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JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 113, B04414, doi:10.1029/2007JB005038, 2008
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Conditions for a crustal block to be sheared off from the subducted
continental lithosphere: What is an essential factor to cause features
associated with collision?
Tetsuzo Seno1
Received 9 March 2007; revised 14 November 2007; accepted 26 December 2007; published 23 April 2008.
[1] Crustal blocks are detached from the subducting lithosphere at various depths. I call
such phenomena shearing-off and investigate the mechanical conditions for shearing-off to
occur in the continental lithosphere. The buoyancy of the crustal block does not work
selectively as a driving force until it has been sheared off and I suppose that shearing-off
occurs when the shear traction at the thrust, whose maximum value is calculated from
the strength along the thrust, overcomes the strength of the boundary faults of the
block, and determine the depth of the leading edge of the subducted crustal block when
shearing-off occurs. The temperatures of the slab and at its surface are calculated by
the steady state formula of Molnar and England (1990) as a function of the surface heat
flow, dip angle, and convergence velocity of the subducted continental plate, as the
shear stress and temperature at the ductile part of the thrust zone are consistent with the
flow law. The shear stress at the brittle part is a strong function of the pore fluid
pressure ratio l. I show that shearing-off of an upper crustal block is possible only for a
small value of l such as <0.4 when the surface heat flow value is <70 mW/m2. I
suggest that the essential factor to cause shallow offscraping of crustal blocks in collision
zones, is not a buoyancy of the continental crust, but a low value of l, which would result
from a little amount of dehydration from the subducted continental plate.
Citation: Seno, T. (2008), Conditions for a crustal block to be sheared off from the subducted continental lithosphere: What is an
essential factor to cause features associated with collision?, J. Geophys. Res., 113, B04414, doi:10.1029/2007JB005038.
1. Introduction
[2] Offscraping of materials from the subducting oceanic
or continental lithosphere and succeeding accretion into the
overriding plate occurs in various scales and depths
(Table 1, e.g., Scholl et al. [1977]; Shreve and Cloos
[1986]; Ben-Avraham et al. [1981]; Taira et al. [1992]).
Sediment accretion/underplating near the toe of the trench
or behind the frontal thrust is one of such phenomena
extensively studied in recent years [Suppe, 1981; Shipley
and Moore, 1986; Taira et al., 1988; Langseth and Moore,
1990; Kimura, 1994; Mugnier et al., 2004]. In a larger
scale, offscraping of the upper or whole continental crust
from the subducting continental lithosphere is observed at
shallow depths in some collision zones. For example,
offscraping of the Indian continental crust has occurred in
the foreland fold and thrust belt of the Himalayan collision
zone [e.g., Molnar, 1984; Butler, 1986; Mattauer, 1986].
Offscraping of the subducted Bonin island arc crust has
occurred intermittently in central Japan [Amano, 1991;
Taira et al., 1992].
[3] In some subduction zones, no sediment accretion is
observed [von Huene and Scholl, 1991]. Similarly, the
1
Earthquake Research Institute, University of Tokyo, Tokyo, Japan.
Copyright 2008 by the American Geophysical Union.
0148-0227/08/2007JB005038$09.00
continental lithosphere can, in some cases, subduct to
depths of 100 200 km as shown by the presence of
exhumed ultrahigh-pressure (UHP) metamorphic rocks in
collision zones [Liou et al., 1994; Coleman and Wang,
1995; Ernst and Liou, 1999; Chopin, 2003]. Such exhumation implies that part of the subducted continental crust
is detached from the rest of the lithosphere at these or
greater depths and then rises up close to the Earth’s surface,
often as a coherent sheet [Philippot, 1990; Wheeler, 1991;
Maruyama et al., 1996]. The W. Alps is a typical place
where exhumation of high-pressure (HP)/UHP terranes has
formed numerous nappes [e.g., Chopin, 1987; Platt, 1986;
Hsu, 1991; Escher and Beaumont, 1997], and shallow
offscraping of the continental crust is rather minor. However, even in the Himalayas, it is known that exhumation of
UHP rocks occurred in its earliest stage of collision
[Kaneko et al., 2003].
