Structural Geology (The Journal of the Tectonic Research Group of Japan), No. ./, .1ῌ0., ,**+

Genesis of Okinawa Trough and thrust development within
accretionary prism by means of ,D ﬁnite element method
Handi Lu* and Daigoro Hayashi**
Abstract : The Okinawa Trough is a back-arc basin opened by crustal extension within
the Eurasia plate. Several two-dimensional (,D) ﬁnite element models are presented tosimulate the stress ﬁeld and fault development in the upper continental lithosphere of
the Eurasia plate. Linear elastic rheology with failure criterion under plane strain
condition is adopted. Two types of displacement boundary condition are considered in
the numerical model. The spreading displacement is applied along the crustal bottom
beneath the Okinawa Trough. The convergence displacement is subjected along theupper side of the Philippine Sea (PHS) plate. From the simulated results, the spreading
displacement along the crustal bottom generates normal faults in the trough, which
ﬁnally leads to the formation of the Okinawa Trough. The subduction of the PHS plate
causes the thrust development within the accretionary prism of the Eurasia plate. The
results from our numerical experiment are in agreement with the earthquake focal
mechanism in the study area.
Key words : Okinawa Trough, ﬁnite element method, spreading displacement, convergencedisplacement, fault development, accretionary prism

Introduction
The Ryukyu trench-arc-back-arc system, Okinawa Trough, Ryukyu Arc and Ryukyu Trench,
is an active continental margin between the Eurasia plate and the Philippine Sea (PHS) plate(Fig. +). Numerous recent observations havecontributed to the genesis of the Okinawa
Trough (Herman et al., +312 ; Lee et al., +32* ;Kimura, +32/ ; Letouzey & Kimura, +32/ ; Sibuet
et al., +321 ; Miki, +33/ ; Park et al., +332).
Based on the kinematics of the Eurasia plate
and the PHS plate (Seno, +311), several ,D ﬁnite
element models with di#erent rheologies andboundary conditions were proposed. Huchon etal. (+320) presented a ,D viscous ﬁnite element
model for simulating a rigid body (the Luzon
Arc) indenting into a rigid-plastic material (theChinese continental margin). Viallon et al. (+320)
gave a ,D ﬁnite element model of the Okinawa
Trough with an elasto-plastic behavior, andReceived +, March ,**+ ; accepted . July ,**+* Graduate School of Engineering and Science, Universityof the Ryukyus, Nishihara, Okinawa 3*-ῌ*,+** Department of Physics and Earth Sciences, University of
the Ryukyus, Nishihara, Okinawa 3*-ῌ*,+-showed that the opening of the Okinawa
Trough behind the Ryukyu Trench could be
explained by a retreating trench model withlateral anchoring due to the collision in Taiwan.
Hu et al. (+330) used a ,D ﬁnite element model ofplane stress with elastic and elasto-plastic rheologies to analyze the relationship between kinematics of convergence, deformation and stress
distribution in the present Taiwan collision occurring between the Ryukyu and Luzon subduction zones.
In this paper we aim to analyze the genesis of
the back-arc trough and thrust development
within the accretionary prism (tip of the Eurasia
plate) by means of ,D ﬁnite element method(FEM) as follows. (+) Based on the P-wave structural proﬁle modiﬁed from the works of Ludwing et al. (+31-), Kimura (+32-), Iwasaki et al.
(+33*), Hirata et al. (+33+), Kodaira et al. (+330)
and Park et al. (+332), the ﬁnite element grid of
the models are produced. (,) ,D and semi--D
stress ﬁelds of the models are simulated whenseveral di#erent combinations of the spreading
displacement along the crustal bottom beneath
the Okinawa Trough and the convergence dis-ῌ 47 ῌ

Handi Lu and Daigoro Hayashi

Fig. +
Index map showing the Okinawa
Trough, Ryukyu Island Arc and Ryukyu
Trench slightly modiﬁed from Kodaira etal. (+330).
Numerical analysis along
southern proﬁle (S-proﬁle) is carried out.

