Time-lag of the earthquake energy release between ... - Springer Link

PAGEOPH, Vol. 139, No. 2 (1992)

Time-lag

0033 4553/92/020293-1651.50 +0.20/0 9 1992 Birkh/iuser Verlag, Basel

of the Earthquake Three

Energy

Release

Between

Seismic Regions

THEODOROS M. TSAPANOS 1 and ][OANNIS LIRITZIS2

Abstract--Three complete data sets of strong earthquakes (M -> 5.5), which occurred in the seismic regions of Chile, Mexico and Kamchatka during the time period 1899-1985, have been used to test the existence of a time-lag in the seismic energy release between these regions. These data sets were cross-correlated in order to determine whether any pair of the sets are correlated. For this purpose statistical tests, such as the T-test, the Fisher's transformation and probability distribution have been applied to determine the significance of the obtained correlation coefficients. The results show that the time-lag between Chile and Kamchatka is -2, which means that Kamchatka precedes Chile by 2 years, with a correlation coefficient significant at 99.80% level, a weak correlation between Kamchatka-Mexico and noncorrelation for Mexico-Chile. Key words: Earthquake energy, cross-correlation, time-lag, Chile, Kamchatka, Mexico.

Introduction The application o f statistical techniques to study the time distribution o f earthquakes is o f great importance in seismology, since such studies m a y bring up new ideas a b o u t the patterns o f earthquake occurrence. The seismic activities can be expressed in terms o f the released wave energies and can be considered as being adequate dynamic parameters to correlate. Correlation o f earthquake strain release patterns f r o m several areas a r o u n d the Pacific suggests that stress is s o m e h o w being affected on a global scale (BERG and SUTTON, 1974; BERG et al., 1977; SKORDAS et al., 1991). KANAMORI (1977) estimated the seismic energy release by the great earthquakes and discussed the temporal variation on a world-wide scale. A certain time-space similarity in the seismic activity between various regions o f the world seems to support the theory o f the plate tectonics. The study o f the space-time pattern in the distribution o f the earthquakes, suggests that past trends

Aristotle University of Thessaloniki, Geophysical Laboratory, 54006 Thessaloniki, Macedonia, Greece. 2 Research Center for Astronomy and Applied Mathematics, Academy of Athens, 14 Anagnostopoulou Str., 10673 Athens, Greece.

294

Theodoros M. Tsapanos and Ioannis Liritzis

PAGEOPH,

will continue. Some linear trends are found in the space-time distributions of large earthquakes in some parts of the circum-Pacific seismic zones (KELLEHER, 1970, 1972; MOGI, 1974, 1979). The cross-correlation method between different seismic regions of the world, as well as in time, is suggested as a useful tool to clarify the complicated space-time pattern (BATH, 1984b). Time-space patterns of seismic activity have always attracted the interest of geoscientists. Especially in the earlier literature, there are numerous investigations of earthquake periodicities as well as relations between earthquakes and various external phenomena (SHLANGER, 1960). Most of this research led to negative results, whereas relations between earthquake activities in different parts of the earth were often inconclusive. Among the early contributions, those of BENIOFF (1951, 1955) are particularly noteworthy. On the basis of strain release diagrams, he concluded that shallow earthquakes of magnitude 8.0 or greater are not independent events, but somehow linked to a single world-wide tectonic system. Although met with interest, this result was only qualitative and appeared somewhat hypothetical at that time. DUDA (1965) confirmed Benioff's result for earthquakes with a magnitude down to 7.0, while OLSSON (1982) maintained that only earthquakes of medium magnitude (7.0 to 7.6) are dependent events. ZHADIN (1984) described connections between large earthquakes in terms of migration. Cycles with radial epicenter propagation inferred a direct connection of the seismic processes with mantle convection. MOGI (1979) found that during several decades, the seismic activity was complementary in regions of low latitude ( < 40 ~ and high latitude ( > 4 0 ~) with low latitude regions active in 1930-1950, highlatitude ones in 1950-1970. In recent decades, the possibilities for investigating global seismic interrelations have improved considerably, especially by the use of global seismograph networks. Moreover, the breakthrough of the plate tectonics theory has made it possible to visualize realistic models for global interactions. Therefore, this topic deserves renewed examination. Typically enough, PAVESE and GREGORI (1985) express this need in the following words: "The rationale provided by plate tectonics does not appear to have as yet been tackled of eventual statistical spatial and temporal correlations of earthquakes occurring in different parts of the world." Global relations are nowadays naturally in several branches of geophysics where relevant observations are more directly available. But it appears the time has come now for tectonophysics to produce a more definite answer to this question, whether yes or no. Bfith has taken up such correlations, first between Sweden and the world (BATH, 1984a), later for Greece and the world (BATH, 1984b; MAKROPOULOSand LIRITZIS, 1985; MAKROPOULOSet al., 1992) and between Greece and Kurile islands (B~TH, 1985). In the latter study the correlation between these two distant areas was highly significant with a time lag of 0 - 5 years, Kurile preceding.

