MAGNITUDE-DISTANCE RELATIONS FOR LIQUEFACTION IN SOIL ...

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83, No. 3, pp. 925 938, June 1993. MAGNITUDE-DISTANCE RELATIONS FOR LIQUEFACTION IN ... One of the most important problems in the study of soil liquefaction from .... 1, Fig. 2). Julius Schmidt, director of the National Observatory of Athens .... Key for data: open circle = 18th and 19th century Greek data (shallow.
Bulletin of the Seismological Society of America, Vol. 83, No. 3, pp. 925 938, June 1993

MAGNITUDE-DISTANCE RELATIONS FOR LIQUEFACTION IN SOIL FROM EARTHQUAKES BY GERASSIMOS A. PAPADOPOULOS AND GEORGIOS LEFKOPOULOS ABSTRACT

The review of a large number of historical documents and scientific publications revealed that at least 30 cases of liquefaction in soil from earthquakes of M s = 5.8 to 7.2 have been observed in Greece since 1767. Liquefaction usually occurs in the epicentral area of earthquakes. However, maximum epicentral and fault distances, R e and Rf, generally increase with the earthquake magnitude, M, which is consistent with similar increase observed in other parts of the world. We propose equations approximating the limiting distances R e and R~ as a function of M. By supplementing the Greek liquefaction data with a worldwide compilation of Ambraseys (1988) and using published observations for recent liquefaction cases in New Zealand, California, Venezuela, Iran, and the Philippines we also propose a slight modification of the M / R e and M / R f relations suggested by Ambraseys (1988). INTRODUCTION

One of the most important problems in the study of soil liquefaction from earthquakes is the investigation of how the maximum distance at which liquefaction can occur increases with earthquake magnitude. Answering this question could substantially contribute to a better understanding of the mechanism of liquefaction occurrence and improving methodologies for the liquefaction hazard assessment. As we will see later, empirical relations have been proposed between maximum epicentral or fault distance of liquefied sites and earthquake magnitude on the basis of regional or worldwide data. Obviously, such relations are sensitive to the case studies considered. As a consequence, any addition of new observations improves the magnitude-distance relations. The long earthquake history of Greece and its high seismic activity provide an excellent opportunity to enhance our knowledge about liquefaction phenomena. Figure 1 is a map of the relative seismic hazard in Greece and adjacent regions. Also, information and discussion of Greek liquefaction cases can be found in several publications (Galanopoulos, 1955; Georgalas, 1962; Andrikopoulou and Roussopoulos, 1980; Ambraseys, 1988; Papazachos and Papazachos, 1989; Ambraseys and Jackson, 1990). In this report we present a compilation of 30 liquefaction cases occurring in Greece from 1767 to 1988. Next, our data are reviewed and evaluated in order to obtain Greek magnitude-distance relations and improve relations proposed by other authors. Observations from some recent earthquakes that took place in several parts of the world have been used and discussed. DATA

Evidence for liquefaction in soil from earthquakes in Greece goes back to 373 B.C. when a large earthquake devastated the ancient city of Helice located only a few km to the east of the modern city of Aeghio in NW Peloponnesus (see liquefaction case 15 in Table 1 and its representation in Fig. 2). According to 925

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G. A. P A P A D O P O U L O S

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Georgalas (1962) and Seed (1968) the town was submerged because of the occurrence of extensive soil liquefaction along the coastal zone. Since t h a t ancient event some additional evidence indicating possible liquefaction phenomena in Greece has been supplied in historical documents. However, only within the last two centuries has reliable information accumulated. Reviewing a large number of such documents and scientific publications revealed t h a t since 1767, at least 30 cases of liquefaction-induced ground failures were observed. Table 1 summarizes information about these liquefaction cases. The first column shows the respective serial number, whereas the next six columns indicate the date, origin time, and focal parameters of the

