The Formation Mechanism of Island Arc – scirp.org

 

 

International Journal of Geosciences, 2013, 4, 1151-1156
http://dx.doi.org/10.4236/ijg.2013.48109 Published Online October 2013 (http://www.scirp.org/journal/ijg)

The Formation Mechanism of Island Arc

Daoxiong Hu
Xibu Drilling Engineering Co., Ltd. of CNPC, Karamay, China
Email: hudaoxiong@cnpc.com.cn

Received April 12, 2013; revised May 16, 2013; accepted June 18, 2013

Copyright © 2013 Daoxiong Hu. This is an open access article distributed under the Creative Commons Attribution License, which
permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

ABSTRACT

The shape of island arc is formed by changing the axis of back-arc basin caused by rock expansion along the long axis
of back-arc basin; that is, island arc is driven to bend along the subduction zone, so that the arc-shaped island is formed.
Rock expansion along the long axis of back-arc basin is attributed to lower part of continental crust melting (underplat-
ing) on the dehydration belt (along the long axis of back-arc basin) due to dehydration of subducted oceanic crust, and
the arched melting plane is formed, so that rocks on the melting plane are subject to differentiated temperature rise and
differentiated expansion. The length of rock expansion along the long axis of back-arc basin is in direct proportion to
the radian of island arc. The arc length of island arc is equal to the sum of the length of the long axis of back-arc basin
and the length of rock expansion. The displacement and the arc length of island arc can be calculated according to the
length of rock expansion; on the contrary, the length of rock expansion can be calculated according to the displacement
or the arc length of island arc. According to the length and the lithology of rock expansion, the value of temperature rise
of rocks above the melting plane, the melting thickness (underplating) at the bottom of continental crust and the settle-
ment depth of back-arc basin can be reckoned.

Keywords: Island Arc; Arc Mechanism; Rock Expansion; Deformation

1. Introduction

of island arc.

The island arc is the arc structure formed at the contact
zone of continental crust plate and oceanic crust plate,
which is divided into oceanic island arc and continental
island arc [1]. Oceanic island arc is the result of the alle-
viation of sediments and volcanic substances on oceanic
crust with the damping impact of continental plate. And
continental island arc is one part of continental margin.
The arc stripe island at the margin of oceanic crust plate
is formed due to sedimentation of fore-arc (back-arc)
basin, rock expansion along the long axis and volcanism.
The formation mechanism of island arc is based on the
surface phenomena such as back-arc rift valley, oceanic
trench antedisplacement and etc. There are mainly two
points in previous explanation: one is tensile movement
whose motive power is magmatic thermal convection in
mantle wedge. The other is oceanic crust drag whose
motive power is dehydration and subsidence of sub-
ducted oceanic crust. The difference of tensile movement
and oceanic crust drag lies in the mode of movement;
that means it is to promote or drag the margin of oceanic
crust plate (island arc) to move towards the direction of
oceanic crust. The common ground of such two points of
view is the agreement that external force leads to the arc

As far as the position where island arc is located is
concerned, it is the zone where continental crust plate
and oceanic crust plate collide. The huge friction and
damping impact between oceanic crust plate and conti-
nental crust plate form horizontal extrusion force among
plates. From the measurement of absolute ground stress
of back-arc basin [2] to the alluvial deposits of oceanic
island arc and fore-arc basin, it can be seen that the zone
is an extrusion environment.

Three contradictions exist in the explanation about
tensile movement: the first one is the contradiction about
the unbalance of tension; the second one is the contradic-
tion about motive power; the third one is the contradic-
tion about the extrusion environment.

Three contradictions also exist in the explanation
about oceanic crust drag: the first one is the contradiction
about unbalance of drag; the second one is the contradic-
tion about the connection relations, the relations between
continental crust and oceanic crust is overlapping instead
of horizontal linkage; the third one is the contradiction
about the direction of force source, that is, the direction
for subduction and subsidence of oceanic crust is contra-
dictory to the direction for drag.

