Vol.2, No.12, 1333-1340 (2010)
doi:10.4236/ns.2010.212162
Copyright © 2010 SciRes. Openly accessible at http:// www.scirp.org/journal/NS/
Natural Science
The earth dynamic system: the earth rotation vs mantle
convection*
Shuping Chen1,2
1State Key Laboratory of Petroleum Resource and Prospecting, China University of Petroleum, Beijing, China;
2College of Geosciences, China University of Petroleum, Beijing, China; csp21c@163.com
Received 18 September 2010; revised 20 October 2010; accepted 25 October 2010.
ABSTRACT
The earth dynamic system is one of the key
scientific questions on the earth science. The
thermodynamic behavior and gravity force of
the earth and the rheology nature of the mantle
prove that mantle convection is the main power
source leading the lithosphere to break and
move. Yet the directivity of both the structures
in the crust and plate movement reminds of the
earth rotation. Here we demonstrate that the
mantle convection and inertia force of the earth
rotation affect each other, the former being the
power source of lithosphere plate break and
motion, and the latter determining the direction
of the mantle convection and plate motion. The
sense of plate motion depends on the mantle
upwells, whose trends are controlled by the
earth rotation. The geometric shapes of the
plate boundaries can adjust the direction of
plate movement.
Keywords: Plate Tectonics; Earth Rotation;
Mantle Convection; Global Dynamics
1. INTRODUCTION
The earth dynamic process has long been a subject for
debate. Tectonic deformation, such as folds and faults, is
a ubiquitous appearance on the Earth’s surface. What
force leads the rock in the Earth to deform? On the other
hand, all structures present orientations either in latitu-
dinal direction, or in longitude direction, or in oblique
direction [1-3]. The present mid-oceanic ridges occur
along longitude or latitude (Figure 1). The transform
faults have good orientation (Figure 2). The flow lines
of the lithosphere plates are parallel to the transform
faults [4-8]. The plate motions also are in certain direc-
tions [4]. The questions are where the dynamic force
comes from and what element controls the directivity.
Several hypotheses of the earth dynamics once emerged
in the earth science, such as the earth expanding hy-
pothesis, the earth contracting hypothesis, the earth
pulsing hypothesis, the earth rotation angular speed al-
ternating hypothesis, mantle convection hypothesis, et al.
[8]. The plate tectonics hold the mantle convection to be
the basic dynamic force of plate movement [9-13], but it
does not touch what controls the direction of plate
movement or deformation direction.
As early as 1910s and 1920s, Wegener considered the
forces related to the earth rotation are the dynamics re-
sponsible for the continental drift [14]). Also, the theory
of geomechanics thought the extraneous forces related to
the change of the earth rotation speed to be the dynamics
of the crust motion [1,2], which resolves the question
about orientation of tectonic deformation, but faces with
the problem on the force magnitude. The change in the
earth rotation speed and deformations related to the earth
rotation has long been noticed [15-19]. The intensive
adjustments of the plates are in sound correspondence to
the changes of the earth rotation speed [12,20]. The
mantle flows along the latitude and longitude, and com-
bined latitudinal and longitudinal mantle flow exists [21].
The relationships among the mantle convection, the
earth rotation, the plate motion and the crust rock de-
formation are worth of insight.
This paper will discuss the relationship between the
mantle convection and the earth rotation in controlling
the plate motion and rock deformation, based on the two
facts of the Earth, the earth’s heat and rotation. And a
carton model was established.
2. LAYER STRUCTURE OF THE EARTH
The Earth is of a layer structure, the crust, the mantle,
and the core according to their component (Figure 3).
The mantle can be divided into upper mantle, transition
zone and lower mantle. The uppermost part of the mantle
*This study is financially supported by the National Natural Science
Foundation of China (No.90814007)
S. P. Chen / Natural Science 2 (2010) 1333-1340
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1334
Figure 1. Present distribution of mid-oceanic ridges. 1-longitudinal mid-oceanic ridge; 2-mid-oceanic ridge circling Antarctica;
3-transform fault; 4-magnetic anomaly belts; 5-Oligocene-Neogene; 6-Paleocene-Eocene; 7-late Cretaceous; 8-early Cretaceous;
9-Jurassic. (cited in reference [4]).
Figure 2. Relationship of transform faults to the Earth rotation.
(cited in reference [22]).
is rheologically similar with the crust, and they make up
the lithosphere, which is cut into plates by deep faults.
The earth mantle under lithosphere has less intensity
than the lithosphere and its deformation mechanism is
flowage. The substance of the mantle is a mixture of the
solid and liquid matter, being very pliable and easily
coming to plastic flow. So it is called the asthenosphere.
