The Co-planarity and Symmetry Principle of Earthquake Occurrence

doi:10.4236/ijg.2010.11005

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International Journal of Geosciences, 2010, 38-43

doi:10.4236/ijg.2010.11005 Published Online May 2010 (http://www.SciRP.org/journal/ijg)

The Co-planarity and Symmetry Principle of

Earthquake Occurrence

Zhe Yin1,2

1Department of Information Management, Beijing University, Beijing, China

2Mathematics Department, Yanbian University, Yanji, China

E-mail: [email protected]

Received February 28, 2010; revised March 26, 2010; accepted April 20, 2010

Abstract

Under the assumption that the earth movement tendency is a sphere, the author does research about the earth-

quakes occurrence between 2001 and 2010 which over 6 scales of magnitude on occurred time (UTC),

magnitude, longitude, latitude and other data, then give out the causal relationship of earthquakes and the

co-planarity and symmetry theory of earthquake occurrence. Also, the author does empirical analysis in the

paper.

Keywords: Earthquake, Co-planarity, Symmetry

1. Introduction (Heading 1)

Research on earthquakes is one of the most important

elements about disaster prevention study, because of its

devastating and destructive. Especially in recent years,

with the rapid development of modern economic activity,

destruction to the Earth was continuous. The frequency

tends to rise and there are more large earthquakes. There-

fore, how to analyze the reason of the earthquake cor-

rectly, and predict earthquakes effectively becomes a hot

topic in nowadays.

Under the assumption that the earth movement ten-

dency is a sphere and mountains fall to the surface of the

earth; estrogens and basin rise to the surface of the Earth.

This article gives out the co-planarity and symmetry the-

ory of earthquake occurrence according to research about

the earthquakes occurrence between 2001 and 2010 which

over 6 scales of magnitude.

2. Questions and Relevant Definitions

The Earth, like a very sensitive being, according to the

laws of nature, it has the desire to achieve a balance of

features. In this process, it will show a particular trend.

As shown in Figure 1, we give some relevant defini-

tions here:

Ecliptic axis: an axis through the center of the Earth

which is a vertical line to the ecliptic plane.

Equatorial coordinate system: a celestial coordinate

system of the equatorial plane and the axis of rotation.

Ecliptic system of coordinates: a celestial coordinate

system of the ecliptic plane and ecliptic axis.

Tangent plane parallel to the equator: the Earth’s

equatorial plane parallel to the tangent plane (Tangent

plane parallel the equator), shown as TPPTE.

Ecliptic line tangent plane: parallel to the ecliptic of

the earth tangent plane (Ecliptic line tangent plane),

shown as ELTP.

Equatorial vertical plane: after the Earth’s surface

Figure 1. Plane figure.

Z. YIN

shock point and the spin axis of the tangent plane (Equa-

torial vertical plane), shown as EVP.

Longitudinal ecliptic plane: after a shock point and

the yellow surface of the Earth axis tangent plane (Eclip-

tic plane vertical), shown as EPV.

Circular symmetry point: Circular , shown as CSP.

Similar point: Similar Point, shown as SP.

Earthquake effects: measure the Earth’s surface; the

intensity level of shock is unstable, the stability of the

boundary tangent plane level. Plane is the ball away from

the more deviation, the more poor results, and the more

unstable and more likely point of this earthquake.

3. Basic Assumptions and the Co-Planarity

and Symmetry Principle of Earthquake

3.1. Basic Assumptions

1) The Earth became positive sphere with earthquakes

which rise or low the ground. That is, because of the ecli-

ptic (23.26 degrees), the Ecliptic Plane TPPTE line tan-

gent planes ELTP have tended to be round;

2) The Earth has tended to balance, and because the

earthquake, to re-balance;

3) Crustal thickness tends to vary. Earth’s core and

mantle movement space tends to a ball space;

4) With the earthquake, the earth rotation axis offset.

When there is a earthquake which makes the low rise, the

earth rotation axis moves to the seismic vertical, those

makes the high low is opposite.

3.2. Co-planarity and Symmetry Principle

After the observation of earthquakes on Earth N (154

earthquakes over 6 scales of magnitude in this article)

times, it is occur time of adjacent earth-

quakes measure with UTC.

H,H

M,M

A) The previous earthquake is a cause of the after. The

tangent plane balances was destroyed, then tend to a new

balance, which Ecliptic line tangent plane generate new

state plane all the times.