[4] Such a variety in depth and time of detachment of
crustal sheets from the subducting lithosphere is also seen in
oceanic plates, although most oceanic plates are subducting
smoothly without obduction, even if they suffer shallow
sediment accretion. Obduction of ophiolites have occurred
occasionally in the shallow part of subduction zones
[Coleman, 1971; Dewey and Bird, 1971; Dewey, 1976;
Ogawa and Taniguchi, 1988]. Furthermore, exhumation of
HP terranes from a depth of about 30– 50 km has also
occurred occasionally [Ernst, 1971; Miyashiro, 1972;
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Table 1. Phenomena Related to Shearing-Off From the Subducting Lithosphere
Depth of Shearing-Off
Shallowest (d < 10 km)
Shallow (d = 1030 km)
Intermediate (d = 3060 km)
Deep (d > 60 km)
Oceanic Lithosphere
offscraping of sediments (rarely seamounts)
ophiolite obduction, offscraping
of aseismic ridges and plateaus
exhumation of high-pressure (HP) metamorphic rocks
exhumation of ultrahigh-pressure (UHP) metamorphic rocks
Banno and Sakai, 1989; Maruyama et al., 1996]. Recent
detailed studies of HP metamorphic rocks of the Sanbagawa
belt, Japan, showed that part of the subducted oceanic plate
was exhumed from the depths of 100 km, close to those of
the UHP rocks in collision zones [Aoya et al., 2003; Ota et
al., 2004].
[5] The fate of subducted crustal and mantle rocks,
therefore, seems to be diverse in both space and time. Many
researchers have tried to solve the mechanism of such
variation by relating the buoyancy of continents, continental
fragments, plateaus, and seamounts to their subductability
[Molnar and Gray, 1979; Nur and Ben-Avraham, 1982;
Cloos, 1993]. They, however, do not seem successful
enough so far in explaining, for example, why a thin sheet
of continental crust is accreted in some places, but not in
others, why UHP rocks are exhumed often in the initial
stage of collision, or why ophiolites are obducted in rare
cases. This would imply that subductability of such features
would not be a simple matter of buoyancy.
[6] In this study, I call separation of the upper coherent
block (sheet) of the subducting continental or oceanic
lithosphere from the rest of it (due to the shear traction at
the thrust, as will be shown later) shearing-off. I use here the
terminology such as subduction and slab also for continental
plates, because it is now known that continental plates can
in some cases penetrate deep into the mantle. The purpose
of this study is to address a question what is a controlling
factor that determines the depths of shearing-off for a plate
capped by a continental crust with enough thickness.
Answering this question seems important to understand
the geological processes associated with collision, where
plates with thick continental crust are impinging beneath the
overriding plate, causing phenomena related to shearing-off
at various depths and times as stated above. It would also
have implications for shearing-off in subducting oceanic
plates as will be shown in the discussion section.
[7] van den Beukel [1992] first investigated the conditions of shearing-off (breakup of the subducting lithosphere
in his term) for the continental plate based on his thermomechanical models of the subducting lithosphere. He assumed that shearing-off occurs when the driving forces
overcome the resistive forces to break the boundary of the
detached block (Figure 1), and I follow his scheme in this
paper. He, however, included the buoyancy force operating
to the crustal block in the driving forces. I show that the
buoyancy force of the subducting crust does not work as a
driving force for shearing-off, and do not include it in the
driving forces.
[8] He also assumed that the pore fluid pressure ratio l,
defined by Pw = lsn where Pw is the pore pressure and sn is
the normal stress at the thrust [Hubbert and Rubey, 1959],
as high as 0.96, which was inferred to be typical for oceanic
Continental Lithosphere
offscraping of continental
and island arc crust
plate subduction [e.g., van den Beukel and Wortel, 1988;
Lamb, 2006]. He used hydrostatic Pw in the block boundary
inside the subducting slab. He obtained the results that
shearing-off occurs when the leading edge of the detached
block reaches at a depth of 3050 km for the continental
lithosphere with a high to moderate surface heat flow
(>60 mW/m2) prior to subduction, and it does not occur
with a low surface heat flow (<50 mW/m2). With these
results, however, it seems difficult to explain the diversity
in depth of shearing-off as stated above in a straightforward
way.
[9] In this study, I take l ranging from 0 to 0.95. This
wider range is because there is no a priori reason to assume
values of l similar to those at the thrust of the subducting
oceanic plate and there has been evidence for little dehydration from the subducting continental or island arc crust
[Seno and Yamasaki, 2003; Seno, 2007]. I show that,
without the buoyancy force, the effect of l is more
important and shearing-off can occur only when l is small,
if the surface heat flow prior to subduction is moderate or
low. I try to demonstrate that a controlling factor to cause
features characteristic of collision, such as shallow offscraping of a continental crust and intense deformation in
the hinterland, is not the buoyancy of the crust but small l. I
also try to explain the observed diversity in shearing-off
among collision zones, e.g., the difference seen between the
Himalaya and the W. Alps, by the different evolution of l
through their histories of collision.