Lithosphere can drift above the asthenosphere.
3. MANTLE CONVECTION
As a thermal system, the earth is in a course of con-
tinual cooling from the beginning of the earth to the
present [23]. Heat conduction and convection are its
cooling methods. The former mainly occurs in litho-
sphere and the latter in mantle [24]. The heat convection
of the earth interior have two methods which are plate
means and mantle plume means [23,25] (Figure 4). As
reckoned, the Rayleigh number of the mantle is at least
3 × 106, which exceeds 2000, the critical value of con-
vection far away. If buoyancy is greater than viscosity
resistance, flowage will happen.
In the earth system, the mantle with high density because
of cooling or phase transition can flow downward, and
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Figure 3. Layer structure of the earth. Not to scale.
Figure 4. Main components of the mantle’s dynamic system (Modified after reference [23]).
the mantle with low density caused by thermal expan-
sion can flow up. According to conservation of sub-
stance, flowage in whatever direction should cause
flowage in opposite direction, forming convection cir-
cles, namely the mantle convection. This is the power
source of the lithosphere plate break and movement, and
the recognized forces moving the plates are ridge push,
slab pull, trench suction and basal drag [26].
4. FORCE ASSOCIAT ED WITH THE
EARTH ROTATION
The change in the earth rotation speed has long been
found [15]. Force relating to the earth rotation includes
S. P. Chen / Natural Science 2 (2010) 1 333-1340
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1336
centrifugal inertia force, latitudinal extraneous force,
Coriolis force and so on [20].
When angular rotation speed of the earth changes, an
extraneous centrifugal force develops with constituents
both in the radial direction F2 and in the longitudinal
direction F1 (Eq.1) [20] (Figure 5).

1
12 sin
2
FmwwwR2
 (1)
where m is the quality of certain unit, w is angular veloc-
ity, Δw is the increase of the angular velocity, R is the
radius of the earth, and α is latitude.
For a terrace with a unit volume, the F1 is as follow-
ing

1
12 sin
2
FwwwR2
 (2)
where the ρ is density. For a homogeneous globe, the F1
has maximum value near the latitude of 45° and de-
creases to zero toward the poles and the equator (Figure
6). There will be action force between two terraces with
different mass or different density, based on Eq.1 and
Eq.2.
Meanwhile, due to the earth is an ellipse, the gravity
has a component in the radial direction P2 and another
constituent in the longitudinal direction P1 (Figure 5). It
can be supposed that there is a state where balances exist
between the F1 and P1 and between the F2 and the P2.
In this case, a terrace in the earth surface is static. When
there is change in the earth rotation speed, either the
component in radial direction or the component in the
longitude will change and the balances will be broken,
and vibrations in the radial direction and movements
along the longitudinal direction will occur.
On the other hand, change of the earth rotation angu-
lar speed may cause force in latitudinal direction F3
(Figure 5) (Eq.3), arousing movement in latitudinal
direction. The maximum of the F3 is at the equator of
the earth, and decrease toward the poles. It has been
proven that the earth rotation angular speed is continu-
ally changing during the earth evolutionary process [20],
while the main reason that causes the earth rotation an-
gular speed change is the earth shrinking or distending
and redistribution of its interior substance, such as man-
tle upwelling or plate subduction.

31co
dw
Fm R
dt s
  (3)
Where m is the quality of certain unit, τ is an coeffi-
cient related to the cohesion between the unit and its
basement, dw
dt is the angular acceleration, R is the ra-
dius of the earth, and α is latitude.
Figure 5. Forces associated with the change of the earth rota-
tion. X-the distance between point A and the rotation axis of
the earth, O-the core of the earth, R-radius of the earth,
α-latitude, F-extraneous centrifugal force, F1-longitudinal con-
stituent of the extraneous centrifugal force, F2-radial constitu-
ent of the extraneous centrifugal force, F3-extraneous latitu-
dinal force, P-gravity, P1-longitudinal constituent of the gravity,
P2-radial constituent of the gravity.
Figure 6. The distribution of extra forces in latitude and longi-
tude.
For a terrace with a unit volume, the F3 can be do-
nated by the following

31co
dw
F
dt sR
 
(4)
where the ρ is density. There will be action force be-
tween two terraces with different mass or different den-
sity.
The Coriolis force comes into being because rotation
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line speed differs in different latitudinal area. For exam-
ple, mobile air can change heading affected by this force.
