~~

3 =.v=.~.~.~.

~..~.=.=__'___'~.v, ~ . . ' . = " . . ~ _ -

i

, ,,_,......a.

a , , ._.] -.,.-_.a._.,,

. . e .

( ( ,

. *. .a ,, e *_.- s , . ' a. n , '.S..a . =. .x. ' .- . '.... a e _* a- '. a. .'a.a a.a.* un a'. _' a.

.- .' .-ov g.,y ., ., 5w.. .. .. 3 .s.

,ues.4,.. ...-a

.. 5. e ,.z,.3.e...

. . ... -.. ..a. 3., ,.e .' ~-= x' na e s: s ' %..i a.

earthquakes. In spite of the deep seated belief cf many seis:clogists gna ....s

. .. .- q..._... . ., . .._3 , _4 . a..-s '.k..a

. . . . '. un,..e. .c"...A. -s us *. a..xi - a~. , '.k . . - _' ~s .a.ssenable approach, given Our current state Of kncvledge, is to assu=e that these

• upper bounds are at rather high levels in all areas.

We are Oberefore forced into the classic method of si=ple extra-polation of linear frequency-nagnitude r frequency-intensity relation-ships. This raises an additional probles which deserves discussion.

In the centext of the evaluation f the seismic risk to :ritical a

structures such as nuclear pcVer plants, we veuld like to establish a vay to determine the size of the earthquake that cecurs vith sete fixed risk probability vithin a given regi:n. yellowing McGuire '19"6} and

, others, we ray usefully set this fixed prcbability at 10- per year. If the earthquake process is stationary Over long periods of tine, such an earthquake vill have a mean return peried of 10,^00 years. If the process is non-stationary, this statement is =eaningless. Ecvever, in practice ve have very little alternative but to assane tha: the avail-able record of earthquakes is representat've Of the rates :f Occurrence o f *.o*vh. s aa' =-~ d ' a. s~ =. =. ar *.* 1 ~ uek = s ' - .' .=. * =a=.'.' s . e - = a . a-A

" -m =. A.-

4a e .r,..,.

. w . . - . a..

t

m. w ,- ., r os.. w ,3 . .-. . a...a. 4 ..w . n_3 4 ., . . s _. v. . . . ..-a. 4.g9 ., s3. .aa. 4 .4.. _ ./ 4. 4.....

,. ..,3

v. .,..y -- ag ..~~s-

. . - ->..a ... n. g c .o .. . . ..-u q . 2. , 2. _. ...

.. . , v.e >- < ..e...- . . . . e _, _. , - , ,.- , a r.y.<.,.e.

. \' v. , ......

.... <..as As...lsge. aw s u , ,. ...a._.<_..,

5.. ~ ~ ~ ,: ',

.y .c C y a .ss.

. - . . . . .u.. s.g-d= J

.. %.g3 5 a. 3 -- .t e - .r=-. 3 .* .J .*y a. . .8_ge.aas"a.s-

-- .-* 3

. #a.y

.  %.." . A w a.3 .ya.-c . a .

'. .b. a. a .a #. .=-.8 *

.. c .a. .s . 3 ,.y

.. .. . .._'.a.

.g

. 3swan3 .a s..ms .

. - .. ..e .,a.

g. 2 . a. .g a..a. . . . ?. . ,

j,,..

.,...u..

..3..

[^.%4....y a * * - ^

. - - - . . . . .s ..

7..4.33

.... -y ., . %..a.*f. _s *

. ,.4

_. ...<.g.,

• a

_,.'...._._...%..4.g a*,,

g .

i l

4

( ( 22 raise.s -he ;cssibility -ha: large earthquakes nay te associated vi:h sc=e long en average level of seismicity which is very different frem the recent shcr: record of s= aller events. It is i=;crtant that research into the stationarity of earthquake precesses in varicus tectenic enviren-ments continue. -

The =ost premising avenues fer future investigations into =aximum possible earthquakes vould appear to lie in three areas. First, ve need more in'or ation on the nature of the strain and stress fields in seismic cones. Second, ve need to improve our understanding of the ulti= ate i strength of crustal materials in a vareity of tectonic settings. It i

seems likely that the tn e upper tcund is controlled by the sice of the regica cf accumulating stress, and the ability of the crustal rock to vithstand that stress. Thirdly, the infor ation from geolc6 ical and r gecmorphciegical data on icas ters fault slip, where surface faulting is visible, sust place scue ecnstraints en the largest possible earthquakes (Smith,1976). This apprcach needs further develo;=ent, thcush the questica cf stationarity say limit its usefulness.

e

. e -

( (

23

2. ANALYSIS JF G'.CSAL CATA; CGS 2.1 Charseteristics of Global Catalogs A logical place to seek " ' 'orsa:ica en the exis;ence of upper bounds to earthquake size, and the variation cf these upper bounds vith tectenic regicn, is within earthquake catalogs. There are basically two kinds of catalogs, those :cmpiled for a limited regien using data " rem a local netwcrk, and those ecmpiled fer the whole vorld using a global network of stations. We have chosen to begin this study by analyzing the global earthquake catalog, since this seems = cst likely to contain evidence.for regional variations, if they exist.

In order to be useful for this study, a global catalog must have two important characteristics.

First, it .sust be eccplete, partiettlarly for large earthquakes, and pre'erably for =edium-sized events as well.

Second, it sust use a clearly defined measure of earthquake magnitude .

which is uniformly applied to all events. As we shall see, this turns out to be a such more restrictive conditica than it appears to be at e.<

. . s . s _4 ._5 . .

Several global catalogs a e available. Those inclwiing events since the early 1900's include Gutenberg and F.ichter '195'a), Duda (1967) and Fothe (1969). Unfortunately, he global distributi:n :f seisni:

, sta-icns was very poor unti; 1960, a-2 -kase :a al:ss si; suffer fres a high iegree of ncn-hetegeneity. With the establishnen: Of the Verld Wide Stindari Seissegraph Ne: veri 'WVSSN) in the early 1960's, a much sore h:=cgenecus data se beca e available. Data fr = this ne: veri,

gether vith a variety Of ista fr:: ::her sta:i:ns va-= 2-='y:ed by tvc Organisati:ns. The U.S. Ocas ani lecde:i: Survey, and its sue:ess0rs the-Na '--** -aa- Survey and -he ~ 3. Secl:si:a1 Survey, have pr:duced

oh

-.. ..  ? .u..e =. ~ v- ,- e . e rn.< .a . . . .. >. r.- a.- . - . . . s 1'

, o,t

- .----/

.-, , t.4 -,.

-- _.. . r o.

r . . . _ -1a- .. e.-., - . . -

issued :n the average abou; 6 =cnths after an even: Occurred. The International Seis=clogical Center (:SC) has chcsen to :clie: all he available -data, including the ?DE bul.letin, and issue a scre ec=prehensive 1

I catales. Typical delays in the publication of the SC catalog ranged frem two to three years. Both the FDE and :SC catalog began eccsisten reutine bulletin production at the beginning Of 19th, and since then have maintained the production of very uniforn :stalogs.

3cth catalogs, since 196h, have recorded a. body vave =agnitude g for essentially all events. This magnitude is based cc the maxiz.:2 peak to peak anplitude in the first few seconds cf -he ?-vave arrival en short period instruments (operating in a rather carrow frequency band centered at about 1 hz). Surface wave nagnitudes M g (at a period Of 9

about 21 seconds) vere recorded very irregularly, and only in the last year or two have atte= pts been made to sessure M, on a routine basis.

The requirement that the catalog be :caplete forces us to "ccus :n the body vave magnitude g . For reasons which are Outlined in the next sections, this is not desirable, but there is little that can be icne about it. Attemets to relate M to a have shcvn a large sea;;er (see, s o for example, Aki, 1972). ,

7 3 .ue aee.4 .

-.m -3

._a. ,3_3 . - ey v. ->.__- 2-_ ......... c ...e -erv ..

. - . . . . ... . ,,._,_ - 3 l

for a very practi:al reasca - it is available in ie: ail :n sa6ne i: tape 4

. .s.e .4 .4. a - 3 a ---

.e.env.4.

a 4. .3- 's

- _-o.). ". k. ..' a- ' a '- ' ' . =. . e s a t o .' a. . /

-. .- .-,'..e.-

analyses Of the very large a:cun Of data ::n=erned. _

i 2.2 Earthe_uake 5:stistics 1

m.%.e-o. gyp. .. ...  %.ga.a- .a. , e. a. g --a e . .s . .m

. a . (. a.

. .'s

.. 1.g . t.3.2.,* ---- .s- u g--s - . s . a. . .: .s .~ 3 i

.J e.*.a. .*a.

gm

a. g. . * . s g f. 3 1. .g_ . e s .

3 9..g.

4 e.g

• g . .- . . . . - 4. 3-..* J .* *. 3 .=.-M J, **

. g *.*.* .s. e. .

l 1

1 1

1 j

. . ( .

25

,,..m.n,...,.. . .-..g-

.,.en ./. . .... -a - -,,..,,,a.,.,.--.>..a,.

. . - - 2. 3 . .. -u. e .. ... .........

..<*a.es t

Gumbeis (1953) theory of extre=es, and is concerned :nly with the largest even vi:hin a given time period. Thcush these two approaches appear to be very different, they give very similar results when applied to the same data set (see, for exa=ple, "hinnery and Rcdgers,1973, and Shakal and Teksos, 1977). Because Of this, and because the frequency-=agnitude approach uses all of the data in a ca: ales, it is to be preferred.

Khepcff and Kagan (1977) have specifies 117 shown that extremal statistics are =uch in*erior in some cases. 7cr this reascn, ve shall use the frequency-nagnitude approa.c h throughout.

Gutenberg and Richter (see Richter, 1958) de=custrated that local ear *hquakes in California Obeyed a frequency-=agnitude relation of the fors:

I les N, = a - tM

- o (2.1) where 3, is the number of earthquakes with =agnitudes in a small range centered en M, and a and b are ecnstants. This for: Of the equation is necessarily discrete (the constant a depends ca the size of the magnitude

._.ervals in which the earthquakes are accumulated). In cany cases, it  ;

l is sore :cavenient to use the :umulative form:  !

los N, = a - tM (2.2)

.gw.-.,. . . ...y, *[ ., 33 . %. . . ..

.e

.. 2. 7.. .. .,. a. ya. w..m a 3'~_ .# .*.* d.a. . M. : ".n' 3.**

a. o. . *. *. .

i i

a.g. e.e.. ...t . e ~- g./ ' e . a. g. e .. a.s. 2 .s g *.a.t .

ne

. e . t ..v.oyg , 2 1.

'. u...n 3 . .

.3 . e. .. .a _-n w.e a. a n.a. s.r*w. a.

~.s. .os ,. ,. aj- .u. . u..

s_sy a .. .s o. ,m .g a.s e...n.

., ,., 2 .. *

.w .-_ *j . . s . a. . .. .

... z. a. . , _ .a A. , .

. s..e n l

l O. F. '.*SOw . . 9 .. ... . 9 we e

w . . M. . O. O M 9. . . $. ..@

... -- .a.

Q W O. M. .M.

m ...*,,g.

d a. . .

g'.gg.

a..

j i

8.

w

. e. .e.g

. . . q. A. . . m... k. ..j

. sef d. A. g- _ g *I

. . ... g g

....g .,o q

9 1

)

• . d . ..

..4.....g.

.. og

.. , . . . ...a . . . .o.M gg

.. ...g .g g e. d .,. g * '..

.. h.. .e g. 8.eg. . . .d .y..g g ,

g

. o.gp.

.s.e. ..-_.2 3..... 8...J.a. .s.*..,.e., --.A .. .A=. ms.e

- g =.  %. e. .s

.-a. 3 m A. A.-A .a 2* m.

-- r E.d.A.a

. Y'f

- -- e .

- y-

'

. u ,

( ( 26 l

d W

i 4

3, log N C

i line=* *-aquency-=agnitude lav t

1 t.

N s

s i

M Magnitude max

. Fig 2: Ideal effect of an up;er tcund to 4

earthquake me r.itude, using :u=ulatite frequeney- agnitude 2 a i3:1:s.

t 1

l

• 9 4

9 4

h

, ...-y _ _ .- -

c ( 27 18-2-12586 1000g C

L L.

L 100 e- -

- E m

a !_

0 L s _

_m C -

0 0

~ lOH ,

> E o h z

• w [ .

D L LOG o 10 N = 7.6 6 -0.93 M s

• x.

W !_

% \.

i w \.

w 1.0 L-F r .\e w -

< h \.

J -

o L s

D

\{

\

o O.1 ;- \

e-y

' P"

~

\ ,.

. I 1 a i \ 6

O.01' '  ! ' ' t 6.0 7.0 8.0 9.0 -

MAGNITUDE (Ms )

ns.  : :c a e = :.=e :ers an'_ n :h:e  :+ - -

l l

l l

28

( (

using Observati: cal -lata, the universality Of a linear rela:icn is net clear. Many of the reasons f:r this vill te discussed in the sections that follev.

In an ideal vorld, the presence of an upper tcund to earthquake magnitude vill reveal itself by a departure frem linearity at the upper end. Figure 2 shevs an idealised representation of this non aa*-'ty.

Unfortunately, there are two other effects that can also lead to a curve similar to Figure 2. First, any measure of sagnitude based en a ibnited spectral band has a built-in saturation property. This is discussed in the next section. And second, seisnic instruments frequently have a limited dynande range, and the magnificatien is often set to record medium sized earthquakes. In this case, large earthquakes vill cause the instrunent to go off-scale, and a =easure of magnitude is impossible.

I As a result, there may be a purely instr.tental upper-tcund to sessureable magnitude for a given instrument. The effect of this en ne:verk determina-tions of event =agnitude is discussed in later sections.

2.3 Saturation of the Magnitude Scale Severd authors (Chinnery and North,1975; Kane=cri and Anderson, 1975, etc) have recently pointed out that because of the shape :f the spectre. of the radiation emitted by an ear.hquake source, any reasr emen:

of sagnitude based en a limited spectral tard of frequency =us: saturate.