2. Conditions for Shearing-Off to Occur
[10] van den Beukel [1992] asserted that the buoyancy
force acts on the subducting crust and serves as a driving
force for shearing-off. However, on the basis of the Archimedes’ principle, the buoyancy force arises from the pressure of the fluid integrated over the surface of the object. If
the crustal and mantle part of the lithosphere is not separated, the asthenospheric pressure does not act at the base of
the crust as far as the lithosphere behaves as an elastic plate.
The buoyancy force acts to the lithosphere as a whole, if it is
embedded within the asthenosphere, by the difference in
asthenospheric pressure at the top and the bottom, not
selectively to the crustal block to be sheared off. Therefore
prior to accomplishment of shearing-off, it is evident that
the buoyancy force does not help to peel the crustal block
off from the rest of the lithosphere. This shows that the
shear stress, or its integrated value, on the top of the block
(Figure 1) is the only driving force for shearing-off.
[11] I assume that shearing-off occurs when the shear
traction at the thrust overcomes the forces necessary to
break the faults (F1, F2, and F3) surrounding the block.
Without the shear traction, all the continental lithosphere
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Figure 1. A schematic cross-section of a subduction zone with the driving and resistive forces for
shearing-off. The crustal block to be sheared off is shaded. The upper surface Fc is the thrust zone where
the driving shear force, whose maximum value is Tc, is operating. F1 and F3 are broken as reverse and
normal faults, respectively. F2 is detached along the ductile shear zone at the base of the upper crust. The
resistive forces, T1, T2, T3, are the tractions necessary to break faults F1, F2, and F3. It is assumed that
when Tc overcomes a sum of these resistive forces, shearing-off occurs.
may be subducted into a greater depth, if an enough amount
of the slab pull is available [Molnar and Gray, 1979]. I
calculate the depth of the leading edge of the block, when
shearing-off occurs. Although the traction provides a driving force for shearing-off, it is often difficult to estimate an
exact amount of this force, because it might vary temporarily due to occurrence of earthquakes at the thrust zone. In
this paper, I therefore use the maximum value of the shear
stress, i.e., strength t c, and its integrated value, traction Tc,
over thrust zone Fc.
[12] T2 is the shear traction to cause shear failure along
F2. On the other hand, fault planes F1 and F3 are broken by
reverse faulting and normal faulting, respectively. Within
the slab near the fault edge, s1 and s3, the principal stresses,
are aligned in the dip and perpendicular directions of the
slab, respectively [Matsumura, 1997, Figure 1]. Let T1 and
T3 be the integrated values of s1 – s3 needed to fracture F1
and F3, respectively, from the upper to the lower ends of
these faults. Because the stress perpendicular to the slab is
close to the lithostatic (Appendix A), these forces to fracture
F1 and F3 are able to be compared with Tc or T2. Then, I
assume that shearing-off occurs when
Tc > T1 þ T2 þ T3 :
ð1Þ
the continental crust [Christensen and Mooney, 1995]. The
densities of the crust and the mantle (rc and rm) are
assumed to be 2800 and 3300 Kg/m3, respectively.
[14] I try to see the effect of Pw on the occurrence of
shearing-off by changing the value of l from 0 to 0.95. The
higher end of this range is the one favored for subduction
zones [van den Beukel and Wortel, 1988; Tichelaar and
Ruff, 1993; Peacock, 1996; Cattin et al., 1997; Lamb,
2006]. The lower end implies that no fluid is supplied to
the pore space. The high value of l in subduction zones is
probably caused by dehydration of subducting altered crust
and serpentinized mantle. Therefore there is no reason to
assume this high value in collision zones, where a small
extent of dehydration of the subducted continental crust is
expected [see Seno and Yamasaki, 2003; Seno, 2007]. m and
t 0 are 0.85 and 0 MPa, respectively, for sn < 200 MPa, and
0.6 and 50 MPa, respectively, for sn > 200 MPa [Byerlee,
1978].
