Study on Correlation of Tidal Forces with Global Great Earthquakes

doi:10.4236/ijg.2012.32041

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International Journal of Geosciences, 2012, 3, 373-378

http://dx.doi.org/10.4236/ijg.2012.32041 Published Online May 2012 (http://www.SciRP.org/journal/ijg)

Study on Correlation of Tidal Forces with Global Great

Earthquakes*

Youjin Su1, Hong Fu1, Hui Hu2

1Seismological Bureau of Yunnan Province, Kunming, China

2National Astronomical Observatories/Yunnan Observatory, Chinese Academy of Sciences, Kunming, China

Email: [email protected], [email protected]

Received February 3, 2012; revised March 6, 2012; accepted April 7, 2012

ABSTRACT

The correlation between the celestial tidal forces and earthquakes has been a controversial problem, although its re-

search history is very long. This paper analyzes the relation between the tidal forces and all the earthquakes of magni-

tudes no less than 7.0 which occurred in the entire world from year 1900.0 to 2000.0 by calculating tidal forces and the

run tests which yields the runs of earthquakes near the extreme and non-extreme values of the tidal forces. It is shown

that the occurrence of an earthquake is relevant to the tidal forces. From the analysis of the relation between the ecliptic

longitudes of the lunar ascending node and the seismic activities of the principal seismic belts and regions in the world,

it is also shown that the lunar node tide is possibly one of the important astronomical contributing factors of the seismic

activities there. The results enrich and support the relevant study of the relation between celestial tidal forces and

earthquakes.

Keywords: Tidal Force; Earthquake; Run Test; Seismic Belt

1. Introduction

The occurrence of a moonquake is closely affected by

tidal forces on the moon generated by the Earth and the

Sun. This has already been studied and confirmed [1,2].

As for the correlation between the celestial tidal forces

and earthquakes, it remains although the research history

is very long and many papers have been published it re-

mains controversial problem [3]. The studies of this sub-

ject carried out both in China and elsewhere can be

roughly divided into two categories:

 The time sequence of certain tidal component is cal-

culated. The statistics of phases corresponding to the

earthquake-generating times or the earthquake-gene-

rating frequencies are evaluated by different methods

[4,5], alternatively, the correlation between the earth-

quakes and tidal-component is directly found values

from the statistics of the tidal periodicity of the

earthquake-generating times [6].

 The tidal-force indeed shear stress in the sliding di-

rection of a causative fault is calculated, mainly based

on the angle of stress. The relation between the earth-

quakes and tidal effects is consequently discussed

from the result in different aspects [7,8].

Different and even contradicting conclusions have

been reached by adopting different methods in these pa-

pers. In this paper the method of run test is used. It is

different from the methods is previous studies. The rela-

tion between the great earthquakes over the world and

the celestial tidal forces is thus studied in the perspective

of entire time sequence, leading to the conclusion that

they do relate to each other. Another difference is that

not the earthquakes in a single region but all earthquakes

in the world are studied, according to the seismic belts or

regions. The phenomenon that earthquakes generally ha-

ppen with a period of 18.6 years in the main seismic re-

gions of the world suggests that the lunar node tide (i.e.

the tidal effect from the Moon at lunar node) should be

an important astronomical factor which influences the

seismic belts or regions hosting potential new earthquakes.

2. Celestial Tidal Force Has Close Relation

to the Occurrence of an Earthquake

2.1. Tidal Force

The resultant of forces (vector difference) of the lunisolar

gravitation exerted on the unit mass of the Earth and the

inertial centrifugal force produced from the revolution of

the Earth round the common center of mass of the Moon

and Earth is called the tide generating force, that is to say,

the difference between the gravitation exerted on some

part of the attracted celestial object and that exerted on

the part with the same mass at the center of the object is

*This work is supported by the tackle key project of the ministry o

science and technology of P. R. China (2012BAK19B01).