placement along the subduction slope of the
PHS plate are subjected as the boundary condition. (-) The development of normal fault in thetrough and thrust fault within the accretionary
prism of the Eurasia plate is analyzed according
to the Coulomb-Mohr criterion. (.) The simulated results are compared with the earthquake
focal mechanism in the study area.
Tectonic setting+. Okinawa Trough, Ryukyu Arc, Ryukyu
TrenchThe Ryukyu Arc and the Okinawa Trough are
typical examples of island arc and back-arc
basin which construct the continental platemargin. The Okinawa Trough is a back-arc
spreading zone between the East China Sea andthe Ryukyu Islands, formed by extension within

continental lithosphere behind the Ryukyu Trench-Arc system as shown in Fig. , (Letouzey &Kimura, +32/). The Okinawa Trough extends
from southwest Kyushu in the northeast to
Taiwan in the southwest. It is only 0*῍+** kmwide in the south and reaches up to ,-* km widein the north. Its maximum water depth is about,-** m in the south and progressively decreases
to ,** m in the north.
The exact timing of the trough opening isalways under argument. Although there is aconsensus about the last two phases of extension occurring in the Okinawa Trough since ,Ma, there is a large controversy about the age ofthe early rifting phase (Sibuet et al., +332). Seismic proﬁles and geological observation in thetrough indicate that the rifting started in thelate Miocene (Herman et al., +312 ; Lee et al., +32*
; Letouzey & Kimura, +320 ; Sibuet et al., +321).

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Structural Geology No. ./Genesis of Okinawa Trough and thrust development within accretionary prism by means of ,D ﬁnite element method

Fig. ,
Idealized cross section of the Okinawa
Trough, Ryukyu Island Arc and Ryukyu
Trench modiﬁed from Letouzey and Kimura(+32/).

Kimura (+32/) suggested that in the center of thesouthern Okinawa Trough spreading initiatedin the early Pleistocene (about +.3 Ma ago). Average half-spreading rate has been up to , cm/y.
The northern Okinawa Trough is in a beginningstage to rift (Letouzey & Kimura, +32/ ; Kimura,+32/). Miki (+33/) gave a two-phase opening
model for the origin of the Okinawa Trough on
the basis of paleomagnetic and geochronologicalresearch, and suggested that the ﬁrst phasewould be between +* Ma and 0 Ma, and thesecond phase at about + Ma.
The Ryukyu Arc extends from Taiwan tosouth Kyushu as shown in Fig. - (Letouzey &Kimura, +32/). It is an elevated ridge marked by
two parallel chains comprising more than +**islands. Islands along the inner arc are volcanoes of Quaternary age, whereas those along theouter arc are non-volcanic outcrops (Iwasaki etal., +33*). The Ryukyu Arc is divided into threesegments by the Tokara Channel and theKerama Gap, which are considered to be leftlateral strike-slip faults (Wageman et al., +31* ;Kobayashi, +32/).
The Ryukyu Trench is usually regarded to be
the boundary between the Eurasia plate and the
PHS plate. The maximum water depth of thetrench is more than 1*** m near the Okinawa
Island while most parts of the trench are not

Fig. Tectonic index map of the Taiwan-RyukyuOkinawa region modiﬁed from Letouzey and Kimura(+32/). Arrows at the trench show the convergence of thePhilippine Sea plate with respect to the Eurasia plate,based on the model of Seno (+311).
Arrows at the
Okinawa Trough show the spreading of the Okinawa
Trough.

ῌ 49 ῌ

Handi Lu and Daigoro Hayashi

Schematic illustration of the focal mechanism of
Fig. .
the shallow-depth earthquakes from Taiwan to south
Kyushu after Shiono et al. (+32*).

deeper than 0/** m. The trench becomes shallower and broader towards the north, where thetrench is with a depth of about //** m.
,. Earthquake focal mechanism
Tectonic features of the Kyushu-Ryukyu Arc
were investigated in detail by Shiono et al.
(+32*), on the basis of seismicity and focal mechanism solution of shallow to intermediate depth
earthquakes with magnitudes around and greater than /.*. The focal mechanism of the shallowdepth earthquakes is summarized, as a schematic illustration in Fig. . (Shiono et al., +32*). From
the focal mechanism, stress is tensional in the
Okinawa Trough, and thrust faults develop
within the accretionary prism as the PHS platesubducts beneath the Eurasia plate.
Finite element modeling
Model geometry
The southern proﬁle (S-proﬁle), a seismic
P-wave structural section, has been constructedon the basis of the works of Ludwing et al.
(+31-), Kimura (+32-), Hirata et al. (+33+) and Parket al. (+332). S-proﬁle is about -,* km long with adepth of about +2 km. (Fig. /). The sedimentarywedge of the continental crust consists of threelayers, whose P-wave velocities are +.2῍+.3, ,.*῍-.0 and ../ km/s at the top of each layer asshown in Fig. /. The +.2῍+.3 and ,.*῍-.0 km/s
layers are assumed to be composed of sandstone,
while the layer ../ km/s is considered to be composed of limestone. The P-wave velocities of
granite layer are 0.,῍0.. and 1.*῍1., km/s. The
Moho depth is deduced to be about +2 km beneath the southern Okinawa Trough. The descending velocity of the PHS plate beneath theEurasia plate is assumed to be 0.- cm/y in the+.