Copyright © 2013 SciRes. IJG

1152

D. X. HU

The author holds that tensile movement and oceanic
crust drag can’t be used to explain the arc mechanism of
island arc. The formation of island arc is not caused by
external force but internal force of rock expansion (the
deformation of rock expansion along the axis of back-arc
basin) [3]. Oceanic island arc is caused by the overlapped
deformation of rock expansion along the long axis of
fore-arc (back-arc) basin, while continental island arc is
caused by deformation of rock expansion along the long
axis of back-arc basin.

2. The Formation Mechanism of Island Arc

The formation mechanism of island arc is constituted by
the factors of dehydration of subducted oceanic crust,
substrate melting (underplating) of back-arc basin, tem-
perature rise of rocks, rock expansion, deformation of the
long axis of back-arc basin and etc.

The origin of the formation mechanism of island arc is
the dehydration of subducted oceanic crust. The dehydra-
tion of subducted oceanic crust leads to substrate melting
[4] of back-arc basin, substrate melting leas to tempera-
ture rise of rocks, temperature rise leads to rock expan-
sion, rock expansion leads to deformation of long axis of
back-arc basin, and the deformation of the long axis
promotes the formation of island arc.

The dehydration of subducted oceanic crust and the
substrate melting of back-arc basin are proved with the
arch up of mantle and a series of volcanic activities of
back-arc basin.

The temperature rise of rocks is also called differenti-
ated temperature rise. It refers to the temperature rise of
rocks above the melting plane due to substrate melting,
that is, the original geothermal gradient is changed, and it
is called the value of temperature rise. When geothermal
gradient is changed, the relatively high heat flow value
occurs at the axial part of back-arc basin (or back-arc rift
valley). Differentiated temperature rise refers to the dif-
ference existing along the short axis of back-arc basin
and in the vertical direction and along the long axis of
back-arc basin above the arc melting plane. And the
value of temperature rise is in direct proportion to the
thickness of melted rocks.

When rocks are expanded, the length of expansion is
direct proportional to the value of temperature rise. As
far as the arc form of melting at the bottom of back-arc
basin is concerned, it means that rocks above the melting
plane are subject to differentiated temperature rise and
differentiated 3D expansion, the length of rock expansion
along the short axis and in the vertical direction of
back-arc basin is one half of the length of that along the
long axis [3].

The deformation along the long axis of back-arc basin
is the change of the distribution form of rocks in three-
dimensional space along the long axis. As far as the

three-dimensional space is concerned, the resistance
caused by the bending of axis reaches the minimum level
only in the direction of the subduction zone, outer arc
bending towards the margin of continental plate is
formed to drive the non-subsiding parts to form island
arc. The deformation along the long axis of back-arc ba-
sin will lead to the phenomena such as broadened back-
arc basin, back-arc rift valley, arc of island arc, ante-
displacement of oceanic trench and etc.

As far as the mechanism of island arc is concerned, the
dehydration volume of subducted oceanic crust deter-
mines the melting thickness of the bottom of back-arc
basin, the melting thickness of rocks at the bottom de-
termines the temperature of rocks (the value of tempera-
ture rise) and the sedimentation depth of back-arc basin,
the temperature of rocks determines the expansion length
of rocks along the axis of back-arc basin, while the ex-
pansion length of rocks determines the arc length and
displacement of island arc.

According to the interrelation among various factors in
the formation mechanism of island arc, on the condition
that the density, distribution scope and structure of rocks
are known, the length of rock expansion along the long
axis of back-arc basin can be figured out according to the
arc of island arc, the displacement of island arc or the
length of island arc. The value of temperature rise can be
figured out according to the length of rock expansion, the
melting thickness can be figured out according to the
value of temperature rise, the sedimentation depth of
back-arc basin can be figured out according to the melt-
ing thickness.