For example, M is usually sessured at abca: 20 seconds peri:d. When s

the source is large encush that fracture prepagation las:s for 10:ger than 20 seconds, the amplitude Of the 20 see td radia-*-- vill no: -

change vi:h increasing si:e, thcush its dura:ict in general vill.

An exa:ple :f this effect vas discussed by "hi .er/ and Ner;h (1975}. Figure 3 shevs the :u=ulative frequency sagni:2ie : r.e f:r

29 large events listed in the :lassi: study of Ou enberg ani ;'-chter (195k).

It appears that the listed =agni udes are very close to presen: day M 3 values (Evernden, 1970).

This diagras has often been used as a basis for discussing the existence of an upper tcund to earthquake =agn'tude (see, for exa=ple, Ecusner, 1970). It is, hcvever, possible o interpret this curve in another way. Figure k shows a cespilation of recen; data relating .

surface wave ma6nitude M s to the seissic moment Mo . The highes': two points correspond to the 1960 Chile and 19eh Alaska earthquakes. 3cth have been extensively studied and sees reasonably reliable. ~'he observa-tional data clearly indicate a saturation of -he M scale which seems to s

begin at about M3=7.5, and be ecmplete at about M,=S.5 The solid line in Figure k is a rough form of the M -M relatica.

x -

s o At this point we can legiti=ately ask if the fall-cff in Figure 3 can be wholly attributed to this saturation. *ie can say this such: if the data in Figure 3 are translated into a frequency-=c ent graph, the result is very linear (see Figure 5).

Kanamori and Anderson (1975) have argued that the frequency- c=en:

graph should be linear, vith a slope of 0.67, if all earthquakes have s the same stress drep. ~t therefere seams reascnable to ;cstulate tha:

. __ss _as .n. . ... se, ,_.d

.. . n...- _- . . _.

._.e .... ... _. .,. .,..c

. . . ..... . . ..s.._.

(Figure 3' :an be explained as saturation Of the M, scale.

m.s.....3,. . .yo 4_.,.c . an . ,c .' - . s

- . .'__a . a_. '. a a '. . . c . ". .' , - . . d.,

. . . T**s.,

.. 1 3_e g_-

s..__,

. . .* s. _c .' .' .- =. . . *. v ' _' _e _ - =. ' . .. _= .. ~.~, ,~ . .  %. c ur_'. .a s,.<.._-__,..,~.u_m..

.r , .. .'_:~:1

, . u , a _. .e. .~_, a. 3.. ,,.,..

. ._ . . . .8. .._- 3. ..,.._.. .: .

.%,.. _. J.. W.u 3

....,..r...:

.y y .. .w.. ......g.....J..

..@ *,J f....._.s..,.  %. 4 .w ,, .

J. . . . . . g... C..... 43._3

.fC .8 _. ., ..

.w  ?. d.g .. .. ,2

( ( 30 18-2-12585 31 10

• CHINNERY AND NORTH 1975 o CHEN AND MOLNAR 1977 10*o - ~

29 e 10 -

_ . o E o o u 28 o sC 10 - ..

> s o u o

- 8 n .o Z 27 .

w 10 -

o 2 .

t o 2 .

26 3 10 -

. s

..l .

25 I *.s.

10 -

I 24 .

10 . I i i 5.0 6.0 7.0 8.0 9.0 MAGNITUDE (Ms )

Fig. i: ~c=plilatica of 87 pfo'ished estimates of se' =~'- ~-a -

l as * ^ ~~ic: Of surface vste zagni nde M 3.

l 1

l 1

l

( (. 3, 18 2-12587 1000t-C L

i 100 -

m m -

a -

c -

A s -

m

e -

i e .

I @

,j ~

10 C

O b

,i z _ .

w _

D -

O W

i e -

u_

w 1.0 2 -

F- -

< r

~

d -

LOG 10 N = 17.47 -0.61 LOG 10 M o .

2 D -

U e

0.1 --

J

_ i 1 i I-i

' 1 0.01 ' ' '

24 25 26 27 28 29 30 31 I

LOG 10 (moment)

~

71 . .: 7:equen:7 - =cce : srs;n :::s: :: ei tr:: 71sures I 1:d .

. + ,

( ( 32 Secend, the i=pertance of =agnitude satura;ien is ienenstrated.

a

• ' hen ve Ocme to examine global :stalegs using the i hz :. scale, ve must expect saturation to occur at icver magnitudes. This # a'aa-'y nake the probles of trf ing to estimate regional variati:ns in =axist:= ea th-quakes very difficult. ,

2.h The ISC Catalog An incremental frequency zagnitude plot Of data in the ISC catal s for the period 1966-70 is shown in the lefthand portion of Figure 6.

Although ISC data are available for a lenger period, ve have chosen to limit ourselves to this 5-year spen in order, as ve shall see, to ecmpare the overall catalog with certain special stations that vere only Operating during this time.

The resulting plot is typical of all frequency-n b

"t" 0"##*'t17

' available (e.g. 3 razee and Stover,1969, 3 razee,1969) . There is no clear linear portion to the graph, and this has led some authors to propose a non-linea- -a'ation (e.g. Shlien and Toksc:, 1970; Mer: and Cornell, 1973; Stewart, 197h). It is theref:re very difficult to determine a unique b-value, though typical attempts to do this lead to high values of up to 1.5 or more (see Figure 6). At icv =agnitudes many events are not reported, and the plot curves icvnvards. At the high end, Of parti:ular interes to us, the graph appears to steepen, and end near n. =6. o 5 Or c.f. y.o ,v,. . , .,.. .u..an :.:. ,,r,ea_

.. .. . - y z.-

. e ..a,.3-a-

- -- - -e a-- -

.a s . - ,.

.teried .

It see=s ressenabic to ask if these :stal:s -'=-** - 'stics =- '- .

any way the result Of the stati

ns used in he analysis. As many as ?:C I

3.,.s..s a a.a z.- .- . . .2C, -,./. . . > . u ,- --

..-n..-,.

. .- .o,,2

. . -_- . .. ,. -.. , . s.,.3--,...-s m.ew a.5e _-o.4., .%4

-J .g.. e 4 . -.-p w s -, 4 ,. w sa. . a. . . .s A- - J .I  %.4g.. . .o --*C 3.s --*

a

.=: y%.. 8=_,%

. , g. -. s . sJ. ..-----

- - - J e:c. . -.-

g ' 4.. *-, [ c# S., * *. , g. .. 2 .gb--.-

3. b wa.: w. .a.,-.=- - - -,w'* ..

=.m....b.,q...

.s..- . ..

o ,

( (

33 the ISC. The staticos used are listed in Table 1. Magnitudes. vere reccmputed as the average of those re;cr:ed by the 23 stati:ns, and a requiresent that at least 3 of the stations =ust have reper:ed the even ,

was superinposed. The resulting frequency-nagnitude graph is shcun in the righthand ;crtica of Figure 6 (the solid ;cints) . A second data se vas formed by applying the station sa6nitude biases determined by :icrth (1977) to the 28 statica network. The results are shewn as open :ireles.

The 23 station network shows very si=ilar characteristi:s to the catalog as a whole. In particular, the general curvature of the graph and the fall-ef' at high nagnitudes are preserved. This is convenient since it allows us to study the 23 statica ne:verk instead of the whole catalog.

t There are reasons to suspect that biases nay be introduced into the network =agnitudes by the process of averaging the reported station sagnitudes. This probles vill be discussed in scre detail in later sections of this re;crt. It suggests, however, that it nay te vorthwhile i

locking at the frequency-n. 0 characteristics Of the events re;cr ed by individual stations.

. Figure 7 shcvs plots of the events re;cr:ed by Keve , Finland, f:r

.:gc :g.

,. n.C

..,e .,..,. ..,

. ... .. ,,u.. ..s 3,.

.g it

.s, . .....,S

. ... rs A 1.

a . . . . - s. .....

. S . ..:

,np. . de .,.

. .... n.u..,>

. . . . _ .v.:.. ,

., a., a. m. .s ..,

... .u.s .. ... a. 2.,<-a

. .-.. .. ,.... . ...> .  ; ,

which ar,e independen; cf source 1: cati:n. The values are :enver:ed in o 3 .a . ' .a. n. "

O

'.v

. S.e .= 7 7.' .' .- . = . '. .- ~..

.. 'a 4.=..=.->.

. =~.y..'..6.da " s-.a....

~%a. o. n.

, e. . a ... .so. %. ,e. -~

. a a. .r ... . .;.. .o, .. .. u..

. .a .sa.. . ggw . ,. .,..,

..g. .V ..

.w ,rs a g....s.

1 ,4...%.,.

. .. d. g -e.

b . %.,.. .4 J.J ,. . = .. ** 7 8 '..$ *

.t ha

.w*g s ,. v a. .*.*. @* 8. . k. . .' 2* .J .# .e a. a =. .* ...g..

. ,. . , * - , l i

.- 4 ,.4... . 4 ., ...3 e. ... .: .. .. .. rg . , e . .w/, .;,.

. . . y ..4.,

. . . , .. ,..,...s.

..we

-4 , -:

..g .. ..

I i

( (

3h "J' GLE 1: 23 STATION NI"4CEX STATICN CODE LCCATION 3IAS (North, 1977)

ALQ Albuquerque, N.M. -0.20 3EA 3roken Hill, Zambia -0.23 3MO Blue.Mtes., Oregon -0.29 3NS Sensberg, Germany +0.20 EUL Bulawayo, Rhodesia -0.07 CAN Canberra, Australia -0.02 CLK - Chileks. Malavi -0.27 COL College, Alaska +0.01 COP Copenhagen, Den = ark +0.36 IUR Eureka, Nevada -0.2k-KEY ~2 Kevo, Finland +0.02 KHC Czechoslovakia +0.10 KJN -

Kajaani, Finland- +0.1h IJU Ljubljana, Yugos1,via +0.29 MBC t Mould Say, Canada +0.14 MCI Noxa, Ger=any +0.02 NCR Nord, Greenland -0.1k t NP- Northwest Territories, Canada 0.00 NUR Nurmijarvi, Finland +0.19 FMG Port Moresby, New Guinea +0.10 PRS " Pretoria, South Africa -0.07 PRU Czechoslovakia +0.0h RSS Resolute, Canada +0.13 SJG San Juan, Puerto Rico +0.2h TFO Tonto Forest, Arizona -0 32 Ttic Tucson, Arizona -0.1h U30 Uinta 3asin, Utah -0.11

~4IN 'dindhoek, South Africa -0.C9 o

l l

i

c22-5585 1966-70 3000 '

ALL EVENTS . 28 STATION NETWORK

.'"**. ' 3 STATION DETECTION 1000 .

, Da.

SLOPE 1.49  : '

• WITHOUT STATION

^

. o BIAS

.o o a WITH STATION BIAS O

IOO i, .  ?

SLOPE 1.47 N -

o

~

, o

.. o o

10 ..

. .+

o .

o

.l. _ _ .1. I I I I I I I I

.__I I

=_I 3.5 4.0 4.5 5.0 5.5 G.0 6.5 7.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 ni b *b F i g , l'. : Freiluency inagasitante data for the IGC catalog, for all listed events (left), and for a y aefected network or 28 stationa (right). The 28 station network is listed in Table 1.

i

KEV c22-n83 1966-70 1000: - -

ALL EVENTS ,

i 30'< A < 90*

i -

l

,1

~

f

(

, .- /

loo r . -

SLOPE 1.41 1

' SLOPE 1.45

/

N l

10 :

. ,r <

g

^

g

-. .t 1 .. __ i . . . . _. t_ __ _ _ t. 2 2 1 - .i i 2 i t_ k i

\

o 0.5 1.0 1.5 2.0 2.5 3.0 4.04.5 5.0 5.5 6.0 6.5 7.0 LOG A/T STATION m b

4 4

5 Fig. *(: Prequency inagnitude data for Kevo, Finland.

PMG cea-s *>

. 1966- 70 IOUO v

ALL EVENTS  :

30* < A < 90*

~

J.

/g  : n 1 -

t Ja

,p

/ SLOPE O.97 / . SLOPE 1.03 loo r / . - /

7

/

N , , , , ,

g 1 e 10 \" r . \

. \ e\ '

l"

.\\ .

\.

5 m

\

i l * *\

) \ i I . . _ ) . _ _ J . ._. L t 1 1., _. i e e t n (3 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 LOG A/T STATION m b

Vig. 8: Frenguency usagnitude data for Port 14oresby, New Guinen.

( ( 38

~4e have ::npiled similar plots fer all of the stations in the 23 statica network. A vide variety of behavi:r is seen. If attespis are made to fit the frequency g plots with a straight line, slopes are found to lie anywhere within the re.nge 0.9 to 1.3 Figv' - 7 and 3 shev clearly the differences that are observed.

There are tvo possible interpretations of these dat % lf the differences in b-value are real, this could indicate an important regicnal variation in seismicity characteristics (clearly ?MG and KE7 sample different portions of global seis$1 city). he second alternative is that station reporting charac'teristics *ra y considerably, and the data are not good enough to define a true b 'ralue.

s Perhaps the most surprising result is obtained when frequency-4 statica ( plots are made for the U.S. VZIA observatories.

"hese are EMO (Blue Mountains, Oregon), U30 (Uinta 3asin, Utah), "?O (Tento Forest, Arizona) and W.O (*iichi a Mountains, Cklaher.a). The four plots are superimposed in Figure'9. 'Zach station has'been adjusted heri: ental'y according to the station biases of North (*977), and small verti:al adjustments have been made to i= prove acincidence, recognizing that there are small differences in the seismicity sa.apled by each station.

Again, only events is the diste.nce range 20' to 90* are incluced.