southern section (Fig. -). The angle between the
strike of S-proﬁle and the convergence directionof the PHS plate is ,0῎. The angle between the
striking of S-proﬁle and the spreading direction
under the trough is 3῎. The dip of the subduction slope of the PHS plate is +3῎ to the horizon(Fig. /).
,. Finite element grid
The ﬁnite element grid of model S is -,* kmlong and +2 km deep as shown in Fig. 0. It is
composed of 0,. nodes and +*.+ triangular elements. In the grid of model S, di#erent kinds ofline (thin, thick and intermediate) indicate sandstone, limestone and granite. The grid of models
S+, S, and S- is the same as model S, but their
two types of displacement boundary condition
are di#erent from each other (Fig. 0, Table ,).
-. Physical properties
The continental crust of the Eurasia plate issimpliﬁed to be composed of sandstone, limestone and granite from top to bottom as a threelayered elastic continuum. Since we have adopted the elastic rheology in the simulation,
physical properties of sandstone, limestone andgranite are listed in Table +.
.. Boundary conditions
Two types of displacement boundary condition but no tectonic force are imposed in ﬁnite
element models. Neither trench suction force
nor overriding plate resistance force is considered in numerical model. This point is also thespeciality of our numerical experiment. The
spreading displacement is applied along the crustal bottom beneath the trough to represent the
spreading of the Okinawa Trough. Since thePHS plate subducts beneath the Eurasia plate,the convergence displacement is subjected tothe upper side of the descending plate along theῌ 50 ῌ

Structural Geology No. ./Genesis of Okinawa Trough and thrust development within accretionary prism by means of ,D ﬁnite element method

Fig. /
P-wave velocity structure of the S-proﬁlemodiﬁed from the works of Kimura (+32-), Hirata et al.
(+33+) and Park et al. (+332). Vertical exaggeration istaken as about +/ : ,. Dashed lines are extrapolations of
the interfaces obtained by the ocean bottom seismometer(OBS) data.

subduction slope.
The boundary conditions of model S are indetail as follows (Table ,). The basal nodes on
the crustal bottom (BG) are constrained to zerovertical displacement but are free horizontally,
though the negative and positive spreading displacements are given along the crustal bottom
under the trough. The nodes at left edge (AB) of
the lithosphere are constrained to zero horizontal displacement but are free vertically. Node B
is ﬁxed. The nodes of the overriding plate on the
subduction slope are applied with the convergence displacement. The convergence displacement decreases gradually from the node (/*. m)at the shallow place to that at the deep place (+02m) on the subduction slope, and the convergencedisplacement decrement is ,2 m.
/. Finite element method
Since the stretch of the Okinawa Trough,Ryukyu Arc and Ryukyu Trench is more than+*** km and approximately perpendicular to theconvergence direction of the PHS plate, linear
elastic rheology with plane strain condition isapplied to analyze the stress ﬁeld of the upper
lithosphere of the Eurasia plate. The ﬁnite element modeling is carried out with the linear
elastic elas.f code (developed by D. Hayashi).
Gravitational body forces are included in themodels.
All the ﬁnite element models are in ,D elastic
state under the plane strain condition. Since ,Dstress ﬁelds of the numerical models are simulated with the elas. f code, the third principal
stress s*, which acts perpendicularly to the section plane, can be obtained from the theory ofplane strain asῌ
s*ῐnῌ῍s+῏s,῎where n is Poisson’s ratio (Timoshenko & Goodier, +31* ; Hayashi & Kazaki, +31,). Since thevalues of s+, s, and s* of each ﬁnite element havebeen calculated, we can deﬁne which principal
stress (s+, s,, s*) is the maximum, intermediate
and minimum principal stress. The semi--D
stress ﬁeld of each model is envisaged with the
newly obtained principal stresses s+, s, and s-.
As the semi--D stress ﬁeld of each model isavailable, it is possible to describe in whichﬁnite element, fault will develop according to
the Coulomb-Mohr criterion. The criterion isexpressed on a linear relationship between theshear stress t and the normal stress sn as
῍tῐc῏snῌtanf
where c is the cohesion strength and f is theinternal friction angle as shown in Fig. 1