[15] For the ductile part of the thrust zone, the shear stress
cannot be given in an a priori manner because the shear
stress depends on temperature Ts at the slab surface through
the flow law, and on the other hand, the temperature
depends on the shear stress through shear heating, as noted
by Lamb [2006]. The ductile shear stress at the fault plane is
represented using the power law rheology by
t c ¼ ½e=A0 3. Driving Force
[13] For the brittle part of Fc, t c is given by the Byerlee’s
friction law, as
t c ¼ ms*n þ t 0 ¼ mðsn Pw Þ þ t 0 ¼ mð1 lÞsn þ t 0 ;
ð2Þ
where m is the coefficient of static friction, s*n (= sn Pw)
is the effective stress, and t 0 is the cohesive stress.
Compressive stresses are taken to be positive throughout
this study. Pw is normalized to sn by Pw = lsn. As shown in
Appendix A, sn is approximated by the lithostatic pressure.
The thickness of the upper crust huc and that of the lower
crust hlc are both assumed to be 18 km, which are typical for
1=n
exp½ðE* þ v*PÞ=nRTs ;
ð3Þ
where e is the shear strain rate, A0 is the constant converted
from the constant A of the triaxial compression experiment
to that of the 2-d simple shear problem, n is the number
close to 3, E* is the activation energy, v* is the activation
volume, P is the lithostatic pressure, and R is the gas
constant. A0 is the same constant in the generalized
constitutive equation and converted from A as
A0 ¼ 3ðnþ1Þ=2 A=2
ð4Þ
(see Appendix B).
[16] To calculate the temperature at the surface and inside
of the slab, I ignore convection in the mantle wedge, and
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Table 2. Parameters Used in the Modeling
Parameter
Definition
tc
Tc
shear strength at the thrust
maximum shear traction integrated
over the thrust
traction needed to fracture F1
traction needed to slip along F2
traction needed to fracture F3
T1 + T2 + T3
pore fluid pressure
pore fluid pressure ratio
coefficient of friction
cohesive stress
fracture angle that satisfies m = cot2q
surface temperature of the slab
temperature within the slab
surface heat flow of the continental
plate 50 – 90 mW/m2
plate thickness
convergence velocity
dip angle of the underthrusting slab
radiogenic heat production at the surface
scaling depth for exponential
decay of radiogenic heat production
thermal conductivity 2.7 W/mk
thermal diffusivity 106 m/s2
thickness of the upper crust 18 km
thickness of the lower crust 18 km
density of the crust 2800 Kg/m3
density of the mantle 3300 Kg/m3
strain rate 104/s in the thrust
1016/s in the slab
T1
T2
T3
Tall
Pw
l
m
t0
q
Ts
T
Qs
a
V
d
A0
D
k
k
huc
hlc
rc
rm
e
Values
65 – 117 km
1.5 – 6 cm/a
15 – 45°
use the expressions derived for the subducting continental
plate by Molnar and England [1990]. Then, temperature Ts
at the slab surface is a function written as
Ts ¼ Ts ðQs ; V; A0 ; D; d; t c Þ;
ð5Þ
where Qs is the surface heat flow of the plate prior to
subduction, V is the convergence velocity, A0 is radiogenic
heat production at the surface, D is the scaling depth for the
exponential decay of radiogenic heat production, and d is
the dip angle of the slab. The formula of (5) is a sum of the
three terms due to advection, radiogenic heating, and shear
hearting [Molnar and England, 1990] and their expressions
are given in Appendix C. I solve (3) and (5) simultaneously
to determine Ts and t c at the slab surface. This is conducted
as follows. Starting from small initial trial values of Ts0 and
t c0 satisfying (5), substituting t c0 into (3), Ts is obtained. If
Ts is larger than Ts0, the next values of t c1 = t c0 + Dt and
Ts1 satisfying (5), where Dt is a small fraction of t c0, are
tried. This process is repeated until Ts becomes smaller than
Tsn, where n indicates the n-th iteration. The obtained value
of Ts has an accuracy smaller than a few to several degrees,
which is enough for the present purpose.
[17] The temperature within the plate at the trench prior to
subduction is determined by the surface heat flow, Qs, that
is varied in the range of 50– 90 mW/m2. Qs is composed of
the mantle heat flow, Qsm, and the heat flow due to
radiogenic heat production in the plate, Qsr. The former
and the latter are assumed to be 60% and 40% of Qs,
respectively [Pollack and Chapman, 1977]. The temperature of the asthenosphere, Tm, is taken to be 1300°C. The
plate thickness, a, is then determined from the heat conduc-
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tion equation as a = (kTmQsrD)/Qsm, where k is the
thermal conductivity, which is assumed to be constant for
the whole lithosphere. I use k = 2.7 W/mk, which is the
average of the crust and the upper mantle values [Schatz
and Simmons, 1972], and D = 10 km. The thickness of the
plate then varies between 58 and 110 km. V and d are varied
between 1.5 and 6 cm/a and between 15 and 45°, respectively. The symbols and values of the parameters used in
this study are summarized in Table 2.