In a word, in the formation mechanism of island arc,
the factors such as the dehydration of subducted oceanic
crust, substrate melting of back-arc basin, temperature
rise of rocks, rock expansion, the deformation of long
axis of back-arc basin and etc. are interrelated and inter-
active. Exactly such kind of interactive relation leads to
the island arc phenomenon.

3. Deformation Force Analysis of the Island

Arc

Island arc located between fore-arc basin and back-arc
basin is deformed from the linear form to the arc form,
and the force comes from rock expansion at the axial part
of back-arc basin. Rock expansion leads to the deforma-
tion at the axial part of the basin. In the process of de-
formation, the force application state of island arc and in
its neighborhood is shown in the following diagram.

In the diagram, Line A is the primitive axis of back-arc
basin, Line B is the present axis of back-arc basin. The
result of rock expansion along the axis of basin is the
deflection of the axis towards oceanic crust plate, that is,
the deformation from Line A to Line B. The direction of
deformation is determined by the crustal structure of the

Copyright © 2013 SciRes. IJG

subduction zone. Continental crust is above oceanic crust,
which is the overlapped relation available for horizontal
movement. If the axis of back-arc basin deflects towards
continental plate, it is required to drive the movement of
continental plate. The resistance is huge as far as the
mass is concerned. It is only available to deflect towards
oceanic crust plate, and it is only required to drive the
margin of continental crust (some back-arc basins, island
arc and fore-arc basins) to move above oceanic crust. The
resistance is relatively small as far as the mass is con-
cerned. Only the overlapped point between continental
crust and oceanic crust is changed, that is, oceanic trench
moves towards oceanic crust (as shown in Figure 1).

The deformation of the axis of back-arc basin will lead
to different result of force application at both sides of
island arc. The area between Line A and Line B is the
tensile area where back-arc rift valley is generated; the
area between Line B and Line C is the extrusion area
where oceanic trench moves forward; the area along
Point D and Point E is the cutting area where sliding
fracture occurs. As far as island arc itself is concerned,
when island arc bears extrusion from the continental side,
crushing collapse occurs; when island arc bears tension
from the oceanic side, volcanoes of island arc are rela-
tively active.

The mechanism of axial deformation also exists in fore-
arc basin. The first dehydration of subducted oceanic
crust also leads to substrate melting of fore-arc basin,
temperature rise of rocks, rock expansion, deformation of
long axis of fore-arc basin and etc. The deformation of
long axis of fore-arc basin is overlapped based on the
deformation of the axis of back-arc basin, so that the arc
of oceanic island arc gets bigger.

The formation of island arc is attributed to the defor-
mation of rock expansion, that is, it is the result of en-
dogenetic action when the existing state of rocks is
changed. In the process of the formation of island arc, the
external side of island arc needs to bear extrusion force
generated in the subduction of oceanic crust, while the
internal side of island arc needs to bear extrusion force
brought by the deformation of rocks at the axial part of
back-arc basin and string tension (extrusion) force brought

D. X. HU

1153

by sedimentation of back-arc basin [3]. The extrusion
force brought by the deformation of rocks at the axial
part mainly exerts impact on the middle section of island
arc, the extrusion force brought by the subduction of
oceanic crust and the string tension brought by the sedi-
mentation of basin will exert impact on both sides of the
whole island arc and form a great number of extrusion
structures.

As far as the force application of island arc is con-
cerned, only the external side of island arc forms tension
along the arc line due to the deformation, the internal
side of island arc forms extrusion force along the arc line
due to the deformation, while extrusion force exists at
both sides of island arc due to the epigene action (sub-
duction of oceanic crust and string tension of arc basin),
no tension of crustal movement exists.

4. Case Analysis of Island Arc

The factor of rock expansion is used to explain the arc
mechanism of island arc, the expansion coefficient of six
rock examples is measured to make conceptual calcula-
tion, the measurement temperature ranges from normal
temperature to the softening point of rocks. See the fol-
lowing table for the expansion rate through the conver-
sion of the measured expansion coefficient.