Remarkably, -hese data are all consistent vi;h a seissicity :urve that is linear, with a slope of abcun 0.9, up to m. =3.3, and -hen -he o

cu:~re tends. devnvards and approaches the vertical in the range n. ='.0 3

to 7.3 This reis, tion, indicated as a s:lii line :n Figu e 9, is remarkably similar to the "rutenberg-Richter M, :ur te .?igure 3} in shape. *i:vev er ,

it differs irsmati:e.117 freer those bserved by ner=al sta-i: s. 20:i:e, fer exs=ple, tha: these :tse: te. ories ree:ri ~*my e tents '- -$a - ge 3"

b

' '=#  ?*2' vh'##*3 #* "#* 1i8=*d i 'U* 30 2'0*105*

( ( 39 tCCC(

l18 2 ;3525 ;l i

.- i I_

I cop *

• K O

x' a

• iCCCr- A y C O

• VELA ARRAYS

' xA ADJUSTED CR STATION BIAS

• , AND SE!SylCITY LEVEL ,

O 1966 70 1970  !

x A

l O *

• x l

A 4

'CC l- 06 b I

'y \ SLOPE 0 93

_ \

_O a N

\ ,

o 1

• SMO a \

0 080 A'40\ r I

• \ '

x 0 x TFO O e \  ;

!OT A \  !

A WMO " \  !

- AA  % \  !

- O '

, xx \ ,

g i 4:

j l

N .

1

._ g l

I t t t  ! 5 1 '

I' 40 4.5 a.C SS 60 6. 5 70 75 b

Fig. 9: heq';e:7f-StatiO3 _] p' 3t 3 f r fTO ~2. 3.

7E!A ObserVSOCrieS.

e

( ho There are a n'.=2ber :f i=portant differecces tetween the TilA arrays and the average anales seismic stati:n. "'he operators cf the 7EIA arrays vere highly trained specialists, who za:1e an unusual attempt to measure magnitudes :arefully and censistently. Mere is;crtant, each of the arrays was equipped with a icv gain channel, which gave the arrays a.

much larger dynamic range than the average station. These pcists strongly suggest that the 7EIA data may be mere reliable than regular station reports. An additional suggestion that this is the case is obtained from the large Aperture Seismic Array (I.ASA) in 31111ngs, Mentana.

' .fe Figure 10 shows data " rem this array for a completely different time

. .? . *- ;2 period (1971). Theseismicit/curveshowninFigure9isanexcellent fit to this data set (in'?igure 10 this seismicity curve has been adjusted e9 vertically for a best fit).

In order to investisete this problem in nore detail, it vould clearly be advantagecus to limit the gecEraphical regica vithis which

. I the events are located'. In this case we say expect a veil defined seismicity curve, and we can test the ability of various networks to detect this curve. This is done in the next section.

2.5 Events in the Aleutian-Kuriles Regien Theanalysksoftheprevioussectionvasrepeatedforeventsinthe Aleutian-K" 'sland area (defined by longitudes 135*3 :o lho**J, and latitudes 20*-90*). The i_.p:rtant seismicity :f Tais a ea lies within the 30 c .9C* range f stations in both Europe and the 'J.3.

Figure il shows he total !3C ista base f:: fais =~aa '-- 196c ~';. -

2e frequency-:agnitude data de no disagree s;r:ngly vith the seismici 7 l 1

ume shevn, which is that shevs in Figure 9 adjusted verti:a'ly f:r a bes; ft . 1* pen : leser excinati:n, i transpiree -ha: the :1:11:6 f:r

. . #r

- c .

i e, ,

C22_5623 1003 _ .

LASA BULLETIN

.  ;

, 1971 ASSUMED BIAS = - O.25 100 _*

N -

f 10 --

1 1 I I I I I 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 M AGNITUDE (mb)

Fig. 10: .Trequen 7-:agni ude~is-Y7:r -he :.arge A er-re Ieissic A: ray (!.ASA' '- "---2 a f:r the year '_; 1.

2.e solid '.ize is -he seisri:1 7 :ur te she c. i .

71 re 9

h2

( (

022-5621 1000_

ALEUTIAN-KURlL EVENTS 1966-70 ALL ISC 100 _- . .,

N

~

/

.s

_.. j

• t

..w 3 .

10 --

1 i L I I I .I t

3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 MAGNITUDE (mb I l Fig. 11: Frec.nene / - ss .itude it.:a f:r C e .ents i: the Aleu;ier.-7.r il a-a* -'s 41 1.. -he :2C.:=_ a'.:g, 1966 .

e

( h3

-his area is heavily biased by the re;cr:s fren the 7ILA bservator'es, par **~ 'a *y for icv and moderate events.

The situation is clarified in Figure 12, which shevs the data for a twenty-five station network (this 's the sa e network as tha- listed in Table 1, with the 75LA sites 3MO, !?O and U20 removed). As before, three station detection is required before an event 's included. Now the shape Of the netverk curve is :learly very different fres the seismicity curve of Figure 9 In fact, it is very difficult to locate the seismicity curve in any "best fit" position by vertical sovement.

On the other hand, data frem the 7ZIA arrays for this area shov excellent agree =ent with the global seismicity curve, as shcvn in Figure 13 Notice again that the 75.A ar sys record many events vi h =agnitudes between 6.5 and 7.3, while the 25 s ation network shows nene (Figure i 12). It is not possible to attribute this effect to the secgraphical location of the stations used, since there are 6 North Anerican stations included in the 25 station network.

We can accentuate the probles further by considering :nly stations in Europe. Figure ik shows the same data for a 10 station European network, which is listed in Table 2. The additica of the biases of North (1977) do not chaege the disagreenent in shape vith the 721A staticcs, tu; they do reduce =any :f -he ne verk tagnitudes. This results fres the generally post-ive tias of Iurcpean stati:ns : Table 2).

If the postulated seismicity :urve (Figures 9 and 13; is real, there are :learly problems vith the nagnitudes reported by the individual

• stati:ns in the ce:verk. As an e:ct=p;e, Figure 15 shcws the :tservati:ns Of Aleutian '~" a avents by stati:n :I7 lXevo, Finland!, whi:h was discussed earlier (?igure 7,'. Zither -he re;or:ei nagnituies are sut,'ee

ha

. (

022-5627 1000 -

_- ALEUTIAN -KURIL EVENTS 1966-70 TWENTY-FIVE STATION

. ., NETWORK o e

.n . - -

e

- o

.., e '

N = ~

e -

t

~

~'

10 -

e 1 I i t i i i

_ i 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 (MAGNITUDE (mb )

Fig. 12: .Wequency-=ag.itude data f:r a. 25 ste.:i:: .e:ve r'.<

(the static:s *isted in 7tble 1, with IMC, TFC s d "3C :mitteC .

i I

( .

h5 022-562k 1000 -

ALEUTI AN-KURIL EVENTS

• 8eze 1966-7O

. A

~

oA 3 . UBO o o TFO

. g o A BMO 100 --

o A 0

.o N -

A

~

I A

O o o

10 *# *

p. .

A o o o .

$4 0

_ A Ao 1 I i i i i ob.o oc 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 MAGNITUDE ( mb)

?i g. 13 : hec,uer.:7-rap.i;;de da a .^ ::. 3 Tl 1 :E75-

.x a - a s .. <- =ver. s , ~' e 5:Lil :::ve is ~'-* *=~^ Ls ;hs; ir. ?ti s e ;, Li'13;ti va '*** 17

.'O r i t 3~, fit.

1

.~

h6

( (

c22-5425 1000- -

ALEUTIANS-KURIL EVENTS 1966-70 5 TEN STATION EUROPEAN Nt.i

e. = WITHOUT BIAS 0 O

• 8. o WITH BIAS 100 -

• 3 .d O*

o N -

o Oe .

r .

10 _

_.

• O

- O O

- O

- O .

O.

1 I c. .

I i t i n . 1 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 l 1

M AGN ITUDE ( mb) I 1

Fig. '_ -: h equency- agni de is:1 ":r a '0 stati:n l

Propean ne:vois. T.e sta:t:r.s used tre listed in Table 2.

. I TABLE 2: 10 5"_'ATION IUP.0?IA'i rCOP.K STAT!0:1 CODE LCCATION BIAS (North, 1977) 3NS 3ensberg, Ger:nany +0.20 COP Copenhagen, Oensark +0.36

G/ Kevo, Finland ~

+0.02

GC Czechoslovakia +0.10

CTN Kajaani, Finland +0.lh LJU Ljubljana, Yugoslavia +0.29 MOX Moxa, East Germany +0.02 NUR Nurmijarvi, Finland +0.19

?RU Czechoslovakia. +0.0h STU Stuttgart, Garzany +0.29 l

1 e

i

- \

. .-  ;

( ( he

22_5626 1000 -

ALEUTI AN -KURIL EVENTS

~

__ KEV

_ 1966 -70 100 -

N -

I

• 10 -

I i.

l.

0 l 1 I . I  ! I i 1 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 t

MAGNITUDE ( m b)

Fig. 15:  ? equency-sap.i ude is:a :':r e ten s i . -he

. Aleutian-:Ori; ares, as :'ese. red a: ~ e r: ,

Finir.d. *he selii :'r te is -he same u these in Tigres 11-1.

, - - rv-

( ( ug o strens tiases, :r the station is ' ailing : re;cr: rany itrge events.

Fcr the reasons discussed in the next secti:n, -he ..e:ter explanati:n see=s =ost likely.

2.6 Intertretatica At this point va a-- " aced with two ;cssibilities. Either the "J.S.

7ELA arrays (and perhaps LASA, teo) have a ;cor_'y calibrated icv gain channel, which leads to the syste=ati: overestinati:n Of -he magnitudes of large events, or the magnitudes of these large events is systemati: ally underestimated by the global ne:verk of anal:s seismic stations. ~4e have been unable to find any independent evidence for the first of these alternatives, and it sust be censidered unlikely. It is possible, however, to suggest an explanation for the second of these alternatives, based on the dynani range of typical analcg stations, and the process e

of averaging which is used to obtain a netverk zagnitude.

Any seismic static can be described by a detection probability curve. The general "orm of this curve, and the parameters necessary ::

define it, are shown in Figure 16. For our present purposes, since ve are examining an earthquake cataleg, ve shculd regard this as the :urve deceribing the probability that the station vill re;cr: an amplitude f an earthquake to the analysis : enter (e.g. She !SC) . If, for exa=;ie, the statica ices nc: Opera:e for a porti:n :' a given -ize peri:d, -he

=azi=cm probability ?g vill be less than 1. .

i The probabili:7 :urve fails c'f a: ic h 1:v =agni uies 'vhere the

,_,a_ ,, . _ __, *yw...

....- _4.

= ._o . __. ._ _. ._.__

. .. ., . . o _a_.. s4. -.,_ ....- _._3__ ...2_.s . . . - ... .. __._._...

. e o.+.>_._,,._.'..

s

. u ,. . ~. s. 4..._<.. y. .-,_.

I

. . . . . _ _ . .. ...y..<..._/.

. . . . . . e ___4_ ..

I 4,

. . _4., ,_,.

. ...___. ._3

..,,3_..=.- .-.a...-..

.4

. 'i...'.-=.

.__a. . ' . ....-$.-.'.-=.

s 1

l

. e .u...

..... ,.......,, _u_,....s 4..._4. ...

. . . .s___-

..s._........_e_._.s....

~

( (. 50 13-2-13521 t--

~~1

.__ p ._ _

R DETECTION SATURATION Q

c:

LI ING CL z

O

') ~

M -

h o

[-

1 w r l F-- I .

w l

- I -

o i  !

G Gs STATION m b

d -

. . u :

- STATION DETECTION PARAMETERS G

d -

7d SPREAD OF DMCTION CUM Gs 50% SATURATION THRESHOLD ~

- 7s SPREAD OF SATURATION CURVE B STATION. MAGNITUDE BIAS P PROBABILITY OF REPORT!NG --

R 713 15: ?cr= :f f..e 2e:e:-icn ?re'ca':lli-/ :;- ee

s seis:L: s:L:i::.

1

. . a

( ( 51 .

d 3.,

. s- e 3.:e. a . . .

".k-- '. s 4 s a . a.d' . d ..- = '. . .--_'.'-a..'...m.

., . vS.. .' . '.. '. a- "..a. .d .o

odel; though it say be One of the res' is; rtan: effects in deter =ining the dynamic range f:r amplitude reperting.

Amplitudes are generally =easured with a rule on the seis:cgras, which is traced by a team of light on photcgraphic paper. "he s=allest amplitude sessurable depends on the line thi:iness, whi:h is typically about 1 mm. One veuld expect amplitudes of a fev =illine:ers to te easily measurable. *41th larger events, hevever, probless arise. Mos operators record the amplitude, :ero to peak, of the firs: sving of the trace. '4 hen this intersects '.he edge Of the paper mest Operators vill ,

not report an amplitude. Also, when the trace amplitude teccmes sore than a few cm, the ability of an Operater te locate the ti.t of the .:eak (or trough) vill depend on the quality of the pho:cgraphic recording, t

which is usually quite variable. And very large events, even if they de not go of*-scale, are usually dif*icult to =easure.

On purely gecmetrical grounds, one veuld expect the dynamic range of a=plitude repor' tin 6 to be between 2 and 3 orders of magnitude 'i.e.

between 2 and 3 3:t units). As we shall see, hcvever, it see=s to be

%e+. Vee. -_ .s.d a O crAe e . s 3s. =ag. .....w. 4...A. 4

. f.r .......

. . e .. . , _.A. -

" ..f....

. 1..." .. . 4.J.gs

......o 3., a3y1.4.ug.s . .. I .s.s e .e.* .,. .r.a . o s. o.s .. 4

.e .. .....

e. . . . . ..s. s

, . . g .4..* J.. /. . . .y.1

. ., _ss

....s . . a., _.y _' a_ _n_t ... . A. .o

. .s .a

. s . .s_S. _ ..A....

s. . . * ~ ag ..-.s .... C.

. . .' s. ._ e . _a . _. . a. ....

. . %. ...a'.

%e..

su .. . .s. . s.a.4 . .. n f.Osw .. .4 -

a*3.4 .4 ...y ... ,..

. . ....e__- a.. .

.u 3

--.2a...... ..... .

