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A note on attenuation of earthquake intensity in Macedonia
Soil Dynamics and Earthquake Engineering 11 (1992) 457-463
A note on attenuation of earthquake intensity in Macedonia L.S. Timiovska IZIIS, 91000 Skopje, Macedonia
Communicated by N.D. Trifunac (Received 16 March 1992; revised version received 29 October 1992; accepted 2 November 1992) The attenuation of intensity of strong shaking is related to the dissipation of earthquake energy. It varies with distance from the epicenter, and depends on the local geological conditions. The 1437 data points have been collected from the Atlas of Isoseismal Maps (Catalogue of Earthquakes) in the UNDP/UNESCO Survey of the Seismicity of the Balkan Region (1974) and from unpublished data on seismic intensities in the Balkan region up to 1989. A regression analysis has been performed to describe the attenuation of earthquake intensity in Macedonia in terms of epicentral intensity, I0, epicentral distance, R, and local geological conditions at the recording site, s (s = 0, 1 or 2 for soft, medium and hard geological site conditions). levels. Intensity levels II to V are determined mainly on the basis of h u m a n response. Damage to structures is usually associated with intensity levels from VI to X. Intensity levels over X often indicate visible changes on the Earth's surface (e.g. slope instability, faulting). All intensity scales are qualitative and descriptive at best, and not quantitative or accurate enough from the point of view of determining the structural response. However, this type of descriptive scaling of earthquake effects on man and his environment will have to be used for some time, as this is usually the only information available on the levels of shaking preceding the early 1900s. 5,6
INTRODUCTION An earthquake is a complex physical phenomenon, with random occurrence in space and in time. The resulting ground motion is complicated by the nonuniform structure of the Earth and by the complex time and space character of the dislocation processes. Considering the characteristics of an earthquake at its focus, the space through which the seismic waves propagate and its manifestations on the Earth's surface, we wish to describe the associated 'strength' of shaking in terms of an intensity scale. This scaling may be considered also in terms of the magnitude scale. 1'2 Both scales can be related to the energy released from the earthquake focus. The intensity describes mainly the earthquake manifestations on the surface of the Earth. The data considered in this paper result from m a n y different reported intensities which have evolved since the sixteenth century. Today, m a n y of these intensity scales are still in use. 3 The M M I scale (Modified Mercalli Intensity scale) as described by W o o d and Newman in early 1930 is used in the U S A ) The G E O F I A N (Institute of Geophysics of the Academy of Sciences) scale was used in the USSR until the introduction of the M K S ~Medvedev, Karnik, Sponheuer) scale in the 1960s7 This scale has 12
DATABASE
The data for this analysis have been collected for the earthquakes which occurred in Macedonia during the period from 1905 to 1985. Table 1 shows a list of all the earthquakes included in this database, and presents information on the time of occurrence of each earthquake, the latitude and longitude of its epicenter, the name of the region where it occurred, the local magnitude, maximum intensity and the focal depth of the earthquake. The positions of the foci in 0-5 ° latitude cross-sections of the crust are illustrated in Fig. 1 for 30-minute latitude intervals from 40o50 ' to 42°301 . As can be seen
Soil Dynamics and Earthquake Engineering 0267-7261/93/$06.00 © 1993 Elsevier Science Publishers Ltd. 457
L.S. Timiovska
458
Table 1. Time-spatial parameters, magnitude, epicentral intensity and depth of analyzed earthquakes in Macedonia Year
Date
Time
Lat.
Long.
Magnitude
Intensity
Depth
1905 1906 1907 1910 1911 1914 1919 1920 1920 1921 1921 1921 1921 1921 1921 1921 1921 1921 1922 1922 1922 1925 1927 1927 1929 1931 1931 1931 1931 1931 1931 1931 1931 1931 1934 1942 1949 1953 1958 1960 1960 1962 1964 1965 1965 1965 1965 1966 1966 1967 1967 1967 1967 1967 1970 1972 1972 1972 1973 1973 1974 1974 1975 1976 1977
24 Oct. 28 Sep. 17 Aug. 22 Mar. 18 Feb. 19 Mar. 26 Dec. 9 Apr. 5 Oct. 15 Mar. 30 Mar. 2 Aug. 10 Aug. 15 Aug. 2 Sep. 10 Sep. tl Sep. 3 Oct. 7 Dec. 7 Dec. 7 Dec. 7 Jan. 23 Jun. 11 Aug. 10 Aug. 7 Mar. 7 Mar. 8 Mar. 8 Mar. 8 Mar. 8 Mar. 17 Mar. 17 Mar. 23 Jul. 13 Sep. 27 Aug. 30 Mar. 7 Jan. 15 Mar. 12 Mar. 12 Mar. 17 Sep. 9 Dec. 19 Mar. 18 May 18 Aug. 11 Oct. 21 Feb. 29 Jun. 27 Jan. 4 Jan. 27 Oct. 2 Dec. 21 Dec. 17 Mar. 12 Aug. 16 Sep. 2 Dec. 19 Aug. 14 Apr. 10 Mar. 21 Jun. 2 Feb. 18 Jul. 17 Aug.