According to the measurement data in Table 1, Kuril
Island Arc and Japan Island Arc are selected to do analy-
sis as follows.

4.1. Kuril Island Arc

The following three points need to be determined to do
analysis of an island arc: the first is to determine two
terminal points of island arc, that is, the point from the
arc to the straight line, e.g., Point A and Point B in Fig-
ure 2, the connecting line between Point A and Point B
is the location before the island arc is subject to deforma-
tion, the string of the island arc now; the second is to
determine the location of the arc line (Arc AB in Figure
2). Consideration shall be taken into the collapse impact
exerted by extrusion at the side of back-arc rift valley
close to island arc, the high points not subject to collapse
shall be put outside of the arc line; the third is to measure
displacement, that is, the maximum point of the arc line
away from the string (CD in Figure 2).

The specific data of Kuril Island Arc are stated as fol-

lows:

Figure 1. Schematic diagram of force applciation of island
arc: continental plate; oceanic plate. (A) Primitive axis; (B)
Present axis Island arc; (C) Fore-arc basin.

At the north end of island arc (Point A), longitude:
155.5005, latitude: 50.8753; at the south end of island arc
(Point B), longitude: 146.1182, latitude: 44.5278. Length
of the string: 1015.66 km, displacement (CD in Figure 2):
67.79 km. According to the string length and displace-
ment, it is calculated that the arc length of island arc (Arc
AB in Figure 2) is 1027.68 km (calculated according to

Copyright © 2013 SciRes. IJG

0.05897

0.16447

0.28375

0.41248

0.54258

0.67057

0.78964

0.90963

1.0439

1.1815

1.2797

100

200

300

400

500

600

700

800

900

1000

1100

1154

D. X. HU

Table 1. Table of expansion coefficient of igneous rocks.

Percentage of linear expansion (10−2)

Change in
temperature (normal
temperature to ˚C)

Olivine rock

Amygdaloidal basalt

Granodiorite

Trachyandesite

Compact massive
basalt

Potassium aplite
granite

0.059445

0.047459

0.048435

0.068418

0.070640

0.12935

0.22676

0.34315

0.47542

0.69674

0.86612

0.91493

1.0367

1.2760

1.4712

0.10732

0.18285

0.26126

0.35243

0.46952

0.59144

0.68954

0.81484

1.0369

1.3339

0.11926

0.21623

0.33205

0.49369

0.74864

0.93889

1.0087

1.0364

1.1730

1.4327

0.22549

0.42736

0.66798

0.98233

1.9145

2.2741

2.3381

2.4634

2.5573

3.1368

0.20323

0.38546

0.61330

0.90200

1.4723

1.6998

1.9367

2.0994

2.3441

2.7652

Softening point

1.4727 (1090.3˚C)

1.3400 (1111.8˚C) 2.2243 (1179.5˚C) 3.5504 (1158.0˚C) 2.9462 (1153.0˚C)

1.3753 (1200˚C
not softened)

Figure 2. Schematic diagram of Kuril island arc.

approximate circular arc).

According to the principle that the arc length is the
sum of the string length and the expansion length, the
length of rock expansion along the long axis of back-arc
basin 12.02 km is got with the arc length less the string
length (see the following diagram).

According to the foresaid data, the rock expansion
along the long axis of back-arc basin of island arc is
12.02 km. According to the corresponding relations of
the percentage of linear expansion and temperature in
Table 1, the value of temperature rise of rocks at the

melting point is calculated with the following formula.

P
E



P
S



PT

(1)

In the formula,
PE: the percentage of linear expansion of calculated

temperature;

temperature;

reckoning.