Vol. 139, 1992

Time-lag of Earthquake Energy Release

295

In the present work an attempt is made to find the time-lag in the seismic energy release, in an 87-year record of three seismic regions of the world (Chile, Kamchatka and Mexico), all of which belong to the Pacific seismic zones, employing for this purpose some statistical considerations.

Data Set and M e t h o d Applied

The seismic energy release depends mainly on the occurrence of great earthquakes and as BATH (1979, 1983, 1984a,b) pointed out this is an advantage, because the magnitudes of great shocks are more easily determined than the small ones. Moreover the collection of the data, which should be accurate, homogeneous and complete, is needless to the studies of seismic energy release, because the great earthquakes are those which govern the release of it. But because our data source is a homogeneous and complete catalogue of earthquakes we shall present, in brief, some information regarding it. TSAPANOS et al. (1990a,b) compiled a new global catalogue of earthquakes, with magnitudes M > 5.5, which is an improved homogeneous one, extending the earlier catalogue produced by TSAPANOS (1985). Earthquakes of all depth subdivisions are listed in this catalogue. The time span covered within this catalogue is 1899-1985 and the size of the earthquakes is quantified on the surface wave magnitude scale. Details of the method used to obtain the completeness of the data and a full review of the content of this catalogue have been described elsewhere (TSAPANOS, 1985, 1990; PAPAZACHOSet al., 1991; TSAPANOS and BURTON, 1991). The seismic regions chosen for the present work are Kamchatka (Kurile islands are also included), Chile and Mexico (see TSAPANOS, 1990). All are parts of the seismically active circum-Pacific belt and certainly are characterized by high seismicity. Examining the seismic energy, release world-wide during the time period 1904-1965 for earthquake magnitudes M > 6.0, we found that this amount is about 172.56 x 1024erg, while for Kamchatka, Chile and Mexico it is 16.66 x 1024, 12.68 x 1024 and 7.02 x 1024erg, respectively. This means that 10% of the global seismic energy is released from Kamchatka, 7.5% is released from Chile and finally 4% is released from Mexico. In order to cross-correlate the seismic energy which is released in the (pre)referred seismic regions, for the time period 1898-1985, we converted the earthquakes magnitude, which occurred in each of the above regions, into seismic energy through BATH's (1958) equation log E = 12.24 + 1.44M.

(I)

Then we calculated the total amount of the seismic energy released in each year and finally expressed this annual amount of energy reduced in 1021 erg. All the above work has been done through a computer program called BATHEN (BATH'S ENergy), compiled for this purpose by the authors.

