Vol. 9 No. 3 429---438 A C T A SEISMOLOGICA SINICA A u g . , 1996

The relat ionships between earthquakes and po- sitions of the sun and moon ( 1I ) ~ S o m e temporal characteristics of the aftershock sequences of strong earthquakes"

WE1 G A O ~ ) ( ~ ~ ) Pu-XIONG L I U ~ ) ( ~ J ' ~ ) SHAO-XIE XUZ)(j.~]:~), =~ XIAO-JIAN LUl l ( ~xl ~ , ~ ) KE-YIN P E N G ~ ( ~ . ~ ) and

1) Center for Analysis and Prediction, State Seismological Bureau, Beijing 100036, China

2) Institute o f Geophysics, State Seismological Bureau, Bei jing 100081, China

Abstract

This paper deals with the distributive characteristics of the occurrence time of earthquakes with respect to the af- tershock sequences of strong earthquakes. The distribution of lunar and solar local hour angles at the time of commencement of moderate and strong aftershocks indicates that the time of commencement of moderate and strong aftershocks is modulated by the positions of the sun and moon and then the earthquake-restrained time zones exists also. In this paper the differences of earthquake-restrained time zones between the preshock se- quences and the aftershock sequences are compared, and the possible mechanism is analyzed preliminarily. And the possible maximum scope of accuracy in predicting the occurrence time of an earthquake is determined as well.

Key words:moderate and strong aftershock, occurrence time, local hour angle, earthquake-restrained time zone, time prediction.

Introduction

From experiences we know, when a large earthquake is occurring, the medium in its source

region will rupture at a large scale in a very short time with the appearance of vast amount of fis-

sures, and the temperature of the medium might be increased because part of the strain energy

has been conversed into thermal energy and at the same time great amount of fluid migration

might be accompanied as well. These macromutations will change the geometric shape, the phys-

ical properties and the mechanical states of the medium in source region in various degrees. And it will be accompanied by a great deal of aftershocks and the readjustment of stress fields, making it reach a new dynamical balance.

The readjusting process is mainly reflected on three aspects(Lu et al. , 1985~ Wu et al. ,

1990) • (1) the local characteristics of aftershocks in the spatial distribution. (2) the fast attenu-

ation characteristics of atershocks in the temporal distribution. (3) the comparative complexity of

attenuation in the intensity. By studying the spatial-temporal active patterns of aftershock se-

quences of strong earthquakes, we can obtain important information about the evolutionary pro-

* Received October 8, 1994~ revised June 12, 1995~ accepted June 12, 1995.

430 ACTA SEISMOLOGICA SINICA Vol. 9

eess of stress-strain state of the medium, the variation of the medium geometric shapes in the source area, and the variation of constitutive relation. Researches and understanding on different types of earthquake sequences are helpful to the understanding of physical mechanism and causes of earthquakes as well as to the better judgement of time parameters on the occurrence of strong

aftershocks in the future. The most prominent feature of the time distribution of aftershocks is Ohmori-Utsu formula

i .e . N ( t ) = K / ( t + c ) e, which demonstrates that the frequence of aftershock decays with time exponential damping. But any useful information about strong aftershocks is not shown while the strain release curves can well reflect the characteristics of the moderate and strong aftershock se- quences. According to statistics the early shapes of strain release of the earthquake sequences of the mainshock-aftershock pattern are in linear relationship with lgt, i.e. the speed of release and adjustment of strain of the medium in the source region is very fast. The above-mentioned expe- rience totally reflects some kinetic characteristics making the source region recover, readjust to be in balance with the enviroment after the sudden changes of the geometric shapes and mechanical states of the medium when a strong earthquake occurs, whose rate of recovery and readjustment is in direct proportion to 1/t v. In the process of fast readjustment, it is a useful attempt to under- stand the process of seismic focus and to predict the occurrence time of strong aftershocks by knowing whether the extraneous actions, especially those changing periodically, playa role of modulation in the readjusting process if the role of modulation can be observed and its mechanism

can be found out.