Y. J. SU ET AL.

374

regarded as the tide generating force (Fang, 1984; Fu

1985; Melchior, 1978). From this the calculation formula

of the tide generating force exerted on a particle with a

unit mass can be obtained as follows [9]:



3cosZ1

KMr

F= D

and

F= 3

3KMrsin2Z

here Fr and Fs are respectively the vertical and horizontal

components of the tide generating force, with Fr being

taken as negative when pointing to the geocentre and Fs

being positive when pointing to the celestial object, K is

the gravitational constant, r is the earth’s radius, and M is

the mass of the celestial object. D is the distance from the

object to the geocentre. Z is the zenith distance of the

celestial object. From the above-mentioned formula it

can be calculated that though the solar mass is 2.7 mil-

lion as much as the lunar mass, the distance between the

Moon and Earth is only 1/390 of the distance between

the Sun and Earth, and therefore the tide raising force of

the Moon is 2.25 times as much as that of the Sun, with

both belonging to the same order of magnitude while the

tidal force on a point of the earth’s surface exerted by

each of the other planets is several orders of magnitude

less than that exerted by the Moon, and therefore the tidal

forces of the other planets can be neglected.

2.2. Run Test

One of the most strong points of the run test is that the

distribution of the stochastic variable need not be taken

into account and it is a nonparametric method. A se-

quence is considered which consists of n observed values

of the stochastic variable x. The variable x is divided into

two kinds which repel each other, and can simply be ex-

pressed with the positive sign (+) and negative sign (–).

The simplest example is the sequence, which is obtained

by throwing a coin, with each observed value being ei-

ther positive (+) or negative (–). The second example,

assuming that a sequential measured value is xi (where i

= 1, 2, 3,, n) and their mean value is x0, and then it is

(+) when xi ≥ x0 and it is (–) when xi < x0. The third ex-

ample, a double sequence consists of two serial observa-

tions xi and yi (where i = 1, 2, 3,, n), where each pair

of the observations are (+) when xi ≥ yi or (–) when xi <

yi. In any case the observed sequence obtained by the

positive sign (+) and negative sign (–) can be written as:

+ + – + + – + + + – + – – + – – + – – –

1 2 3 4 5 6 7 8 9 10 11 12

A run is defined as a segment of the sequence to in-

clude the same category of outcomes as many as possible.

There are N = 20 of runs observations in the above illus-

tration, with the number of runs being r = 12. The num-

ber of an observational sequence shows whether the out-

comes of the stochastic variable are independent or cor-

related. The run test can be directly used for analyzing

data and a test for the existence of systematic pattern of a

single observational sequence may be given as follows.

Let the assumption be that there is no clear pattern in a

sequence which consists of N independent observations

of the same stochastic variable. Under the assumption

that the observations with + are equal to those with −, the

sampling distribution of the number of runs in the se-

quence is determined by the run-distribution theory.

From the comparison of the observed number of runs to

the opened interval (rn, 1−α/2, rn, α/2 ), the assumption can

be tested under any required level of significance α,

where n = N/2. If the number of runs lies inside this

opened interval the assumption is accepted within the

confidence level. Otherwise, the assumption is rejected

as not having sufficiently confident evidence [10].

2.3. Test of the Influences on Great Earthquakes

from the Celestial Tidal Forces

Engdahl and Villasenor [11] collected the statistics of

seismic records of all countries in the world and found,

as a result, that the records of earthquakes of M ≥ 7.0

have been complete and reliable since 1900. In order to

determine whether the occurrence of an earthquake is

correlated with the celestial tide generating force or not,

and to let the conclusions obtained from analysis be reli-

able and reveal the true characteristics of the matter, all

the earthquakes events analyzed in this article are se-

lected from the “Global seismicity: 1900-1999” with

Engdahl and Villasenor (2002). There occurred 1553

earthquakes of M ≥ 7.0 in the whole world in the time

interval from 1900.0 to 2000.0, and there were 67 earth-

quakes of M ≥ 8.0 during that same interval. The analysis

in the present paper is carried out for all the earthquakes

with M ≥ 7.0.

It is common knowledge that the energy E released by

an earthquake and its magnitude M have the following

relation [12]:

E = 1011.8+1.5M (2)

here M correspond the magnitude determined by surface

wave. Unit of E is erg. Form which it is not difficult to

know that if earthquake is one order greater than another

in magnitude the energy released by the former will be

30 times greater than the latter. Thus as far as the energy

released by earthquakes is concerned, it is mainly con-

centrated on great earthquakes. The destruction caused

by earthquakes mainly also comes from the great earth-

quakes.

