A STATISTICAL REAPPRAISAL IN THE RELATIONSHIP BETWEEN GLOBAL AND GREEK SEISMIC ACTIVITY

A STATISTICAL REAPPRAISAL IN THE RELATIONSHIP BETWEEN

GLOBAL AND GREEK SEISMIC ACTIVITY

I. L IRITZIS ~ , D. D I A G O U R T A S 2 and C. M A K R O P O U L O S 2 t R esearch Center for Astronomy and Ap~lied Mathematics, Academy of Athens, 14

Anagnostopoulou Str., Athens 10673, Greece ; Department of Geophysics, University of Athens, Athens 15784, Greece

(Received 10 November 1994)

Abstract. For the period 1917-1987, Greek seismic activity exhibits a very significant positive correlation to the preceding global activity with a time-lag of 15 years. It seems that all Greece and the two characteristic areas in which we have separated it (Greece without Arc, and the area of the Greek seismic Arc), follow the global seismic activity but with a time-shift of 15 years. Moreover, it seems to exist an intrinsic interaction mechanism between the Greek seismic arc and the rest of Greece, which may be deduced by their different behavior exhibited when they are correlated with the global activity, as well as from the correlation between themselves, where a very significant positive correlation has been found with a time-lag of 3 years, for Greece without arc preceding. A quasi-periodic term of 30-yrs is also observed in these detailed four seismic time-series.

The cross-correlation analysis of seismic time-series, as shown, is served as a powerful tool to clarify the complicated space-time pattern of the world wide mosaic of tectonic plate motions. The implications of spring-block model of tectonic plates interaction is invoked, considering the earth's rotation rate changes as their triggering agent.

Particular emphasis is given to the potential of such studies in earthquake prediction efforts from local or regional scales to a global scale and vice-versa.

EaEWEAER

T

p

~rt

1. Notation

seismic wave energy (ergs) of Greece (G), world (W), Greek arc (A) and rest of Greece (R), respectively

correlation coefficient

probability of r being accidental

Earth's rotation rate.

2. Introduction

It has been demonstrated that the seismic activity of Sweden and Greece since 1928 is significantly correlated to the worldwide activity (Bath 1984a,b).

Greece, having the highest seismicity in Europe (Figure 1), should be closely related to the world activity because of its location at the front of the collision of Eurasian and African plates with a weil defined arcuated seismic active belt, the so called Hellenic Arc. (Figure 2) (Main and Burton, 1989; La Pichon and Angellier, 1981).

Greek seismicity and tectonics are complex but the interaction between hellenic trench rollback and back-arc spreading is now reasonably weil understood.

Earth, Moon and Planets 69- 69-86, 1995. @ 1995 Kluwer Academic Publishers. Printed in the Netherlands.

7 0 I. LIRITZIS ET AL,

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Fig. 1. Total Greek seimicity. Key to symbols refer to magnitude and focal depth.

THE RELATIONSHIP BETWEEN GLOBAL AND GREEK SEISMIC ACTIVITY 71

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Fig. 2. Hellenic arc seismicity. Key to symbols refer to magnitude and focal depth.

72 I. LIRITZIS ET AL.

Due to this particularly complex tectonic setting and the recent studies, a detailed correlation study of the Greek seismic activity gives reasonable tectonic rationale for splitting the catalogue into the activity of the Greek seismic arc and the activity of the rest of Greece. These two characteristic areas give a different earthquake pattern.

Therefore we have performed the correlation studies between these two Greek regions, the whole of Greece and the Globe as follows:

1) Between Global and whole Greek seismic activity 2) Between Global and Hellenic arc 3) Between Global and rest of Greece 4) Between arc and rest of Greece. The aim is to examine the existence of a possible space-time relationship

between these four active areas.

3. Observational Material

The seismic activity is expressed in terms of the annual energy release, being adequate dynamic parameter to correlate.

Therefore, our observational material consists of annual sums of seismic energy release. The energy values refer to the total release, except for possible contribution from the ultralong-period range, for which reliable statistics are not available. In other words, we are dealing with the energy of a restricted time interval.