1 Methods and results of data statistics

As far as the present level of understanding on the causes and mechanism of earthquakes, the research methods on earthquake sequence chiefly depend on statistical methods, which re- quires the features and numbers of research samples should meet certain condition. Through the study (Gao et al. , 1995) we found that there existed a so-called earthquake-restrained time zone because the occurrence time of earthquakes above a certain scale in the future seismogenic zones of strong earthquakes is modulated by the lunar and solar local hour angles. The process of after- shock is different from the foreshock one, reflected mainly on two aspects: intensity and time. Taking the figure of M - t of the moderate and strong aftershock sequences of the earthquakes in Tangshan and Haicheng as examples(Figure 1), we know that the parallel processes of condensa- tion and rarefaction exist on three different temporal scales. In the process of comparatively fast decay, we try to find whether the phenomenon of modulation still exists in the aftershock se- quence, i.e. whether the earthquake-restrained time zone exists in aftershock sequences. In this paper we will investigate the aftershock sequences of earthquakes in Xingtai, Tonghai, Haicheng and Tangshan, the principal situations of the aftershock sequences investigated are listed in

Table 1.

Table 1 The data of the aftershoek sequences studied in this paper

Name Time interval Epicenter range Lower limit

Xingtai 1966-03-08~1992-12-31 Aftershock coverage 5.0

Tonghai 1970-01-05~1992-12-31 Aftershock coverage 4.5

Haicheng 1975-02-04 ~ 1992-12-31 Aftershock coverage 4. 5

Tangshan 1976-07.-28~1992-12-31 Aftershock coverage 5.0

Geneally speaking, earthquakes occurred at different time correspond to different lunar and

No. 3 G A O , W . eta/. : T H E E A R T H Q U A K E S A N D P O S I T I O N S O F T H E S U N A N D M O O N 431

7 i/i) ll i 3

1 28

1976-07

1 07

I976

5

3

1 ~ 1976 1980

(a)

29 30 31 06 t/d

( b )

08 09 1 0 t/mo

(c )

, ,], 198-I

t / a

7

5

3

04

ll, l 12

) 1 I1 02

I J 1992

E I 1988

IItlIB 05

1975-02 t/d

(e)

II tl,ll, 04 06

1975

(f)

197 1978 lqSI t / a

! 08 10

?'too

1 1 I I I It'S4 1987

I 07

12

II 1090

Figure 1 The M-t pattern of moderate and strong aftershock sequences of Tangshan earthquake ML~5. 0 (a ,b ,c ) and Haicheng earthquakeML~4. 5 (d,e d ) .

solar local hour angles. In the light of the occurrence time of earthquake we can calculate the lu- nar and solar local hour angles in correspondence with the moment. Thus, from the astronomical fomula, the local hour angles of Hs and Hm which the sun and the moon correspond to the ones in seismic focus can be obtained:

/ H m = 15*(t0 -- 12) + h -k L -- am ( 1 )

[ H . ----- 15*(t0 - - 12) -1- h -q- L - - a.

Where h is the mean longitude of the ecliptic, L is the longitude of seismic focus, a, and am are the right ascensions of the sun and the moon, to is the Greenwich Mean Time (GMT) at which the earthquake occurs.

In the process of comparatively fast decay, the distribution of the lunar and solar local hour angles at the time of commencement of the moderate and strong aftershocks in Tangshan, Xing- tain, Haicheng, and Tonghai is shown in Figure 2. From which we find that the distribution of the solar local hour angles at the occurrence time of earthquake is of significant distinction and statistics. To earthquakes in Tangshan, the solar local hour angles at the occurrence time of earthquake are primarily within the time zones of 0 6 ~ 1 2 and 1 8 ~ 2 4 local time, in which dis- tribute uniformly, while the prominent blank time interval of the distribution of the lunar local hour angles is in the time zone of 11 ~ 17 local time, i.e. the earthquake-restrained time zones of the sun are 0 0 ~ 0 6 and 12"--18 local time, and the moon is 11"-'17 local time. The data used here ranges from the occurrence of the earthquake ML7. 2 on July 28 , 1976 to the end of 1992.