LIQUEFACTION IN SOIL FROM EARTHQUAKES

927

corresponding earthquake. The remaining four columns give information about the most distant liquefied site, its epicentral and fault distances, R e and R f, and the source of information; R e and R f are defined in the next section. The error, (r, involved in the epicentral coordinates ~bN° and AE° , is included in the distance R e and R f so that ~ is equal to about 30 km, 20 km, 15 km, and 10 km for data from 1767 to 1910, 1911 to 1964, 1965 to 1980, and 1981 to 1988, respectively. When R e > 10 km, the azimuth of the liquefied site with regard to the earthquake epicentre is indicated in the column of R e. The error in the earthquake magnitude is generally no more than 0.5, 0.3, and 0.2 for magnitudes from 1767 to 1910, 1911 to 1964, and 1965 to 1988, respectively, with some possible exceptions. In some particular cases the error in magnitude, as suggested by Ambraseys and Jackson (1990), is given in parenthesis in the column M~ in Table 1. The liquefaction cases listed in Table 1 (Fig. 2) commonly occur in beach sand, deltaic, lake, or alluvial deposits. Ground fissures (Fig. 3), vent-fractures, ground settlements, and depressions associated with lateral spreading are the most usual liquefaction-induced ground failures observed. Sand boils have also been reported, in some cases being quite impressive, such as near Aeghio in the epicentral area of the 1861 Aeghio (case 5) earthquake where m u d volcano cones had a diameter of up to 10m and a height of up to 1 m (Schmidt, 1867a). Comparison of Figures 1 and 2 shows that liquefaction commonly occurs, as expected, in regions of high seismic activity such as the seismotectonic segments 2, 3, 8, and 18 (Fig. 1). They are also regions of high sedimentation rate. Liquefaction also frequently occurs in the eastern part of segment 10. This has relatively low seismic hazard but is a region of high sedimentation rate. However, the most prominent feature of the spatial distribution of liquefaction sites is the nonoccurrence of liquefaction on Crete Island (segment 4) and Dodecanese Islands (segment 5 and eastern part of segment 9), which are of high seismic hazard. It is not certain whether this is due to poor liquefaction reporting or to lack of susceptible conditions. A very important characteristic is that the liquefied areas in Greece are as a rule rather small with respect to those observed in other regions of the world. We attribute this feature to the high lateral heterogeneity in the soils, thus reflecting the complex geological structure and geomorphology in Greece. There are some exceptional cases, however, indicating the possibility for liquefaction of large areas as well. In the epicentral area of the 1861 Aeghio (case 5) earthquake, coinciding with the epicentral area of the 373 B.C. large shock of Helice, the settlement of 2 to 3 m and associated soil densification of deltaic deposits of about 15 × 106 m 2 in area, has been reported (Schmidt, 1867a). Similar ground settlements of loose alluvial deposits were observed (Georgalas, 1962) in the epicentral area of the 1953 Sousaki earthquake (case 22), the most extensive settlement of 0.6 to 4 m being 12 km in length and 3 to 4 m in width. The most distant site at which liquefaction was observed in each case is indicated in Table 1. However, considering that the minimum liquefactionassociated surface-wave magnitude is M s = 5.8, one m a y easily observe that in 22 of 30 cases the observed liquefaction is confined to distances of no greater than 20 kin. We would like to make specific comments regarding cases 5, 27, 29, and 30 of Table 1. As for the 1861 Aeghio earthquake (case 5), sand boils were observed not only at the epicentral area b u t in the Kalamaki region as well (see Table 1, Fig. 2). Julius Schmidt, director of the National Observatory of Athens

928

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at t h a t time, wrote an excellent m onogr aphy about the 1861 Aeghio e a r t h q u a k e (Schmidt, 1867a). In his s t udy it is clear that, while at the coastal village of Kalamaki, he observed sand boils spouting m u d d y material 12 or 15 min after the cessation of shaking. Regarding the 1978 Volvi Lake e a r t h q u a k e (case 27), Gazetas and Botsis (1981) discussed the possibility of liquefaction having t a k e n place in a 6-m thick s a t u r a t e d loose layer of silty sand u n d e r the m o n u m e n t a l "White Tower" located in the city of Thessaloniki at an epicentral distance Of about 28 km. However, t h er e has been absolutely no indication of any liquefaction-induced ground failure. The Alkyonides Islands e a r t h q u a k e sequence of 24 and 25 F e b r u a r y 1981 ( M s = 6.7 and 6.4) and 4 March 1981 ( M s = 6.24) (case 29) created soil liquefaction at m a n y sites. However, ground failures produced by the first two shocks have been mas ke d by the effects of the subsequent event(s). To avoid confusion and erroneous results only the dat a available for t he third shock have been