3 s w' al *. V'3_.' '. *. ," t ~a ^. ~ n ~. '* . e

~ ~

.d. ~ . . ~ . * . . = ~ . .* = *~..

a~ ~w E~. . - ' 3 ' a $ _~ .' .' .' . .* ~. .' ~. ~- ** *

(.ne *a....

_ .... _.... a.. .J 3 ...

.. . .. . ..s,3 3 .ea.y ....s.

.....-a

.s ,

~ , e.........

s..4 4..

. . . . - .a..

..g,. 9

. .w .

. s...e

. 4..,.,.4...

... .. .a . .. .s.a r.

s

.e. . .4 .... . . .... ...a ...s.. . . .... .e ..s e

4....a

.s ._.s...

_ .4e ..... e - . . -2 . . . . k.

.a..... e ,...

.w..... .., .s ....s..

...s... ... .. . s .a. a.

.. 4..........4..

. ~ r

. . t

,. ,. }

( ( 52 j s

I in Figure 17, 2ecause of scattering, an even cf nagnitude a vill lead t g

e to a distributica cf observed =agnitudes at a ne:vork cf staticns. Sis l' i

s distributica is often rou6hly nornal vi*.a standard deviation about 0.3 )

mb units (7 n Seggern,1973), and its mean (in the absence of station 5 bias) vill be an estimate of m. Ecvever, when the magnitude of the event approaches either the detection threshold er the cli; ping threshold

• 3 of the stations, the distribution beccces skeved.

Effects near the detection threshold have been discussed by Ringdahl (1976) and by Christoffersson et al (1975). Those staticas where scatter- M ing produces a lov amplitude vill not report, whereas these where a large amplitude occurs vill report. 31s leads to a net positive bias when the statien reports are averaged to produce a network magnitude.

Methods can be devised for including the fact that sc=e stations did not p 05 report an event (the maximum likelihcod method) but these =ethods a e

i cumberscce, an(I require a detailed kncvledge of the detection probability ~

1

curves. It does not appear possible to apply then to a data set such as .~

the ISC catalog. ~

I

'g An equivalent bias arises at the clipping threshold of stations,

.h.

S4 although this has not been discussed in the litere.:ure. 't is, of ji course, reversed in sign. When a large event cccurs, . hose statiens where scattering produces a la se amplitude vill usually act re;crt , *I 1

vhile those stations that receive a icv amplitude vill repert. he g resul . is a egative bias to the netver% cagnitudes re;cr =' '- ge N events. "his negative bias vill te quite substantial, up to 0 5 Or 1 M)

W M

=agnitude unit, a.d can adequately .cccunt f:r '-a d' "a-a ce be:veen UE sq h s-the '.T.J. sei.sicity :u re and the ~5C :stal:g seis=i:ity :urve. r C.

A B

( 53 4

~

i j

Number

.o v.

Observa?. ions I

i l

Approximately ner:a1 l 3 -

3.3 =b Units r  !

I l

i s Observed Station Magni ude f

24 . ,* w ,,,

3 _. .me .....

.. . ..,, s _...e

.. 4_..

. 3 2

n,.,.,

< . . 2.a.ea.

ga .y.... . . > .ge

. a...a.,.

..a.__

. e nd .o s -

0. . .- ~. . .* *.u . .* ~. n ~. .* =a 3~.. .' . . .' =. s s .

a .e - . 4, 1 o a... _. .. <. .. ,. s .

. .u .s a. .s .a . . . . . .. a.

a...... .

. is usually appr:xicately ncr:al.

Y

( ( 5s Ve :an illustrate our arg.=ent by using iata fr:s a single stati:2.

Figure 13 shcws the da:a ter IL7 (Eureks., Nevada: . ne left hand ;cr:i:n of this figure shows a ccnventional interpretation of the reporting characteristics of this station. An arbitrary straight line is fitted to the data, and detectica and clipping thresholds (indicated by arrows) are :letermined at g=h.5 and 6.3 respectively. In the right hand ;crtien of the figure, the 721A seismicity cu.w.e is used (E3 is quite close to the observatory UBO). In this interpretation the station fails to report many events for g greater than 5 5 The thresholds are nov i.3 and 6.1, and "ccmplete' reporting is limited. to the range h.7 to 5 5 A similar interpretation for staton KI7 using Figure '.5 sussest that this station carries out "ccmplete" reporting ever an even smaller range, perhaps as little as 0.3 g units (frcm 5 2 to 5 5).

A different representation of the sa=e phencuenen for station K'R is shown in Figure 19 Here, for each interval of 0.1 s units of UEO b

reported magnitudes, ve have ' averaged the difference in reported magnitude between EUR and UE0 for events in the ISC catales during the period 1966-70. The theoretice.1 interpretation of such a :iata set has been discussed in detail by Chinnery and Lacoss (1976). If the detection probability curve for EUR vere horizontal (Fire.re 16) then this ple, should be hori: octal co. he prese ~ ~ ' ' h =- '-- *'--ashold shevs as pronounced ;ositive biases as lov =agnitudes. There is a hin of a fla ;crtien of the curve in the vicinity Of 5 0-5.5, and then the data

en-inue teceming =cre negative. his must be in;erpreted as being due _

o a : lipping threshold. 1: seneral te: s, 7 tree 19 is entirely :ensis-ten; vith the right hand ;reterred inter;re a:i:n :t Firre 13.

t

c22-ssa7 EUR

. 1966-70 1000:  : g

! r}N j A m E

100 :  :

. .g

~*

T N

~

• \

. .\

-.. .. .. x.

\

10 .

g  : i-

\  :

\

\ n\

\  : \ -

4 \

3 y.

1 ._.4 i- .i 1. t _.1.i , , , , , . ,\ ,

3.5 4.0 4.5 5.0 5.5 6.0 s.5 7.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.o STATION m STATION m b b F l y. . 18: 'rwo interteretuLions of the reporting frequency of uLullon h2111 (Eureku, Nevadu).

The rig!L hurul litterpretation 10 preferred.

. e-i

( ( ,

C22-D61-e 0.5 - EUR - U B0 o 1966-70 co ,

o e e W

Q D

F_-

e* ,

z o e e 2 e i O.O -

. .. e n

cc

• o w

e*

ee e w

• O O

D '

ee t- e e z e e

e s -0.5 -

e e O

l- I  ! I I t

, 5.5 4.0 4.5 5.0 5.5 6.0 MAGNITUDE (UBO) i i

-\

l 1

Fig. 19: Ia:h ;cint is the aterase difference ':e veen the stati:n  !

=agni u<ies :f IU3 sed 'J3C '-- ' a .'ents listed in -he :5C esia' 06, ;;:::ed as s hneti:n :f the ~20 cap.i uie.

l l

4 l

27 2.~ 31scussien The results described abcve ;r: vile :envincing evidence that instru-mental clipping of analog stations is an importan problem, and that the 4

magnitudes of larger e tents published in the ISO catalog are biased *.ov and unreliable. A corollary to this cenelusien is that it is virtually impossible to study the seismicity :haracteristi:s of differen: regions using this (cr similar) catalegs, since each regica is "=o:.1:cred" by a different set of stations, with different operating and reporting character-istics.

l The VILA arrays appear to be unique in their vide dynamic range, and, until a global netverk of digital stations becemes available and has accumulated a substantial data set, the 7I'd 1sta is the :nly reliable

,, scurce of information en upper bounds. So far, ve have not discovered any evidence for regional variations in seismicity using these arrays.

As an example, Figure 20 shevs data for shallev seismicity along the South American subduction :ene. The gicbal :urve (?i.1.re 7 9) is again an excellent fit.

If we assume that the 7ILA seismicity curve is valid and represents j l

saturation of the :L scale, ve can use similar argunents : these :f  ;

O Chinne.nr and North (1975) to construe; an m.-memen relati::.shi;.

Assuming tha: he relati:cship be:->>-- ~ =-d M a: 1:v =agnitudes is 3 s m

b

• M s

+05 (2.3)

( see , fo'r ~ example , Lamber; et al,197h', then the fers Of the . -ccmen:

Ourte is as shevs in Figure 21. Scme 10 b; abeu- -he ::nstan- is equatica 2.3 remains, 3: the hori: ental 10 cati:n :f the m. -ccmen :ur.e is :00 vell-define 1.

. ( (

58 C22-57h3 1000 -

SOUTH AMERICAN EVENTS 1966-70

• QA a6 o . UBO

.o o . O TFO .

• ^ 0 A BMO 100 : o *

. A N -

O

_ O A o' 0 0O 10 _-

O A

O O

A d O

' I i ' i 1 '.c.A 3.5 4.0 4.5 5.0 5.5 6.0 6.5 6.0 I

MAGNITtJOE ( mb )

711 20:

~

7-e:;;ency-:2.p.it;ie ia:1 f:r 301:-h Ameri ' - i?* 3 2':3*P7'i a  ; 7rA a_rsys. S.e 2 _ii : eve is '-* **-' 13 ih' i

~

Ti f;re 3, adj' 30di '*erii d'-7 f r i ;e30 fiI-

. , 6

( ( 59 C22-5622 9

M s ~ 8.6 8 -

'M s ~ 7. 2 m '

7 -

b W

o \

i mb ~ 7.3 3

s m

b ~ 5.8 z

o6 -

2 ys t

5 -

4 -

!  ! I I I I I  !

22 23 24 25 26 27 28 29 30 31 LOG (moment)

Fig. 21: An esp 4 ' "' =b-sc=ent reisti:cship :ensister: vith the 72LA seis=icity Ou.-ve l71rire 3.1 ~he M 3 - ccent re_ati:n-i ship frem Chi:r.e./ ar.d, North !" 975' is shcc. for ::sparison.

. I 1

G l

-l l

l l

g 60

. 1 The inter;re a.:icn that the : rve in the *C A seismici y relati:nship is due entirely to sat r ation of -he s. scale see=s reasonatie. ~"ne shape Of the n.-ncment c' ave in Figre 21 is similar to tha: Of the M -

o s oment relati:n, and (at least qualitatively) g appears to sat r ate at about the expected magnitude. It theref:re see=s unlikely that any information alcut upper bound magnitudes :an te obtained fr:ct the existing

global g :etalegs.

2.8 Conclusions .

The conclusions of this' study are very negative. It does :o appear that the test earthquake catalog data can shed any light en the problem of the existence or the regional variation of maximum earthquale sise. This leaves only the much less ecmprehensive catalogs Of Gutenberg and Richter (195h) and others, collected before 1960. *4hile these older g catalogs are useful for event times and locations, there are growing indications that the assigned magnitudes in these catal0gs are ereliable (e.g. Chen and Molnar, 1977). At least part of this unreliabi'.ity probably arises from the instrumental probless described ateve.

I a

e i

. . j. .

4--

e r.v. :m..rJC:S

• References marked by an asterisk are included f:r completeness, but vere nc; used during this study.

Many have not been translated into Inglish.

Aki, K. , Scaling lav of earthquake sour:e ti=e-functi:n, Geophys. J. ,

3.1., 3-26, 1972. .

'Anan'in, I. V., Assessment of the seismic activity and the =axista possible energy of earthquakes in individual seis=cgenie :::es in the Caucasus regien, in Seis:cgeni: Structures and Seis=1: ,

Dislocations, 73II Geofizika, Moscev,1973 Archambeau, C. , Estimation of non-hydrostatic stress in the earth by seismic metheds: lithospheric stress levels along the ?acifi: and Nazca plate subduction zones, manuscript, in press, 1973.

3ath, M. , Earthquake energy and magnitude, in Physics and ~he=ist y of the Earth, Volume 7, Pergamon Press, 1966.

Berg, J. W., Gaskell, R., and Rinehart, 7., Earthquake energy release and isostasy, 3u11. Seism. Soc. Am., ih,, 777-78k, 196h.

• Bonilla, M. G. , and Buchanan, J. M. , Interin report en vorldvide his:crie

,6

' surface faults, Open file report, NCE2, U. S. Geological Survey, 1970.

Borisov, 3. A., and Reyoner, G. I., Seis=c- ectoni: pregnosis of the maximus magnitude of earthquakes in the Carpathian Region, ::vestia, Earth Physics, no. 5, 21-31, 1976.

• 3orisov, 3. A. , Reysner, G. I. and Sholpo, 7. N. , On the prepara:ics and use of geological-geophysical data for the i-dentificati:n Of :enes with different Mmax values in the outer :ene of the Alpine f:1ded region, Symp. On Search for ?.arthquake Fredi:ters (Abstracts:,

MGGG3, MAS 7ZN, Tashkent, 1974.

3ra:ee, R. J., Parther reporting en the distributi:n f earthqua.<es with respecc :o magnitude sb, Zartheuske Nc:es, LO, 51, ';69 _

3ra:ee, R. J. , and Stover, O. W. , The distribution of earthquakes vi h 1 respect to magnitude sb, 3u11. Seirs. Scc. Am., 12,, 1015-101 , 1969 i

l 3ru=e, J. N., Seissi =ccent, seissi:ity, '-d'-a e Of slip aleng raj:r I fault :enes, w.. vecphys. ,es., _73, ,-. .23, --rec.

43une, 7  !. , Kirill:va, :. 7. , Anan'in, :. 7. , 7vedenskaya , N. A. ,

Reysner, 3. I., and Shel;o, 7. N., A :e=pt :: esti= ate :he - H---

seismic risk: exas;1e :f the Caucasus, Prebie=s of Ing. Zeir=.

no. la, Science lNauka: Press, Mes::v, 13";. )

i l

l l

. ( t 62

• Sune, 7. C., and ?clyakcya, T. P., Correla i:n Of the saximum possitie

earthquakes in the Caucasus region and Asia Minor with seis=ic l activity, in Investigation of Seismie 0

nditions, "Stiintsa",

! Kishinev, 197h.

• 3une, 7. I., Turbovich, I. T., 3erisov, 3. A., Gitis, 7. G., Reysner, G. I., and Yurkov, 3. ?., Method of devel:;sent of a relatienship between the earthquake magnitude and the te :eni: parameters of l s region, Proc. Acad. Sci. USSR, 21h, 197h.