4 37 2 30 11 51 2 6 21 35 3 20 9 29 20 32 12 25 1 40 15 5 11 55 14 10 8 23 9 41 3 20 15 17 12 30 16 22 16 37 22 4 11 6 19 14 1 34 9 40 9 16 1 50 1 50 2 11 2 26 5 3 18 2 20 28 3 8 4 5 6 14 22 30 1 18 6 27 11 54 12 2 19 44 18 28 4 35 18 29 4.49 6.37 20 30 0 49 10 19 8 16 23 59 12 44 0 9 17 0 23 47 14 6 19 48 16 33 2 15 21 51 1 9 21 12 22 9 22 32
42.10 40.90 41-30 41.20 40.90 41.50 41.20 42.10 42-30 40"40 41-70 41-40 43-30 42.30 42-40 42"10 42-10 42.10 41'80 41.70 41.70 42.00 41'70 41.80 41'40 41.30 41.30 41.30 41'30 41.30 41.30 41.20 41.30 41.60 41.30 41-60 41-90 41.30 40-50 41.90 41.90 41.10 41.10 41.30 42.00 41-90 42.00 42.20 41.40 42.00 42'00 41"90 41"30 42.00 41.40 41-10 41-50 41.60 41.40 40-80 41"00 41-30 40"50 41"10 41.40
21.80 20.70 22-50 22-00 20.30 20'50 20.60 21.60 21.40 21.00 20-50 21-10 21-40 21-40 21.40 21.40 21.40 21.40 20.50 20.70 20'70 22.40 22.70 22'20 22.30 22'30 22.50 22.50 22.50 22.60 22.50 22.60 2.50 22.40 20'90 29.40 20.90 20.60 21.20 20.90 20'90 20.80 20.70 22-80 21-40 22-00 21.50 21.50 20.40 21-30 21.40 21"00 20"30 21.00 20.90 22.80 20.90 21.00 20.50 20.80 21'30 22-80 21"40 22"50 21.00
5-0 6.0 4.9 5.0 6.7 4'5 4.1 4.6 4"6 4.1 5'3 4.4 5'7 4.7 4.4 3"9 4.1 4.4 5.7 5.5 4.6 4.7 4.9 4.3 4.5 6.0 4.9 6"7 4'1 3.6 4.6 4.3 4.3 4.1 4.3 6'0 3.4 5.6 5"3 5.7 4.0 4.4 4.5 4.5 2-5 3"6 3-8 3-8 4-6 3-2 3"5 3"4 5"3 4-6 4.5 4.8 4.0 4.0 4-0 4.0 4"2 4-7 4.3 4"0 4.0
6-5 8.0 7-0 8.0 9.0 6'0 5.5 6'0 7'0 6"0 8'0 6"0 8'5 7.0 7.5 6-0 6.0 7-0 7-0 7.5 6.0 5"0 6'0 6.0 5"5 8.0 6.0 10.0 6"0 7.0 7.0 6"0 6.0 6.0 6'0 8.5 6.0 6"5 7.0 8.0 6"0 6"0 7.0 6.0 6.0 7.0 6.0 7"0 7.0 6.0 6"0 6"0 8"0 6-0 6"0 7.0 6"0 5.0 5-0 5.0 6"0 6-0 5'0 6'0 5'0
19-00 20.00 6.00 10.00 15.00 6'00 17'00 14.00 5'00 6"00 13.00 14.00 20.00 6-00 3-50 7-00 6-00 3'50 17.00 15.00 7.00 30"00 21.00 4.00 18.00 17.00 32.00 16.00 8.00 4.00 6-00 13.00 10.00 15.00 7.00 12.00 4.00 19.00 16-00 6'00 7.00 9.00 11.00 14.00 2"50 2.50 5'00 3'00 7.00 3.50 5'00 4.00 14-00 9.00 16"00 15.00 14.00 20.00 20-00 20.00 15.00 25.00 32"00 10-00 13"00
459
A t t e n u a t i o n o f e a r t h q u a k e intensity in M a c e d o n i a Table
1. Continued.
Year
Date
1978 1978 1979 1979 1980 1980 1981 1982 1982 1982 1983 1983 1983 1984 1985 1985 1985 1985
24 Jun. 18 Aug. 23 Jan. 26 Feb. 9 Feb. 19 Jul. 7 Sep. 28 Feb. 14 Jul. 17 Dec. 25 Feb. 26 Aug. 5 Sep. 8 Jul. 21 Feb. 2 Oct. 1 Oct. 28 Sep.
Time
Lat.
Long.
Magnitude
Intensity
Depth
0 20 4 22 12 0 17 13 16 10 18 16 8 3 2 2 13 14
41'70 41'70 40.90 41'60 41.00 41'40 41.40 41.20 42.20 42'00 41.90 40.90 41.30 41.20 41.60 41.50 41.50 41.50
20"40 20"30 20'70 20.60 21.00 20.50 22'60 20.50 21'40 20.80 21.60 22.50 21.00 22.50 20.50 22.20 22.20 22'20
4" 1 5"0 4'2 4.5 4.1 4.8 4.0 4'3 4.0 3"3 4.5 4.2 4-2 3"9 4.3 4.2 4-0 5.1
6"0 7"0 5-0 6"0 5"0 6"0 6"5 6-0 6-0 5"0 6"0 6-0 6-0 6"5 6-0 5-5 5"0 7-0
13"00 20"00 25-00 18"00 23"00 27"00 12-00 17.00 12'00 10.00 20'00 15.00 14-00 8-00 16.00 18"00 21-00 21.00
14 53 11 9 59 37 43 1 14 15 22 15 31 31 35 32 25 50
in this figure, m o s t o f the events have o c c u r r e d at a shallow d e p t h . T h e h y p o c e n t e r s are c o n c e n t r a t e d between 20°30 , to 21°00 ' a n d 22000 ' to 23°00 , longitudes in a V - s h a p e d p a t t e r n . INTENSITY ATTENUATION
Here, I 0 a n d E 0 are the epicentral intensity a n d energy a n d I a n d E are intensity a n d energy at some distance f r o m the epicenter. A s s u m i n g t h a t the energy p r o p a g a t e s f r o m a p o i n t source, the a t t e n u a t i o n o f the energy density d e p e n d i n g on the h y p o c e n t r a l distance can be described by
EQUATION
E = E* (TrR)-" e x p ( a g ) T h e a t t e n u a t i o n o f e a r t h q u a k e intensity d e p e n d s on the h y p o c e n t r a l distance a n d the energy a b s o r p t i o n a l o n g the wave path. T h e f o r m u l a relating intensity, /, to energy, E, for a large n u m b e r o f physical p h e n o m e n a is o f the f o r m I -- a + b l o g ( E )
where a = energy a b s o r p t i o n coefficient n = r a d i a l scattering n e a r the focus E* = focal sesmic energy
(1)
T h e relation between the focal seismic energy a n d the surface wave m a g n i t u d e M~ is o f the f o r m
E q u a t i o n (1) implies the intensity a t t e n u a t i o n ( I 0 - I ) which is
log(E*) = c~ + / 3 M s
(2)
d I = Io - I = b l o g ( E o / E )
Generally,
(4)
log(E*) ~ 1.5(M)
20.30
21.00
22.00
21.30
I
-.I-
22.30
I 1 . ." . . ~
/
eI
T
t
J_
.s
i
/ ,li 4,.oo1 / l~J
.,
.