As far as the global activity is concemed for the period 1917-1977 and from earthquakes with M > 7.0, the energies calculated by Bath (1984a,b) were used, whereas for the period 1978-1987, earthquake magnitudes listed on PDE and ISC catalogues were used. Thus the data set covers a period of 71 years. With this data set, we are concemed with activities that are relatively homogeneous on the large scale, thus avoiding any bias due to some increased activity in the beginning of the century (Abe and Noguchi, 1983).

The material for the Greek region is restricted to the area 33.0-42.5 °N and 19.0-29.0 °E. For the years prior to 1917 the data become increasingly unreliable. That is why the material referring to the period 1917-1928 can be accepted as relatively reliable after the revision of magnitudes by Makropoulos (1979) and by Makropoulos and Burton (1981) despite the reservations by Bath (1984b). The material for the Greek area is based on the catalogue by Makropoulos, Drakopoulos and Latoussakis (1989). We must mention that there is a partial overlap between Ew and EG for particular years of about 0.35%. The overlap therefore is insignificant and it is right to correlate the computed seismic energies.

The observational material is summarized in Table I.


4. Analytical Method and Discussion

4.1. STATISTICAL ANALYSIS

The statistical analysis is a follow up of the work initiated by Bath (1984a,b) and refers to the calculation of correlation coefficients between Ew, EG, EA and E~, not only for simultaneous seiles but also for time shifts from - 1 9 to +19 years. (cross-correlation method).

The time is extended so as to include the first significant extreme of the correlation coefficient. The statistical significant the correlations is investigated in each individual case, because the correlation coefficient depends on the amount of data used. The significance of the higher correlation coefficient was checked applying t-statistic distilbution, Fisher's transforrnation and the probability distribution for linear correlation coefficient P(r, N), as follows:

a) The t-statistic which is given by

/(;v- 2)

has a t-distribution (nearly normal) with u = N - 2 degrees of freedom and it examines whether the computed (r) is large enough to be considered significant compared to zero. If t > t (critical), the r is significant

b) Fisher's transformation. This examines whether the (r) of a sample population is significantly different from some stated hypothesized value (e.g., zero) of ~), the correlation coefficient of the population. The calculated Z-value is given by

Z r -- Z0

(x-3)

and it is compared with Zi from tables at higher than 95% two-tail critical values, where ZT = 1/2[ln(1 + r) / (1 - r)] and Z« = 1/2[ln(1 + 6)/(1 - L))].

If Zi is outside the range (-Zi, +Zi) then (r) is significantly different from r = ~ (Davis, 1973).

c) Probability P(r, N), where a random sample of N observations will yield a correlation coefficient (r) for those two sets greater than the computed linear correlation coefficient (r) in terms of a percentage.

The annual energy values may not always be the best representation of the seismic activity. Thus, Bath (1984a,b) performed also a computation for "totaled", that is, partially cumulative intervals of 2, 3, 4 and 5 consecutive years. In this study it is prererred to smooth the data using the "running means", by replacing every data value by the mean of an area around it. The size of this area determines the size of the desired smoothing. The "running means" is chosen because this method


TABLE I

Annual seismic energies in 1022 erg, for World (W), Greek (G), rest of Greece (R) and Hellenic arc (A) regions, 1917-1987