It is considered that all over the word the earthquakes

of M ≥ 8.0 are too few while those of M < 7.0 are too

Y. J. SU ET AL. 375

many. In addition, there are some earthquakes of M < 7.0

caused by artificially created factors (such as the nuclear

explosion, construction of large dams and reservoirs,

etc.), and the reliability of the catalogue of the earth-

quakes of M < 7.0 is not good as that of M ≥ 7.0. Based

on these reasons all the earthquakes of M ≥ 7.0 are se-

lected by us as the object for analyses. As for analyses of

every year we take the frequencies of the earthquakes of

M ≥ 7.0 in that year and do not compute their energies.

Based on the time of occurrence of an earthquake and

the longitude and latitude of the epicenter, the celestial

tidal force exerted on the epicenter when the earthquake

occurs is calculated and the run tests are respectively

given to three sequences of the tidal force (i.e., the resul-

tant, vertical component and horizontal component of the

tide generating force), or the runs at which the earth-

quake occurs near the extreme and non-extreme values

are calculated. It is found from the results that for the

resultant, vertical component and horizontal component,

the runs at which the earthquake occurs near the extreme

and non-extreme values are respectively 1030, 1046 and

510. The null hypothesis is taken as that the occurrence

of the earthquake has no relation to the celestial tidal

force, then for the level of significance α = 0.05, the ac-

ceptance region of the assumption n = N/2 = 776 should

lie in the opened interval (656, 906). Evidently, all the

runs of the above mentioned three sequences lie outside

this opened interval, and therefore the null hypothesis is

rejected. In other words, the occurrence of an earthquake

and the tidal force have obvious potential tendency, i.e.

the occurrence of an earthquake has some relation to the

celestial tidal force.

3. Seismic Activities of Principal Seimic Belts

in the Whole World and Lunar Node Tide

3.1. Existence of Period of 18.6 Years in Seismic

Activities in Principal Seismic Belts in the

World

As already pointed out, among various celestial tidal for-

ces the lunar-origin tidal force is the greatest, and the

next important is the solar-origin tide fore. Therefore the

tidal force of the lunar origin becomes the prior subject

in our study. During the studies of the characteristics of

seismic activities, many researchers have found that the

earthquakes in a certain region or belt have periodicity in

activities [13,14]. There were 5 active periods of strong

earthquakes and 5 calm periods in China in the 20th cen-

tury [15] with the period being 18.6 years [16]. There

may be similar periodicity of earthquakes over the entire

world as well. If the earthquakes of M ≥ 7.0 in the entire

in the 20th century are collectively analyzed, there is no

evidence for such periodicity. However, the period of

18.6 years apparently exists for the earthquakes in a lim-

ited region associated with boundaries between tectonic

plates. The phases of the cycles of earthquake frequent-

cies in different seismic belts or regions are different.

This causes the period of 18.6 years not seen in the data

covering the entire world. The differences in phases are

understandable. Because the occurrences of earthquakes

are related to certain geological structures, only in the

areas with the same or similar seismotectonics, their

seismic activities can have the same or similar laws.

Therefore, the earthquakes in different regions need to be

studied separately, otherwise little pattern of the seismic

activities can be found. It is the very reason why the

regularity of the seismic activities has not been revealed

from the analyses of the combined data of all earthquakes

of M ≥ 7.0 over the world.

As pointed out by Chen Yong, regularity and random-

ness coexist in seismic activities, of which above 90%

are distributed near the boundaries between tectonic

plates [17]. The theory of tectonic plates holds that the

crust of the Earth consists of some rigid blocks or plates,

the interior of a plate is relatively stable, many phenomena,

such as submerging, colliding and shearing, occur at the

boundaries between the plates and the mutual movements

between the plates cause the formations and occurrences

of earthquakes. A plate drifts under the joined influence

of the centripetal force from the Earth rotation and the

mantle plume heat convection. The Celestial tidal forces

periodically trigger the release of the stress energy ac-

cumulated along the boundaries between plates, in the

forms of the seismic energy and volcanic energy [18].

Since the major earthquakes are mainly concentrated

near the boundaries between the tectonic plates [19,20],

we divided the seismic belts of the major earthquakes

over the world along the plate boundaries into 11 regions

(Figure 1). We find for separate analysis that the seismic

activities of each region have a period of 18.6 years.