In those data there are 24 times of M L ~ 5 . 3 earthquakes, and only once the solar local hour an-

432 ACTA SEISMOLOGICA SINICA Vol. 9

gle at the time of commencement of earthquake ML5.4 at 05 • 23 on July 31, 1976. It is not within the time zone of 06~12 and 18"~24 local time. And since 1981 the solar local hour angles of ML>~5.0 earthquakes are also within the time zones of 06"12 and 18"-24 local time. There are two most prominent erthquakes. One is ML5.2 at 19 : 02 on May 29, 1991 and the other is MLS. 6 at 07 : 06 on May 30, 1991. The interval of their occurrence times is about 12 hours. From Figure 2(c,d) we can find that the earthquake-restrained time zones of the sun and moon are 06"-12 and 03"-15 local time corresponding with the strong aftershocks ( M L ~ 5 . 3) in Xing- tai. The earthquake-restrained time zone of the Sun acting upon the aftershocks(ML~4. 7)in Haicheng is 06"-.12 local time, while it seems that the earthquake-restrained time zone of the Sun on the strong aftershocks ( M L ~ 5 . 0 ) in Tonghai is 12"18 local time. Accordingly we hypothe- size from the point of statistical check, that the occurrence time of moderate and strong afetr- shocks in the source region has no connection with the lunar and solar local hour angles at that time, then the appearance chances of the sun or moon in any one of angular areas are equal in one earthquake. Therefore the event of m celestical bodies in the same angular zone a for n times of earthquakes is n multiple Bernoulli trial which is in line with the binomial distribution, then the probability of events occurring more than m celestial bodies in the angular aera a is shown as fol- lows :

" , ~ n ! V,,(k >~ m) = ~-~P,,(k) = ~ k ' (~-Z. k) ' pkq.-, (2)

k = m k ~ m * •

Where p=a/2~, q = 1--p. Table 2 is the results of the probability of appearance of the earth- quake-restrained time zone of aftershocks of the above-mentioned earthquake exceeding the actual number of celestial bodies and X 2 check. The figure shows that there are three times of the prob- ability of predicting the occurrence of events of earthquake-restrained time zone for four earth- quakes bigger than 0. 97 that the X ~ check denies primary hypothesis at 0. 01, 0. 05, and 0. 25 significant level, i.e. solar local hour angles have various effects of modulation on the occurrence time of aftershocks of the above-mentioned earthquakes. It is identical that the lunar local hour angle also have effects of modulation on the strong aftershocks of earthquakes in Tangshan and Xingtai. In other words, the solar local hour angles have strong restraining effects on the occur- rence time of the moderate and strong post shock sequencse in Tangshan and other places.

Table 2 T h e r eauks of probabi l i ty s tat is i t ies and X 2 check

Name ,, n ms P ~ mm P m X~ 2 X2= as am

Tangshan 24 2 0. 9999 20. 16 0. 01

Xingtai 21 2 0. 9833 4 0. 9992 4.58 13. 76 0.05

Haicheng 32 4 0. 9748 4. 16 0.05

Tonghai 22 4 0. 8394 1.51 0. 25

0. 01

The previous statistical results demonstrate that the earthquake-restrained effects of the sun are prevalent while the effects of the moon are weaker in comparison with the sun. Next we mainly take the effects of the sun as research object. The same method can also be applied to the moon, but only by altering some parameters for research, i.e. changing some parameters of the sun to the corresponding ones of the moon.

2 Analyses and discussion

From the group characteristics and statistical results of the distribution of solar or lunar local

No. 3 GAO,W. et ad... THE EARTHQUAKES AND POSITIONS OF THE SUN AND MOON 433

12 12

12 12

1 8 ~ 6 1 8 ~ 6

0 0 12 12

0 0 12 12

0 o

Figure 2 The distributive patterns of the lunar and solar local hour angles at the time of commencement of the aftershocks in Tangshan Mu~ 5. 3 (a, b), Xingtai ML~5.3 (c,d), in Haicheng ML~4. 7 (e,f) , and Tonghai ML~5. 0(g, h).