B) Seismic vertical and seismic vertical

are on the same plane at the time or . That is

parallel to the cut-plane in the equatorial plane or Eclip-

tic line cut the ecliptic plane, or longitudinal vertical

plane or equatorial plane.

MK+1

HK+1

C) If the tangent of the plane where seismic vertical

and seismic vertical are tends to round, or

fall-rise movement in the earthquake tends to stable,

and tends to symmetry in the circle; other-

wise, coplanar circle from the difference of the most un-

stable point will have an earthquake.

K+1

D) After earthquake on occurs, if the most unsta-

ble point (poor seismic effect) is still, earthquake

will take place near the same point.

K+1

4. Research Basis and Calculation Method

Assumptions (1), (2), (3) are prerequisite of conclusion

(A), (B), (C) and (D); symmetry points including the spin

axis symmetry, yellow axis symmetry and geocentric

axial symmetry. With the existence of the ecliptic obliq-

uity (ecliptic plane and the equatorial plane angle 23.26

degrees) and the Ecliptic plane tangent line, parallel to

the equatorial plane tangent tends to a circle, the shape of

the earth tends to a sphere becomes possible. This can be

concluded with (C) and (D). Assumptions (4) decided the

longitudinal movement of the after . As-

sumptions (1) and (3) show the possibility that the

earthquake and the earthquake potential basis for the

order. Be noted that symmetrical points at any time

change the fact that, in the premise revolution, a startled

different points of the Ecliptic OK UTC timing of your

cutting surface is subject to change, and cut parallel to

the equatorial plane remain unchanged.

K+1

Earthquake time: the time the earthquake is very

important, when the earthquake occurred; it generates

and identifies Ecliptic line tangent plane, tangent plane

parallel to the equator, the ecliptic plane and the equato-

rial vertical longitudinal cut tangent plane, as well as the

corresponding point of the plane of symmetry at the

same time.

Symmetrical points on the calculation: Earth auto-

biographical spherical coordinates on the equatorial

plane symmetry coordinates of points on the simple cal-

culation, the same latitude, longitude 180 degrees plus or

minus 180 degrees. The following calculation Ecliptic

coordinate system on the surface of the ball symmetric

point computation of positions is shown in Figure 2.

Figure 2. Caculations.

40 Z. YIN

Shock point set M of lat = W, long = J, time (UTC) = a:

b, then 0



= 90 – W, 0



= J +（a + b/60）× 15

Step2:

sin cos

sin sin

cos























000360 ,18



 



Step3: To the counterclockwise rotation 23°26', then

cos23 26sin23 26

sin2326cos 2326

xx z

zx z













M point symmetry point assignment

Step4: Clockwise rotation to 23°26', then

''' '

'' ' '

cos23 26sin23 26

sin23 26cos23 26

xx z

zx z



















Step5

sin cos

sin sin

cos











 



 



 



Step6: symmetry point, lat = 1

W=90



－, long = 1



– (a + b/60) × 15

5. Results

According to the information of 154 earthquakes over 6

scales of magnitude over the world from the USA Earth-

quake Observation Council, the causal relationship com-

mon area, symmetry of them can be concluded as fol-

lowing (Table 1) [1]: in the Comments, the next item

TPPTE cut parallel to the earthquake in the equatorial

plane, ELTP that the next seismic line cutting in the

Ecliptic plane, EVP that the next earthquake in the verti-

cal plane perpendicular to the equator, EPV that the next

earthquake in the vertical longitudinal ecliptic plane. A

total of circular symmetry point, then increasing the CSP,

such as TPPTECSP; similar point with the SP said. Two

adjacent seismic Mand Mt present, earthquake

moment K

H, when the total surface, then added 1;

when the time after the earthquake , when the total

surface, then added 2.

K K1,

Table 1. Original data.