PS: the percentage of linear expansion of softening

PT: the percentage of linear expansion of graphic

It is assumed that the thickness of continental crust is

Copyright © 2013 SciRes. IJG

D. X. HU

1155

35 km, which is the original thickness of continental
crust of back-arc basin. Under the circumstance of linear
geothermal gradient, the melting thickness at the bottom
of continental crust can be calculated.

Through calculation based on the expansion rate of
compact massive basalt, the value of temperature rise is
737˚C, the melting temperature of compact massive
basalt is 1090˚C, the melting thickness at the bottom of
continental crust is approximately 23.67 km.

Through calculation based on the expansion rate of
olivine rocks, the value of temperature rise is 977˚C, the
melting temperature of olivine rocks is 1200˚C, the
melting thickness at the bottom of continental crust is
approximately 28.49 km.

According to the above measurements and calculations,
the string length of island arc is 1015.66 km, the arc
length is 1027.68 km, the length of rock expansion along
the long axis of back-arc basin is 12.02 km. Due to
different rock expansion rate, under the circumstnace of
constant length of rock expansion, different rocks have
different value of temperture rise. The value of tempera-
ture rise of compact massive basalt is 737˚C, the value of
temperature rise of olivine rocks is 977˚C. Under the
circumstance of the same geothermal gradient, different
value of temperature rise shows different melting thick-
ness at the bottom of continental crust. The melting thick-
ness of compact massive basalt is about 23.67 km, the
melting thickness of olivine rocks is about 28.49 km.

According to the data of Kuril Island Arc, the average
thickness of the crust of island arc is 33 km. And the
crust thickness of back-arc basin is 10 km. 23 km sub-
strate is melted, which is close to the melting thickness of
compact massive basalt.

The melting thickness of substrate of back-arc basin
exerts impact on the subsiding depth of the basin. The
melting thickness of substrate can be verified according
to the subsiding depth. In the subsiding process of back-
arc basin, the melted magma at the substrate forms the
interbedding of volcanic rock and sedimentary rock at
back-arc basin in the form of volcanic eruption. When
the melting thickness of substrate at back-arc basin is cal-
culated, the thickness of the sedimentary deposit of back-
arc basin shall be subtracted.

4.2. Japan Island Arc

At the north end of island arc (Point A), longitude
139.3945, latitude 42.1797; at the south end of island arc
(Point B), longitude 130.8911, latitude 34.3797. The
length of string is 1152.27 km, and the displacement is
74.14 km, the arc length of island arc is 1164.95 km, the
length of rock expansion along the long axis of back-arc
basin (AB) is 12.68 km (see the following diagram).

According to the foresaid data and conditions, the
value of temperature rise and the melting thickness are

calculated respectively.

Through calculation based on the expansion rate of
compact massive basalt, the value of temperature rise is
668˚C, and the melting thickness at the bottom of conti-
nental crust is about 21.45 m.

Through calculation based on the expansion rate of
olivine rocks, the value of temperature rise is 907˚C, and
the melting thickness at the bottom of continental crust is
about 26.45 km.

The thickness of the crust of Japan Island Arc ranges
from 37 km to 43 km. The thickness of the crust of Japan
Sea (back-arc basin) is 9 km [5]. This shows that at least
28 km crust of back-arc basin is melted, which is close to
the calculation result of olivine rocks (as shown in Fig-
ure 3).

5. Calculation of the Arc Island

The calculation of arc island mainly depends on the re-
lationship of the deformation of arc island. That is, string
length subtracted from the arc length (straight line AB
in Figure 2) gives the length of rock expansion. Accord-
ing to the length of the rock expansion, the increment of
rock temperature and thickness of rock melted at the
bottom can be calculated. The calculation measure is as
follows:

1) Calculation of the Arc Length.
It can be calculated as on geometric relationship of the

arc length and the radius.

2) Calculation of the Length of the Rock Expansion.
The string length subtracted from the arc length gives

the length of rock expansion.

3) Calculation of the Temperature Increment of the

Rock.