Year Ec Ew EA ER

1917 0.19 1 2 . 6 0.042 0.145

1918 0.22 6.1 0.147 0.070

1919 2.30 5.1 0.160 2.136

1920 0.21 7.6 0.131 0.078

1921 0.14 1.8 0.069 0.076

1922 2.15 3.0 1 . 9 5 1 0.204

1923 0.59 4.8 0.036 0.555

1924 0.03 3.7 0.007 0.022

1925 0.12 0.8 0.000 0.120

1926 10.21 3.0 0.210 10.001

1927 0.45 2.5 0.056 0.398

1928 7.72 3.6 0.000 7.717

1929 0.00 6.7 0.000 0.000

1930 0.64 0.4 0.169 0.472

1931 1.28 3.5 0.010 1.272

1932 3.38 3.5 0.059 3.325

1933 1.19 1 2 . 1 0.010 1.182

1934 0.26 4.2 0.020 0.241

1935 4.19 2.2 0.154 4.035

1936 0.01 1.0 0.014 0.001

1937 0.03 1.9 0.014 0.021

1938 0.27 12.0 0.107 0.161

1939 2.14 8.0 0.020 2.117

1940 0.13 3.3 0.130 0.001

1941 0.66 9.4 0.000 0.633

1942 0.48 10.0 0.090 0.393

1943 0.13 6.0 0.082 0.051

1944 2.37 3.0 0.051 2.324

1945 0.30 2.5 0.010 0.286

1946 0.14 5.6 0.121 0.014

1947 1.04 1.6 0.947 0.091

1948 6.21 3.3 6.042 0.167

1949 2.18 2.5 0.000 2.177 1950 0.01 11.0 0.007 0.000

1951 0.06 1.3 0.042 0.021

1952 0.70 7.3 0.638 0.064

1953 15.66 1.4 7.585 8.074

1954 0.87 0.5 0.010 0.859

1955 2.33 1.1 0.000 2.331 1956 12.17 1.2 0.010 12.157

1957 5.72 5.4 4.146 1.576

1958 0.48 7.1 0.433 0.051

1959 1.92 2.1 1 . 8 4 1 0.080


TABLE I

Continued.

Year E6 Ew ÆA ER

1960 0.41 2.5 0.070 0.335 1961 0.32 0.7 0 .025 0.293 1962 1.05 0.5 0.380 0.667 1963 0.37 2.0 0 .046 0.325 1964 2.27 3.8 0 .038 2.232 1965 1.47 2.2 0.140 1.331 1966 0.29 3.7 0 .104 0.187 1967 1.75 0.7 0 .028 1.723 1968 4.33 8.0 0 .141 4.186 1969 0.83 2.9 0 .286 0.543 1970 0.24 2.2 0 .069 0.173 1971 0.03 4.7 0 .010 0.015 1972 0.53 7.3 0 .383 0.148 1973 0.14 2.9 0 .138 0.000 1974 0.03 1.5 0.010 0.018 1975 0.95 2.3 0.050 0.904 1976 0.28 3.9 0 .276 0.000 1977 0.24 3.0 0.211 0.029 1978 0.38 2.3 0 .036 0.344 1979 2.02 3.4 1.972 0.048 1980 1.00 1.5 0 .569 0.431 t981 5.62 2.1 0 .063 5.557 1982 1.67 1.0 0 .046 1.624 1983 4.60 3.1 2 .461 2.139 1984 0.13 1.1 0 .103 0.027 1985 0.12 4.7 0.060 0.060 1986 0.16 3.4 0 .086 0.074 1987 0.06 4.3 0 .053 0.070

gives a better smoothing and also keeps the same number of data. The cumulative intervals, ("totaled" by Bath), reduced the number of data, reduce the inherent

resolution and the obtained correlation coefficients become less reliable.

It was found that the best representation our data is succeeded with "running

means" of 5 data points (terms). It is considered that the "running mean" of 5 terms

provides the best smoothing data that can be achieved for this study, without losing

the physical meaning of the correlation. With higher smoothing it is possible to

average out some significant changes of the annual energy and loose information that affects the correlation study.

76 1. LIRITZIS ET AL.

i. Correlation study between Global and Greek seismic activity ( Ew) Figure 3a shows the results of the cross correlation between (Ew - Ec) and Figure 3b shows the cross correlation when a 5-terms smoothing is applied. In both figures we can see clearly a very significant positive correlation that exists between the global and Greek activities with a time-lag of 15 years (At = ÷15), the global one preceding. In Figure 4a the correlation coefficient is r = 0.5 which is very significant, since the probability of being accidental is P < 0.001. It is • = 4.2 >

t(critical) = 2.70 at less than 1% level (t0.995) , and Z = 3.93 > Zcrit (at 0.2%) = 3.08. In Figure 4a there appears a tendency for negative, not significant, correlation coefficients around At = 0. This tendency is also seen in Figure 4b, but with a very significant correlation (r -- -0 .35 with/9 < 0.005); t = -2 .74 < t c r i t ---- -2 .70 (<1% level), and Z = -2 .67 < Zcrit = -2 .58 (<1% level).