[18] Because the thrust zone is the plate interface, and the
upper plate material in contact with the slab changes from
the upper crust, through the lower crust, to the mantle. The
material of the lower plate in contact with the upper plate is
always the upper crust of the subducting continental lithosphere. Because the weaker material deforms mainly at the
shear zone [Yuen et al., 1978], I regard that the ductile shear
zone at the plate interface forms in the surface layer of the
lower plate, whose rheology is represented by that of granite
[Carter et al., 1981]. The rheological parameters used for
the crust and mantle materials are listed in Table 3. The
activation volume of 17 106 m3/mol of olivine [Kirby,
1983] is used for both the crust and the mantle, because that
of the crust is not well known. The strain rate at the ductile
shear zone of the thrust is taken to be 1014/s, which
corresponds to a differential velocity of 5 cm/a across the
shear zone having a width of 2 km. This width is a
representative one observed for outcrops of shear zones
[Nicolas et al., 1977; Ponce de Leon and Choukroune,
1979].
[19] Figure 2 shows examples of calculation of t c and Ts
along the thrust with V = 3 cm/a, d = 30°, and Qs = 70 mW/m2
for l = 0.95 and 0. For l = 0.95, t c is small and the brittleductile transition occurs at a downdip distance of 83 km
from the trench (42 km depth), due to low shear heating.
For l = 0, t c is larger, and the brittle-ductile transition occurs
at a downdip distance of 16 km from the trench (8 km
depth) due to large shear heating. In this case, Ts in the ductile
shear zone does not rise quickly along with the depth,
because the combination of (3) and (5) forms a feedback
system that stabilizes Ts. For example, if t c becomes larger,
Ts becomes larger through (5) due to shear heating. This
makes in turn t c smaller through (3), and then making Ts
smaller through (5). Therefore t c at the thrust zone falls
gradually as shown in Figure 2b. This is important to provide
an enough amount of Tc to cause shearing-off for small l.
4. Resistive Forces
[20] From the Coulomb-Mohr fracture criterion, the
strength for F1 and F3 in the brittle part is,
s1 s3 ¼ 2 tan qt 0 þ tan2 q 1 s3 ;
ð6Þ
Table 3. Rheological Parameters for Crust and Mantle Materialsa
Section
Material
A
E*
n
Ref
U. crust
L. crust
Mantle
granite
diabase
dunite
1.26E-9
5.2E2
3.4E4
105.8E3
356E3
544E3
2.9
3.0
3.5
Carter et al. [1981]
Caristan [1982]
Zeuch [1983]
a
A and E* are in the unit of (MPa)ns1 and J/mol, respectively.
Activation volume of 17*106 m3 /mol [Kirby, 1983] is used for all
materials.
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Figure 2. Profiles of shear strength t c (solid line) and temperature Ts (dotted line) at the thrust zone
(Fc) plotted versus distance from the trench in the downdip direction. V = 3 cm/a, d = 30°, and Qs =
70 mW/m2. (a) l = 0.95. The large pore fluid pressure makes the fault brittle down to a distance of
83 km (42 km depth), and then the fault becomes ductile further below. (b) l = 0. The fault becomes
ductile at a distance of 16 km from the trench (8 km depth) due to the high rate of shear heating. The
shear stress, however, does not drop rapidly due to the feedback mechanism discussed in the text.
where s1 and s3 are the principal stresses aligned in the
downdip and perpendicular direction of the slab (see
section 2), q is the fracture angle that satisfies m = cot2q,
where m is the internal friction. Equation (6) is obtained from
the geometry of the Mohr circle and the friction line tangential
to it as
ðs1 s3 Þ=2 ¼ ½ðs1 þ s3 Þ=2 þ t 0 tanð180° 2qÞ cosð180° 2qÞ:
The values of m and t 0 in section 3 are used here. Although
these values are for static friction [Byerlee, 1978], they seem
appropriate for fractures within the crust. q determines the
fault geometry, as it is the angle between the fault normal and
the direction of the larger principal stress. Because different
values of m give different values of q, as q = 60.5° for m = 0.6
and q = 65.2 for m = 0.85, I use q = 60.5° for the fault
geometry. For the calculation of the strength, appropriate
values of q and m are used depending on sz.