Bune, 7. I., Turbovich, *. T., Borisov, 3. A., Gitis, 7. G., Reysner, j G. I. , and Turkov, E. F. , Method of pregnestiestin8 the saximum ma6nitude of earthquakes, Isvestia, Earth ?hysics, no.10, 31 i3,1975

a j Caputo, M. , A mechanical model for the statistics of earthquakes , .=agnitude, i acment and fault distribution, Bull. Seism. Sec. Am., 61, Sh9-861, i i 1977 Ii li Chen, *J.-P. , and Molnar, ?. ,' Seismic =cments of najor earthquakes and

)' the average rate of slip in Central Asia, J. Geophys. Res. , 82,,

29k5-2970, 1977

I i Chinnery, M. A., Theoretical fault models, o ubs. Oco. Obs. Ottava, 27, 211-223, 1967. I i Chinnery, M. A. , and Lacoss, R. T. , Magnitude differences between station f pairs, in Seismie Discrimination, Semi-Annual Technical Sum =ary, I Lincoln Laboratory, M.I.T., 30 June 1976.

!I

! Chinnery, M. A., and North, R. G., The frequency Of very large earth-quakes, Science, 190, 1197-1198, 1975 Chinnery, M. A., and Redgers, D. A., Earthquake statistics in Southern NewEngland,Ea-hquakeNotes,]L.,- h 89-103, 1973.

Christoffersson, L. A., Lacoss, R. T., and Chinnery, M. A., Statistical models for magnitude determination, in Seismic Discrimination _,

Semi-Annual Technical Sunmary, Lincoln lateratory, M.I.T., 31 December l

1

} 1975 i Ocnnell, C. A., 2ngineering seismic risk analysis, Sull. Seiss. Sce. As.,

- fjl,1583-16c6,1968.

Connell, O. A. , and Merz, 3. A. , Seismi: risk analysis of 3osten,

, , ASCE 'Jatienal Strue ural Ingineering Meeting, Cincinnati, Ohio, ,

April 197h. i ennell, C. A., and Mer:, H. A., Seissi: risk analysis :f 2csten, o.

m,. rue.

,a

- v., --,2% s , . _e_,

_,, no.

s.-.3,.r...-- se - e.i, , .y.n-;.

Ocsentino, F. , Ficarrs, 7. , and Lucie , D. , Trnn a ed ex;cnential frequency-nagnitude relationship in earth uake statisti:s, St:1. I Seiss.Sce.As.,j,, 1615-1623, 19~~.

,, - --m-,-,_ ,-,-y, .~ y , . ,- .

- - - , , - - - ,3 m.. ,.- , ,,

. ( 63 Cosentino,  ?., and u:fo, 3., A generalisation :f -he frequency-ragnitude relation in the hypothesis Of a =aximum regi:na; =agni;ude, Ann.

i Geofis. (Rc=e), 29, 1-2, 1976.

i Davies, G. F., and Brune, J. N., Regional and gletal fault slip rates frcm seismicity, Nature, 229, 101-107, 1971.

and Stepanenko, N.' y., Map of the maxinun possible earth-Drumya, A. 7.,

quakes of the Vrancea seismic region, I:vestia, Earth Physics , no.10, 77-78, 1972.

Duda, S. J., Secular seismic energy release in the Circum-Pacifi: telt.

Tectonophysics, 2, hC9 h52, 1965 b

'D:hibladze, 3. A., Seismi: activity and the =aximum earthquakes in the Territory of Georgia and its vicinity, in Study of Seismie Danger, "yan", Tashkent, 1971.

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• Esteva, L., Seismicity prediction: a 3ayesian approach, Prec. hth W.C.E.3., 1, Santiago, Chile, 1969 Esteva, L., Seismic risk and seismic design decisiens, in Seismie Oesign

, for Nuclear Power Plants, M.I.T. ?ress, 1970.

Evarnden, J. F. , Study of regional seismicity and related probla=s, Bull. Seism. Soc.Am.,10,393kh6,1970. 0 Gayskiy, 7. N. , and Katok, A. P. , The applica:icn Of the theory f extreme values to the proble=s of recurrence :f large ear-hquakes (in Russian), in Dynamics of the Earth's Crust, AN SSSR, Nauka, Moskov, 1965 Gelfand, I. M., Guberman, S. A., and Keilis-3crok, 7. I., Pattern recognition applied to earthquake epicesters in Calif;rnia,

J. Phys. Earth Plan. In .,., 227-233, 1976.

Gortuneva, . 7., A maximus-earthquake sap f:r he Ner.hern ien 5han, I:vestia, Earth Physics, nc. 11, 3-13, 1969 Gumbel, 3. J., Statistics Of Ixtre=es, Oclumbia University Press, 1953. Outenberg, 3. , and Richter, C. F. , Seissi:i y f -$a "* -" =-d Related

?hencmena, ?rinceton 7aiversi:7 Press, 195a.

Hailey, J. ?., and Devine, J. F., Seis ctec:eni: ra; : he Ias ern

                                     *J. S. , J. 3. Oecleg' -+'

• vey, Misc. Fieli 5 uiy My-620, 13 .

                               *E*"'iten, 3. , Final safety analysis re;cr , ;iab_: any:n ::u:; ear ;;ser
                                     ?lant, A;;endix. 2. 50,             1 4 en- ;;, p. 2. 3:6 -6 , 19- .

l t

   .   . e
     .                                     (                                 (                  6h
               *3ofmann, 3. 3. , Sta e of the art f:r assessing earthquake ha:ards in the United States, Sept. 20. 3, U. 5. A- ;/ Ing. Watervsy I:cp. Stati:n ,

71cksburg, Miss., Misc. Paper 5-73-1, 19?h. Housner, 3. W., Design spectrum, in Eartheuake Engineering, ed. 3. L. Wiegel, Frentice-Hall, Inc., 1970.

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Tashkent, 1971. 4 Kanancri, H. , and Anderson, D. L. , Theoretical basis for reme e=piri:al relations in seismology, 3u11. Seiss. Sec. Am., 6],, 1073-1095, 1975 Kanasori, H. , and Cipar, J. J. , Fecal process of the great Chilean Zarthquake , May 22, 1960, Phys. Earth Plan. Int., p., 128-136, 19Th. Kanemori, H., and Jennings, P. C., Deter =ination of-local magnitude XL frca strong-motion accelerogrens, Eull. Seism. Sec. Am., 68, h71 h85, 1978. Karnick, 7. , and Hubnereva, Z. , The probability of cccurrence Of largest earthquakes in the European area, Pre and A;ol. 3eophys. , 3, 61-73, 1968.

 ,            Knoperf, L. , and Kagan, Y. , Analysis of the theory of extremes as applied to earthquake problems. , J. Geophys. Res. , g, 56h7-5657,1977 Kogan, L. A. , and Shakirova, T. D. , Assessment of Keax by means of Gumbel's first =ax1=us distribution, in h oblems in the Assessment of the Seismic Danger, "'iauka", Mosecv,197h,

• Lambert, D. G., Tolstoy, A. I., and Becker, 3. S., 7ela Ne:verk Evaluation and Autematic h ocessing Research, Technical Repor No. 7, Texas Instruments !nc., 9 Decenter 197k.

Lee, W. N. K. , and 3rillinger, D. R. , A preliminary ana*ysis of the ~hinese earthquake history, paper presented at the U.S. Geolegical Survey Conference on Seismic 3aps, 3osten, May 1973. Lemnit:, 0., Statistical prediction Of earthqu.tkes, Rev. 3eophys.,i,37~- 394, 1966. McGarr, A. , Upper limit to earthquake si:e , 'lat're , 262, 373-3~9, 19~6. McGuire, 3. K. , Me-hedclogy for incorporating persmeter uncertainties into seismi hazard analysis for 1:v risk design intensities , ~ presented a ; Int. Symp. On Iarthq. 3: rue:. Irg., 3:. ;cuis, Augus-  ; 2, ,o' . Mer:, 3. A. , - and Connell, C. A. , Seissi: risk s.na'ysis based :n a quai- a:i: i

                    =agni ;ude-frequency law, 3 :'.1. Sei =. Icc . Am., H , 1999-20C6, 19~3 1

( ( - e5 Milne, '4. G. , and Davenpert, A. G. , Iarthquake probability, Pubs. :ca. Obs. Ottava, Seism. Series ,1966 L ,19pp. ,1968. Neunhofer, H. , Non-linear energy frequency curves in statisti:s :f earthquakes, Pageoph, 2,76-63,1969 New= ark, N. M. , and Rosenblueth, E. , Funder:entals of Earthcus2e Ir.gineering, Prentice-Hall Inc., 1971. - Nordquist, J. M., Theory of largest values applied to earthquake

                        =agnitudes, h ans. Am. Geop'.fs. nien, 26, 29-31, 19k5 North, R. G.,      Station Magnitude 31as, Its Determination, causes and Effects, Lincoln Laboratory, X.I.T., Technical Note 1977-24, 1977 Otsuka, M. , Cut-off of seissie energy, 2. Phys. Zarth, g, 119-123, 1973 Papa:achos, 3. C. , Dependence of the seismic parameter b on the =agnitude

] range, Pageoph, 112, 1059-1C65, 197h.

                ?'ei-shan, C.,        and Pang-Lui,         L., An application Of statistical theory Of extreme values to moderate and icng-interval earthquake predicti:n, Acta Geochys. Sinica, '6,, 6-2k,1973 (Plenus Publishing Corp.

translation, 1975).

*Perkins, D. , ~'he search for sax!: rum magnitude, NCAA Iarthe . nf. 3ul'.,

18-23, July 1972.

                *?utrushevskiy, 3. A.,            On the relationship between the earthquake of maximus intensity and the geci:gical state, 3u11. Council Seism.,

no. 3, 1960. Richter, C. F., Elementary Seis= ology,~4. H. Freeman and Ocmpany, 1953. R111:ake, T., Statistics of ultimate strain of the earth's : rust and probabilityofearthquakeoccurrence,Tectenochysics,jf,,1-21, i 1975. Ringdal, F., Maximun-likelihecd estimatica of seissi: =agnitude, Eull. ann ,-n-se4sm. sec. ..m., _co_, ..a9 eve, -y. . Ri:nichenko, T. 7., Possibilities ^**'-"'*-ing naxi=us ear;hquakes, Sans. (Sudy) Inst. Phys. Ear-h, Acad. Sci. SSR, g , 192, 1962. Ri:nichenko, Y. 7. , Relati:nship between the energy Of the str:nges-earthquakes and seissi: activity, Ocklady Akad. Nauk 2333, li', 1352-13?i, 196ha. -

               'Ri:ni:henko, I. 7.,          Determination :f the energy flux :f earthquake f::i

n the basis of seissi: activity, Oeklair Akad. Maux :se.. _; ,

                      . <,  .-ee,    ,:c'Lb.

i

           .      a 6o-i              'Ri:nichenko, T. 7., Seismi: activity and the energy of the larges l;                        earthq:skes, in hcblems of the Gec;hysi:s of Soviet Central Asia j                     Kazakhstan, Science (Nauka) Press, Mcse:v, 1967.

i

    ;               *Ri:nichenko, T. 7., The generalized lav of earthquake occurrence, ji                        Soll. 11 Geofis. Theer. ed. A;olie. , _2_, no. h8,1970.
                    "Ri:nichenko, Y. 7., The strongest possible earthquakes, Iarth and 4 ,                       Universe (2cmlya,i 7eslennaya), no. 3, 1971.

4 6

                    *Ri:nichenko, T. 7. , Determination of seismic danger, in hablers in the Ctuantitative Assessment of Seismi: Ca.ger, "Nauka", Mosecv, 1971 Riznichenko, Y. 7.,                and Zagdosarova, A. M., The strongest possible earth-quakes of Japan, Izvestia, Earth Physics, no.11, ih-32,1975
                    *Riznichenko, T. Z., Dru ya, A. V., Stepanenko, N. Y., Crustal seismic activity and the maximum possible earthquakes in the Carpathian-i 3alkan Regica, in Regional Studies en Seismic Regime, Shticitsa,

). Ushinev, 197h. l Ri:nichenko, Y. 7. , and Dzhibladze, 3. A. , Determination of the axist:2

    ;                     possible earthquakes n the basis of the ecmprehansion data of the 1                     Caucasus Region, Izvestia, Earth ?hysics, no. 5, 6h-85,197h.

L Riznichen'<.o, T. V. , and- Zakharova, A. I. , Generali:ed lav of earthquake occurrence, T:vestia, Earth Physics _, no. 3, 29-38, 197'..

Rothe, J. P. , The Seismicity of the Earth 1953-1965, UNISCO Publica

icn, 4

1969 Shakal, A. F., and Toksoz, M. N., Earthquake hazard in New I Eland,  ; Science,- 195, 171-173, 1977 , Shebalin, N. 7. , *he maximun magnitude and =aximum scale intensity Of an earthquake, Izvestia, Iarth ?~. ysics , no. 6, 12-20, 1970. Shebalia, N. 7. , Isti=ation of the size and positi:n of the f:cus Of the Tashkent earthquake frem =acrcseisni: and i:strr. ental ia. a, in "he Tashken Iarthcuake Of 1966,'.*:tek Sranch, Acad. Sci.

                       ,  USSR ?ress, 1971.

Shebalin, N. W.,. Assessment of the maxi =u: seissic ianger in '-a - '-aa-i !, Tamansk, region, in Se'smicity, 3+1ssi: Canga- ' - '- a ' '-a* *-> Seis=cstability of Structures , "Nauh:vaya Ci=&a", Kiev, 19 3 . ll' i i shenk:va, :. , and Karnik, 7. , he ;r:bati' ity :f :e:rrecca ' _ ges: , earthquakes in -he Tur: peat a. es - 7tri !!, ? re and A 01. :ec:hys., 2 0 , *_:, _) .* *. _ , *-2, 7 6 . 2'-a '< va , 2. , and Kartik , 7. , Occparis:: :f se:heis f * ':::g

                          -he larges: ;cssitie earthquakes, ::restia, Ia- h Physi:s, cc. *.1,
                          . . a, ..= , ._s i                                                                                                                                I l

         =.