LIQUEFACTION IN SOIL FROM EARTHQUAKES

931

FIG. 3. Sand boils emanated from a surface fissure near Bouka during the 1988 Kyl]ini earthquake (case 30, Table 1).

listed in Table 1. From the existing information it is clear t h a t Kalamaki is the most distant site where liquefaction in soil was observed in t h a t case. The 1988 Kyllini e a r t h q u a k e (case 30) is of crucial importance in defining magnitude-distance relations and, therefore, is examined in detail in the following section. Almost all the liquefaction cases listed in Table 1 are associated with shallow mainshocks with the exception of the 4 March 1981 Alkyonides Islands aftershock (case 29). Only one case of liquefaction in Greece is known to be associated with i n t e r m e d i a t e depth e a r t h q u a k e (Table 1, case 12). MAGNITUDE--DISTANCE RELATIONS Results regarding m a x i m u m source distance to a site of liquefaction has been discussed by several authors. F r o m observations in J a p a n , Kuribayashi and T a t s u o k a (1975), investigated the correlation between m a x i m u m epicentral

932

G. A. PAPADOPOULOS AND G. LEFKOPOULOS

distance, Re, at which liquefaction has been reported, and associated earthq u a k e m a g n i t u d e , M. T h e y s h o w e d t h a t t h e d i s t a n c e R e (in k m ) m a y be

approximated by log R e = 0 . 7 7 M -

3.60.

(1)

E q u a t i o n (1) is s h o w n as d - d in F i g u r e 4. O t h e r a u t h o r s s u p p l e m e n t e d t h e s e d a t a w i t h case h i s t o r i e s f r o m o t h e r p a r t s of t h e world. Y o u d (1977) a n d Youd a n d P e r k i n s (1978) d e v e l o p e d u p p e r b o u n d lines for e p i c e n t r a l a n d f a u l t dist a n c e s , r e s p e c t i v e l y , for l i q u e f a c t i o n p h e n o m e n a of s e v e r a l e a r t h q u a k e s . K e e f e r ' s (1984) b o u n d i n g curves, s h o w i n g e x p o n e n t i a l i n c r e a s e of d i s t a n c e s w i t h i n c r e a s ing e a r t h q u a k e m a g n i t u d e , w e r e b a s e d on 40 w e l l - d o c u m e n t e d h i s t o r i c a l e a r t h q u a k e s . T h e s e c u r v e s e n v e l o p e t h e c o r r e s p o n d i n g lines s u g g e s t e d b y K u r i b a y a s h i a n d T a t s u o k a (1975), Y o u d (1977), a n d Y o u d a n d P e r k i n s (1978). H o w e v e r , t h e i n d i s c r i m i n a t e u s e of m a g n i t u d e s d e r i v e d f r o m d i f f e r e n t scales c o n s t i t u t e s one of t h e m o s t i m p o r t a n t u n c e r t a i n t i e s in m o s t of t h e d a t a s e t s used. A m b r a s e y s (1988) a d d e d n e w d a t a , u s e d u n i f o r m e a r t h q u a k e m a g n i t u d e s , a n d p r o p o s e d f a u l t d i s t a n c e , R f, as a m o r e a p p r o p r i a t e m e a s u r e of t h e d i s t a n c e to a site of l i q u e f a c t i o n f r o m t h e s o u r c e of seismic e n e r g y release. Finally, h e listed 137 l i q u e f a c t i o n cases r e p o r t e d in s e v e r a l r e g i o n s of t h e world, 7 of t h e m in Greece, a n d c o r r e l a t e d t h e d i s t a n c e s R e a n d R f w i t h t h e m o m e n t - m a g n i t u d e , M w. R e is defined as t h e m a x i m u m e p i c e n t r a l d i s t a n c e m e a s u r e d f r o m t h e e a r t h q u a k e e p i c e n t r e to t h e m o s t d i s t a n t site w h e r e t h e r e w a s c l e a r e v i d e n c e of l i q u e f a c t i o n - - i n d u c e d g r o u n d failures. R f is d e f i n e d as t h e m a x i m u m d i s t a n c e