ῌ 51 ῌ

Fig. 0Finite element grid of model S. The grid is composed of 0,. nodes and +*.+ triangular elements. Thin, thick and intermediate lines indicate sandstone, limestone andgranite. Physical properties are listed in Table +. Lines with arrow represent the two types of displacement boundary condition (see text and Table ,). The grid of models S+, S,
and S- is the same as model S.

Handi Lu and Daigoro Hayashi

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Structural Geology No. ./Genesis of Okinawa Trough and thrust development within accretionary prism by means of ,D ﬁnite element method

Table ,

Two types of displacement boundary condition subjected in ﬁnite element models.

Table +

Physical properties applied for sandstone, limestone and granite.

Fig. 1
Linear Coulomb-Mohr criterion demonstrating the concept ofproximity to failure after Melosh andWilliams (+323).

(Melosh & Williams, +323) and listed in Table +(Clark, +300). Failure develops when the Mohr’s
stress circle touches the Coulomb-Mohr failureenvelope. This takes place when the radius of
the Mohr’s stress circle, (s+ῐs-)/,, is equal to or
greater than the perpendicular distance fromthe center of the circle, (s+῏s-)/,, to the failureenvelope.
The proximity to failure Pf is calculated foreach ﬁnite element of the models using the fol-lowing equations (Melosh & Williams, +323).
῍῍s+ ῐs-῎ ῌ ,῎failure ῑcῌcos f῏῍῍s+ ῏s-῎ ῌ ,῎ῌ
ῌ
sin f
῍
Pfῑ῍῍s+ῐs-῎ῌ,῎ῌ῍῍s+ῐs-῎ῌ,῎failure
We can evaluate whether faulting occurs in certain ﬁnite element according to the value ofparameter Pf. If the value of Pf is less than +.*,
the Mohr’s stress circle is inside the failure envelop and no fault develops, but faulting occurs
whenever Pf exceeds +.*. Thus the parameter Pf

ῌ 53 ῌ

Fig. 2Magnitude and orientation of the principal stresses in the semi--D stress ﬁelds of models S, S+, S, and S-. Straight lines represent compression, and lines with arrow
represent tension. Note that the boundary condition is di#erent in the four models.

Handi Lu and Daigoro Hayashi

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Structural Geology No. ./Genesis of Okinawa Trough and thrust development within accretionary prism by means of ,D ﬁnite element method

is taken as an indicator to deﬁne whether thefault develops or not.
Modeling results
Stress ﬁeld
The semi--D stress ﬁelds of models S, S+, S,
and S- are simulated as shown in Fig. 2. s+ and srepresent the maximum and minimum principal
stresses, and compression is taken as positive.
The spreading displacement of 2* m and theconvergence displacement varying from /*. m
to +02 m are subjected to model S as the boundary condition (Table ,). The main feature of thestress ﬁeld of model S is that s- is tensional in
the southern Okinawa Trough and that compressive s+ is nearly horizontal within the accretionary prism of the Eurasia plate. In thesouthern Okinawa Trough, compressive s+ is
nearly vertical while tensional s- is nearly horizontal. In the southern Ryukyu Arc, compressive s+ is nearly horizontal while compressive sis nearly vertical at the shallow place (*῍+, kmdeep). However compressive s+ and s- are inclined at the deep place (+,῍,0 km deep).
Within the accretionary prism, compressive s+ is
nearly horizontal and compressive s- is nearlyvertical. s+ is compressive and nearly vertical in
the trough while compressive s+ is nearly horizontal within the accretionary prism. The maximum values of compressive s+ and s- are 2/.
MPa and -*. MPa, respectively. The absolute
maximum value of tensional s- is 3.- MPa.
The spreading displacement of 2* m but noconvergence displacement is applied as the boundary condition in model S+ (Table ,). The
stress distribution of model S+ is similar to thatof model S in the trough, but is di#erent frommodel S within the accretionary prism of theEurasia plate where compressive s+ is roughly
vertical in model S+. The convergence displacement varying from /*. m to +02 m is loaded as
the boundary condition in model S, (Table ,). In
the trough, the stress ﬁeld of model S, is di#erent from model S since s- is compressive inmodel S,. Within the accretionary prism of theEurasia plate, the stress ﬁeld of model S, issimilar to model S. Neither the spreading displacement nor the convergence displacement issubjected to model S- as the boundary condition+.