-.• •
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40.30
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:.
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I
I I
I .4. "
Oo
I
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o
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23.00
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:"
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for
Longitude (degrees)
4k : 20.00
(3)
I
I
Fig. 1. Distribution of earthquake foci in Macedonia.
B
M _> 7
and
460
L.S. Timiovska
log(E*) ~ (M) for M _< 7, and dI(I0 - Ii) = b l o g { ( R , / h ) " e x p [ a ( R i - h)]}
(5)
where h = focal depth R i = hypocentral distance Ii = intensity at some hypocentral distance
(8) and (10) enables one to obtain the values of C k l , Ck2 and C m l , and Cm2 constants, i.e. Cn and Ca. In this case, an empirical equation for the intensity-magnitude and hypocentral distance relationship is obtained. Many equations for the intensity versus epicentral or hypocentral distance and focal depth have been derived (e.g. Refs 7, 8), of the form: I=Kl
One can search for a basic of such a formula by representing the energy density by E = (E*/47rr~)(ro/r)" exp[-c~(r - r0)]
(6)
which is the result of the assumption that the spreading of the elastic energy of P and S waves is of a spherical nature, where E* = 10K; focal seismic energy determined at a 'reference' sphere. n = scattering indicator c~ = absorption and scattering coefficient of seismic energy r -- [(x0 - x) 2 + (Y0 - y)2 + h2]1/2 = hypocentral distance, in which xo,Yo are the coordinates of the epicenter and x, y are the coordinates of the observed points The linear log relationship between the intensity and the density of seismic energy represents a rough description of the complex physical situation. Adopting the intensity energy density of relationship of the form I = a + b log(E)
(7)
and using eqn (6), eqn (8) is obtained: I = Ckl + C k 2 K - C~ log(r/ro) - Cc~(r - ro)
where C k l = a - b log 47rr0
(11)
Here, the proportionality of the intensity to the log of energy density [eqn (1)] at some site (or the log of the amplitude) is equivalent to I+Ka
+ K5 l n E
(12)
The energy attenuation is described by E = (E0/47r)A -b e x p ( - c A )
(13)
where E0 is the total released energy, b is the constant of attenuation and c is a constant representing the energy absorption. Substituting eqn (13) into eqn (12), I + K 4 + K 5 ln(E0/47r ) - K s b ( l n A ) -- K 5 c A
Io = K4 + K s l n ( E o / 4 7 r ) - K s b ( l n H )
- KscH
al = Ksb(ln H ) + K s c H bl = K s b C1 = K5c
and eliminating E in eqns (14) and (15), I0 + al - bl lnA -- clA
There is a similar alternative to eqn (12). It may be considered that intensity is proportional to the density of seismic energy, (17)
I = K ( E o / 4 7 r ) P A -bp e x p ( - c P A )
Ca = ba log e
(18)
and the intensity at the epicenter is
and K is the logarithm of energy released by an earthquake. In macroseismic eqns (7) and (8) the intensity of an earthquake is thus expressed via K. The relationship between K and M is of the form t (9)
Substituting eqn (9) in (8) there follows I = C m 1 + Cm2 - C , log(r/ro) - C a ( r - ro)
(16)
By combining this with eqn (13) it follows that
Cn = bn
K = al + bl M
(15)
Adopting the new constants
I = KE p Ck2 = b
(14)
At the earthquake epicenter,
I(8)
+ K2 l n A + K3A
(10)
where Cml = Ckl + Ckza Cm2 - Ck2b
The processing of macroseismic data by using the eqns
Io = K(Eo/47v)PH p e x p ( - c P H )
(19)
Dividing eqn (18) by eqn (13) gives I = Io Hbp e x p ( c P H ) A
bp
(20)
In eqns (16) and (20) the coefficients c characterize the energy dissipation, the coefficients b define the exponential absorption and the coefficients a refer to the conditions at the earthquake source. Recently, many authors have considered the attenuation equations of the form I(I0, R) = I o + a + b R + c l o g R
(21)
where I(Io, R) is the intensity at a distance R from the
Attenuation o f earthquake intensity in Macedonia Table 2. Regression coefficients in eqn (23)
epicenter, I 0 is intensity at the epicenter, and a, b and c are constants. Including the effects of the local geological conditions, the equation for the intensity is further modified 9 to I(I0, R, s) = Io + a + bR + c log R + ds
a b c d
(23)
The coefficients of the regression analysis were estimated by using eqn (22) and are presented in Table 2 along with their 95% confidence intervals. Plots o f the estimated intensity levels versus epicentral distance are illustrated in Fig. 2, for s = 0. The quality o f fit has been tested and the correlation coefficient c o m p u t e d f r o m N(Iobs -- lobs )E(Iest -- lest.) ' " " N(Iobs. -- lobs.) 2 ~(Iest. lest.) 2 -
0'1624-0-230 -0"023 4- 0"002 -0'577 4- 0-156 -0"520 4- 0"260
intensities are plotted in Fig. 3. This yields a correlation coefficient r = 0-883. T h e estimate for d = 0.52 suggest that intensities recorded on sediments (s = 0) tend to be a b o u t one intensity level higher than the intensities recorded on the basement rock sites (s = 2). In their study o f the attenuation of seismic intensity in the Balkan countries Trifunac and coworkers 7'8 considered 'natural' seismological zones originally p r o p o s e d on the basis o f the differences in the regional tectonic environment by Sheballin et al. 4 These natural zones (adjacent to M a c e d o n i a ) are: (1) the outer area o f the Dinarides and the Illyrides, (2) from the Hellenides to Crete and Rodos, (3) inner parts o f the Balkan peninsula west of R o m a n i a and Bulgaria (including Macedonia) and north of Greece, (4) central and eastern Greece and the Aegean Sea and (5) inner parts of the Balkan peninsula covering m o s t of R o m a n i a and Bulgaria. O u r results in this p a p e r suggest that the
I(Io, R , S ) = I 0 + 0-162 - 0.023R
r =
-= = =
(22)
The following scaling relation is obtained in this analysis:
- 0.577 log R - 0.520s
461
(24)
-
where lobs. is the m e a n of the observed intensity, and/est. is the m e a n o f the estimated intensity level. The estimated intensity levels versus the observed
I
10
I S=0 Io=X IX VIII VII VI V
_6
I I
~5
t
\ \
'
4
9 10
20
30
40
50
60
80
\
\
100
200
250
Epicentral Distance(km)
Fig. 2. Site intensity versus epicentral distance (in km) for I 0 = V, VI,..., IX and X and for sites on sediments (s = 0).