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Re (Kin) FIG. 4. Maximum epicentral distance, R e, of liquefied sites versus moment magnitude, Mw, of shallow earthquakes. Key for data: open circle = 18th and 19th century Greek data (shallow shocks), hexagon = case 12 (Table 1) of intermediate depth shock of 1898, semi-solid circle = Greek data of 1902 to 1954, solid circle = Greek data of 1965 to 1988, open triangle = Edgecumbe (New Zealand, 1987) earthquake, solid triangle = Loma Prieta (California, 1989) earthquake, square = Falcon State (Venezuela, 1989) earthquake. Key for curves: a-a and b-b = Greek earthquakes of 5.8 < Ms < 5.9, and M~ > 5.9, respectively (present paper), c-c = worldwide data (Ambraseys, 1988), d-d = Japanese data (Kuribayashi and Tatsuoka, 1975), e-e = modification of c-c (present paper).

LIQUEFACTION IN SOIL FROM EARTHQUAKES

933

of liquefaction from the seismic source and is in general the fault distance. To calculate R f Ambraseys (1988) used information about surface-break, aftershock sequence, and geodetic measurements. For shallow earthquakes he found t h a t the data points M w and R e are bounded by the equation M w = - 0 . 3 1 + 2.65 x 10 8R e + 0.99log(Re)

( R e in cm),

(2)

whereas the data points M w and R f are bounded by the equation M w = 0.18 + 9.2 X 10-8Rf + 0.901og(Rf)

( R f in cm).

(3)

The curves of equations (2) and (3) are similar to those of Keefer (1984) and are represented by c-c and a - a in Figures 4 and 5, respectively. Ambraseys (1988) concluded t h a t these equations imply t h a t for distances larger t h a n R e and R f, liquefaction is very unlikely for practically all sites--except, perhaps, where conditions are ultra s o f t - - a n d t h a t for distances smaller t h a n R e and R f , liquefaction is likely but dependent on other factors t h a t determine in situ strength. On the basis of the data listed in Table 1 we define M s / R e and M J R y bounding equations for earthquakes in Greece and revise the worldwide curves proposed by Ambraseys (1988) by adding the data from Greece to his worldwide data and incorporating some recent liquefaction observations made in New Zealand, California, Iran, the Philippines, and Venezuela. In Figure 4 the data points from earthquakes in Greece, M s and Re, are plotted along with the data points from the Edgecumbe, New Zealand earthquake of 2 March 1987 (Franks, 1988), from the Loma Prieta, California, earthquake of 17 October 1989 (U.S. Geological Survey Staff, 1990; Papadopoulos, 1990) and from the Falcon State, Northwestern Venezuela earthquake of 30 April 1989 (Audemard et al., 1990; Audemard and De Santis, 1991).

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Rf (Krn) FIG. 5. Maximum fault distance, Rf, of liquefied sites versus moment magnitude, Mw, for shallow earthquakes. Key for data: all gymbolsas in Figure 4, + = conventionalplot for Re = 0 of cases 27 and 28 (Table 1). Key for curves: a-a = worldwide data (Ambraseys, 1988),'b-b = modificationof a-a, c-c = Greek shocks of 5.8 < M s < 5.9 (present paper).