It is noted that the correlation coefficients in this study are somewhat lower from those obtained by Bath, though more significant, due to the fact than Bath has used series of 50 data points, while we have used seiles of 71 data points.

It is important to consider the possibility that some outstanding maxima in the two series could give a false indication of a high correlation. This possibility has been investigated in all cases of high correlations, by comparing the trends of the shifted smoothed data that we correlate, so that a visual compailson can also be made. For example Figures 5 and 6 show the "running mean" of 5-terms curves of the seismic time-series of World and Greece, with a time shift of At = + 15 years and At = 0 (simultaneous), respectively. A similar time-shift has been found by Bath (1984a).

ii. Correlation study between Global and Hellenic Arc seismic activity (Ew- EA) Figure 3c shows the cross correlation of this study. Figure 3d shows the cross correlation of the smoothed data of 5-terms. In Figure 3c the higher and significant correlation exists again for the time-shift of 15 years, (r = 0.5, P < 0.001); t = 4.2 > tcrit = 2.70 (< 1% level), and Z = 3.93 > Zc~it = 3.08 (0.2% level) However, a difference with the previous study is noted here; there exists, also, another significant correlation coefficient for the time-shift of 7 years, (7" = 0.29, P < 0.02); T = 2.38 > tcrit -- 2.00 (< 1% level) (t0.975) , and Z = 2.26 > Zcrit - -

1.96 (5% level). In the smoothed data of Figure 3d, there appear two very significant negative

correlation coefficients, for time-shifts of - 6 and - 7 years, (r = -0 .33 for both and P < 0.01); t = -2 .75 < tcrit = -2 .66 (0.5% level), and Z = -2 .66 < Zcrit = - 2 . 5 8 ( 1 % , level). In this figure the higher positive correlation is now for a time-shift of 11 years, which is a very good example of the effect of smoothing masking the real correlation coefficients. The change of this higher correlation is due to another significant coefficient which appears in Figure 3c for time-shirt of +7 years. Therefore, it seems that this smoothing helped to reveal the very significant


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Fig. 3. Cross-correlations between World-Greece of unsmoothed (a) and 5-terms smoothed (b) data, and between World-Arc of unsmoothed (c) and smoothed with 5-terms data (d). Black columns indicate high significance with probability P of being accidental P < 0.05.

corre lat ion coef f i c i ents for t ime-sh i f t s - 6 and - 7 years, but apparently m a s k s the t w o p o s i t i v e s ignif icant coef f ic ients o f Figure 3c.


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Fig. 4. Cross-correlations between World-rest of unsmoothed (a) and 5-terms smoothed (b) data, and between Arc-rest of Greece of unsmoothed (c) and 5-terms smoothed (d) data. Black columns indicate high significance with probability P of being accidental P < 0.05.

iii. Correlation study between Global and rest of Greece seismic activity

(Ew - E~) The results of this correlation study can be seen in Figures 4a and 4b. Figure 4a shows a very significant correlation coefficient for time-shifl of +15 years, (r =

8

THE RELATIONSHIP BETWEEN GLOBAL AND GREEK SE1SMIC ACTIVITY

19t7 T~

E~ t4

T t2

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5-

4-

3

2

ergs 10 22

EW

ergs 10 ~~

-8

6

4

932 t~42 IS52 t~2 1972 t ~ Y~A~s T E

Fig. 5. Comparison between World and Greek annual seismic energy release of smoothed data and with A~ _--. 15 years, World being kept constant.

E~ 7" 8 t4

S. -- GREECEI /I

' WORLD

i t

E,,,

S .

t

2 -4

i~i7 Isi7 ' Is37 ' Is47 is~ ' Is~7 ' is~ ' isi7 "I"EA R..S

Fig. 6. Comparison between World and Greek annual seismic energy release of smoothed data, without any shift A t = O, where the anticorrelation is noticeable.

8 0 I. LIRITZIS ET AL.