2001

Date Time

(UTC) PlaceLat.Long. Magnitude Comments

Jan 1317:33Salvador13.04-88.66 7.7 ELTPCSP1

Jan 2603:16India23.3970.23 7.7 TPPTECSP1

Feb 1314:22Salvador13.67-88.94 6.6 ELTP1

Feb 2818:54 USA47.11-122.6 6.8 EPV2

Jun 2320:33 Peru -16.3-73.55 8.4 ELTPCSP1

Nov 1409:26 China36.290.9 7.8 ELTP1

2002

Date Time

(UTC) PlaceLat. Long. MagnitudeComments

Feb 307:11Turkey38.573 31.271 6.5 TPPTE1

Mar 312:08Afghani-

stan 36.543 70.424 7.4 SP1

Mar 2514:56Afghani-

stan 36.06 69.32 6.1 TPPTE1

Jun 2202:58Iran 35.63 49.05 6.5 TPPTE1

Oct 3110:32 Italy 41.79 14.87 5.9 ELTPCSP1

Nov 322:12 Alaska,

USA 63.52 -147.4 7.9 EPV1

2003

Date Time

(UTC) PlaceLat.Long. Magni-

tude Comme nts

Jan 22 02:06Mexico18.8-104.1 7.6 TPPTECSP1

Feb 2402:03China39.61 77.23 6.3 TPPTE1

May 1 00:27Turkey39.01 40.46 6.4 TPPTE1

K+1

Z. YIN

May 21 18:44 Algeria 36.96 3.63 6.8 TPPTE1

Sep 25 19:50 Japan 41.82 143.91 8.3 ELTP2

Nov 17 06:43 USA 51.15 178.65 7.8

Dec 22 19:15 USA 35.71 -121.1 6.6 ELTP2

Dec 26 01:56 Iran 29.00 58.31 6.6 ELTP1

2004

Date Time

(UTC) Place Lat.Long.

Mag-

nitude Co mmen ts

Feb 5 21:05 Indonesia -3.61135.53 7.0 ELTP1

Feb 24 02:27 Gibraltar 35.14-3.99 6.4 TPPTE1

May 28 12:38 Iran 36.2951.61 6.3 TPPTE1

Sep 5 10:07 Japan 33.07136.62 7.2 SP1

Sep 5 14:57 Japan 33.14137.07 7.4 ELTP1

Oct 9 21:26 Nicaragua 12 -86 7.0 ELTPCSP1

Oct 23 08:56 Japan 37.3138.8 6.6 EVP1

Nov 11 21:26 East Timor -8.15124.87 7.5 ELTPCSP1

Nov 15 09:06 Colombia 4.7 -77.51 7.2 ELTP1

Nov 20 08:07 Costa Rica 9.6 -84.17 6.4 TPPTE1

Nov 21 11:31 Islands 15.68-61.71 6.3 TPPTECSP1

Nov 26 02:25 Indonesia -3.60135.40 7.1 EPV1

Nov 28 18:32 Japan 42.94145.28 7.0 EVP1

Dec 23 14:59 New Zealand -50.24 160.13 8.1 ELTP1

Dec 26 00:58 Indonesia 3.3095.87 9.1 ELTP1

2005

Date Time

(UTC) Place Lat.Long.

Magni-

tude C omme nt s

Feb 22 02:25 Iran 30.72656.817 6.4 TPPTE1

Mar 20 01:53 Japan 33.54130.12 6.6 EPV1

Mar 28 16:09 Indonesia 2.0897.11 8.6 ELTPCSP1

Jun 13 22:44 Chile -19.89-69.12 7.8 EPV1

Jun 15 02:50 California 41.284-125.9 7.2 TPPTE1

Aug 16 02:46 Japan 38.259148.98 7.2 EPV1

Sep 9 07:26 New Guinea -4.539153.47 7.6 TPPTE1

Sep 26 01:56 Peru -5.68-76.4 7.5 EPVD2

Oct 8 03:50 Pakistan 34.4373.54 7.6 TPPTE1

Nov 26 00:49 China 29.7115.7 5.2 TPPTE1

Nov 27 10:22 Iran 26.7755.86 5.9 EPV1

Dec 5 12:19 Tanzania -6.21229.599 6.8 EPV1

2006

Date Time

(UTC) Place Lat. Long.

Mag-

nitude Comments

Jan 811:34Greece 36.250 23.498 6.7 EPV1

Feb 2222:19Moza m-

bique -21.32 33.58 7.0 EPV1

Apr 2023:25Russia 61.075 167.08 7.6 EPV1

May 315:26Tonga -20.13 -174.1 8.0 EVP1

May 1610:39New Zea-

land -31.55 -179.2 7.4 ELTP2

May 2722:54Indonesia 7.977 110.31 6.3 EPV1

Jul 1708:19 Indonesia -9.334 107.26 7.7 EPV1

Aug 2003:41Scotia Sea-61.02 -34.37 7.0 EPV1

Sep 1014:56 Mexico26.339 -86.56 5.9 TPPTE1

Oct 1517:07 USA 19.801 -156.0 6.7 EPV1

Nov 1511:14 Russia 46.616 153.22 8.3 ELTP1

Dec 2612:26Taiwan21.818 120.53 7.1 ELTP2

2007

Date Time

(UTC) Place Lat. Long.