L.S. Timiovska
462
Correlation Coefficient = 0.883 /
/
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6 Estimated
I
I
8
10
Intensity
Fig. 3. Observed versus estimated intensities, indicating correlation coefficient equal to 0"883. attenuation of intensities in Macedonia is very close to their results for Bulgaria (their natural zone 5), suggesting that it might be better to include Macedonia in the natural zone 5. Our results on the intensity attenuation in Macedonia are also close to their inferences for regions 2, 4 (including south Albania and north-western Greece) and 1 (including Albania, but for epicentral distances between 20 and 150 km only, the regions bordering Macedonia to south and to east. Gupta and Nuttli l° used "7 = 0.1/deg (= 0.0009/km) for eastern United States, in the equation
I(R) = I o + CI + C2("7R lOgl0 E + logl0 R) and found C1 = 3-7 and C2 = - 2 . 7 , for epicentral distance R > 20 km. They used "7 = 0-60/dy (= 0.0054/kin) for California. The results in this paper suggest "7 ~ 0.0009 for Macedonia, which is smaller than 7 for regions 1 to 5 and 7, but is larger than "7 for region 6 according to Trifunac et al. 7
acceleration amplification (recorded on s = 0 and s = 2) in California and in Yugoslavia, the present results are also consistent with the interpretation that the quality coefficient Q appears to be larger in Macedonia for high frequencies, 11 thus implying more prominent consequences of wave amplification by sediments in Macedonia relative to Southern California.
REFERENCES
1. Richter, C.F. Elementary Seismology, Freeman and Co., San Francisco, 1958. 2. Trifunac, M.D. M sM. Soil Dynamics and Earthquake Eng., 1991, 10, (1), 17-25. 3. Trifunac, M.D. & Brady, A.G. On the correlation of seismic intensity scales with the peaks of recorded strong ground motion. Bull. Seism. Soc. Amer. 1975, 65 (1), 139 62. 4. Shebalin, N.V., Karnik, V. & Had2ievski, O. Catalogue of earthquakes. In UNDP/UNESCO Survey of the Seismicity of the Balkan Region, UNESCO, Skopje, Yugoslavia, 1974.
CONCLUSION This paper includes the effect of the variation of the local geological conditions on observed earthquake intensities in Macedonia. Its results are consistent and in qualitative agreement with other related studies in California (e.g. Ref. 9), but the implied site effects are twice as large as in California. Together with results from Ref. 6, which showed differences in peak
5. Trifunac, M.D. & 7.iv~i6, M. A note on instrumental comparison of the modified Mercalli intensity (MMI) in the western United States and the Mercalli--Cancani Sieberg (MCS) intensity in Yugoslavia, European Earthquake Eng., 1991, V (1), 22 26. 6. Trifunac, M.D., Ziv~i6, M. & Mani6, M. On the correlation of Mercalli Cancani Sieberg intensity scale in Yugoslavia with the peaks of recorded strong earthquake ground motion. European Earthquake Eng., 1991, V (1), 27 33. 7. Trifunac M.D., Lee, V.W., Cao, H. & Todorovska, M.I.
Attenuation of earthquake intensity in Macedonia Attenuation of seismic intensity in the Balkan countries, Dept. of Civil Eng. Report No. CE 88-01, Univ. of Southern California, Los Angeles, CA, 1988. 8. Trifunac, M.D. & Todorovska, M.I. Attenuation of seismic intensity in Albania and Yugoslavia. Earthquake Eng. and Structural Dynamics, 1989, 18, 613-7. 9. Lee, V.W. & Trifunac, M.D. Attenuation of modified Mercalli intensity for small epicentral distance in
463
California, Report No. CE 85-01, University of Southern California, Los Angeles, CA, 1985. 10. Gupta, I. & Nuttli, O.W. Spatial attenuation of intensities for central US earthquakes, Bull. Seism. Soc. Amer., 1976, 66, 743-51. 11. Lee, V.W. & Trifunac, M.D. Frequency dependent attenuation of strong earthquake ground motion in Yugoslavia, European Earthquake Eng., 1992, VI (1), 3-13.