(Table ,). The stress distribution of model S- is
deﬁnitely di#erent from model S in the troughand within the accretionary prism. In model S-,
s- is compressive in the trough and compressives+ is nearly vertical in the accretionary prism of
the Eurasia plate.
,. Inﬂuence of displacement boundary condition to stress ﬁeld
The stress ﬁelds of models S, S+, S, and Sshow di#erent features from each other. In thetrough, s- is tensional in models S and S+ while
the spreading displacement of 2* m is applied as
the boundary condition. However no tensional
stress occurs in models S, and S- with no spreading displacement subjected. The stress ﬁelds ofmodels S, and S- are similar to each other in thetrough, though their convergence displacementboundary conditions are di#erent. The stressﬁeld of model S+ is similar to model S in thetrough, whereas their convergence displacement boundary conditions are di#erent. Thus
the spreading displacement loaded as the boundary condition raises up tension in the trough.
The convergence displacement subjected as theboundary condition hardly a#ects the stress distribution in the trough.
Within the accretionary prism of the Eurasia
plate, compressive s+ is nearly horizontal inmodels S and S, while the convergence displacement varying from /*. m to +02 m is loaded as
the boundary condition. However compressives+ is nearly vertical within the accretionary
prism in models S+ and S- as zero convergencedisplacement is applied. The stress ﬁeld ofmodel S is similar to model S, within the accretionary prism, though their spreading displacement boundary conditions are di#erent.
The stress ﬁeld of model S+ is similar to model S- within the accretionary prism, whereas theirspreading displacement boundary conditions
are di#erent. Thus the convergence displacement generates horizontal compressive s+
within the accretionary prism of the Eurasia
plate. The spreading displacement has little
e#ect on the stress distribution within the accretionary prism.
-. Inﬂuence of displacement boundary condition to fault development
The style of fault development is di#erent inmodels S, S+, S, and S- as shown in Fig. 3. In theῌ 55 ῌ

Fig. 3
Fault development in models S, S+, S, and S-. The maximum and minimum principal stresses are illustrated just for the ﬁnite element with Pf῍+.* in the four models.
Straight lines represent compression, and lines with arrow represent tension.

Handi Lu and Daigoro Hayashi

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Structural Geology No. ./Genesis of Okinawa Trough and thrust development within accretionary prism by means of ,D ﬁnite element method

trough, normal faults develop in models S and S+ with the spreading displacement subjected as
the boundary condition. On the other hand nonormal fault develops in models S, and S- aszero spreading displacement is applied. Within
the accretionary prism of the Eurasia plate,thrust faults develop in models S and S, inwhich the convergence displacement varying
from /*. m to +02 m is loaded. However nothrust fault develops in models S+ and S- as zeroconvergence displacement is subjected. Thus
the spreading displacement generates normal
faults in the trough and it hardly a#ects thrustdevelopment within the accretionary prism.
The convergence displacement causes thrust development within the accretionary prism of theEurasia plate and it has little e#ect on the fault
development in the Okinawa Trough.
Discussion
All the ﬁnite element models here are assumed
to be elastic in the simulation. The elastic assumption is based on the theory of plate tectonics (Turcotte & Schubert, +32,). The continental
lithosphere is considered to be internally rigid.
The rigidity of the lithosphere allows the plates
to transmit elastic stresses during geologic intervals. Generally the continental lithosphere
has a thickness of more than +** km, though the
thickness of our numerical models is less than ,*km in the Eurasia continental plate. Although
the entire lithosphere is not e#ective in transmitting elastic stresses, the upper half of it issu$ciently rigid. This fraction of the lithosphere is referred to as the elastic lithosphere.
We think that the elastic assumption is acceptable for the following reason. The principle strains in our numerical models are mostly lessthan +ῌ and few are +῍,./ῌ. The maximum
shortening or elongation of sandstone is up to,./ῌ when the axial di#erential stress s+῎s- isless than failure strength under the conﬁning
pressure of /* MPa as shown in Fig. +* (Hoshino
et al., +31,).
The simulated result of model S, in which the
spreading displacement of 2* m and the convergence displacement varying from /*. m to +02 m
are subjected as the boundary condition, is inagreement with the earthquake focal mecha-