296


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The seismic wave energy is the only dynamical parameter available to us. It is therefore natural that it receives a certain significance in these studies. Correlating total magnitudes is obviously (eq. 1) equivalent to correlating the logarithm of the energies, a method to be found in the statistical literature for the reduction of outstanding maxima (e.g., AGTERBERG, 1974). The energy as an obvious measure of the dynamics of the earthquake phenomena, is thus assigned the greatest weight. A first observation is that there is a number of "missing years," which seem to be years with no release of seismic energy, for the data sets of each region. This is not true. We also have earthquakes and their corresponding seismic energy release, but these shocks do not fulfill the completeness condition (TSAPANOS, 1990). It was proven (BURTON, 1979) that if the "missing years" are less or equal to 25% of the total years in the time series, then the calculated parameters may be estimated without noticeable loss of accuracy. In our case Kamchatka has 14 "missing years" (16% of the total annuals), while Chile and Mexico have 19 (21%) and 14 (16%) "missing years" and their percentage of the total annuals respectively. Although our "missings" are less than 25%, we consider for these years the minimum seismic energy release, which was found for each of the data sets. This was because the applied method (BATH, 1984a) needs a seismic energy release per year. These three data sets were cross-correlated for time-lags between - 2 4 to +24 years. Subsequently the significance of the higher correlation coefficient was checked, applying T-statistic distribution, Fisher's transformation and the probability distribution for linear correlation coefficient P(r, N).

Statistical Analys& of the Data Sets Table 1 shows the annual seismic energy release in units of erg/yr and a summary statistic for the three regions of Chile, Mexico and Kamchatka for the period 1898-1985 (Fig. 1). Tables 2, 3 and 4 give the correlation coefficient (r) for various time-lags and Figures 2, 3 and 4 the corresponding plots. Correlation coefficients reflect the relative overall trends of any two series (e.g., as displayed in Fig. 1). The method is simple, reliable and efficient and is applicable to curves of any shape, periodic as well as nonperiodic. It is, therefore, natural that it has found extensive application in geophysics, recent examples being offered by LUGOVENKO and PRONIN (1982, 1984) and in paleomagnetic data series (CREER and TUCHOLKA, 1982; XANTHAKIS and LrRITZlS, 1991). A correlation coefficient (r) is calculated as r=

~ [(x -- )2)(y -- )5)]

IY. (x- ~),2Y~(y-;)~l "~

(2)

Vol. 139, 1992


297

Table 1 The data sets o f the three seismic regions Sismchil, Sismmex and Sismkam are the energy released in Chile, in Mexico and in Kamchatka, respectively. The calculated seismic energy was reduced in 1021 erg. Nos. I and 87 in the row corresponding to 1899 and 1985

row

Chile sismchiI

Mexico sismmex

Kamchatka sismkam

1 2 3 4 5 6 7 8 9 10 l1 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 25 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44

109.6 3.7 3.8 3.7 56.0 3.7 3.7 2167.0 3.7 3.7 152.7 40.5 40.6 3.7 3.7 109.6 3.7 109.6 3.7 262.4 97.0 56.5 3.7 1625.6 3.7 3.7 29.0 20.9 69.6 575.4 109.6 3.7 40.8 l 1.7 81.4 63.0 4.0 48.3 7.9 15.7 375.2 104.8 3.7 35.9

522.7 491.7 152.7 1269.6 842.2 0.2 0.2 02 685.0 296.4 78.7 0.2 291.5 20.9 219.3 219.3 29,1 29.1 130s 0.2 0.2 0.2 109.6 0.2 0.2 0.2 62,7 0.2 0.2 658.5 41.7 0.2 327.6 1455.4 15.7 57.7 93,7 20.9 185.1 15.7 19.4 7.7 233.7 440.4

413.0 4.7 413.0 29.1 4.7 1511.1 152.7 20.9 119.2 29.1 4.7 4.7 152.8 4.7 20.9 4.7 728,2 4.7 296.5 1329.6 4.7 50.0 4.7 120.4 1693.5 154.8 77.4 4.7 77.4 4.7212.8 29.1 23.7 8.0 52.3 37.7 4.7 122.6 117.6 15.0 11.9 7.7 28.6 89.5

row

Chile sismchil

Mexico sismmex

Kamchatka sismkam

45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 6t 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87