In the first, please consult the Table 1. Then you can
select the rock whose the expansion rate has been known.
Thus formula 1 can be used to do the calculation. The
estimated linear expansion rate (PT) subtracted from the
linear expansion rate (PS) of rock softening temperature
gives the linear expansion rate of calculated temperature
(PE). The calculated linear expansion rate is corres-
ponding to the rock temperature before the melting. The
temperature before melting subtracted from the softening
temperature is equal to the temperature increment.

For example, Kurile Arc Island and linear expansion
rate of tight blocky basalt have been selected to do the
calculation. If we get the linear expansion rate (1.4727)
of tight blocky basalt (softening temperature, 1090˚C),
string length 1015.66 km, arc length 1027.68 km, expan-
sion length 12.02 km of the Kurile Arc Island, thus the
linear expansion rate is 1.1835. And the linear expansion
rate of tight blocky basalt deducts 1.1835 (linear expan-
sion rate of the Kurile Arc island) is equal to 0.2892,
˚
which is corresponding to 353 C in Table 1. Because the

Copyright © 2013 SciRes. IJG

1156

D. X. HU

Figure 3. Schematic diagram of Japan island arc.

softening temperature of tight blocky basalt is 1090˚C, so
we can get the difference 353˚C, which means the tem-
perature increment is 737˚C.

4) Calculation of the Continental Crust Melting Thick-

ness.

Melting thickness of the continental crust refers to the
melted basement rock of the back arc basin. Let’s sup-
pose that the original continental crust thickness is about
35 km. And tight blocky basalt softening temperature is
1090˚C as the sample we have selected. Under the linear
temperature gradient condition, the rock temperature is
353˚C at the depth of 11.33 km, and the temperature in-
crement is 737˚C. That is, the basement of the continen-
tal crust is melted under the depth of 11.33 km, and the
melted thickness is about 23.67 km.

The above analysis is only a concept proposed. The
accurate analysis of an island arc needs to figure out the
following issues: the first is the lithology of substrate of
back-arc basin; the second is the expansion coefficient
and compression coefficient of rocks; the third is the im-
pact of back-arc rift valley; the fourth is the superposition
impact of deformation.

About the formation mechanism of island arc, the au-
thor presents the internal force factor of rock expansion.
It can be seen from the foresaid analysis and calculation,
the formation of island arc is relevant to the dehydration
of subduction oceanic crust, substrate melting, tempera-

ture rise of rocks, rock expansion and etc. The structure
phenomenon that the force generated by the deformation
of rock expansion forming specific dimension in crustal
movement is a kind of non-negligible motive power to
promote crustal movement.

REFERENCES

[1] C. Z. Song and D. L. Qian, “Discussion on Serial Origin
of Northwest Pacific Island Arc,” Geological Review, Vol.
39, No. 1, 1993, pp. 1-8.

[2] Y. J. Li, L. Lin and B. J. Zhao, “The New Mode of the
Origin Mechanism of Faulted Basin at the Mesozoic Era
and the Cenozoic Era in East China,” Geology of Petro-
leum and Natural Gas, Vol. 9, No. 4, 1988, pp. 334-345.

[3] D. X. Hu and M. H. Cai, “Discussion on the Origin of
Arc Basin,” Xinjiang Petroleum Geology, Vol. 33, No. 1,
2012, pp. 120-124.

[4] G. Z. Zhu, Y. L. Shi and H. Zhang, “New Progress of the
Study on Subduction Dynamics in the Deep Part of Plate
Bar,” Progress of Geophysics, Vol. 23, No. 2, 2008, pp.
333-342.

[5] W. Luo, Z. L. Luo and S. P. Chen, “Vertical Deformation
Field of Island Arc Structure and Horizontal Displace-
ment Field and Tectonic Movement and the Features of
Seismic Activities,” China Earthquake, Vol. 11, No. 4,
1995, pp. 351-360.

Copyright © 2013 SciRes. IJG