Stress-strain curve for Furukawa sandstone,
Fig. +*
HSF (S32) after Hoshino et al. (+31,).

nism in the Okinawa Trough. From the focal
mechanism, stress is tensional in the trough as
illustrated in Fig. . (Shiono et al., +32*). The
simulated stress ﬁeld of model S shows that s- is
tensional in the trough (Fig. 2). The simulated
result of model S also coincides with the earthquake focal mechanism within the accretionary
prism of the Eurasia plate. According to the
focal mechanism, thrust faults develop within
the accretionary prism as shown in Fig. .
(Shiono et al., +32*). The simulated result also
shows that there are some ﬁnite elements with
Pf῏+.* within the accretionary prism in model S,
where thrust faults develop (Fig. 3).
The spreading of the Okinawa Trough is simpliﬁed as the spreading displacement along thecrust bottom. As the PHS plate subducts beneath the Eurasia plate, the convergence litho-ῌ 57 ῌ

Fig. ++
Magnitude and orientation of the principal stresses in the semi--D stress ﬁelds of models S-A, S-B, S-C and S-D. The value of the spreading displacement varies in thefour models while the values of the convergence displacement are ﬁxed.

Handi Lu and Daigoro Hayashi

ῌ 58 ῌ

Fig. +,
Fault development in models S-A, S-B, S-C and S-D. The maximum and minimum principal stresses are illustrated just for the ﬁnite element with Pf῍+.* in the fourmodels. Note that the intensity of the spreading displacement regulates the development of normal fault in the trough.

Structural Geology No. ./Genesis of Okinawa Trough and thrust development within accretionary prism by means of ,D ﬁnite element method

ῌ 59 ῌ

Fig. +Magnitude and orientation of the principal stresses in the semi--D stress ﬁelds of models S-I, S-II, S-III and S-IV. The value of the spreading displacement is ﬁxed whilethe values of the convergence displacement vary in the four models.

Handi Lu and Daigoro Hayashi

ῌ 60 ῌ

Fig. +.
Fault development in models S-I, S-II, S-III and S-IV. The maximum and minimum principal stresses are illustrated just for the ﬁnite element with Pf῍+.* in the fourmodels. Note that the intensity of the convergence displacement controls the thrust development within the accretionary prism of the Eurasia plate.

Structural Geology No. ./Genesis of Okinawa Trough and thrust development within accretionary prism by means of ,D ﬁnite element method

ῌ 61 ῌ

Handi Lu and Daigoro Hayashi

sphere induces a secondary convection cell (Turcotte and Schubert, +32,). The positive and negative values of the spreading displacement indicate the two di#erent directions of the mantle
convection under the trough. This is the signiﬁcance of the spreading displacement under thetrough in numerical models.
The convergence displacement is appliedalong the subduction slope in ﬁnite element
models. The application of the varying convergence displacement is somewhat arbitrary. To
get a similar simulated results with the earthquake focal mechanism (Shiono et al., +32*), thevarying convergence displacement is appliedalong the subduction slope and thrust faults
develop within the accretionary prism. On theother hand no thrust development occurs as theconstant convergence displacement is imposed
along the subduction slope. More detailed discussion about the varying convergence displacement or the slip deﬁciency along the subduction slope is beyond the scope of this paper.
Although the role of the two types of displacement boundary condition to the fault development is shown up, the inﬂuence of the intensityof the spreading and convergence displacements
is unknown. In order to make out the inﬂuenceof the intensity of the spreading displacement to
the development of normal fault in the Okinawa
Trough, stress ﬁelds of models S-A, S-B, S-C and
S-D are simulated (Fig. ++). The spreading displacement varies in the four models while theconvergence displacements are ﬁxed (Table ,).
The ﬁnite-element grid of the four models is thesame as model S.
The stress ﬁelds of models S-A, S-B, S-C andS-D show di#erent features from each other. In
the trough, tensional s- becomes stronger andoccupies more extensive area as the value of the
spreading displacement increases. Within theaccretionary prism of the Eurasia plate, thestress distributions of the four models are similar to each other. Thus the intensity of the
spreading displacement decides the magnitude
and area of tensional stress in the Okinawa
Trough.
The development style of normal fault in thetrough is di#erent in models S-A, S-B, S-C and
S-D as illustrated in Fig. +,. In the trough,normal faults develop at the deep place in model