0.35, P < 0.01); t = 2.74 > tcrit = 2.69 (0.5% level), and Z = 2.62 > Zcrit = 2.58 (<1% level). Figure 4b, with the smoothed data, indicates the appearance of a very significant negative correlation (r = -0.30, P < 0.01); t = -2 .6 < tcrit = -2 .38 (<1% level), and Z = -2 .47 < Zcri t • -1 .96 (~2% level). The importance of these coefficients has been verified in the discussion section below.

iv. Correlation study between Hellenic Arc and rest of Greece Seismic activity (ÆA - ER) This last correlation study is of great interest for the Greek region, (Figure 4c and 4d). Figure 4c illustrates a very significant correlation coefficient for time- shift +3 years, (r = 0.30, P < 0.01); t = 2.55 > tcrit = 2.39 (1% level), and Z = 2.4 > Zcrit = 1.96 (2% level). One should mention that in Figure 4d, with the smoothed data, this correlation is stronger with r = 0.41 and P < 0.001; t = 3.65 > tcri t = 2.66 (< 1% level), and Z = 3.47 > Zcrit = 3.08 (0.2% level). In this figure, one can also see another significant correlation for At = 0 with r = 0.35 and P < 0.005; t = 3.1 > tcrit = 2.66 (<1% level), and Z = 2.8 > Zcrit = 2.58 (<1% level). There is also an anticorrelation for a time shift of - 9 years with r = -0 .35 and P < 0.005; t = -2 .90 < tcrit = -2 .66 (0.5% Ievel), and Z = -2 .8 < Zcrit = -2 .58 (<1% level).

The correlation for At = 0 years implies a strong simultaneous relationship between the seismic activity of the Hellenic arc and rest of Greece. The correlation for At = +3 years (arc leading) indicates that the Hellenic arc has its own mechanism for earthquake occurrence.

From the above we could suggest that the arc seismic energy release activates the rest of Greece and could trigger earthquakes after a time period of three years. All these obtained high correlations have been verified by comparing the curves or the smoothed data with the appropriate time-shift.

Figure 7 shows that in every peak of the time series of the Arc there is also both, a simultaneous peak of the time series of Rest of Greece (this verifies the real existence of the simultaneous high correlation), and another peak with a lag of about 3 years (this verifies the high correlation, for At = +3 years).

5. Earth's Rotation Rate as Triggering Agent to Global Seismicity

In our attempt to further clarify the complicated space-to-time pattern of the worldwide mosaic of tectonic plate motions with regional seismic pattems, the earth's rate of rotation variation over the past two centuries was considered.

Figure 8 shows the work for rate of rotation by Morrison (1979) and Brouwer (1952) and Guinot (1977) together.

There seems to exist a correlation between the world increased seismic activity tum-points and the fairly sharp minima in the earth's rotation rate ~~ (1907, 1940,


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Fig. 7. Comparison between Arc-rest of Greece annual seismic energy release of 5-terms smoothed data, where we notice the triggering of arc on the rest of Greek area for At = 0 and A t ---- 3 years,

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TABLE Il

Earth's rotation rate data; angular velocity (w~), kinetic energy (Ekin), angular accel- eration (7) and rate of change in seconds (AT), for different time intervals.

Time Aw~ AE~n A T 3' A T (X 10-12 rad/sec) (erg) (s) (rad/sec 2) (years)

1830-55 1.1 4.3 × 102o 0.001 0.14 x 102o 25

1870-1905 6.5 1.5 × 10 22 0.008 0.6 X 10 .22 35 1940-70 2.0 1.4 × 1021 0.0024 0.2 × 102o 30

1970). These minima are followed by increase of the earth's rotation rate of the order of 2-3 × 10 .22 rad/sec which occur over approximately 15 to 30 years.

Such sudden impulses in the earth's rate of rotation may be interpreted as triggering mechanisms of increased global seismic activity.

In fact such change may act as a sudden applied torque in the mantle, that causes a change in the kinetic energy, AEki n. Table II gives various physical parameters regarding Earth's rotation. Thus, for moment of inertia of the mantle In = 7.2 × 1037 kg.m 2 and Aa;~ = 6.5 × 10 -22 rad/sec, the larger observed for 1870-1905, the/kEki n = 1.5 × 1022 erg. In particular, we may note that, the magnitude of such a kinetic energy is of the same order of the annual seismic energy release of regional interest, e.g. for Greece, Japan, Sweden.