509.6 44.5 29.1 36.8 3.7 3,7 538.6 590,4 10.7 4.0 112.9 29.8 34.8 49.7 320.2 18,0 127.0 3.7 38.5 98.8 21.0 12.1 58.6 221.7 79.2 4.2 3.7 47.2 ! 140.9 12,6 11.8 61.6 47.7 163.7 181.3 62.3 14.9 17.0 47.0 8.0 74.0 28.0 359.2

149.9 39.9 26.5 83,0 20.9 79.5 41.7 109.4 34.1 7.7 36.7 50.0 88.3 26.5 127.7 7.7 33.5 2.8 7.3 30.1 7.0 87.8 178.6 3.6 0.2 46.4 4.3 35.9 4.6 9.0 144.8 1.0 8.5 10,0 0.4 61.4 82.6 57.0 61.6 8.8 62.3 8.2 1335.4

7,7 40.6 48.3 75.9 56.3 7.7 10.7 4.7 40,6 1116.8 170.7 50.2 119.8 191.9 33.8 4.7 287.2 61.6 26.9 23.5 950.6 67.7 45.3 13.5 16.3 12.2 54.3 141.2 179,9 38.8 57.4 82.8 15.6 47.3 22.8 770,3 4.7 30.6 36.6 72.6 72.4 119.2 23.7

298

Theodoros M, Tsapanos and Ioannis Liritzis Table 1

Sample size Avrg. Median Vrac. S.D. S.E.

PAGEOPH,

(Contd)

Chile

Mexico

Kamchatka

87 178.1 40.5 254081 504.06 54.04

87 140.8 35.9 79360.7 281.71 30.20

87 223.3 45.3 493869 702.76 75.35

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Figure 1 The annual energy release (erg/yr) in the three examined seismic regions. Single lines represent the energy released in Kamchatka, while broken lines and dot lines show the energy released in Chile and in Mexico, respectively.

299


Vol. 139, 1992

Table 2

The estimated cross-correlation between Chile and Mexico Lag

r

Lag

r

Lag

r

Lag

r

--24 --20 16 12 -8 --4 0 4 8 12 16 20 24

--0.09217 0.07197 --0.06543 --0.04679 -0.02736 0.10716 -0.06622 --0.00879 -0.02253 -0.07425 -0.06512 -0.01443 -0.07369

--23 - 19 - 15 -- 11 -7 -3 1 5 9 13 17 21

0.00487 0.08153 0.04261 0.03895 0.07071 0.06687 --0.00496 0.00851 -0.02500 -0.02220 -0.08928 -0.04932

-22 - 18 -14 - 10 --6 --2 2 6 10 14 18 22

-0.01017 0.11088 --0.01800 -0.07543 0.00519 -0.09934 --0.04463 --0.01557 0.12461 0.08202 --0.05120 0.04528

-21 - 17 - 13 -9 -5 --i 3 "7 11 15 19 23

--0.02107 0.01348 -0.08907 -0.05326 -0.05969 --0.06570 --0.06029 -0.04507 -0.07122 -0.02341 0.00322 --0.03039

-

-

-

-

where x, y are the annual energy release data of the two time-series; ~, 37 their respective averages. In order to determine the significance of the obtained correlation coefficient, a test is required which will indicate if (r) is large enough to be considered significant. Three such tests were employed: a) The T-statistic distribution which is given by

/(_N_u_2)

t

(3)

rx/( 1 - r 2)

has a t-distribution (almost normal) with v = N - 2 degrees of freedom and it Table 3

The estimated cross-correlation between Chile and Kamchatka Lag

r

Lag

r

Lag

r

Lag

r

-24 -20 --16 --12 -8 -4 0 4 8 12 16 20 24

--0.02016 -0.04514 --0.04492 --0.06115 0.13060 0.02516 -0.06447 -0.06623 0.03307 0.02712 --0.05840 -0.04609 --0.01303

--23 --19 --15 - 11 -7 -3 1 5 9 13 I7 21

-0.03828 -0.00879 --0.05657 --0.06282 0.01560 -0.07165 0.08071 -0.03436 0.10807 --0.04120 0.03969 -0.05657