hour angles of the occurrence time of generalized preshock sequential earthquakes above moderate scale before strong earthquake and the occurrence

time of moderate and strong aftershocks after strong earthquake. It is known that certain effects of the sun and the moon have some modulating ef- fects on the kinetic process of the source region of strong earthquakes. Now we analyze the possible physical mechanism of the modulation. First we hypothesize that the constitutive relationship of the medium in source region is linear, and the occur- rence of earthquakes only change the boundary val- ue conditions and the original state of the medium. Owing to the linear property of kinetic equations, the occurrence of each earthquake will be corre- spondingly accompanied by one time changes of o- riginal state and boundary values of the medium. F is the sum of all body forces acting upon the medi-

um, i.e. F=~fi,

~2Ui ~ik - - + F i (3) POt 2 -- ~xk

Because the motion equation is of linear, the contribution of each term in body force F to the medium motion can be considered individually. Therefore the sum of contribution from each term equals to the one resulting from force F. Here we hypothesize f , is the body force resulting from solar effects. Letrs compare the patterns of earthquake- restrained time zone of earthquake within the medium in source region from the sun before and after strong earthquakes. Figure 3 is the correla- tive synoptic diagram of earthquake-restrained time zone of the generalized preshock sequence and of

the strong aftershock sequence after strong earthquakes, which the sun acted upon earthquakes in Tangshan, Xingtai, Haicheng and Tonghai, Figure 3 shows that the earthquake-restrained time zones before and after the strong earthquakes in Xingtai are identically 06"~12 local time, and the ones in Tangshan are complementary, 06 "-~ 12 and 18"-~24 local time before the shock while 00---06 and 12"--18 local time after the shock, in Haicheng are 18~24 local time before the shock and 06 --~ 12 local time after the shock, in Tonghai are 00 "~ 12 or 00~06 local time before shock and 12 --~ 18 local time after the shock. The above results demonstrate the earthquake-re- strained time zones of preshocks and afteshocks of different earthquakes before and after strong earthquakes are different, whereas their ways of changing vary in a form of equvalent multiple, i.e. inereased and reduced at the intergral mutiple of 6 hours, K = 0, ± 1, + 2. The earthquake- restrained time zone before and after earthquakes in Xingtai did not alter, i.e. K = 0, K = ± 1 in Tangshan, K = ± 2 in Haicheng and Tonghai. We know that earthquakes in Xingtai are swarm

434 ACTA SEISMOLOGICA SINICA Vol. 9

types, i.e. the release of strain energy in source region is completed through a series of earth- quakes. Thus the adjustment of tectonic stress field is also completed gradually, and the direction of stress field is not changed fundamentally in the whole process. Accordingly we can conclude that the earthquake-restrained time zone should be remained unchanged, so should the mecha- nism of modulation. Earthquakes in Tonghai and Haicheng are major shock-after shock type, then the strain release of their major shocks may lead to three results. (1) excessive release, (2) inadquate release, (3) moderate release. If it is excessive release, the aftershocks should first ad- just against excess; if it is the inadquate release the aftershocks should first adjust toward further moderation; if it is the moderate release, the aftershocks should adjust toward global eqilibrium. On the other hand, there are many types of ruptures existing in major shocks(Fu et al. , 1985). simplex rupture, duplex rupture, simultaneous rupture of conjugate interfaces. The combina- tion of several types will give rise to many possi- ble results, so the mechanism of strong earth- quakes may exist several patterns. The aforesaid statistical results show that the earthquake-re- strained time zones act stronger restrained ef- fects on generalized preshocks than on after- shocks, which may have connection with the strong aftershocks restricted by strong earth- quakes while ordinary aftershocks dually re- stricted by strong aftershocks and strong earth- quakes. As far as the kinetic mechanism is con- cerned, the phenomenon of earthquake-re- strained time zone is the result of what exogenic force acting on the kinetic system of medium is not in favor of the occurrence of earthquakes in

Tangsban

Post-earthquake [t)-,~N~" ~ 12 [~',.'~.~N~"~] 2 4 I t /h

Pre-earthquakc]' Xingtai ~ i ! Post .-earthquake ]0 [~'.~.~X]l 2 2 4

L r/h

Prc-earthquake Haieheng

Post-earthquake 0 k'x-.\\\~.~-] 12 24 t /h

, T o n g h a i Pre-carthquake ~ , x ~ - ~ . - x ]