6. Discussion

The above four correlation studies yield the following comments. a) The Global energy release activates Greece with a time-shift of 15 years.

This agrees with Bath's (1984b) results although he used a less detailed approach. This agreement is due to the fact that the existence of such a correlation is strongly supported by the data. The simultaneous anticorrelation between Global and Greek seismic activity indicates that when the Global energy release is maximum the Greek one is minimum.

b) Global energy release also activates both Rest of Greece and the Arc with the same time shift of 15 years.

c) There is an intemal interaction mechanism between the Hellenic Arc and Rest of Greece. This can be seen very cleafly in the correlation study between Arc and Rest of Greece, since apart from the expecting simultaneous relationship, there is also a very significant positive correlation for time lag +3 years. Thus, within the limits the uncertainties involved and the limited number of data available, this indicates that the Rest of Greece may be seismically activated after about three years from the activation of the Hellenic Arc.


One possible explanation for this correlation is the mechanism oftrench rollback (Le Pichon and Angellier, 1981) where back-arc spreading is caused (and hence must be preceded) by the moving of the hellenic trench followed by the resulting gravitational stretching of the lithosphere in the back-arc. The time lag of 3 years could be the time constant consistent with stress diffusion over these distances.

d) The importance of all the above correlation studies with the present time seiles of 71 years is reenhanced considering also the apparently obtained periodicity (3, 4.5, 6.5, 8-9, 14-20 and 31-34 years) in the release of the seismic energy (Liritzis and Tsapanos, 1992a; Xanthakis, 1982). The time distance between a positive peak and the successive negative one of a cross correlation is a good indication of a quasi-periodic term for this time-series. This quasiperiod of about 15 years, is seen in the histograms of Figures 3 and 4. Therefore, we are dealing with a period of about 30 years. This hypothesis is furthermore reenhanced by the shape of the four time-series of Figure 9. Here the peak-to-peak distance in all time-series of about 30 years is noted. However, it should be mentioned that our data set is not long enough to clearly visualize this periodicity, because we have only two large seismic energy peaks in the world time-series and three in the Greek time-series. Nevertheless, the high significance of the correlation coefficients and the existence of a period of 30 years, which has, also, been found in spectrum analysis of global seismic energy release, provides a very strong indication of a (quasi) periodic variation in the world and Greek annual seismic energy release.

e) There seems that the drastic changes in ~~ during short time intervals correspond to an increased seismic activity. This implies an anticipated increased seismic activity follow up since 1975, should the a~~ continue increasing, which is so far the case.

The latter observation is commensurable also, with the expected 15-years and 30-years recurrence of seismic energy release, any time, within the coming decade.

f) Clearly, the resultant seismic energy release curve consists of several laged (quasi-) periodic components, which depend upon many triggering parameters, thus attaching to the seismic trend a seemingly chaotic behavior.

The implications of spring-blocks model of tectonic plare interaction can, once more, be revisited and framed within the global plate tectonic dynamics (Tsapanos and Liritzis, 1992b).

g) The cross-correlation function even for two ideally-correlated seiles has the form of a sine function [sin(z)/z] of finite width, rather than an ideal spike, due to the finite length of the catalogue and the discrete nature of the data. The size of the first lobe of the sine function in this work is then equivalent to the resolution limit in the time domain, as applied for example in the spatial domain in optical interferometry. In the present work the width of the first lobe which establishes the significant positive correlation on the smoothed data appears to be ±3 years for a catalogue length of 70 years, which seems not unreasonable. Thus, the 3-year


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i / ~ : i i ! ! , , i l ~ ) i ! i :

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: / : i • k . / ' ~ ; - J \ ~ f ............. ~~.......: ........................ ~..:&.......~ ............ ~.........«. ............

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i ~ i ' ! ! ' : « . . . . . . . . . . . . . . . . . . . . . . . . . . . ; . . . . . . . . . . . . . « . . . . . . . . . . . . . . . . ! . . . . . . . . . . . . . . ; . . . . . . . . . . . . . ~ . . . . . . . . . . . . . . . . : . . . . . . . . . . . . . .