A note on attenuation of earthquake intensity in Macedonia L.S. Timiovska IZIIS, 91000 Skopje, Macedonia
Communicated by N.D. Trifunac (Received 16 March 1992; revised version received 29 October 1992; accepted 2 November 1992) The attenuation of intensity of strong shaking is related to the dissipation of earthquake energy. It varies with distance from the epicenter, and depends on the local geological conditions. The 1437 data points have been collected from the Atlas of Isoseismal Maps (Catalogue of Earthquakes) in the UNDP/UNESCO Survey of the Seismicity of the Balkan Region (1974) and from unpublished data on seismic intensities in the Balkan region up to 1989. A regression analysis has been performed to describe the attenuation of earthquake intensity in Macedonia in terms of epicentral intensity, I0, epicentral distance, R, and local geological conditions at the recording site, s (s = 0, 1 or 2 for soft, medium and hard geological site conditions). levels. Intensity levels II to V are determined mainly on the basis of h u m a n response. Damage to structures is usually associated with intensity levels from VI to X. Intensity levels over X often indicate visible changes on the Earth's surface (e.g. slope instability, faulting). All intensity scales are qualitative and descriptive at best, and not quantitative or accurate enough from the point of view of determining the structural response. However, this type of descriptive scaling of earthquake effects on man and his environment will have to be used for some time, as this is usually the only information available on the levels of shaking preceding the early 1900s. 5,6
INTRODUCTION An earthquake is a complex physical phenomenon, with random occurrence in space and in time. The resulting ground motion is complicated by the nonuniform structure of the Earth and by the complex time and space character of the dislocation processes. Considering the characteristics of an earthquake at its focus, the space through which the seismic waves propagate and its manifestations on the Earth's surface, we wish to describe the associated 'strength' of shaking in terms of an intensity scale. This scaling may be considered also in terms of the magnitude scale. 1'2 Both scales can be related to the energy released from the earthquake focus. The intensity describes mainly the earthquake manifestations on the surface of the Earth. The data considered in this paper result from m a n y different reported intensities which have evolved since the sixteenth century. Today, m a n y of these intensity scales are still in use. 3 The M M I scale (Modified Mercalli Intensity scale) as described by W o o d and Newman in early 1930 is used in the U S A ) The G E O F I A N (Institute of Geophysics of the Academy of Sciences) scale was used in the USSR until the introduction of the M K S ~Medvedev, Karnik, Sponheuer) scale in the 1960s7 This scale has 12
DATABASE
The data for this analysis have been collected for the earthquakes which occurred in Macedonia during the period from 1905 to 1985. Table 1 shows a list of all the earthquakes included in this database, and presents information on the time of occurrence of each earthquake, the latitude and longitude of its epicenter, the name of the region where it occurred, the local magnitude, maximum intensity and the focal depth of the earthquake. The positions of the foci in 0-5 ° latitude cross-sections of the crust are illustrated in Fig. 1 for 30-minute latitude intervals from 40o50 ' to 42°301 . As can be seen
Soil Dynamics and Earthquake Engineering 0267-7261/93/$06.00 © 1993 Elsevier Science Publishers Ltd. 457
L.S. Timiovska
458
Table 1. Time-spatial parameters, magnitude, epicentral intensity and depth of analyzed earthquakes in Macedonia Year
Date
Time
Lat.
Long.
Magnitude
Intensity
Depth
1905 1906 1907 1910 1911 1914 1919 1920 1920 1921 1921 1921 1921 1921 1921 1921 1921 1921 1922 1922 1922 1925 1927 1927 1929 1931 1931 1931 1931 1931 1931 1931 1931 1931 1934 1942 1949 1953 1958 1960 1960 1962 1964 1965 1965 1965 1965 1966 1966 1967 1967 1967 1967 1967 1970 1972 1972 1972 1973 1973 1974 1974 1975 1976 1977
24 Oct. 28 Sep. 17 Aug. 22 Mar. 18 Feb. 19 Mar. 26 Dec. 9 Apr. 5 Oct. 15 Mar. 30 Mar. 2 Aug. 10 Aug. 15 Aug. 2 Sep. 10 Sep. tl Sep. 3 Oct. 7 Dec. 7 Dec. 7 Dec. 7 Jan. 23 Jun. 11 Aug. 10 Aug. 7 Mar. 7 Mar. 8 Mar. 8 Mar. 8 Mar. 8 Mar. 17 Mar. 17 Mar. 23 Jul. 13 Sep. 27 Aug. 30 Mar. 7 Jan. 15 Mar. 12 Mar. 12 Mar. 17 Sep. 9 Dec. 19 Mar. 18 May 18 Aug. 11 Oct. 21 Feb. 29 Jun. 27 Jan. 4 Jan. 27 Oct. 2 Dec. 21 Dec. 17 Mar. 12 Aug. 16 Sep. 2 Dec. 19 Aug. 14 Apr. 10 Mar. 21 Jun. 2 Feb. 18 Jul. 17 Aug.