Mag-

nitude Commen ts

Jan 1304:23Russia 46.288 154.44 8.1 ELTP1

Jan 2111:27Molucca Sea1.207 126.29 7.5 EPV1

Feb 1211:27Portugal 36.09 10.26 6.0 ELTP2

Mar 605:49Indonesia -0.490 100.52 6.4 ELTP2

Mar 2500:40Vanuatu -20.59 169.41 7.1 EPV1

Mar 2500:42Japan 37.537 136.43 6.7 EPV1

Apr 120:39Islands -8.474 156.95 8.1 ELTP1

May 1608:56Laos 20.470 100.70 6.3 ELTP1

Jun 221:34 China 23.013 101.05 6.1 ELTPCSP1

Jun 1319:29 Guatemala13.628 -90.73 6.7 ELTPCSP1

Jul 1601:13Japan 37.574 138.44 6.6 ELTP2

Jul 1817:30 Tanzania -2.586 36.281 5.9 ELTP1

Aug 117:08 Vanuatu -15.67 167.60 7.2 EPV2

Aug 202:37 Russia 47.259 141.75 6.2 EPV1

Aug 817:04 Indonesia -5.968 107.65 7.5 ELTPCSP2

Aug 1523:40 Peru -13.32 -76.50 8.0 ELTPCSP1

Sep 1211:10 Indonesia -4.517 101.38 8.5 ELTP1

Sep 2813:38 USA 21.980 142.68 7.5 EPV1

Sep 3005:23 New Zealand-49.39 163.84 7.4 SP1

Oct 1512:29 New Zealand-44.68 167.21 6.8 EPV1

Oct 2421:02Indonesia -3.909 101.06 6.8 ELTP2

Oct 3103:04 USA 37.432 -121.7 5.6 ELTP1

Oct 3103:30 USA 18.854 145.31 7.2 ELTP2

Nov 1415:40 Chile -22.18 -69.84 7.7 ELTPCSP1

Nov 2516:02 Indonesia -8.294 118.36 6.5 EPVD1

Nov 2919:00 France 14.951 -61.24 7.4 EPV1

Dec 907:28Fiji -26.15 -177.4 7.8 EVP1

Dec 1909:30Alaska, USA51.495 -179.4 7.1 ELTP1

Z. YIN

2008

Date Time

(UTC) Place Lat.Long.

Mag-

nitude Co mmen ts

Jan 5 11:01 Canada 51.299-130.7 6.6 ELTPCSP1

Feb 3 07:34 Congo -2.31428.896 5.9 EVP1

Feb 14 10:09 Greece 36.64621.833 6.9 ELTP2

Feb 20 08:08 Indonesia 2.75195.966 7.4 EPV1

Feb 21 15:26 (Norway) 77.4114.48 6.1 ELTP1

Feb 21 14:16 USA 41.076114.77 6.0 TPPTE1

Apr 18 09:37 USA 38.45087.890 5.2 ELTP1

May 7 16:45 Japan 36.141141.54 6.9 ELTP2

May 12 06:28 China 31.099103.27 7.9 ELTP2

May 24 19:20 Colombia 4.447-73.67 5.9 EPV2

May 29 15:46 Iceland 63.992-21.01 6.3 ELTP2

Jun 8 12:25 Greece 38.02921.464 6.4 TPPTE1

Jun 13 23:43 Japan 39.122140.67 6.9 ELTP2

Jul 15 03:26 Greece 35.98327.785 6.4 ELTP1

Jul 19 02:39 Japan 37.627142.11 7.0 SP1

Jul 23 15:26 Japan 39.807141.46 6.8 ELTP2

Jul 29 18:42 California 33.955-117.7 5.5 ELTP2

Aug 21 12:24 China 25.06697.737 6.0 EPV2

Aug 25 13:21 China 30.89383.614 6.7 ELTP2

Aug 30 08:30 China 26.277101.91 6.0 EPVD2

Sep 8 18:52 Vanuatu -13.51166.96 6.9 ELTP1

Sep 10 11:00 Iran 26.82355.825 6.1 ELTP1

Sep 11 00:20 Japan 41.979143.62 6.8 EPV1

Sep 29 15:19 New

Zealand -29.87-177.6 7.0

Oct 5 15:52 Kyrgyzstan 39.51573.768 6.6 ELTP2

Oct 6 08:30 China 29.75990.302 6.3 ELTP1

Oct 11 09:06 Russia 43.27146.262 5.8 ELTP2

Oct 16 19:41 Mexico 14.443-92.42 6.7 ELTP2

Oct 19 05:10 Tonga -21.85-173.8 6.9 ELTP2

Oct 28 23:09 Pakistan 30.65367.323 6.4 ELTP1

Nov 16 17:02 Indonesia 1.290122.10 7.3 EPV1

Nov 24 09:02 Okhotsk 54.194154.31 7.3 EPV2

2009

Date Time

(UTC) Place Lat.Long.