I s'

• o s.

Sh11en, S., and Toksc:, M. :i., Frequency-=agnitude statistics of earth-quake Occurrence, Iarthquake :Ictes , d, 3-13,19'O. Smith, S. *4. , Octerminati:n Of taxi =um earthquake magnitude, Gecphys. Res. letters, 3, 351-352, '.976. Stevart, 1. C. F., On the use Of the saximum likelihecd esti=ater for recurrence curves, Zarthcuake : Totes, M, 17-22, 197h. ~

                  *Osuboi, C., Isostasy     and : axis.:2  earthquake energy, pree. !:ro. Acad.

Jape.n, M , 19h0. Tsubci, C. , Earthqua'<e energy, earthquake volume, aftershock area and strength of the earth's crust, J. Phys. Zarth, i, 63-66, 1956. SUspenskaya, "'. A. , Fr;erience obtained in calculating the sap of maximum possible earthquakes in the Pribai'<al region, in Study of Seismic Danger, "?an", Tashken , 1971. Veneziano, D., Probabilistic and Statistical Models for Seis=ic F.isk Analysis,, M.I.T. Dept. of Civil Ing. , uo blica:ica 375-3h,19T5 Von Seggern, D. , Joint magnitude determination and anal / sis of variance for explosien magnitude estimates, Bull. Seism. Sec. Am., 63, 827-Sh5, 1973 i Yegulalp, 7. M. , and Kuo , J. T. , Statistical predi::ics of the cecurrence of maximum magnitude earthquakes, 3ull. Seism. Sec. h ., _6h., 393 kih, 197h.

                 *2akharova, A. I. , Ccmputer program for calculating L_.ax maps, in Investigation of Seis=ic Conditions, "Stiintsa", Kishinev,197h.
                 *Zonin, T. A. , and :Tovoseleva, M. P. , Prediction f 1:cg-ters seismic activity On the basis f the geoccrphoicgical and gecphysical' parsneters of the Pritai :a1 region, in " roble =s in the Quantitative Assessment of Seismi: 2 anger, ":Tauka", Mosecv, 197h.

i i I i i i 1 _i l

            .                                                                                              1

     .                                                            (                                                                 (                                           sa
                                                                                  -a r.D,.$

M. -s

                     ? regress Ee; ort:                   New Ingland Crust and ";;er Mantle Structure The recent establish =ent of the northeastern seissi-                                                          =--ay has allowed us to :onstruct a preliminary 2cdel :f the crust and upper
                     =antle structure beneath New England.                                           3ecause the array has only been in full operation for approximately 2 years, the dataset is lL=ited, and ve have analyzed the data using a variety Of techniques including:

1. observati:ns of relative J3 residuals

2. a time ters analysis using S =- *vals n

3 three-di=ensional modeling using eleseissic ?-vaves

                                !s .      analysis of array diagrens a

i 5 refractica studies Preliminary results indicate a crustal thickening under central New

 '                   Hampshire coupled with a slight crustal thi:hening vestward tevaris the North American craten. There is also sc=e suggestica of a regien :f J

relatively low velocity in the upper mantle beneath central New Ze;upshire and southern Maine. Methods of Analysis and Results The relative arrival times of telesa*='d-

• vaves were read fr:n enlarged copies :f 16 nm develecorder fiin. In general, the first fev cycles exhihi :cherence across the array : relative arrival reasure=ents ve-a. ake.n #-en 2 -.- -*- . - e .. . ,- a.--a .-. .. ^ % -

a. .a .

                                                                                                                      .r ' n 4
                                                                                                                                    - e 3 . s----- =~.          ~'.=
                    , roc a.d.".*. a. vas --."'-ad                '-- a      "unhe.          ' vaa'< s
                                                                                                       ----         .a. -d- ed. . e ' a..s a. '. .e . .=
                   ..,s-.--.n     .u,.

s

s. ... , .,

                                                       . . - -             . o -,   . .. e,. . , . ..      s-..-,3 7

s

                                                                                                                                      ..o . a. e .       --

f . y._.y , ,-.- ,,- ,.

                                                 .a
                                                 .-- e=.       ..   -.s .e , egg -,.a. .- ...
                                                                                                               .              r.
                                                                                                                                    .    . a .     ,
                                                                                                                                                     -.-....s,,
                                     ,sa -

e . ,.. , , - , - . c . .--.. --, 2 , . , .,

                                                                               ,-a. g ;22-s  -.  ,..,. .. ,- , .. , s ,. , e ~ . , 2. . y
                                                                                                                                                            .s v..+, : J.
                           . , n,    ,-2 a s .,a v - -
                                              -#   ----g        ..a.
                                                                  ..-@  a. .,.., . .. ,. 4 . d . .a ....
                                                                                                      . ,.. ....,.--     a...3.

   -                                                                                                                     f                                                -

c9 Absolute travel tine res'iuals vere cal:ulated vi h respe : c J3 tables and are defined to be 9<<J3

                                                              = m.< obs _ v J3 where R,j"3 is the absolute residual with respect to J3 tables for station i, event j; Tg bs is the etserved travel :Lae using cr* gin times from PDE bulletins; T,,                                 3 is the theoreti:a1 travel time through a
                                                                          .o J3 earth.

The residuals were reduced by calculating relative residuals with respect to a mean residual ecmputed for each event; N J3 1 JB 9 =R - R

                                                 ' ij          ij             N                ij i=1 vhere N is the number of stations reporting ? arrivals for a given event. The utilization of relative residuals reduces source effects and i

mislocation errors, removes errors in origin tine, and reduces effects of travel path through an inhemogeneous mantle. In this way, positive residuals represent late arrivals where the waves have been sicved 'n the crust or upper mantle teneath the array. There are several consistent trends in the teleseissi: ? vave residuals which suggest the presence of large scale regional structures in the crust and upper santle teneath the array. The data shev to:h . azimuthal variations in resiiual values, and varia;i::s in average i 1 I station residuals across -he array. 1 _ u_e .as. . s ye.- .. _ _s .y,. . . ,.a. . , . 2 a. ,. p .. _. . o .+ .,5 c 2. 2 . o _ _ e_ _ ... ,. .. -

                                                                                                                                                 . .. .. .. _a : _ . .
                   .J a .      .
                            .a. _C 4.. s.* 4 .g s. ,.c hn_Js .,i..

_ . a. .*-4.4 ,... ,,*_ . /. _* *f .v'. O. ,. ha.sy . %_.

                                                                                                                                              . _ms.

_w e..,.._

                   ,.a_.

_3 .,gn__.a.g

                                                     .u. e .,..se..
                                                               .. _..            .._..s
                                                                                   > , .,g_             e,-_--._.>-,,_a_,,*-
                                                                                                                                                ._,      _.y
                  ........ . a . ./ <- _ e
                                                         .. ___._.  ..    ,      ,1,_,.-_.-          _..-,-
                                                                                                   . . . _ _      .7,. ~. =_ ,____, , u a _ ,   ,.a       ..

a..._.,.._

                  .g a _. ., .
                                    . u_ s_   ..,,.>,g..a.....
                                              .._. . . . _                . . _s _.  ...,....~c'..".~.-..**.*_>.=.=2~,a.__=__-f".'..'..
                                                                                             ...             s               _     .
                                                                                                                                         ~       ' '*

he Me20*ci: '4 hit e MCu.". ai.". ;1": .".i 3 erie 3. is thcugh; tha; -he , l

s* . ( 70 scur:e of -hese in rusive ::=plexes is deep-seated ' Chap =an,19~:',, and it is possible that this anc:aly is related to the f:r:a-icn Of these

               .....c,s.

S time tern analysis using ? arrivals indicates tha: the varia icns in average station residuals may be due to varisticcs in crustal thickness and/or velecity. This is in contrast to the Observed a:i=uthal dis:ritu-tien of residuals 'or each station which is pro'cably due to deeper effects. It was assumed that the distribution o' average residuals is caused by crustal thickness variations, and the data vere inverted to find a crustal thickness cap 'of New England. The resulting map suggests a crustal thickening beneath central New Hampshire, vith more nor=al thicknesses in Massachusetts and Maine. 2.e con: curs of the ap paral el the northeasterly trend of the Appalachians. t The variations in crustal thickness observed across the network are also supported by anal / sis of array diagrams. "nese are sterecgraphi:  ; crojections

               .                   of sicvness and a:isuth anenalies Observed frec a plane vave                                                      1 fit to the wavefrcct traversing the netverk.                                    These studies indi:ste a Mcho which dips 2* or less to the northwest.                                    This is not surprising
                                                                                            'd because it is expected that the crust vould                                         =- '- a the continental
               =argin tovards the Ncrth Anerican cra:cn.

In additice to the above centi:ned studies, an average :rustal

                 .                                                                                                                                   4 l

velocity sedel has been :0mpiled for eastern Massachusetts and set;hern

                                                                . "-- . s . .-^. m . ' ~ ~-'- -"

Tev as sk'-.

               .                 . be/ .- ..- *.
                                                        -s . a.
                                                              - =                              , a -.- . .v '. i s- s . a-     "..'..'e 1

I

               .,_t.,-. .ar3
                        .s       .
                               ,.,.a_ys.a.s
                                            .            ..ne-
                                                   ~_ u_e._.

• t.

a .....a.... s 'e......ew a_3 .a A s.

                                                                                                                  ... - a.
                                                                                                                         -. s .- %. .s . . , 4 .a s..

1 1

               ..C3.4      3 ....  ,.*.     . . , - 9
                                            ---{*-         -*  ..g    43          s.**.

3. ---- yg. l

                 .      .      . 6-  --                      --           -

• i i

    . w ,-
              .1 . .

t , g ( \ 71 iayer (km)  ? velceity lkn/se:: 0 - 7.3 5.68 7.3-26.1 6.26 P. 26.1-38.0 7.33 - Moho 3.13 Puture Studies Studies for the next year vill be abned at impreving the preliminary crust and upper nantle model for New Ingland. This vill be achieved by using additional teleseismic ? and Pk? data. The database is currently being expanded to include readings frem shcr: pericd stations in Connecticut and eastern New ?crk. The structural models derived from the residual studies vill be

  ,                      ccmpared to these from long period surface wave dispersion studies.

4 Phase velocities are presently being cceputed as a function cf seinuth i frcm the Quebec-Maine bcrder event of June 15, 1973, and sispie :rustal models vill be developed. Phase velocities vill aisc be reasured using the tvc station teennique. More elaborate medels vill be generated by perfcrsing a st=ul:anecus inversica of phase veiccity and attenuation folleving the techniques cf Lee and Sciccca (1975). A study cf the Lg phase, a shcr; peri:d higher nede icve vave, vill 1 be initiated ;o compare the effec of regicnal geci:si: strue ure :n ig I prcpaga'i:n. The data vill be ecliected using three :: penent, iigital receriing even: 1e:ecters devel:;ed a: :CT.

         -                                                     u                           -        -

 . . 6
   -                              (.                              I                   72 References Aki, K., A. Christoffersson, and I. 3. Husebye, Cetermination of the three-dimensional seismic structure of the lithesphere, i. Geophys.

Res, 8_2, 2 277-296, 1977

           ?apman, O. A. , Structural evolution of the White kuntain magna series, Geol. Soc. M , Mem., ih6, 291-2C0, 1976.

lee, W. 3. and S. C. Sole =en, Inversion sche =es for surface vave attenus-tion and Q in the crust and the mantle, CeophIs. [. R. Astron. Soc. , M, k7-71,1975 4

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p .L. t' ii t Bullete of the snsmoior.calsociety of Amenca.Vol49. Niipp. 757 ~1 June 19*9 1 A COMPARISON OF THE SEISMICITY OF THREE REGIONS OF THE g \\ (/; EASTERN U.S.- <..

                                                                                                                                ,             20CK27D T-BY MtcHAEL A. CHINNERY                                           -7 tg=;.-3           -

I ABSTRACT, ,, UM i 2 Gc0*~ Frequency-intensity data from the Southeastern U.S., Central Mississippi $ 3ff'h % M~ Valley, and Southern New England are compared. They are all quite parallel to '-h # $O one another and consistent with a slope of about 0.57. There is ao evidence for .,

                                                                                                                                              ""U the existence of upper bounds to maximum epicentral intensity in these data                                          "

XeN'. sets. Linear extrapolation of the frequency-intensity data to intensitios of X leads _- to expected probabilities for the occurrence of large earthquakes. The largest f events which have occurred in these three regions are consistent with these l probabilities. i i INTRODUCTION

            ;                Recently there have been rather detailed analyses of the seismicity of three
           ;

sections of the Central and Eastern U.S. Bollinger i1973) has described an extensive j sat of data for the Southeastern U.S., which includes the seismically active zones cf i Maryland, Virginia, West Virginia, North and South Carolina, Georgia, Alabama, and Tennessee, for the period 1754 to 1970. Nuttli (1974) has listed the known events in the central Mississippi Valley seismic region for the period 1833 to 1972. And [ Chinnery and Rodgers (1973) have analyzed the data of Smith (1962,1966) for the

           !              Southern New England region for the period 1534 to 1959.The purpose of this paper i              is to compare these three studies, and to bring cut the similarities between them.
           !                 The discussion of seismic risk inevitably involves plotting frequency-intensity (i.e.,

I maximum epicentral intensity) diagrams. In what follows we use this type of plot, i since magnitude data are not available for all three regions. This raises a difficult

           ;              point, ainee within each of these regions, the . seismic activity is not uniform. The
           ;         -

selection of the boundaries of the area to be studied is much akin to the problem of

           ,              the definition of a tectonic province (which is required, for example, by the Nuclear i              Regulatory Comnussion Rules and Regulations, Part 100, Appendix A).

i For the moment, we shall make the following assumptions: First, we assume that l all subregions within a given region have a linear frequency-intensity relation of the i form i

           ;                                                         log N,= a,- bl I

where N, is the cumulative number of events in the :th subregion with intensities greater than or equal to I, and a, is a parameter desc:ibing the level of seismic activity of the ich subregion. We assume that the slope b is common to all subregions. Second, we assume that the maximum possible intensity in each subregion, if one exists which is lower than the nominal maximum of XII, is larger than the largest event recorded within that subregion during the period of the earthquake record. These assumptions sound very drastic, yet they are really implicit whenever we j plot a frequency. magnitude or frequency-intensity curve. Furthermore, at least in 1 -

• The ne'ws and conclusierts contained in thi.s docurr.ent are those the contractor and should not be interpreted a.s necema:.ly represenar.4 the o5cial pclicies, etther espressec or aplied. of the t,'ruted
• States Covertunent.