Post-earthquake 10 121".\\\~\",~ 2~4 t/h

Figure 3 The correlative synpotic pattern of earth- quake-restrained time zones before and after the Tangshan (a) , Xingtai (b) , Haicheng (c) and Tonghai (d) earth- quakes.

certain time interval. Here the exogenic force is called the earthquake-restrained force. Accord- ing to the questions considered, the earthquake-restrained force can be simplified to the normal- ized form f ( t ) , and f ' ( t ) , the earthquake-restrained force of the four generalized preshock se- quence in Xingtai, Tangshan, Haicheng and Tonghai, can be obtained and shown separately as follows(Gao et al. , 1995) •

"fb(t ) = a~coswlt + ab3cosw3t

fb ( t ) = bgsinto2t

fb ( t ) = ablcos~ol t + a~cos%t ,fb(t) = a ~ c o s m l t -+- abcos%t

-4- ~sinwzt + bbzsin%t -+- b~sinto3t

+ b~sinwzt + b~sinwzt + b~sin~o3t

+ b~sinwat + bbzsin%t + b~sinto3t

(4)

Now we will analyze the variation in shape of the solar earthquake-restrained force before and after the four earthquakes. First, we normalize the earthquake-restrained force of the strong aftershock sequence as did on fb ( t ) , then fa (t) is obtained. Suppose that the curve shape of fa (t) is identical to the one of fb( t ) . Under these conditions in mathematics, f a ( t ) is equivalent to the changes of the starting point of time of f~( t ) , i.e. the starting time is t=to instead of t = 0, thus obtaining the corresponding fa ( t ) only by delaying one moment ( t0>0) of f~( t ) , i.e.

fa ( t ) = fb( t -- to) (5)

No. 3 G A O , W . e t a l . : THE E A R T H Q U A K E S AND POSITIONS OF THE SUN AND MOON 435

as for Xingtai earthquake to = 0 (hour), for Tangshan earthquake to = 6 (hour), for Haicheng and Tonghai earthquakes to = 12 (hour). By substituting the above to and o~= 2k~/2 T for Formu- la (4) and (5), we can obtain the corresponding i f ( t ) through simple calculation. The formulae are shown as follows:

' f " ( t ) = fb ( t ) f ' ( t ) = - - fb ( t ) f~ ( t ) = - - f b ( t ) -F 2b~ sin%t (6)

. f ' ( t ) : -- f b ( t ) -F 2b~ sin%t

+1[ Xing ta i~N~ . ( t ) , f f ( t ) {a~

- I ~ t/h

Tonghai

n [ ! I iX i i / I I ! I \ i I " 0 12 1 24

- 1 [ t/h

+1 r- Haicheng/'~N f'( t

L / \ h i \ I I A I I I~, J J )J ] J I ' ~ ~ 12 24

, L t/h

F i g u r e 4 T h e s y n p o t i c d i a g r a m of t h e so la r

e a r t h q u a k e - r e s t r a i n e d force s h a p e s

before and after the Xingtai (a), Tonghai (b) , Haieheng (c) and Tangshan (d).

If the ways of changes of certain parameters deter- mining the occurrence of earthquakes before and af- ter violent earthquakes can be known, then we can decide time interval of their triggering time zone. These results make us know that the changes of the way the sun modulated these four earthquakes be- fore and after their occurrence are that there is no change in Xingtai earthquake, but vice versa in Tangshan earthquake, partial changes in Haicheng and Tonghai earthquakes. In ideal situation, the shapes of earthquake-restrained foces f f (t) and f f (t) before and after the four earthquakes are shown in Figure 4. The above analytical results demon- strate that the changes of earthquake-restrained time zones before and after main shock in the same source region are the results of altering the signs before am- plitude of some periodic modulation terms or of the adding or subtracting some periodic terms. The rea- sons of changes might be decided by the focal mech- anism of strong earthquakes, for the occurrence of corresponding strong earthquakes changes the condi- tions of boundary values and the orginal states to the greatest degree.