4 37 2 30 11 51 2 6 21 35 3 20 9 29 20 32 12 25 1 40 15 5 11 55 14 10 8 23 9 41 3 20 15 17 12 30 16 22 16 37 22 4 11 6 19 14 1 34 9 40 9 16 1 50 1 50 2 11 2 26 5 3 18 2 20 28 3 8 4 5 6 14 22 30 1 18 6 27 11 54 12 2 19 44 18 28 4 35 18 29 4.49 6.37 20 30 0 49 10 19 8 16 23 59 12 44 0 9 17 0 23 47 14 6 19 48 16 33 2 15 21 51 1 9 21 12 22 9 22 32
42.10 40.90 41-30 41.20 40.90 41.50 41.20 42.10 42-30 40"40 41-70 41-40 43-30 42.30 42-40 42"10 42-10 42.10 41'80 41.70 41.70 42.00 41'70 41.80 41'40 41.30 41.30 41.30 41'30 41.30 41.30 41.20 41.30 41.60 41.30 41-60 41-90 41.30 40-50 41.90 41.90 41.10 41.10 41.30 42.00 41-90 42.00 42.20 41.40 42.00 42'00 41"90 41"30 42.00 41.40 41-10 41-50 41.60 41.40 40-80 41"00 41-30 40"50 41"10 41.40
21.80 20.70 22-50 22-00 20.30 20'50 20.60 21.60 21.40 21.00 20-50 21-10 21-40 21-40 21.40 21.40 21.40 21.40 20.50 20.70 20'70 22.40 22.70 22'20 22.30 22'30 22.50 22.50 22.50 22.60 22.50 22.60 2.50 22.40 20'90 29.40 20.90 20.60 21.20 20.90 20'90 20.80 20.70 22-80 21-40 22-00 21.50 21.50 20.40 21-30 21.40 21"00 20"30 21.00 20.90 22.80 20.90 21.00 20.50 20.80 21'30 22-80 21"40 22"50 21.00
5-0 6.0 4.9 5.0 6.7 4'5 4.1 4.6 4"6 4.1 5'3 4.4 5'7 4.7 4.4 3"9 4.1 4.4 5.7 5.5 4.6 4.7 4.9 4.3 4.5 6.0 4.9 6"7 4'1 3.6 4.6 4.3 4.3 4.1 4.3 6'0 3.4 5.6 5"3 5.7 4.0 4.4 4.5 4.5 2-5 3"6 3-8 3-8 4-6 3-2 3"5 3"4 5"3 4-6 4.5 4.8 4.0 4.0 4-0 4.0 4"2 4-7 4.3 4"0 4.0
6-5 8.0 7-0 8.0 9.0 6'0 5.5 6'0 7'0 6"0 8'0 6"0 8'5 7.0 7.5 6-0 6.0 7-0 7-0 7.5 6.0 5"0 6'0 6.0 5"5 8.0 6.0 10.0 6"0 7.0 7.0 6"0 6.0 6.0 6'0 8.5 6.0 6"5 7.0 8.0 6"0 6"0 7.0 6.0 6.0 7.0 6.0 7"0 7.0 6.0 6"0 6"0 8"0 6-0 6"0 7.0 6"0 5.0 5-0 5.0 6"0 6-0 5'0 6'0 5'0
19-00 20.00 6.00 10.00 15.00 6'00 17'00 14.00 5'00 6"00 13.00 14.00 20.00 6-00 3-50 7-00 6-00 3'50 17.00 15.00 7.00 30"00 21.00 4.00 18.00 17.00 32.00 16.00 8.00 4.00 6-00 13.00 10.00 15.00 7.00 12.00 4.00 19.00 16-00 6'00 7.00 9.00 11.00 14.00 2"50 2.50 5'00 3'00 7.00 3.50 5'00 4.00 14-00 9.00 16"00 15.00 14.00 20.00 20-00 20.00 15.00 25.00 32"00 10-00 13"00
459
A t t e n u a t i o n o f e a r t h q u a k e intensity in M a c e d o n i a Table
1. Continued.
Year
Date
1978 1978 1979 1979 1980 1980 1981 1982 1982 1982 1983 1983 1983 1984 1985 1985 1985 1985
24 Jun. 18 Aug. 23 Jan. 26 Feb. 9 Feb. 19 Jul. 7 Sep. 28 Feb. 14 Jul. 17 Dec. 25 Feb. 26 Aug. 5 Sep. 8 Jul. 21 Feb. 2 Oct. 1 Oct. 28 Sep.
Time
Lat.
Long.
Magnitude
Intensity
Depth
0 20 4 22 12 0 17 13 16 10 18 16 8 3 2 2 13 14
41'70 41'70 40.90 41'60 41.00 41'40 41.40 41.20 42.20 42'00 41.90 40.90 41.30 41.20 41.60 41.50 41.50 41.50
20"40 20"30 20'70 20.60 21.00 20.50 22'60 20.50 21'40 20.80 21.60 22.50 21.00 22.50 20.50 22.20 22.20 22'20
4" 1 5"0 4'2 4.5 4.1 4.8 4.0 4'3 4.0 3"3 4.5 4.2 4-2 3"9 4.3 4.2 4-0 5.1
6"0 7"0 5-0 6"0 5"0 6"0 6"5 6-0 6-0 5"0 6"0 6-0 6-0 6"5 6-0 5-5 5"0 7-0
13"00 20"00 25-00 18"00 23"00 27"00 12-00 17.00 12'00 10.00 20'00 15.00 14-00 8-00 16.00 18"00 21-00 21.00
14 53 11 9 59 37 43 1 14 15 22 15 31 31 35 32 25 50
in this figure, m o s t o f the events have o c c u r r e d at a shallow d e p t h . T h e h y p o c e n t e r s are c o n c e n t r a t e d between 20°30 , to 21°00 ' a n d 22000 ' to 23°00 , longitudes in a V - s h a p e d p a t t e r n . INTENSITY ATTENUATION
Here, I 0 a n d E 0 are the epicentral intensity a n d energy a n d I a n d E are intensity a n d energy at some distance f r o m the epicenter. A s s u m i n g t h a t the energy p r o p a g a t e s f r o m a p o i n t source, the a t t e n u a t i o n o f the energy density d e p e n d i n g on the h y p o c e n t r a l distance can be described by
EQUATION
E = E* (TrR)-" e x p ( a g ) T h e a t t e n u a t i o n o f e a r t h q u a k e intensity d e p e n d s on the h y p o c e n t r a l distance a n d the energy a b s o r p t i o n a l o n g the wave path. T h e f o r m u l a relating intensity, /, to energy, E, for a large n u m b e r o f physical p h e n o m e n a is o f the f o r m I -- a + b l o g ( E )
where a = energy a b s o r p t i o n coefficient n = r a d i a l scattering n e a r the focus E* = focal sesmic energy
(1)
T h e relation between the focal seismic energy a n d the surface wave m a g n i t u d e M~ is o f the f o r m
E q u a t i o n (1) implies the intensity a t t e n u a t i o n ( I 0 - I ) which is
log(E*) = c~ + / 3 M s
(2)
d I = Io - I = b l o g ( E o / E )
Generally,
(4)
log(E*) ~ 1.5(M)
20.30
21.00
22.00
21.30
I
-.I-
22.30
I 1 . ." . . ~
/
eI
T
t
J_
.s
i
/ ,li 4,.oo1 / l~J
.,
.