There are 1416 earthquakes of M ≥ 7.0 in the 11 regions

in total making up 91.2% of all the earthquakes of M ≥

7.0 of the world. The remaining 137 earthquakes of M ≥

7.0 did not appear to be in the 11 regions.

3.2. Lunar Node Tide Is an Important

Earthquake-Pregnant Astronomical Factor

in the Principal Seismic Belts and Regions in

the World

The period of 18.6 years equals to the period of the Earth

main nutation term, and also of the motion of the lunar

node. The Moon revolves around the Earth in its orbit,

while the lunar orbit shifts under the action of the solar

gravitation. Therefore, the node of the lunar orbit on the

ecliptic (i.e., the plane of the Earth’s orbit) moves west-

ward, causing the ecliptic longitude of the lunar ascend-

ing node to steadily decrease. The ecliptic longitude of

the lunar ascending node is expressed by the equation

[21]:

Y. J. SU ET AL.

376

Figure 1. The studied region of 18.6 years recurrence of the great earthquakes in the world.

as much as that of the solar origin. During the steady

westward motion of the lunar ascending node, the obliq-

uity between the lunar orbit and to the ecliptic varies in

the range 4˚57' to 5˚19', thereby causing the obliquity

between the lunar orbit and the Earth equator to vary, in

the range18.4˚ to 28.8˚, with a period of 18.6 years. The

variation in the obliquity between the lunar orbit and the

Earth equator translates into the variation in the range of

the declination of the lunar motion in a tropical month

and ultimately the latitude range of strong tidal effects of

lunar origin on the Earth surface, thereby controlling the

range of motion of the Moon in the equatorial zone and

evidently controlling the latitude zone of the tidal force

on the Earth’s surface affected by the Moon. Therefore,

the influence of the inclination of the Moon’s path with

the equator results in the tidal force exerted by the Moon

on the Earth’s surface.

Ω = –125˚02'40.280" – 1934˚08'10".539T

+ 7".455T2 +0".008T3 (3)

where T is the number of Julian centuries elapsed from

J2000.0. This equation can be used to calculate the lon-

gitude of the lunar ascending node for the moment of any

earthquake. The distribution of the ecliptic longitudes of

the lunar ascending node at the time of earthquakes in the

region under study can thus be obtained. This allows us

to find potential concentration patterns of the ecliptic

longitude of the lunar ascending node at the time of oc-

currence of the earthquakes in each studied region, i.e.

including the periods of the seismic activities there. By

taking the uniform distribution as the null hypothesis we

carry out the χ2 test for each region. A sampling point is

taken in the active period or in the calm period, and the

degree of freedom evidently equals to one. Under degree

of freedom is equal to 1, if χ2 > 3.841, the null hypothesis

can be rejected with the 95 percent this confidence level,

and the periodicity of earthquakes to concentrate within

the mentioned active period is highly likely. The test of

results show that the values of χ2 are all greater than

3.841 as listed in Table 1. Therefore, the seismic activi-

ties in each region studied have significantly shown a

period of 18.6 years. The interval of strong seismic ac-

tivities N is associated with an opened interval of the

ecliptic longitude of the lunar ascending node in the Ta-

ble 1.

It is well known that the pattern of seasons in the

southern hemisphere of the Earth is opposite to that of

the northern hemisphere due to the difference between

the amounts of solar radiation received (which in turn

depend upon the incident angles of the sunlight beams),

e.g., when there is a hot summer in the southern hemi-

sphere, there is a severe winter in the northern hemi-

sphere (Pen & Lu, 1983). The most fundamental reason

for this phenomenon is that there exists the obliquity of

the ecliptic from the equatorial plane of the Earth. Simi

larly the obliquity of the Lunar orbit from the terrestrial

equatorial plane is probably the astronomical factor

causing the latitude dependence of the seismic activities.

The tidal forces of solar and lunar origins not only

cause the sea tides on the Earth surface but also deform

the elastic Earth mantle, consequently redistribute the

matter and change the gravitational field of the Earth

[22,23]. The tidal force of the lunar origin is 2.25 times

4. Discussion

1) A new method, which is to study earthquakes in

Y. J. SU ET AL. 377

Table 1. Statistic results of seismic recurrence of 18.6 years of the principal seismic regions in the whole world.