934

G. A. P A P A D O P O U L O S

A N D G. L E F K O P O U L O S

In all the liquefaction cases considered, the surface-wave magnitude, Ms, falls into the magnitude range in which M s = M w. It is evident t h a t the Japanese curve ( d - d in Fig. 4) of Kuribayashi and Tatsuoka (1975) does not envelope the Greek, Loma Prieta, and Falcon State data points whereas most of the data lie within the worldwide bound curve (c-c in Fig. 4) of Ambraseys (1988). Observations of liquefaction sites from the Manjil, Northern Iran, earthquake ( M s = 7.5) of 21 J u n e 1990 (Eshghi, 1990) and the Luzon, Philippines earthquake (M s = 7.8) of 16 J u l y 1990 (Wieczorek e t a l . , 1990) imply t h a t the associated liquefaction sites are confined within the limiting distances predicted by t h a t curve. However, in the Kyllini earthquake (case 30) the distance R e = 25 km is clearly larger t h a n the distance predicted by the curve c-c of Figure 4 for M s = 5.9. The survey within the macroseismic field of the strong earthquake of 16 October 1988 in Kyllini (Papadopoulos and Profis, 1990; Papadopoulos, 1990) leaves no doubt t h a t liquefaction-induced ground failures appeared in the saturated deltaic deposits of the Pinios river at a position named Bouka (Fig. 3). The susceptibility to liquefaction of buried river channels, such as in Bouka, has been shown to be very high (Youd and Perkins, 1978; Franks, 1988). The Kyllini earthquake (case 30) has been well-recorded in 10 seismographic stations of the Seismological Institute of the National Observatory of Athens (Bulletin of SINOA, 1988), with good azimuthal distribution and low phase residuals so t h a t the error involved in its epicentral location does not likely exceed 10 km. Location has been determined using a crustal model in the Hypo 71 computer program. The magnitude has been determined as equal to M L = 5.5 (M s = 5.9) from the m a x i m u m trace amplitudes recorded by a s t a n d a r d Wood-Anderson torsion seismograph at distance 242.2 km, implying t h a t the error is no more t h a n about 0.2. The most distant site liquefied by the Falcon State, Venezuela, earthquake also seems to be located at an unusually long distance. From the map of liquefaction sites presented by Audemard and De Santis (1991) it appears t h a t the most distant site is located at about R e = 28 km. The earthquake magnirude, as reported by Audemard e t a l . (1990) and Audemard and De Santis (1991) is m b = 5.7 or M s = 6.0. This determination agrees well with those edited by Person (1990): mb(GS) = 5.9, Ms(GS) = 6.0, Ms(BRK) = 6.4, Me(PAS) = 6.0. The liquefaction distance limit from the Falcon State earthquake is plotted in Figure 4 assuming t h a t R e = 28 km and M e = 6.0. Visual inspection of Figure 4 indicates t h a t the straight lines M s = 5.647 + 0.1811ogR e, 5.8 =< M s < 5.9 ( R e i n k m )

(4)

M e = 3.686 + 1.584 log Re, Ms > 5.9 (R e in kin)

(5)

and

provide good approximations to the limiting distances, R e (curves a - a and b - b in Fig. 4). However, the data from earthquakes in Greece, the worldwide data by Ambraseys (1988), and the Edgecumbe and Falcon State earthquake data discussed earlier, impose modification of equation (2) M w

= - 0 . 4 4 + 3 × 10-SRe + 0.981og R e ( R e in cm)

(curve e - e in Figure 4).

(6)

LIQUEFACTION IN SOIL FROM EARTHQUAKES

935

The fault distance, R f, for the Greek liquefaction cases has been determined by considering alternatively either the length of surface fault break or the l e n g t h , /10, of the central axis of the 10-day aftershock area. In the absence of such information either the earthquake focal mechanism (Ambraseys and Jackson, 1990) or general trends of the seismotectonic field (Papadopoulos et al., 1986) have been used to estimate the seismic fault orientation. The relation log/10 = - 3 . 6 8 + 0.8 M s (Papadopoulos and Skafida, 1990) for recent welllocated aftershock sequences in Greece has been applied to calculate the length of the central axis of the 10-day aftershock area. In the 1898 and 1899 Peloponnesus earthquakes (cases 12 and 13) RFvalues h a v e not been determined because the first is a subcrustal event whereas the focal mechanism of the second is very uncertain, and there are no other means to determine Rf. Rf determination for the Loma Prieta earthquake has been made on the basis of the aftershock spatial distribution presented by U. S. Geological Survey Staff (1990). From the fault breaks and liquefaction locations associated with the Edgecumbe, New Zealand, earthquake, as studied by Franks (1988), Rf is on the order of 6 km. From the existing information we were not able to determine Rf for the Falcon State earthquake. Figure 5 shows the plot of the Greek, Loma Prieta, and Edgecumbe earthquake data points M s and Rf. It is evident that Rf from the Greek liquefaction cases 5, 29, and 30 (Table 1) as well as that of the Loma Prieta e a r t h q u a k e are clearly larger than the corresponding limiting distances predicted by equation (3) ( a - a in Fig. 5), and that there is need for modification resulting in

M w = - 2 . 5 x 10 3 + 9 . 2 5 x 1 0 - S R f + O . 9 1 o g R f ( R f i n c m )

(7)

( b - b in Fig. 5). However, considering solely the Greek data it seems that the straight line (c-c in Fig. 5) Ms =5.623+0.2091ogRf

(Rfinkm)

(8)

provides a better approximation for 5.8 =< M s 5.8 have occurred. Liquefaction has commonly occurred in beach sand, deltaic, lake, and alluvial deposits. The surface area of the liquefied zones in Greece is, as a rule, small with respect to areas observed elsewhere, thus reflecting regional geologic and geomorphic features. However, there are some exceptional cases of large liquefaction surface areas as well.