-.• •
' "
40.30
: •
I
*
:.
"
. .
~ I I
I
I I
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Oo
I
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:
~•°"
o
I "
B
I
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l
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,
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I
." . I,
I
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I
I
I
23.00
I
:"
42"00/I/
for
Longitude (degrees)
4k : 20.00
(3)
I
I
Fig. 1. Distribution of earthquake foci in Macedonia.
B
M _> 7
and
460
L.S. Timiovska
log(E*) ~ (M) for M _< 7, and dI(I0 - Ii) = b l o g { ( R , / h ) " e x p [ a ( R i - h)]}
(5)
where h = focal depth R i = hypocentral distance Ii = intensity at some hypocentral distance
(8) and (10) enables one to obtain the values of C k l , Ck2 and C m l , and Cm2 constants, i.e. Cn and Ca. In this case, an empirical equation for the intensity-magnitude and hypocentral distance relationship is obtained. Many equations for the intensity versus epicentral or hypocentral distance and focal depth have been derived (e.g. Refs 7, 8), of the form: I=Kl
One can search for a basic of such a formula by representing the energy density by E = (E*/47rr~)(ro/r)" exp[-c~(r - r0)]
(6)
which is the result of the assumption that the spreading of the elastic energy of P and S waves is of a spherical nature, where E* = 10K; focal seismic energy determined at a 'reference' sphere. n = scattering indicator c~ = absorption and scattering coefficient of seismic energy r -- [(x0 - x) 2 + (Y0 - y)2 + h2]1/2 = hypocentral distance, in which xo,Yo are the coordinates of the epicenter and x, y are the coordinates of the observed points The linear log relationship between the intensity and the density of seismic energy represents a rough description of the complex physical situation. Adopting the intensity energy density of relationship of the form I = a + b log(E)
(7)
and using eqn (6), eqn (8) is obtained: I = Ckl + C k 2 K - C~ log(r/ro) - Cc~(r - ro)
where C k l = a - b log 47rr0
(11)
Here, the proportionality of the intensity to the log of energy density [eqn (1)] at some site (or the log of the amplitude) is equivalent to I+Ka
+ K5 l n E
(12)
The energy attenuation is described by E = (E0/47r)A -b e x p ( - c A )
(13)
where E0 is the total released energy, b is the constant of attenuation and c is a constant representing the energy absorption. Substituting eqn (13) into eqn (12), I + K 4 + K 5 ln(E0/47r ) - K s b ( l n A ) -- K 5 c A
Io = K4 + K s l n ( E o / 4 7 r ) - K s b ( l n H )
- KscH
al = Ksb(ln H ) + K s c H bl = K s b C1 = K5c
and eliminating E in eqns (14) and (15), I0 + al - bl lnA -- clA
There is a similar alternative to eqn (12). It may be considered that intensity is proportional to the density of seismic energy, (17)
I = K ( E o / 4 7 r ) P A -bp e x p ( - c P A )
Ca = ba log e
(18)
and the intensity at the epicenter is
and K is the logarithm of energy released by an earthquake. In macroseismic eqns (7) and (8) the intensity of an earthquake is thus expressed via K. The relationship between K and M is of the form t (9)
Substituting eqn (9) in (8) there follows I = C m 1 + Cm2 - C , log(r/ro) - C a ( r - ro)
(16)
By combining this with eqn (13) it follows that
Cn = bn
K = al + bl M
(15)
Adopting the new constants
I = KE p Ck2 = b
(14)
At the earthquake epicenter,
I(8)
+ K2 l n A + K3A
(10)
where Cml = Ckl + Ckza Cm2 - Ck2b
The processing of macroseismic data by using the eqns
Io = K(Eo/47v)PH p e x p ( - c P H )
(19)
Dividing eqn (18) by eqn (13) gives I = Io Hbp e x p ( c P H ) A
bp
(20)
In eqns (16) and (20) the coefficients c characterize the energy dissipation, the coefficients b define the exponential absorption and the coefficients a refer to the conditions at the earthquake source. Recently, many authors have considered the attenuation equations of the form I(I0, R) = I o + a + b R + c l o g R
(21)
where I(Io, R) is the intensity at a distance R from the
Attenuation o f earthquake intensity in Macedonia Table 2. Regression coefficients in eqn (23)
epicenter, I 0 is intensity at the epicenter, and a, b and c are constants. Including the effects of the local geological conditions, the equation for the intensity is further modified 9 to I(I0, R, s) = Io + a + bR + c log R + ds
a b c d
(23)
The coefficients of the regression analysis were estimated by using eqn (22) and are presented in Table 2 along with their 95% confidence intervals. Plots o f the estimated intensity levels versus epicentral distance are illustrated in Fig. 2, for s = 0. The quality o f fit has been tested and the correlation coefficient c o m p u t e d f r o m N(Iobs -- lobs )E(Iest -- lest.) ' " " N(Iobs. -- lobs.) 2 ~(Iest. lest.) 2 -
0'1624-0-230 -0"023 4- 0"002 -0'577 4- 0-156 -0"520 4- 0"260
intensities are plotted in Fig. 3. This yields a correlation coefficient r = 0-883. T h e estimate for d = 0.52 suggest that intensities recorded on sediments (s = 0) tend to be a b o u t one intensity level higher than the intensities recorded on the basement rock sites (s = 2). In their study o f the attenuation of seismic intensity in the Balkan countries Trifunac and coworkers 7'8 considered 'natural' seismological zones originally p r o p o s e d on the basis o f the differences in the regional tectonic environment by Sheballin et al. 4 These natural zones (adjacent to M a c e d o n i a ) are: (1) the outer area o f the Dinarides and the Illyrides, (2) from the Hellenides to Crete and Rodos, (3) inner parts o f the Balkan peninsula west of R o m a n i a and Bulgaria (including Macedonia) and north of Greece, (4) central and eastern Greece and the Aegean Sea and (5) inner parts of the Balkan peninsula covering m o s t of R o m a n i a and Bulgaria. O u r results in this p a p e r suggest that the
I(Io, R , S ) = I 0 + 0-162 - 0.023R
r =
-= = =
(22)
The following scaling relation is obtained in this analysis:
- 0.577 log R - 0.520s
461
(24)
-
where lobs. is the m e a n of the observed intensity, and/est. is the m e a n o f the estimated intensity level. The estimated intensity levels versus the observed
I
10
I S=0 Io=X IX VIII VII VI V
_6
I I
~5
t
\ \
'
4
9 10
20
30
40
50
60
80
\
\
100
200
250
Epicentral Distance(km)
Fig. 2. Site intensity versus epicentral distance (in km) for I 0 = V, VI,..., IX and X and for sites on sediments (s = 0).