No. Studies region Total sample Seismic active interval

Sample N (˚)

1) Himalayas and its region 48 45 (260 180) 9.000

2) Mt.Tianshan and Baikal 45 37 (0 270) 4.900

3) Eastern Alps plate 19 15 (0 200) 5.221

4) Nalay Penisaula-Sund Islands 110 86 (70 330) 3.958

5) Weslern Philipping sea plate 187 162 (150 80) 8.480

6) Philippine sea-Northeast Japan 236 168 (130 10) 16.041

7) Aleut-North Mexico 132 73 (0 250) 6.303

8) New Guinea-Cumtuok 371 355 (350 330) 7.851

9) South Cumtuok 30 26 (330 200) 8.244

10) Central America Caribbean 71 59 (60 330) 4.187

11) West of southern America 167 126 (350 230) 9.674

Total 1416 1152

Total sample is the time of occurrence of an earthquake in the studies region from 1900.0 to 2000.0; N is an opened interval of strong seismic activities with the

ecliptic longitude of the lunar ascending node; Sample is the time of occurrence of an earthquake in the opened interval N.

separate regions and employs run tests, is adopted in this

paper. If the earthquakes of the entire world are consi-

dered collectively, there is no evidence of the period of

18.6 years. The situation changes little if the earthquakes

in apparently ill-defined regions are studied. The key to

the question is to divide earthquake regions reasonably.

Through the run tests of the occurrences of earthquakes

near the extreme values and non-extreme values of the

celestial tidal forces we reach the conclusion that the

occurrences of earthquakes are related to the celestial

tidal forces. We thus emphasize the importance of adopt-

ing proper regions of seismic activities and using the run

tests in probing the influences of tidal forces on earth-

quakes.

2) The contribution of astronomical factors on the

earth is a global effect. However, at different time one of

the astronomical factors plays a role in different region

on the earth. Response regions are confined to the area

where potential movement in the atmosphere and crust is

highly unstable. Therefore natural calamities induced by

astronomical factors are regional effects [24].

3) The variation of the obliquity of the lunar orbit

causes variation in the tidal force of the lunar origin. The

amplitude of the tidal force of the lunar node is smaller

than that of the tidal force at the semidiurnal diurnal, or

leading to semi-monthly tides (Gao, 1997). Studies have

already verified that the tidal forces of the semidiurnal,

diurnal, and semi-monthly tides play triggering roles in

the earthquakes in some regions [25-30]. According to

the theory of dissipative structures, when the earthquake-

formation and energy accumulation have already been in

an extreme unstable state, which is far away from the

equilibrium, any small fluctuation can be enlarged to

cause the giant fluctuation of the geological system, there-

by inducing an earthquake [31]. The so-called trigger

means that an earthquake may be triggered at any mo-

ment when the earthquake-pregnency has arrived at the

moment of occurrence of the earthquake. So that the lu-

nar node tide may not play a trigger role in the occur-

rence of an earthquake or may and probably it partici-

pates in the earthquake-pregnant activities, or the long-

term action of the lunar node tide joins the earthquake-

pregnant process in the seismic belt and the accumulative

effect of its action is added to the accumulation of the

regional energy and to deviate the area from slowly sta-

ble [32,33]. The details of such modulation mechanism

need to be studied in future.

4) The period of 18.6 years in the seismic activities is

only statistical. From Table 1 it can be clearly seen that

except for the phase differences, the patterns of cycles of

different regions are also different: some have longer

active times and some have considerably short active

times. An earthquake is an extremely complicated pro-

cess, as it is affected by many factors internal and exter-

nal to the Earth’s (the internal factors are more important,

since the external factors affect through the internal fac-

tors), and therefore, earthquakes cannot have exact peri-

odically.

5. Acknowledgements

We heartily thank for the referee’s valuable comments.

In response to our request, Professor E. R. Engdahl of the

University of Colorado at Boulder (USA) sent us twice

their paper and computer readable catalogue of global

earthquakes, which is adopted in this paper. He also gave

Y. J. SU ET AL.

378

us tremendous help in the process of this work. Dr. Chen

I-wan, British (ancestor Chinese), Advisor of Committee

of Natural Hazard Prediction of China Geophysics Soci-

ety gave us valuable discussion and help. We express our

heartfelt thanks to these colleagues.

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