--22 - 18 --14 - 10 --6 --2 2 6 10 14 18 22

--0.06956 0.04027 -0.04627 -0.04744 -0.08451 0.75074 --0.04121 -0.06896 -0.06418 -0.03933 0.04061 -0.06043

-21 - 17 --13 -9 --5 - 1 3 7 I1 15 19 23

-0.04160 -0.06190 0.16627 --0.06427 0.01106 -0.01235 0.05914 --0.03619 -0.04362 0.02118 0.00385 --0.04989

300


PAGEOPH,

Table 4

The estimatedcross-correlation betweenKamchatka and Mexico Lag

r

Lag

r

Lag

r

Lag

r

-24 -20 16 - 12 -8 -4 0 4 8 12 16 20 24

0.00958 -0.04280 -0.06529 -0.04907 -0.03674 -0.04916 -0.10956 -0.00373 -0.02229 -0.01808 0.23101 0.09022 0.02623

-23 - 19 - 15 - 11 -7 -3 1 5 9 13 17 21

-0.04352 -0.03652 -0.00273 -0.07147 0.05653 0.00202 0.03820 -0.01629 -0.04058 -0.03335 0.00458 0.15235

-22 - 18 - 14 -10 -6 -2 2 6 10 14 18 22

0.00184 -0.05917 0.06079 0.01975 -0.04269 -0.06775 0.04702 -0.06858 0.00602 -0.05898 -0.05576 -0.04376

-21 -17 - 13 -9 -5 -1 3 7 I1 15 19 23

-0.03237 -0.00391 -0.00854 0.07710 -0.01251 -0.05888 -0.05714 -0.06773 -0.03157 0.09179 -0.05974 -0.00531

-

examines w h e t h e r the c o m p u t e d (r) is large e n o u g h to be c o n s i d e r e d significant c o m p u t e d to zero. I f t > t(critical), the r is significant. b) F i s h e r ' s t r a n s f o r m a t i o n . This examines w h e t h e r the (r) o f a s a m p l e p o p u l a tion is significantly different f r o m some stated h y p o t h e s i z e d value (e.g., zero) o f p, the c o r r e l a t i o n coefficient o f the p o p u l a t i o n . The c a l c u l a t e d Z - v a l u e is given b y Z - ( Z , - Zp)

(4)

( U - 3)

a n d is c o m p a r e d with Z = 1.96, the 9 5 % two-tail critical value, where Zr = 1 / 2 1 n ( l + r ) / ( 1 - r ) a n d Z o = l / 2 1 n ( l + p ) / ( 1 - p ) . I f Z is outside the range ( - 1.96, + 1.96) then (r) is significantly different f r o m 0 = r (DAVIS, 1973). c) P r o b a b i l i t y P(r, N), where a r a n d o m s a m p l e o f N o b s e r v a t i o n s will yield a c o r r e l a t i o n coefficient (r) for those two sets greater t h a n the c o m p u t e d linear c o r r e l a t i o n coefficient (r) in terms o f a percentage.

Comparison Between the Seismic Regions (a) Results of Comparisons F r o m the a b o v e b r i e f i n t r o d u c t i o n o f the terms used, the following r e m a r k s are drawn. i) Chile-Mexico: T h e highest (r) is 0.124 for a n u m b e r o f o b s e r v a t i o n s N = 77 a n d the time-lag is equal to 10 years. A c c o r d i n g to the precedent, it is t = 1.078 < t(critical) - - 1 . 6 7 a n d Z = 0.125 < Zcnt(at 5 % ) = 1.96, which indicates t h a t r is n o t

Vol. 139, 1992

Time-lag of Earthquake

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~ ime- lag(y~ars) Figure 2 Estimated cross-correlation between Chile and Mexico.

significant. P(r, N) is about 60% or insignificant too, implying that the two seismic records taken from a parent population are uncorrelated. Therefore, all above tests confirm that Chile and Mexico seismic regions are not well correlated. ii) Chile-Kamchatka: The highest (r) is 0.750 for N = 85 and the calculated time-lag is - 2 years, i.e., K a m c h a t k a precedes Chile. It is t = 10.33 > t(critical) = 3.40 or r is significant at 99.9% level. Also, Z = 8.78 > Z m t = 3.09 or r is significant at the 99.8% level and P(r, N) = 99.9% all, indicating a highly significant correlation between their annual seismic energy releases, K a m c h a t k a preceding by 2 years.