In view of the deduction, when the mantle moves from
the deep to the Earth’s surface or from low latitude to
high latitude, it is affected by the Coriolis force due to
speed changing. And the mantle flow will change
movement direction.
5. RELATIONSHIP
It is assumed that magnitude of tectonic stress caused
by alteration of the earth rotation rate is 10-2 to several
Pa, which is much less than magnitude of tectonic stress
actually measured from ancient to modern [5,27], hence
the force relating to the earth rotation inertia force fails
causing lithosphere plate to break or move.
Probability of mantle convection and gravitation re-
lating to the mantle convection are enough to cause
breaking and movement of the plate. The associated
forces with the mantle rising and the plate movements
include gravity and drag forces related to the mantle
convection and the dynamic slab of a subducting plate.
Mantle convection is relevant to the earth heat. The
mantle starting to move up from the core-mantle bound-
ary or transition zone base may arouse redistribution of
the earth interior substance. Thereby they cause altera-
tion of the earth rotation angular speed, developing in-
crement of the earth rotation inertia force. Whereas this
rotation inertia force restrains and regulates the initial
mantle convection, hence decides the direction of plate
movement at last and in turn decides the orientation of
deformation.
If the change of angular velocity is great, and
w
the angular acceleration dw
dt is small, the longitudinal
extraneous force will be significant. And the trend of the
possible mid-oceanic ridge will be parallel to latitudinal
line (Figure 7(a)). When the earth rotation becomes
slow, the lithosphere plates will move to the North and
South Pole, and the possible mid-oceanic ridge trend
will be along the equator. When the earth rotation be-
comes fast, the lithosphere plates will move toward the
equator, and the possible mid-oceanic ridge trend will be
in the north and south half globes and parallel to
the latitude lines. If the angular acceleration dw
dt is
great, and the latitude extraneous force will be dominat-
ing. The upwelling mantle will prefer to grow in the lon-
gitudinal direction, and the trend of the possible
mid-oceanic ridges will be along the longitudinal lines
(Figure 7(b)).
If the difference between the longitudinal extraneous
force and the latitude extraneous force is small, the trend
(a) (b)
Figure 7. Possible mid-oceanic ridge trend when either longi-
tudinal extraneous force (a) or latitudinal extraneous force (b)
is dominating.
of the possible mid-oceanic ridge will controlled by both
of the two forces, and it will be along the “possible
mid-oceanic ridge” in Figure 8. The line of the possible
mid-oceanic ridge can be divided into five segments.
The segment DD’ is nearly parallel to the longitudinal
line, and parallel to the longitudinal line in the equator
where the longitudinal extraneous force is zero. The
segment DC or D’C’ connects with the longitudinal lines,
and it trends NE or NW in this case like Figure 8(a),
while the earth rotation speed becomes slow. The seg-
ment CN or C’S concave to the west and its trend
changes from NE to NNE northward in the north half
globe, or from SW to SSW southward in the south globe.
This is due to that the decrease in magnitude of the lon-
gitudinal extraneous force is faster than that of the lati-
tude extraneous force as indicated in the Figure 6. The
lengths of the five segments depend on the relative mag-
nitude of the latitudinal extraneous force to the longitu-
dinal extraneous force. When the latitudinal extraneous
force is bigger than the longitudinal extraneous force,
the segment DD’ will become long and the other seg-
ments will become short. The trend of the possible
mid-oceanic ridge will parallel to the longitudinal line.
When the latitudinal extraneous force is less than the
longitudinal extraneous force, the segment DD’ will be-
come short and the other segments will become long.
The trend of the possible mid-oceanic ridge will be NE
or SW.
In the case that the earth rotation becomes fast, the
lithosphere plates will move toward the equator, the
shape and the relationship of the trend of mid-oceanic
ridge to longitudinal line do not change (Figure 8(b)).
The trend of mid-oceanic ridge line will in the east half
globe and symmetrical to the trend of mid-oceanic ridge
in Figure 8(a).
Although the force related to the earth rotation can not
break or move a plate, it can control the growing trend of
an upwelling mantle. In turn, it controls the directions of
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Latitudinal extraneous force α
(a) (b)
Figure 8. Possible trend of the mid-oceanic ridge when the magnitude difference
between the longitudinal and latitudinal extraneous forces is small. (a)the earth ro-
tation velocity becoming slow, (b)the earth rotation velocity becoming fast. Given
the sense of the latitudinal extraneous force is westward. The longitudinal line is of
no longitude value, which is applied here to indicate its relationship to the trend of
mid-oceanic ridge. The α becomes big from point O to certain point C’’ in the line
of NS which matches the point C along latitudinal line. From point C’’ northward,
the α becomes small.
plate movements for the plates move perpendicular to
the mid-oceanic ridge and parallel to the transform faults.