S-A, and develop within more extensive area inmodel S-B. As the value of the spreading displacement increases, normal faults develop
within almost all the ﬁnite elements in thetrough. However within the accretionary prismof the Eurasia plate, thrust development is similar in the four models. Thus the intensity of the
spreading displacement controls the occurrence
and area of normal fault in the Okinawa Trough.
In order to know the inﬂuence of the intensityof the convergence displacement to the thrustdevelopment within the acretionary prism of
the Eurasia plate, stress ﬁelds of models S-I, S-II,
S-III and S-IV are simulated (Fig. +-). The valueof the spreading displacement is unchanged in
the four models while the values of the convergence displacement are varied (Table ,). The ﬁnite-element grid of the four models is the same asmodel S.
The stress ﬁelds of models S-I, S-II, S-III and
S-IV show di#erent features from each other.
Within the accretionary prism, compressive s+
tends to be nearly horizontal, and increases its
area from the shallow to deep place as the valuesof the convergence displacement increase. However, in the trough, the stress distribution issimilar in the four models. Thus the intensity of
the convergence displacement changes the orientation and area of horizontal compressive s+
within the accretionary prism of the Eurasia
plate.
The style of thrust development within theaccretionary prism is di#erent in models S-I, S-II,
S-III and S-IV as shown in Fig. +.. No thrustfault develops in model S-I. There are few ﬁnite
elements with Pf῍+.* at the shallow place within
the accretionary prism in model S-II, where
thrust faults develop. As the values of the convergence displacement increase, thrust faults
develop within almost the whole accretionary
prism. However the development of nomal fault
in the trough is similar in the four models. Thus
the intensity of the convergence displacement
regulates the occurrence and area of thrustfaults within the accretionary prism of the Eurasia plate.

ῌ 62 ῌ

Conclusions
In this paper, semi--D stress ﬁelds of the Eura-

Structural Geology No. ./Genesis of Okinawa Trough and thrust development within accretionary prism by means of ,D ﬁnite element method

sia plate are simulated with a series of ﬁnite
element models. The spreading displacement
along the crustal bottom under the Okinawa
Trough and/or the convergence displacement
attached along the upper side of the PHS plate
are subjected as the boundary condition. The
development style of normal fault in the backarc trough and thrust fault within the accretionary prism of the Eurasia plate is analyzed. The results obtained from the numericalexperiment allow us to draw the following conclusions.
The spreading displacement under the troughis one type of displacement boundary condition
for numerical model. Tensional stress appears
and normal faults develop in the trough as the
spreading displacement is applied as the boundary condition. On the other hand there is no
tension and no normal fault develops in thetrough with zero spreading displacement subjected. The spreading displacement along thecrustal bottom beneath the trough raises up
tensional stress and generates normal faults inthe trough. The intensity of the spreading displacement controls the area of tensional stressand normal fault in the trough. However theconvergence displacement has little e#ect on
the stress distribution and development style ofnormal fault in the trough. Since normal faults
in a tensional terrane often leads to the formation of a trough structure (Melosh & Williams,+323), the genesis of the Okinawa Trough is the
spreading along the crustal bottom beneath the
back-arc trough.
The convergence displacement attached along
the upper side of the PHS plate is the other typeof displacement boundary condition for numerical model. Thrust faults develop within theaccretionary prism of the Eurasia plate as theconvergence displacement is loaded. However
no thrust fault develops with zero convergencedisplacement subjected. The convergence displacement causes thrust development within
the accretionary prism. The intensity of theconvergence displacement controls the area ofthrust fault within the accretionary prism, but
the spreading displacement hardly a#ects thestress distribution and style of thrust development within the accretionary prism of the Eurasia plate. The genesis of the thrust development

within the accretionary prism is the subductionof the PHS plate beneath the Eurasia plate.
Acknowledgements
H. Lu would like to express his appreciation to
Ministry of Education, Culture, Sports, Scienceand Technology and Association of International Education, Japan for the ﬁnancial support ofscholarship to this work.
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