, ù . ù ~ . , ù , i , , ~ , . ; , , ù , ~ ,

L~~.S I~2S ~,-~0~ 1~laS ~.g55 1 9 a 5 ~.~'75 ! ~ e ~ ~995

Timm,(~Im¢~)

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,~: ............. ~,...',d ............... :J.....:.-L...;,-.......:.../..f, ............... :..

r / k l , : ~ ~ ~ J L , ' i : . ~ :

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.oa .

Z

ù - ; " " " :~ : . . . . . . . . . . . . . . . . " x ' : "< . . . . . . . . . . . . . . . . . . . . . . . . . . . . . :,.1 . . . . . . . . . . . . . i'-

....... ~ .............. ~ ............. ~ ............ !~ ............. i ............. ! ............. ~ ............. i- i • i i ~ i t ! ~ i l ~ . . . . . .

. . " .............. :. . . . . . . . . . . . . . . :, ........... ;...... l : : : . I ............. ; .............. : .............................. ; , - ]

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I : : i ': Il i i ; i 1

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i L I '. ~ | i ~ . ] / • J : : ;

r ......... ~ ..... tx: ............... ~-.~ ................. ,~ ........... : - ~ : ............... 7

[ ~!!!( ' l / , , ' i / t • ......... I ........ ~, !.!. .i

CSZ5 ~s25 ¢9=S ¢9<~ XSSS ¢S65 ¢9T5 1~e6 19s5

T¢m~,(~aar~j TLma,(~$ar«)

Fig . 9. Annual seismic energies of 5-years smoothed data for World, Greece, Arc and rest of Greece. Notice the 30-years recurrency of respective p e a k s .

t ime- l ag o f the back-arc se i smic i ty , t h o u g h interest ing, is o n l y just o n the bounds o f the reso lu t ion o f the m e t h o d , at least unti l m o r e data b e c o m e avai lable .

Re lated to this c o m m e n t is the fact that the apparent "negat ive correlat ions", a l luded to in the text, at different t ime- lags , m a y s i m p l y represent the higher- order l odes o f a p o s i t i ve corre lat ion (w here s i n e ( x ) < 0), and cannot , therefore be interpreted w i t h o u t further statist ical tests as nega t ive corre lat ions in their o w n right.


The individual spikes in the unsmoothed data set seems to reflect statistical noise in the raw data due to fluctuations introduced by individual events, since these fluctuations die out into the expected sine function as the data is smoothed.

As a result, we attach significance to the values of (r) in the smoothed data set, though a comparison of smoothed/unsmoothed correlations is still useful.

7. Conclusion

In the present work the global seismic energy release activates Greece, as well as the Arc and rest (whole of Greece without arc) with a time-shift of 15 years, while there has been found an intemal interaction mechanism between Hellenic arc and the rest of Greece, with a simultaneous and a three year lag relationship.

Furthermore, calculations have shown that the drastic changes in earth's rotation rate (a:~) cause changes in kinetic energy of the same order of annual seismic energy release of regional interest.

From the abovementioned it becomes clear that the cross-correlation method of analysis extended both in space and time, and to longer and approximately chosen observational seiles, yields valuable information on the global space-time properties of the tectonic plate motions. That is, if the world annual energy release is kept as a standard parameter to correlate, the obtained cross correlations between characteristic areas will provide a world space-time pattem of seismic energy release migration.

Such simple statistical techniques, albeit competent, enhance our knowledge about global tectonics yielding useful results which i) clarify the space-to-time pattem of the regional seismic activity, ii) lead to consider certain factors e.g the earth's rotation rate or devise models, as possible triggering agents to ear~hquake occurrence and iii) aid earthquake prediction.

Acknowledgements

We thank Dr. K. Makropoulos for supplying the earthquake data and Prof. Bath for constructive comments.

This is an extended and updated version of the abstract presented to the 1992 EGS conference in Edinburgh.

References

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A STATISTICAL REAPPRAISAL IN THE RELATIONSHIP BETWEEN GLOBAL AND GREEK SEISMIC ACTIVITY

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