Mag-

nitude Comments

Jan 3 19:43 Indonesia -0.510132.78 7.6 ELTPCSP1

Jan 8 19:21 Costa Rica 10.197 -84.15 6.1 ELTPCSP2

Jan 15 17:49 Russia 46.862 155.15 7.4 EPV1

Feb 11 17:34 Indonesia 3.902126.40 7.2 ELTP1

Mar 19 18:17 Tonga -23.05-174.6 7.6 ELTPCSP2

Apr 6 01:32 Italy 42.334 13.334 6.3 ELTPCSP2

Apr 7 04:23 Islands 46.088 151.49 6.9 ELTPCSP1

Apr 16 21:27 Afghanistan 34.197 70.065 5.4 ELTPCSP1

May 2808:24Honduras 16.730 -86.20 7.3 TPPTECSP1

Jul 911:49China 25.619 101.08 5.7 EPV2

Jul 1509:22New Zealand-45.75 166.58 7.8 EPV1

Aug 910:55 Japan 33.144 138.04 7.1 ELTP1

Aug 1019:55 Andaman 14.013 92.923 7.5 EPV2

Sep 207:55 Indonesia -78.09 107.25 7.0 TPPTE1

Sep 1220:06 Venezuela10.70 -67.92 6.3 ELTP1

Sep 2917:48 Samoa 15.509 -172.0 8.1 ELTP1

Sep 3010:16 Indonesia -0.725 99.856 7.6 ELTP2

22:03-13.05 166.18 7.6 SP1

22:18-12.55 166.32 7.8 SP1 Oct 7

23:13

Vanuatu

-13.14 166.29 7.3 ELTP1

Dec 1913:02Taiwan 23.763 121.68 6.4 ELTP2

2010

Date Time

(UTC) Place Lat. Long.

Mag-

nitude Commen ts

Jan 3 22:36Solomon-8.912 157.30 7.2 ELTP2

Jan 1000:27California 40.645 -124.7 6.5 EPV1

Jan 1221:53Haiti 18.451 -72.44 7.0 ELTPCSP1

Feb 2620:31 Japan 23.472 123.71 7.0 ELTPCSP1

Feb 2703:34 Chile -35.84 -72.71 8.8 SP1

Feb 2715:45 Argentina 6.1 ELTPCSP1

Mar 40:18 Taiwan 6.4 EPV1

Mar 523:29Sumatra 6.5 ELTP1

Mar 84:32 Turkey 6.0 ELTP1

Mar 1111:39Chile -34.25 -71.88 6.9 ELTPCSP1

Mar 149:57Indonesia 6.4 EPV1

Mar 148:08Japan 6.6 ELTPCSP1

Mar 162:21Chile 6.7 EPV1

Apr 422:40Mexico 2.128 115.3 7.2 ELTP1

6. Analysis

According to the information of 154 earthquakes over 6

scales of magnitude over the world from the USA

Earthquake Observation Council, the causal relationship

common area, symmetry of them we can get the follow-

ing results, as shown in Table 2:

Table 2. Results.

Type Equatorial level

Line plane

Which

Symmetry

Ecliptic

Line plane

Among

Symmetry

Vertical

Flat

Similar

point

Other Not

coplanar Total

Quantity 22 (Four) 77 (23) 45 7 3 154

Percentage of total 14% (3%) 50% (15%) 29% 5% 2% 100%

Z. YIN

7. Conclusions

This study allowed existence of the errors, but those er-

rors do not interfere the co-planarity and the symmetry

principle. Errors may come from the inaccuracy of ob-

servation time, perhaps the errors accelerate the process

of the Earth becoming to sphere. In the next step of our

research, we plan to study on earthquake prediction and

the relationship between earthquake and economic de-

velopment.

8. References

[1] Http://earthquake.usgs.gov/recenteqsww/quakes/quakes_

all.html