According to the earthquake-restrained phe- nomena of preshocks and aftershocks and the above analysis and discussion, we can make the judgement of what time zone intervals within 24 hours is liable to the occurrence of strong aftershocks on the basis of earthquake-restrained time zones most possibly existing in the earthquake sequences before strong

earthquakes and early moderate and strong aftershocks. Taking Tangshan earthquakes as exam- ples, on the basis of preshock and the seismic data of the earthquake ML7. 2 in the afternoon of July 28, 1976 through October 23, 1976, we try to predict the possible time intervals of com- mencement of the strong aftershocks within one certain day. We have known the earthquake-re- strained time zones of the sun before strong earthquake are 06~ 12 and 12 "~ 18 local time. Ac- cording to Figure 5 we know that the earthquake-restrained time zones after strong earthquakes are 00~06 and 12~18 local time, which suggests that main shocks result in drastic changes of

436 ACTA SEISMOLOGICA SINICA Vol. 9

the conditions of boundary value and the original states of medium in source regions. Thus we

can predict that ML>~5.3 earthquakes in the future will be prone to occurring at the time inter-

vals of 0 6 ~ 1 2 and 1 8 ~ 2 4 local time within 24 hours a day. Figur 6 is the distributive patterns

of the lunar and solar local hour angles of the time of commencement of whole ML>~5. 3 earth-

quakes happened later and earthquakes ML~5. 0 after the year 1984, which are listed in Table

3. If other ways can be used to determine the occurrence data of strong aftershocks, in a sense, prediction of the occurrence time of moderate and strong aftershocks would be determined within

24 hours.

12 12 12

, S ~ 6 1 8 ~ 6 1 8 ~ 6 0 0 0

Figure 5 The distributive pattern of the lunar and solar local hour angles at the time of commencement of earthquakes ML~5.3 after the quake MLT. 2, on July 28, 1976 until October 23, 1976.

12 12 12

0 0 0

Figure 6 The distributive pattern of the lunar and solar local hour angles of the occurrence time of moderate and strong aftershocks after October 24, 1976.

As to the present level of observation as well as the understanding of the physical mechanism of earthquakes, we can estimate the accuracy of time prediction of earthquakes. The earthquake- restrained time zones of generalized preshock sequences and aftershock sequences within 24 hours a day, which are 12 consecutive hours(for example Tonghai earthquake) or two consecutive 6 hours at 6 hour interval, apply to the minimum time interval of 6 consecutive hours that is sub-

ject to the occurrence of earthquake, and the distribution of the sun within 6 consecutive hours is

of uniform, i.e. there is not any one time interval which is more special and conducive to the oc- currence of earthquakes. Thus we can infer that if the time prediction of earthquake is measured by an hour, tp is the time of occurrence predicting future earthquake(event E ) , t, is the actual time of occurrence of the earthquake predicted, then ~t=tp--t,, when tp>~6 h , if P ( E I tp, t t )= 1, then I~tl>~3 h , when 3~<tp<6 h , if P(Ettp, t , ) = l , then I~tl>~tp/2, when 0 < t p < 3 h , if P ( E Itp, 6 ) = 1 , then I~tl>~3 h. Thus we know that t,, the occurrence time of earthquake,

might be of randomness within the scope of :k 6 hours, i .e. the minimum time interval in the state of impending earthquake in 6 hours. Within its minimum time interval, earthquake may oc- cur at any moment. Accordingly it is meaningless to make accurate prediction(unless for the pur-

pose of statistical prediction) within 6 hour. It is a general opinion:

No. 3 G A O , W . et a l . : T H E E A R T H Q U A K E S A N D P O S I T I O N S O F T H E S U N A N D M O O N 437

I~tl ~ 3 h

T a b l e 3 T h e c a t a l o g o f m o d e r a t e a n d s t r o n g a f t e r s h o c k s e q u e n c e a f t e r 1 9 7 6 - 1 0 - 2 4

(7)