302

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cross-correlation

3

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Chile

and

Kamchatka.

iii) M e x i c o - K a m c h a t k a : The highest (r) is 0.231 for N = 71 and the time-lag is equal to 16 years, Mexico preceding. It is t = 1.97 < t(critical) = 1.99, Z = 0.235 < Zcrit = 1.96 at the 5% level and P ( r , N ) = 95%, all converging to the weak significance of this correlation. As the three seismic data sets are samples of a common parent source, the global seismic energy release, a test to examine whether indeed these seismic records derive from the same parent distribution was applied. The K o l m o g o r o v Smirnov two-sample test provided an estimated overall m a x i m u m distance ( D N ) between the cumulative distribution functions of the two records and an approximate significance level (ASL) (see Table 5). In all cases D N was not large and

Vol. 139, I992


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Iime-lag(years)

Figure 4 Estimated cross-correlation between Mexico and Kamchatka.

Table 5 The Kolmogorov-Smirnov two-sample test between Chile and Kamchatka, Chile and Mexico, Kamchatka and Mexico

Estimated overall statistics (DN) Approximate significance level (ASL)

ChileKamchatka

ChileMexico

KamchatkaMexico

0.247 0.011

0.207 0.048

0.229 0.020

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ASL < 0.05 which implied that these seismic distributions were similar at a 95% level.

Co) Discussion of Statistical Evaluation However, particular attention must be devoted to cases where correlated curves exhibit one or a few outstanding maxima, which may have important consequences for the values of the correlation coefficients (e.g., the two very large earthquakes in 1958 and 1960). Although one may dismiss such results in the belief that one or a few single events, even if large, are not statistically significant or~may bias the obtained statistics, we consider this conclusion incorrect, as such large peaks do represent large magnitude events whose weights correspond to the released wave energies. And, even more important, they are not isolated events but preceded by many years of strain energy accumulation. Such developments cannot be disregarded as insignificant, neither statistically nor physically. Therefore, the statistically significant correlations are truly significant. But we must remember that correlations measure the degree of parallelism between two curves and that this measure is taken in relation to their respective averages. In our cases, this means that the significance refers to the overall shapes of the curves correlated, but not to details in the curves. In other words, the significant correlations refer to scales of certain extensions along the horizontal axis (time) or the vertical axis (energy, etc.), with a certain lag between two regions, whereas minor features along the two axes may not correlate significantly. Removing the two high results of 3739.9 for Chile and 5974.2 for Kamchatka and replacing them with the minimum value of missing years of 3.7 and 4.67 respectively, the significant correlation with time-lag 2 years is still present. However, we would need to see such correlation studies for more time-series of corresponding lengths to be convinced about their physical significance. The problem is not only that required observation series are not available, but also that such a procedure may be inconclusive. The global tectonics is probably more complex than merely to present the same correlation between two areas for any period of time. We must consider that all other areas of the earth are also part of the tectonic development and may therefore interfere.

(c) Physical Significance of Correlation Studies As a general rule, once statistical significance is achieved, it is justified to seek physical interpretations. However, in the present case, caution is required considering the limitations of statistical significance as described above. We are only entitled to look for physical phenomena on a sufficiently large scale in time and energy. This inference conforms to our impression that it is rather the tectonics, acting over longer periods of time, that is correlated, rather than the momentary release in

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earthquakes. Lacking the availability of long time intervals, correlation studies of various regions in the globe are a worthy pursuit. Therefore, the significant correlations of (e.g., Greece-Kurile islands, Greece-world, continental GreeceGreek arc, Sweden-world, Sweden-Greece) demonstrated earlier (BATH, 1985; MAKROPOULOS and LiRrrZiS, 1985), may suggest that global tectonic relations are a reality. These could be the fractal results of global interactions of a mantle circulation system triggered by various external (planetary) influences (springblocks, see below). Even though the results, so far, are only minor contributions to a major problem, they seem to justify the undertaking of detailed and extensive investigations of the time-space relations of the global mosaic of tectonic plates. Once these relations have become more clarified a base is provided for the deduction of possible general rules for the tectonic behavior as well as of its physical background.