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                                                                                                                                    }

t 758 MICHAEI. A. CHINNERY pnneiple, they are testable. It is easy to plot frequency. intensity diagrams for portions of a region and examine both the linearity of the results and the constancy of the slope b. In practice, of course, scatter in the data often makes such a test inconclusive. However, a substantial breakdown of any of the above assumptions should be apparent in the data for the region as a whole, either by the appearance of nonlinearity in the frequency. intensity statistics, or by variations in estimates of b using different data sets. as we examine and compare the seismicity of the three areas under consideration, we shall look for information related to these assump-tions. -

                                                                                                                                    ;

Perhaps the most important question which we shall address is as follows: Each ' of these areas has had one moderately large earthquake in its recorded history (the  ! 1755 Cape Anne, 1811-1812 New Madrid, and IS$6 Charleston events). Are these large events consistent with the record of smaller earthquakes that have occurred rnore recently? Clearly, this question has a direct bearing on the very fundamental problem of how to extrapolate from a short record of seismicity to the occurrence of low probability events, which is particularly important in the assessment of the potential seismic hazard to critical structures such as nuclear power plants. We shall disregard questions of the lack of stationarity of the earthquake process in these three areas, in spite of their potential importance (Shakal and Toksoz, 1977). It is very difficult to document this nonstationarity w thin time periods of 100 to 150 years, because of the small number of events concerned. Tne DAra Southeastern U.S. Bollinger (1973) describes the seismicity of four seismic zones in the Southeastern U.S. for the period 1754 to 1970 (see Figure 1). In this study we ' shall restrict ourselves to the two southernmost zones, the Southern Appalachian seismic zone and the South Carolina. Georgia seismic zone. The combined area of these two zones is given by Bollinger to be 307,000 km2 . Since we would like to . exclude the 1886 Charleston earthquake from consideration, we have analyzed  ! events during the period 1900 to 1969. Even this period is probably too long for the adequate recording ofintensity III events, so these have been accumulated for the i period 1930 to 1969 only. Total events listed by Bollinger (1973) are shown in Table ' 1. These data are easily converted into a cumulative frequency intensity plot, and ' this is shown in Figure 2. The usual interpretation of such a diagram is to fit the data points with a straight line, recogmzmg that the data at the lower intensities is likely to be incomplete. Such a fit is shown as the solid line in Figure 2. This line corresponds to _the equation log N, = 2.31 - 0.461. (1) The slope of this line is low compared to other similar regions, as we shall see below. The occurrence of three intensity VIII events danng this 70 year period seems high, and in fact one of them has been shown to be an explosion (G. A. Bollinger, personal communication . Certainly a line such as the dashed line in Figure 2, which has the equation I i log N, = 2.33 - 0.55I 42 cannot be ruled out. The slope of 0.55 in this equation is very close to the s!cpe 0.56

1 i i

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760 .St!CHAEL A. CHINNERY

                                      = 0.0S found by Bollinger t1973) for the whole Southeastern U.S. For the moment, we will retain both equations (1) and (2) as possible interpretations of the data.

Central .Vississippi Valley. Nuttli (1974) has given a list o(events in the central Mississippi Valley for the period 1833 to 1972. The epicenters of these events are shown in Figure 3. The total area of this zone is given by Nuttli to be 250,000 km 2.

             '                        Since he lists few events before IMO, we have restricted ourselves to the period 1840 to 1969. Table 2 lists the events duririg this period as a function of intensity. As TABLEI Evests tx Sot:Turax APPALACHIAN AND Sot;TM CArot.tsA-Geor.ctA Stzsuic Zosts a                                                     iam                   renoa             .w or E III               1930-1969                 10 IV                1900-1969                49 V                 1900-1969                46 p

VI 1900-1969 17 8 VII 1900-1965 5 VIII 1900-1969 3 1 j oS

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                                                                                              !NTENSITY
                                   . Fic. 2. Cumulatiye frequene.v.tnte:uity plot for :he data in Table 1. Two possible stra:ght line

nterpretat: ora are snown. ,

e l 4 i k before, smaller events are only counted for the more recent portion of this time period. Since many events are listed with intensities intermediate between two values tsuch as III to IV), where this occurs one. half event has been accumulated

                                                                                                                                                             ;   !

into each value. This accounts for the fractional events listed in Table 2. Figure 4 shows a cumulative frequency. intensity plot for the data in Table 2. A .l reasonable linearity is obtained. corresponding to the equation log .V, = 2.77 - 0.55I. (3) l

( ( strS111 CITY COh!PARISON-T!!REE RECloNS OF THE EASTERN t.'.5. 761 Southern .Vew England. The seismicity of Southern New England has been discussed by Chinnery and Rodgers (1973), using data of Smith t1962,1966) for the period 1534 to 1959. The region defined as Southern New England is shown by the solid line in Figure 5 which also shows the epicenters in Smith's listing. Following Chinnery and Rodgers (1973). we note that many of the listed epicenters are 3o. . 3 s as-

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          ]                             mth permission, from Nuttli (1974L 4
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TABLE:

            ;                                                                         Evrsts tx Crxtaat. Niisszss PPI VALLEY j                                                                      towna.y                         F.,=4                  mi E..au II                     1930-1969                            22.5 III                    1900 1069                            94.5

[V 1870.I969 14J.5 V 1870-1969 63.0 VI IM O.1969 31.5

            ..                                                                    VII                     IMO-1969                             10.5 VIII                    1840-1963                              1.0
            ,                                                                     IX                      1849 1969                              1.0 clustered in a region extending from Bosto through central New Hampshire. We have outlined this area in Figure 5. and refer to i: as the Bos:en.New Hampshire                                                                              -

seismic zone. The areas of the two zones in Figure 5 are approximately 100.000 km 2

                                       . Southern New England) and 27.000 km'(Boston.New Hampshire zone). Since we wish to exclude the 1755 Cape Anne earthquake from the data set. events have been i

                    ......(.....                                .       . . . _ . . . .   ..(            _     ..__ .J 762                                  MICHAEL A. CHINNERY                                         l t.

accumulated in both the Southern New England region and the Boston.New Hampshire zonc for the period 1800 to 1959. These are listed in Tables 3 and 4, respectively. As before, small events are ordy accumulated for she most recent portion of the record. The cumulative frequency-intensity plot for Southern New England is shown in Figure 6. The straight line through the data has the form Log N, = 2.36 - 0.59I. (4) In spite of the rather low numbers of events, this line is a reasonable fit to the data. In the case of the Boston.New Harnpshire zone, however, the number of events l 1.o , l MISSISSIPPI VALLEY

        ;                                                                   1840 -1969 i                                                    .

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                  . becomes low enough that it becomes difficult to formulate a linear 5t with any certainty. A straight line through the upper four data points has a shallow slope (about 0.50), which is significantly different from the other areas studied, and which leads to high estimates of risk for large events. We prefer to interpret these data with a line such as the one shown, which has the equation log N, = 115 - 0.59I.                           15)

With this interpretation, the number of intensity VII earthquakes is anomalously high. due either to poor data or a statistical :1uctuation. At least equation '5 should lead to reasonably conse.vative estimates for risk at high intensity levels.

                                           . .                                                                       ~y

     .                                                                                                                            /~

s ( ( sErsMic:TY COMPARISON-THREE REGIONS OF THE EASTERN U.S. 763

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scale N wit.E S Fic. 5. Epicenters i.n New England. 'ro:n Srt; h (19%. The solid line :t.:hnes :he reron ca2ed Southe- . New England in thu study. The broken line mdics:es :he Bos:on New Ha:npsh:re zone 'see Chinnery and Roogers.19~3). COMPARISON OF FREacENcy INTENSITY DATA The frequency-intensity data shown in Figures 2,4. 6. and 7 a.re show together in Figure S. In this case we have omitted the individual interpretation using :itted straight !ines, and show the data alone. This emphasizes the very simdar character of the four recurrence curves. There is some scatter. but each of the curves is i

                                                                                                                                                .B

( k 764 x,rcHAEL A. CHINNERY j consistent with a slope somewhere in the range 0.55 to 0.60, and we show a slope of 0.57 which seems to be a reasonable average. In view of the rat %r inferior quality of rnuch historical intensity data, it is surprising how consistent the slopes of cumulative frequency. intensity data appear TABLE 3 , Evtsis IN SocTMtu.s Nzw Exct.aso

m.w, e. .d . .s.. w v. .-w 11 19 5 1959 32.5 III 1928-1959 09.5 i IV 1900-1953 43.0 V 1860-1953 24 0 VI 1900-1959 4.0 VII 1600-1959 J.0 TABLE 4 Evexis ts Bostox-Nzw Haxesurrt Zost

         ;                                       latewity         Perme               h .4 F.ent.                       .

t II 1928-1959 16.0

                                              !!!               1928-t953                  IJ.5 IV           '    1900-1959                  1 *.5 V                 1860-1959                  12.0 VI                1800-1959                   3.5 VII               1800 '959                   J.0 to l

l SCUTH12N NC# EZLA.NQ I 18co - 1959 - l 6 i t **W e 1

                                                     #~

Log g e 2.34 -o.591 } h -o s,- t' j 2 . I  ! s I

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t I

                                                 -2 3 *-

2 2 I 4 NTENS.TY Fro. 6. Curulative frequency..ntusity plot for :he 1.tta in Table 3. J l to be. Both Connell and Men (1975) and Veneziano (19756 have surveyed a number of estimates of this slope. and many of these are consistent with the present data.

                                                                                                                                                         ~

The mean of the 11 estimates quoted by Veneziano is 0.53, but hia list contains some low values which are probably n:: realistic. Of particular interest are the

                                                                                                                                                ..g i
                                                                                                                                                  ~l I

_ . . . . . . . . . . . ( ( SE! Sat! CITY CO.4IPAR150N-THREE REGIONS OF THE EASTERN t .s. 765 values 0.59 for the whole J.S. (Connell and Merz,1975) and 0.54 for California ( Algermissen,1969). A recent estimate for the area around the Ramapo fault in New York and New Jersey is 0.55 0.02 ( Aggarwal and Sykes,1978). It is interesting to compare a slope of 0.57 with the value that one would predict from known magnitude intensity relationships. A selection of these relationships .

       ,                   have been given by Veneziano (1975), in the form M = ai + ad.                                 (6)

Values of the constant a2 have been estimated as 0.67 (Gutenberg and Richter, 1956), 0.69 (Algermissen.1969), and 0.60 tChinnery and Rodgers,1973; Howell, os SCSTON-NEW HAMPSHIRE 1800 -1959 o - e l

• Log Nc = 2. 5 - 0.59 I

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{ INTENSITY Fic. 7. Curaulative frequency.intenat:y plot far the data in Table 4. 1973). The latter estimates of 0.60 were obtained from data in the Eastern I'.S.. and may be the best estimates for our present purposes.

             .J                There is an abdunance of frequency-magnitude data, which is usually represented by the form log .V, = a - bM                                (7) where the slope b often lies between 0.9 and 1.0 (see, for example, Chinnerv and North,1975>. Combining this expression with equation (6), with a: = OA0. would lead to a sicpe of the frequency intensity relation between 0.54 and 0.60. Clearly the

( ( 1 766 MICHAEL A. CHINNERY

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3 1 3 ~i3 1 NTENSITY Fic. 8. Comparuon of the frequency intensity data ' rom Figures 2. 4. and 7 t o utssiss.Fot .AJ l

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9 s

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sEISMICtTY COMPARISON-THREE REGIONS OF THE EASTERN L*.5. I67 0.57 value shown in Figure 8 is eminently reasonable and consistent with other information. The similarity between the four sets of data shown in Figure 8 can be further emphasized by normalizing for the areas of the seismic regions. After this normali- - zation. Figure 9, the recurrence curves are found to lie almost on top of one another (we have chosen to normalize to 1,000 km2 , but this choice is completely arbitrary). - The apparent similarity in seismic activity per unit area is entirely fortuitous, and is simply due to the particular regions chosen for each study. The true levels of activity in the three regions differ markedly (see, for example, the return periods I calculated in Table 5). However, one is tempted to note that the activity per unit area in the Boston-New Hampshire zone is slightly larger than that in the South-eastern U.S. Is there really any good reason why an event the size of the Charleston earthquake could not occur in the Boston-New Hampshire zone?

         .f  ;                 It is interesting to search these data sets for evidence that there may be an upper bound intensity in some of these areas. Cornell and Merz (1975), for example, have proposed a frequency-intensity curve for a site in the Boston area that curves downward and becomes vertical (parallel to the ordinate axis) close to intensity VIL Since this calculation is for a single site, it is crucially dependent on our ability to predict the location of large events near Boston. Certainly, if large events could occur anywhere within the Boston-New Hampshire zone, the present data show no indications of an upper bound. Given our present knowledge concerning the mech-anisms oflarge events in regions like the Boston-New Hampshire zone, it does not seem reasonable to propose such an upper bound.