Date T i m e Ep icen te r M a g n i t u d e

a - m o - d h : min fN /rE

1 9 7 6 - 1 1 - 1 2 21 : 13 39054 ' 118°49 ~ 5 . 4

1976 -11 - 15 21 : 53 39°24 ' 117°50 ~ 7 . 1

1 9 7 6 - 1 2 - 0 2 08 z 42 39°35 ~ 117°32 ~ 5 . 8

1977 -01 - 15 06 : 46 39°41 r 118°46 ~ 5 . 3

1 9 7 7 - 0 1 - 3 0 12 : 11 39°33 ' 118°13 ' 5 . 5

1977 -03 - 07 08 : 28 39°54 ' 118°52 r 5 . 9

1977-05 -12 19 : 17 39°23 ~ 117°48 ~ 6 . 5

1977 -06 - 10 08 ." 40 39°28 ~ 118°04 ' 5 . 4

1977 -11 - 27 06 -" 46 39°12 ' 118°01 ' 5 . 8

1982 -10 - 19 20 : 46 39°53 ' 118°59 ~ 5 . 3

1984-01 -07 19 "- 18 39°43 ' 118°45 ~ 5 . 2

1985 -04 - 22 11 : 31 39045 ' 118046 ' 5 . 0

1985 -10 - 05 12 : 01 3 9 ° 4 T 118°27 ' 5 . 0

1991-05-29 19 : 02 39°43 ' 118°18 ' 5.2

1991-05-30 07 : 06 39°41 ~ I18°16 s 5. 6

By now, the earthquake-restrained force (or the modulation force) which is discussed is a scalar quantity, whereas the state of load of the medium is depicted in the form of stress tensor,

that is •

0"12 (YI3 l

LO'31 0"32 0"33..]

In the coordinate system of principal axis ao= 0(i:z~j), a0ve0, if the surface of maximum shear stress firstly ruptures, then f ( t ) , the earthquake-restrained force, might actually corre- spond to the term of max(ao--ajj)(i~z:j) or the term of confining pressure etc. From the addi- tion and subraction of the periodic terms of earthquake-restrained force of some earthquakes we can infer that there might exist a pheomenon of resonance in the system of medium. In the future we will make furthur discussion on problems with respect to modulation, to the mechanism of changes of the earthquake-restrained time zones, and to the process of changes of the geometric shapes and mechanical states of medium in source region.

3 Conclusions

The above examples of earthquakes provide us with the following knowledges: ( 1 ) The lunar and solar local hour angles modulate the time of commencement of the moder-

ate, strong afershock sequences of a strong earthquake, and there exists an earthquake-restrained time zoe.

(2) The changes of earthquake-restrained time zones before and after earthquakes in the source regions of violent earthquakes might be determined by such factors as the focal mechanism of strong earthquakes and the changes of geometric conditions of the medium.

(3) As far as the aftershock sequence is concerned, solar effects play more popular role

438 ACTA SEISMOLOGICA SINICA Vol. 9

than lunar ones with respect to earthquake restraint. (4) The error accuracy of deterministic prediction

quake is I ~ t l ~ 3 h . of the occurrence time of earth-

This paper is supported by the Eight Five Year Target of the State Seismolgoical Bureau, China.

References

Fu, C. Y. , Chen, Y. T. and Qi, G. Z. , 1985. Fundamentals o f Geophysics. Beijing: Science Publishing House. 447 pp (in

Chinese).

Gao, W. , Xu, S. X. , Liu, P. X. , et al. , 1996. Relationships between earthquakes and positions of the sun and moon

( I ) - - s o m e temporal characteristics of generalized preshoek sequence in the seismogenie zones of strong shocks. Acta

Seismologica Sinica, 9(1) : 91~101.

Lu, Y. Z. , Chen, Z. L. , and Wang, B. Q. et al. , 1985. The Seismological Methods in the Prediction o f Earthquakes, Bei-

jing : Seismological Press. 268pp (in Chinese).

Wu, K. T. , Jiao, Y. B. , and Lfi, P. L. et al. , 1990. An Introduction to Earthquake Sequence. Beijing: Peiking University

Press. 250 pp (in Chinese).