L.S. Timiovska
462
Correlation Coefficient = 0.883 /
/
10
/
/
/
/ / /
/
>
,/
/ / / ,/ ,I
®
/
O
-x-// /
/
/
/
P
/
/ / / /
/ /
/
/
/
/
/ I 4
I
6 Estimated
I
I
8
10
Intensity
Fig. 3. Observed versus estimated intensities, indicating correlation coefficient equal to 0"883. attenuation of intensities in Macedonia is very close to their results for Bulgaria (their natural zone 5), suggesting that it might be better to include Macedonia in the natural zone 5. Our results on the intensity attenuation in Macedonia are also close to their inferences for regions 2, 4 (including south Albania and north-western Greece) and 1 (including Albania, but for epicentral distances between 20 and 150 km only, the regions bordering Macedonia to south and to east. Gupta and Nuttli l° used "7 = 0.1/deg (= 0.0009/km) for eastern United States, in the equation
I(R) = I o + CI + C2("7R lOgl0 E + logl0 R) and found C1 = 3-7 and C2 = - 2 . 7 , for epicentral distance R > 20 km. They used "7 = 0-60/dy (= 0.0054/kin) for California. The results in this paper suggest "7 ~ 0.0009 for Macedonia, which is smaller than 7 for regions 1 to 5 and 7, but is larger than "7 for region 6 according to Trifunac et al. 7
acceleration amplification (recorded on s = 0 and s = 2) in California and in Yugoslavia, the present results are also consistent with the interpretation that the quality coefficient Q appears to be larger in Macedonia for high frequencies, 11 thus implying more prominent consequences of wave amplification by sediments in Macedonia relative to Southern California.
REFERENCES
1. Richter, C.F. Elementary Seismology, Freeman and Co., San Francisco, 1958. 2. Trifunac, M.D. M sM. Soil Dynamics and Earthquake Eng., 1991, 10, (1), 17-25. 3. Trifunac, M.D. & Brady, A.G. On the correlation of seismic intensity scales with the peaks of recorded strong ground motion. Bull. Seism. Soc. Amer. 1975, 65 (1), 139 62. 4. Shebalin, N.V., Karnik, V. & Had2ievski, O. Catalogue of earthquakes. In UNDP/UNESCO Survey of the Seismicity of the Balkan Region, UNESCO, Skopje, Yugoslavia, 1974.
CONCLUSION This paper includes the effect of the variation of the local geological conditions on observed earthquake intensities in Macedonia. Its results are consistent and in qualitative agreement with other related studies in California (e.g. Ref. 9), but the implied site effects are twice as large as in California. Together with results from Ref. 6, which showed differences in peak
5. Trifunac, M.D. & 7.iv~i6, M. A note on instrumental comparison of the modified Mercalli intensity (MMI) in the western United States and the Mercalli--Cancani Sieberg (MCS) intensity in Yugoslavia, European Earthquake Eng., 1991, V (1), 22 26. 6. Trifunac, M.D., Ziv~i6, M. & Mani6, M. On the correlation of Mercalli Cancani Sieberg intensity scale in Yugoslavia with the peaks of recorded strong earthquake ground motion. European Earthquake Eng., 1991, V (1), 27 33. 7. Trifunac M.D., Lee, V.W., Cao, H. & Todorovska, M.I.
Attenuation of earthquake intensity in Macedonia Attenuation of seismic intensity in the Balkan countries, Dept. of Civil Eng. Report No. CE 88-01, Univ. of Southern California, Los Angeles, CA, 1988. 8. Trifunac, M.D. & Todorovska, M.I. Attenuation of seismic intensity in Albania and Yugoslavia. Earthquake Eng. and Structural Dynamics, 1989, 18, 613-7. 9. Lee, V.W. & Trifunac, M.D. Attenuation of modified Mercalli intensity for small epicentral distance in
463
California, Report No. CE 85-01, University of Southern California, Los Angeles, CA, 1985. 10. Gupta, I. & Nuttli, O.W. Spatial attenuation of intensities for central US earthquakes, Bull. Seism. Soc. Amer., 1976, 66, 743-51. 11. Lee, V.W. & Trifunac, M.D. Frequency dependent attenuation of strong earthquake ground motion in Yugoslavia, European Earthquake Eng., 1992, VI (1), 3-13.