RANDOMNESS OF THE CATAt.OGS Before attempting to calculate the risk of large events in the three areas under consideration, we should briefly address the nature of the statistical model to be used. It is usual to assume that catalogs such as these are random, i.e., described by the simple Poissonian distribution. This problem has received ample treatment in the literature (see, for example, Lomnitz,1966). In some cases the Poisson distribution has been shown to be a good description for large events, Epstein and Lomnitz (1966), and Gardner and Knopoff (1974) have shown that the Southen California catalog, with aftershocks carefully removed, is Poissonian. Other studies have indicated departures from Poisson statistics (e.g., Aki,1956; Knopoff,1964; Shlien and Toksoz,1970). However, these departures are small, and may be disregarded for our present purposes. One graphic method of demonstrating the approximately Poissonian character of a sequence of earthquakes is to plot the interoccurrence times (Lomnitz,1966). In a purely Poisson crocess, the probability P that an inte: val of time T will contain at k least one event is given by P( T) = 1 - e -". (8) Here T3 is the mean return peried for events in the sample.

                             'If the time between events in the sample is the variable t, then the frequency distribution of tis given by                                                                 -

1 F( t) = T, e " ^ i9t F e

                                                                                                                    !i 768                                     MIcHAEt, A. CHINNERY l

It is easy to show that the observed interoccurrence times are quite closely , represented by equation (9). Figure 10 shows a plot of these interoccurrence times  ! for the central Mississippi Valley catalog for events with intensity greater than or equal to V during the period 1900 co 1972. Clearly, the exponential distribution is a j; good description of the data. The anomalously large number of events at small  ? interoccurrence times can be attributed primarily to the presence of aftershocks in  ; the catalog. A similar plot for Southern New England data is shown in Figure 11. ) Data from the Southeastern U.S. were not available in a form that would permit a  ? similar plot to be made, but this is probably not necessary. On the basis of Figures 9 10 and 11, we feel justified in using the Poisson model, and in particular equation (8), to calculate probabilities. L In passing, Figures 10 and 11 make another point. It is easy to use the quantity f mean return period of earthquakes in a sequence as ifit has a deterministic meaning. j These figures are a reminder that the mean return period is entirel) a statistical j g _

                                                                                                                       \
                                       ~

t , Missi$$iRR' VAdY ' 19Co -1972 D 2sr 84 EVENTS AIT* t 22  ; RETURN RERIOo r, e C $7 YEAR $ { g f T '

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                                       !        i l                           M N I 3          .        2          3       4        5    6                          H E

INTERCCetJRRENCE '.ME ( yemi { Ac.10. Interoccurrence :2::es using Nuttli's (1974) data for :he central .\fississippi Valley. The exponential curse would be ez;e::ed for a Poisson distribution. b' 1 quantity, and that its only real meaning is as one of the parameters describing the f probability distribution that corresponds to the catalog under consideration.  ? THE PaosAsttirY or LAacE EvtNTs k i With the above model it is now possible to address the question posed in the 5

         . introduction. In each of the three areas under consideraticn a large earthquake                          p occurred shortly before the periods of data that we have analyzed. Are 'these large                        V l

earthquakes consistent with the later record of smaller events? ' g Our procedure is simple. We take the linear relations fitted to the frequency- , intensity data, extrapolate them to larger intensities sr4 make estimates of the I mean return periods of these larger intensities. We then use equation (S) to estimate @ -) the probability that at least one of these larger events will occur in any 200 year U l period, and specifically relate this to the 200 year period ending at the present time M ta 300-year period was chosen for New England, since the largest event occurred in D the 1700'sL k 8 s$ r b

SEtsslictTY COS!PAttISON-THREE REGIONS OF Tite EASTERN l'.5. 769 The results are shown in tabular form in Table 5. We do not pretend that these

         ;              numbers are very accurate. In fact, because of the subjectivity that has to be used in obtaining the linear relations [ equations (1) to (5)], thue is no way to make a realistic assessment of errors. We therefore view the numbers in Table 5 as being a qualitative indication of risk, rather than quantitati,e. The results for the individual areas are discussed below.

w { to SOUTHERN NEW ENGLAND 1860 -1959 32 EVENTS WITH I 2 "T i RETURN PE5100 7o 2 3.13 YEARS 8 r D z i 6b o la l

                                                      ~

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• I

[ 't i t t t i i , o 5 to 'S 20 g INTERCCOURRENCE TIME ( years ) l

       !t                     Fic.11. Interoccurrence times for Southern New England ' rom the data of Smith t1962.1966).
        ,t
        'I TABLE 5 PaosAatLITY Or LARGE Evests :s Fot a Rtczoss or retr. EASTERN (*.S.
           $,                                                                        p rmhehtis:w ..f de Lu. One bens i rqueen t;w                                     rim. s,.on           .. em.a r . .i         ;
                                                             .m snu                                    rnmei\an avf!I      stX        RX                    EVtil        atX      3x     i l

Southeas:ern L*.S.,1900- 1 23 68 195 200 99 95 44 1 1969 2 33  !!7 417 000 99 32 3d Misatssippi Vs'. ley. ING- 3 43 151 537 000 99 ?J 31 1969 Southern New England. 4 229 391 3467 J00 73 29 3 i 1800-1959 Boston-New Ha=pshire. 5 J71 1445 5623 000 55 :9 5 1900.!953 The earthquake catalog for the Southeastern l'.S. described by Bollinger (1973) is approximately 200 years long. Table 5 shows that, on the basis of the most recent 70 years of this catalog (which may logically be expected to be the most complete at , lower intensities), there is a substantial probability of the order of 50 per cent that  ! at least one earthquake ofintensity X or greater will occur in a 200. year period. We i conclude. therefore, that the Charleston earthquake of 1*S6 < intensity X. Bollinger. 1977) is entirely consistent with the 1900 to 1969 data. i

                                      .(
                                                                                       .                   ._ j 770 MICHAEL A. CHINNERY Without any question the largest earthquakes during the past 200 years in the central .fississippi Valley were the 1811 to 1512 New Stadnd events. Nuttli (1973)                  '

lists the maximum observed intensity during this sequence as X to XI, at New 5fadrid,511ssouri: Gupta and Nutcli (1976) have recently revised this upward to XI to XII. Some question perhaps remains as to the validity of this value as a true epicentral intensity, since some amplification by the alluvium in the area might be expected. Table 5 lists the probability of an event of intensity X or greater during a 200-year period as being about one. third. The New Stadrid events were therefore reasonably consistent with the data for IMO to 1969. Ifit could be shown that these , j were the largest events in the last 300 years in this area (which is not unlikely), or i that the true epicentral intensity was somewhat less than X, it would be easy to increase the calculated probability to 50 per cent or more. l

                                                                                                                   ;

The record of earthquakes for Southern New England is about 300 years long (Smith,1962,1966). During the period 1800 to 1959, Smith lists 3 events with } intensity VII, and there are none any larger. Table 5 shows that there is a respectably high probability (about 75 per cent) that an earthquake of intensity VIII will occur q somewhere in Southern New England in a 300-year period. The probability of such an event in the Boston New Hampshire zone is about 50 per cent. The epicentral intensity of the 1755 Cape Anne earthquake is not well defined. Smith (1962) lists - [ this event as intensity IX, which is probably somewhat high. The Earthquake j History of the United States (NOAA publication 41 1, 1973) lists this event as r l intensity Vill. Other unpublished studies have deduced intensities close to VII. I Whichever is correct, it cannot be said that this event is inconsistent with the subsequent seismic record. An equally important result for the Southern New England region is that the j probability ofintensity IX and X events occurring within a 300-year period is quite s low.The absence of these events in the historical record is therefore again consistent

                                                                                                                 ;

with the 1800 to 1959 data. Notice, too, that the return period for intensity VIII is 229 years, which is consistent with the absence of such an event during the period l 4 1800 to 1959. ' t f CONCLt'ston G e, We can make several conclusions from this study j

1. The four frequency-intensity plots that we have considered show a remarkable s

uniformity. All show a pronounced linearity, and have slopes which are cor,sistent with a value of about 0.57. This, m turn, corresponds to a magnitude b value in the range 0.9 to 1.0. This uniformity, and the fact that 0.57 is very close to slopes j a observed in other areas of both Eastern and Western U.S., suggests that frequency-intensity data can usefu!Iy be applied in seismic dsk analysis. In areas where data 68 are poor or sparse, it would appear possible to combine data from as little as one y intensity value with the apparently universal slope of about 0.57 to construct a local g y frequency-intensity relationship. Such a procedure may be more reliable than some h of those in current use.

2. The uniformity cf the shape of the frequency-intensity relation over regions ranging from the Boston-New Hampshire :one and the Ramapo fault zone i Aggarwa! [

r a - and Sykes,1978) to the whole of the continental U.S. suggests that the problem of M nonuniformity of seismicity within a region is no impediment to the use of frequency-intensity statistics. The assumptions outlined in the introduction to this paper seem to be useful working hpotheses. y[ I E [ lt u 3

t

   .                                                      (                                                      (

III sEssat! CITY CoatPAR! SON-THREE REGIONS OF THE EASTERN l'.s.

3. The question of the existence of upper bounds to maximum earthquake intensity fless than the scale maximum of XII) remains unanswered. There is no

          '                 reason within the data themselves to suggest that the three large events that we have considered are the largest that could occur in these regions. Similarly. there are no statistical arguments that a very large event could not occur in other areas (such as Southern New England outside of the Boston.New Hampshire zone) that have not recorded such an event. A rational, conservativ'e approach to the estimation of the seismic risk at a site would include the possibility of events with intensity X or more anywhere in the Eastern U.S. This topic will be discussed more fully elsewhere.

4. The validity of linear extrapolation of the frequency-intensity data has been

             ;,              tested by predicting the probability of occurrence of large earthquakes in the historical record, and comparing this probability with the known occurrence oflarge earthquakes in each of the three areas.The Charleston and Cape Anne earthquakes are both consistent with more recent data from small events (calculated probabilities of these events are 50 per cent ore more). The New Madrid sequence is only slightly anomalous. The chance that such an event would occur during the past 200 years is about 30 per cent, but the chance that it would occur in a 300 year record approaches 50 percent. Thus, it appears that linear extrapolation of frequency intensity data to intensities of IX and X is a valid procedure in these areas.

ACKNOWI.EDG51ENT This research was supported by the Nuclear Regulatory Commission. The author appreciates the helpful commenta on this paper received from O. W. Nutt!i and G. A. Bollinger. REFERENCES

 '                            Aggarwal. Y. P. and L R. Sykes (1978). Earthquakes, faults. and nuclear poner plants in Southem New York snd Northern New Jersey, Science 200,425-429.

Aki. K. (1956). Some problems in statistical seismology. Zism 5,205-223.

       ~                       Algermissen. S. T. (1969). Seismic Risk Studies in :he Unard States. Pme. u*orld Cani. Earthquake Eng., 4th. Santia go.

Bollinger. G. A. G973). Seismicity of the Southeastern Cruted Statcs. Bu!L See.sm. Soc. Am 63,17?$- 1808. Bollinger. G. A. (19-~). Reinterpretation of the intensity data for the ISe6 Charleston. South Carolina, earthquake,in Studies Related to the Charleston. .%uth Carolina. Earthquake ai!?66-A P elim. inory Report. U.S. Geol Survey Profess. P:per 1023.17-32. Chinnery. St. A. and R. C. North H975). The frequency of very large earthquakes. Science 190, 1197-119S. Chinnery, St. A. and D. A. Rodgers 0973). Earthquake stattsticsin Southern New England. Earthqucke Notes 44,39-103. Cornell. C. A. and H. A. Siera (1975). Seismic -isk analysts of Boston. J. Struct. Dir. ASCE 201. no. STIO. 0027-2')43.

               'l              Epstem. B. and C. Lomnitz (1966). A model for the occ r ence of !arge earthquskes. Nature 211, 954-956.

Gardner. I. K. and L Knopoff (1974). Is tne secuence of ear hquakes in Southem Califorma. with aftershocks removed. Poissonian? Bull Seu i. Soc. Ar 44,1063 '.067. Gupta 1. N. and O W. Nutdi C9 6L Spatial attenunion ofintensi:ics for centrr1 U.S. earthquakes. Bull Scum. Soc. Am. 66. 740-751.

Gutenberg. B. and C. F. Richter (1956L Earthquake m.tgnatude, intennty and accelernion. Sull. Sebrt.

I Soc. Ant. 46.'05-145. Howell. 3. F. Jr. d9~3L Earthquake hazard in the Eastern Cruted States. Earth MineralSec. 42,41-45. Knopoff. ' i1964L The s stisues cf earthquakes in Southern California. Bull Scum. Soc. Am. 54. "371-l l 1873. ~

• 1.omrutz. C. N. Stat stical prediction of earthquakes. ?ct. Gemhys. 4,377-J93.

Nut:li. O. W. 1973L The Siisatssippi Va!!ey earthqua.ces :(1911 and !!!2 intenstries, ground motion and l magm uoes. Sull. Scum. Soc. Am. 43,027-24d. i l

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772 MICHAEL A. CHINNERY  ; i Nuteb. O W. 41974). .\tagnitude recurrence relation for central MUsta tppi Valley earthquakes. Sull i Ses.sm. Soc. Am. 64, 1169-1207. Shakal. A. F. anc St. N. Tokson (1977). Ear.hquake haurd in New England. Scrence 194. 171-173. Shben. 3. and $1. N. Toksoz e1970L A cluster rig model for earthquase occurrences. Bull. Sosm. Soc. Am 60,1741787. Smith W. E. T. t1962). Earthquakes of Eastera Canada and adjacent areas.15M-1927, Publ Dom. Obs. Ottaa a 26,2 1-301. Snuth. W E. T. (1966). Earthquakes of Ea.itern Canada and adjacent areas. 1923-1959 Pabl Dom. Obs. Ottan a 32,87-121. Venevano, D. (1975). Probab:lklic and Statkrical Models for Sebmic R:sk Anal.nas. 51.LT. Dept. of Civil Eng., Publication R75-34. AreLIED SEtsuotocy Gaottr Liscot.s LASCR.% TORY, .N1.I.T. 42 CAALETON STREET CAxsatocE. .\f AMACHUsErrs 02142 31anuscript received October 17,1973 f s b I i l. I t e i

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