Regarding the plates in the north half globe or in the
south half globe, the trends of possible mid-oceanic
ridges may be parallel to the longitudinal lines, latitu-
dinal lines or may trend northeast or northwest, depend-
ing on both the relative magnitude of longitudinal extra-
neous force to latitudinal extraneous force and the
change of the earth rotation velocity.
6. DISCUSSION
The established models of mid-oceanic ridges (Figure
8) match well with the distribution and trends of present
mid-oceanic ridges (Figure 1). The Atlantic mid-oceanic
ridge and the east branch of the Indian mid-oceanic ridge
are identical to the possible mid-oceanic ridge in Figure
8a. The changes of the trend of mid-oceanic ridges near
the equator are resulted from the disharmonic deforma-
tion between the north half globe and the south half
globe [7] or are related to the Coriolis force, which
caused the north half globe move westward relative to
the south half globe [20]. The geometric shape of the
Pacific mid-oceanic ridge is similar to that of the possi-
ble mid-oceanic ridge in Fig.8a, but the relationship of
the Pacific mid-oceanic ridge to the longitudinal lines is
different from that in the Figure 8(a). If the Pacific
mid-oceanic ridge is rotated by an angle of 20˚ clock-
wise, it will nearly parallel to the Atlantic mid-oceanic
ridge, and will match the possible mid-oceanic ridge in
Figure 8(a). This indicates another place of the earth
rotation axis when the Pacific mid-oceanic ridge formed.
In other word, it can be deduced that the earth rotation
axis drifts from the formation of the Pacific mid-oceanic
ridge. The west branch of the Indian mid-oceanic ridge
trends northeastward, which may be affected either by
the increase in the earth rotation velocity or by the
northward movement of the all plates of the earth due to
the Africa superwell [28].
Furthermore, the extensive activities of the plate tec-
tonics are sound related to the changes of the earth rota-
tion speed (Figure 9). The hotspots in Hawaiian Islands
show that the Pacific plate moved toward north from
Paleocene to Eocene, and moves toward NWW or W
from Oligocene to the present [28]. The moving direc-
tion change corresponds to the change of the earth rota-
tion speed from a slow decrease to a fast decrease (Fig-
ure 9). The longitudinal extraneous force dominated for
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the former, and the latitudinal extraneous force domi-
nated for the latter. The two forces prefer to form
east-west trend mid-oceanic ridge and north-south trend
mid-oceanic ridge, respectively. The corresponding plate
movements are toward the north or west, respectively.
These match the viewpoints indicated in the Figure 7.
Some other problems should be noted. Where one
plate collides with another plate, their movement direc-
tions will change. As a result, the deformation direction
will change depending on the collision and the geometric
shape of the plates. In the models like Figure 7 and Fig-
ure 8, if the Coriolis force and some other force relating
to the earth rotation are accounted, the mantle movement
situation will be more complex. For example, when a
mantle plume, which has considerable impact on tec-
tonic evolution of plates [25], moves from the deep to
shallow, it will deflect westward because line speed in
shallow layer is greater than that in deep layer.
In fact, these forces associated with the earth rotation
operate connectively at the same time. This will cause
complex pictures of plate movements at various latitude
and longitude. In turn, this will lead complicated crust
deformation assemblages like what can be seen today. It
is worth further study.
Finally, on deciding plate movement, relationship
between mantle convection and the earth rotation can be
represented with a carton model (Figure 10), called the
Є
Figure 9. The change of the earth rotation speed in the Phan-
erozoic (Modified after reference [20]).
Figure 10. Carton of the Earth Dynamic Car.
“Earth Dynamic Car”. In this dynamic system, the mantle
convection is the power source, accounting the engine of
one car and being the power source of the plate break
and movement. While the force relating to the earth rota-
tion accounts the steering wheel of the car, restraining
the direction of the plate movement.
7. CONCLUSION
The earth basic dynamic system should include the
content in two aspects, namely the mantle convection,
relating to the earth heat and gravity, and the earth rota-
tion. The mantle convection is the power source of the
plate break and movement, while the earth rotation re-
strains the growing trends, and in turn controls the direc-
tion of the plate movement. Above both are two parts of
dynamic system that can not be separated. The model
connects the thermal and the rotation of the earth.
8. ACKNOWLEDGEMENTS
The author thanks Prof. Ma Zongjin and Prof. Jin Zhijun for their
guidance on his research work and creative suggestions in the prepara-
tion of this paper.
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