Discussion

An explanation of these statistical correlations can be given in terms of plate tectonics and continental drift rates. The coincidence of plate boundaries with belts of seismic activity has been confirmed, with the majority of earthquakes appearing along the ocean ridges, probably arising from shears across transform faults connecting a section of ridge (SYKES, 1967). The rates of divergence at ocean ridges are estimated reasonably reliably from the scale of the magnetic strips which flank them, in terms of the established time scale of geomagnetic field reversals. Figure 5 shows the three regions of interest and their correspondence to rigid plates that are in relative motion (STAcEY,1977). If the drift rates and direction of plates are to be related to the degree of interaction and their triggering mechanism for seismic energy release between two regions (from Figure 5), it seems that Kamchatka and Chile are interrelated excessively more than Kamchatka-Mexico, or Chile-Mexico, especially, considering their high drift rates of ~ 9 cm/yr and the stretching in opposite direction of Chile, with 9.1 cm/yr and 9.3 cm/yr. The plate motion towards Kamchatka may result in stress accumulation, which in two years is released as seismic energy, and it is an appropriate quantity to trigger seismic energy in Chile via a migration process. The weak significance found for Kamchatka-Mexico and no-correlation for Mexico-Chile, two close regions, imply that the interaction between seismic active regions does not necessarily depend upon their distance (time-space relationship) as much as on other dynamic parameters, e.g., prominent direction of seismic wave stress periodic transmission giving rise to a mechanism of sheer rip--not a pull apart one--which begins at Kamchatka epicenters and runs along the KamchatkaChile directions; that is, an exhibit of oscillations and especially migration of

Theodoros M. Tsapanos and loannis Liritzis

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120

150

180

-150

-120

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-90_

-60

3o

0

-60 Figure 5 Division of the earth's surface into limited number of rigid plates that are in relative motion. Lines of divergence (oceanic ridges) are marked with lines of dots. The lines of convergence are marked by arrow heads showing directions of motion of downgoing slabs. Arrows with numbers give motions of plates (in cm/yr) as estimated by MINSTERet al. (1974). The single lines mark transform faults of their extensions (after STACEY, 1977). CHI is Chile, M E X is Mexico and K A M is Kamchatka.

earthquake activity. P r o b a b l y the relative motions o f tectonic plates, considered as spring-blocks, f o r m a fractal, which, when viewed from a short time interval seems to exhibit a nonconvincing r e s u l t - - d u e to either chaotic behavior or a seemingly fortuitous significant correlation due to lack o f physical modeling and relevant arguments on its c a u s e - - b u t for a longer time-interval an order m a y emerge. F o r the latter mechanical analogue o f tectonic plates c o m m u n i c a t i n g via spring as a frictional surface in the f o r m o f h a r m o n i c oscillators (F = - k x ) , the Mexico-Chile spring is very stiff, having very large value for the force constant, kl, while for K a m c h a t k a - C h i l e the spring is compressed x < 0, F positive, k2 small. Further

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investigations of the mantle geology in this ridge and the surroundings, coupled with the drift rates of plates, may elucidate the obtained correlations. Extensions of similar investigations on a world-wide basis and to longer observational series could yield valuable information on the global space-time properties of the tectonic plate motions. For this purpose, the correlation studies offer a particularly useful, straightforward and unambiguous supplementary method. Besides increasing our knowledge of global tectonics, such studies could also aid earthquake prediction efforts from local or regional scales to a global scale as suggested by BM'H (1979).

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