International Journal of Geosciences, 2010, 38-43
doi:10.4236/ijg.2010.11005 Published Online May 2010 (http://www.SciRP.org/journal/ijg)
Copyright © 2010 SciRes. 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: yinzhe@ybu.edu.cn
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
39
1
1
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.
KK
H,H
KK
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.
K
MK+1
M
K
HK+1
H
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
M
K
M
K+1
M
K+1
M
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
M
K
M
K+1
M
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
MK
M
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.
Copyright © 2010 SciRes. IJG
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:
00
00
0
sin cos
sin sin
cos
x
y
z
00
000360 ,18

 

'
'
Step3: To the counterclockwise rotation 23°26', then
''
'
''
cos23 26sin23 26
sin2326cos 2326
xx z
yy
zx z




M point symmetry point assignment
Step4: Clockwise rotation to 23°26', then
''' '
''
'' ' '
cos23 26sin23 26
sin23 26cos23 26
xx z
yy
zx z






Step5
11
11
1
sin cos
sin sin
cos
x
y
z



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
a
K+1
H
Copyright © 2010 SciRes. IJG
Z. YIN
41
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
Copyright © 2010 SciRes. IJG
Z. YIN
Copyright © 2010 SciRes. IJG
42
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
Copyright © 2010 SciRes. IJG
43
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