936

G. A. PAPADOPOULOS AND G. LEFKOPOULOS

L i q u e f a c t i o n u s u a l l y occurs w i t h i n t h e e p i c e n t r a l a r e a . H o w e v e r , m a x i m u m e p i c e n t r a l a n d f a u l t d i s t a n c e s , R e a n d RW, g e n e r a l l y i n c r e a s e e x p o n e n t i a l l y w i t h t h e e a r t h q u a k e m a g n i t u d e as h a s b e e n e m p i r i c a l l y r e c o g n i z e d in o t h e r p a r t s of t h e world. We p r o p o s e e q u a t i o n s t h a t a c c o m o d a t e t h e i n c r e a s e d l i m i t i n g d i s t a n c e s R e a n d R f of t h e G r e e k l i q u e f a c t i o n d a t a . By a d d i n g t h e s e d a t a to t h e w o r l d w i d e d a t a c o m p i l e d b y A m b r a s e y s (1988) as well as e x i s t i n g l i q u e f a c t i o n o b s e r v a t i o n s for s o m e r e c e n t e a r t h q u a k e s in N e w Z e a l a n d , California, V e n e z u e l a , I r a n , a n d t h e P h i l i p p i n e s , we slightly m o d i f y t h e w o r l d m a g n i t u d e d i s t a n c e c u r v e s s u g g e s t e d b y A m b r a s e y s (1988). A p a r t f r o m t h e i r i m p o r t a n c e in e a r t h q u a k e e n g i n e e r i n g , b o u n d i n g e q u a t i o n s for t h e m a x i m u m R e a n d R f a p p e a r to be e x t r e m e l y u s e f u l in liquefaction h a z a r d a s s e s s m e n t . C u r r e n t l y , a n a t t e m p t h a s b e e n m a d e ( P a p a d o p o u l o s , 1991) to f o r m u l a t e a p r o b a b i l i s t i c a p p r o a c h for t h e d e t e r m i n a t i o n of t h e liquefaction h a z a r d a t specific s u s c e p t i b l e sites. T h i s a p p r o a c h i n t e g r a t e s t h e M / R e a n d M / R f l i m i t i n g d i s t a n c e r e l a t i o n s , t h e e x p o n e n t i a l d i s t r i b u t i o n of e a r t h q u a k e m a g n i t u d e s , t h e P o i s s o n t i m e d i s t r i b u t i o n of e a r t h q u a k e s , a n d a n e m p i r i c a l l y d e t e r m i n e d p r o p o r t i o n of "liquefaction seismic e v e n t s " into a unified e x p r e s s i o n of overall p r o b a b i l i t y . T h i s a p p r o a c h does not consider c a l c u l a t i o n of d y n a m i c s h e a r s t r e s s e s in t h e soil, l a b o r a t o r y t e s t r e s u l t s , or soil g e o t e c h n i c a l p r o p e r t i e s , as h a s b e e n m a d e in o t h e r a p p r o a c h e s ( F a r d i s , 1979). T h e l i q u e f a c t i o n susceptibility is c o n s i d e r e d only on t h e b a s i s of t h e soil p a s t history. T h e efficiency of t h i s a p p r o a c h s h o u l d be t e s t e d b y its a p p l i c a t i o n to r e a l l i q u e f a c t i o n d a t a . ACKNOWLEDGMENTS We are grateful to two anonymous reviewers for their constructive comments. The first author expresses his sincere thanks to M. N. Fardis (Patras, Greece), G. Gazetas (Athens, Greece), Ch. Tsatsanifos (Athens, Greece) and N. N. Ambraseys (London, United Kingdom) for useful discussions and for supplying reprints, and to F. A. Audemard (Caracas, Venezuela) for sending a preprint. 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SECTIONOF GEOLOGYANDGEOPHYSICS HELLENIC AIR FORCEACADEMY DEKELIA,ATTIKA,GREECE (G.A.P., G.L.)