[21] For F1 which is the reverse fault, using the result that
s3 = sz in Appendix A, equation (6) gives
s1 s3 ¼ 2 tan qt 0 þ tan2 q 1 sz
s1 s3 ¼ ½e=A00 1=n
exp½ðE* þ v*PÞ=nRT;
ð9Þ
where A00 is the constant converted from the constant A of
the triaxial compression experiment to that of the plain
strain problem (Appendix B), as
A00 ¼ ð3=4Þðnþ1Þ=2 A
ð10Þ
ð7Þ
Similarly, for F3 which is the normal fault, using the result
that s1 = sz in Appendix A, equation (6) gives
sz s3 ¼ 2t 0 = tan q þ 1 1= tan2 q sz :
For faults F1 and F3, I assume Pw = 0 (l = 0). This is
because dehydration by compaction of the cracks in the
granitic crust would be finished at shallow depths and the
breakdown of white mica and biotite occurs at depths
>100 km [Ernst et al., 1998]. The small extent of
dehydration from the subducting continental lithosphere
will be discussed later. However, because van den Beukel
[1992] assumed a hydrostatic Pw within the slab, I also test
such a case, i.e., l = 1/3.
[22] The differential stress for the ductile part of these
faults can be estimated from the power laws of the crustal
and mantle material, strain rate, and temperature T and
pressure P in the subducting plate, using
ð8Þ
I calculate temperature T within the slab using the
expressions of Molnar and England [1990], on the basis
of temperature Ts at the slab surface obtained in section 3
(see Appendix C). I use the rheological parameters listed in
Table 3. The strain rate within the plate is lowered by a
factor of 100 from that at the thrust zone.
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Figure 3. Strength s1 – s3 (solid line) and temperature T (dotted line) along (a) F1 and (b) F3 plotted
versus distance from the slab surface perpendicular to it. V = 3 cm/a, Qs = 70 mW/m2, and l = 0. The
upper edges of F1 and F3 are placed at 10 and 100 km on the slab surface from the trench. The shallowest
parts of these faults become ductile by the high temperature due to high shear heating at the thrust zone.
The weak zone at the base of the upper crust is used as fault F2.
[23] Examples of the calculation of strength profiles
along F1 and F3 are shown in Figure 3. The strength minima
appear at the bases of the upper crust and the lower crust. It
is required that F2 is along these minima. I assume that F2 is
located at the base of the upper crust, i.e., that only the
upper crust is sheared off, because shearing-off of the lower
crust requires a few times larger driving force. Consistently,
subduction of the continental plate leads generally to the
detachment of the upper crust only [van den Beukel, 1992,
p. 316]. Shear traction T2 along F2 is calculated by using
equation (3), with the same strain rate for F1 and F3.
Tractions T1, T2 and T3 required to fracture F1, F2 and F3,
respectively, are obtained by the integration of the strength
over these faults.
5. Depths Where Shearing-Off Occurs
[24] As the length of Fc becomes larger, Tc becomes
larger, and if equation (1) is satisfied, shearing-off occurs.
If not, the continental crust will subduct deep into the
mantle. In this study, the updip end of F1 is fixed at a
distance of 10 km from the trench on the thrust zone, taking
into account that the shallowest portion of the subduction
boundary has a low stable friction [Byrne et al., 1988;
Scholz, 1998]. The values of T1, T2, and T3, and the sum of
them, Tall, are calculated as a function of the distance of the
updip end of F3 along the thrust. The values of l are set to
be zero for these intraslab faults and it is varied only for Fc.
Figure 4 shows an example of a plot of these tractions, with
Tc, versus the distance from the trench, for l = 0, V = 3 cm/a,
d = 30°, and Qs = 70 mW/m2. The value of Tall increases with
the distance because T2 increases with it. T2 also increases
due to the activation volume effect. In contrast, T3 does not
increase significantly because the effect of the activation
volume and that of the temperature counteract each other.
The activation volume effect on T2 makes the curve of Tall
concave upward, and Tc does not cross Tall at all if it does not
before Tall starts to deflect upward.
[25] Figure 5a shows the depths of the updip end of F3 at
which shearing-off occurs versus Qs for various l ranging
from 0 to 0.95 (V = 3 cm/a and d = 30°); no symbol for Qs <
70 mW/m2 means that there was no solution. As Qs
becomes higher, shearing-off occurs at shallower depths,
as noted by van den Beukel [1992]. For Qs as high as
90 mW/m2, l as large as 0.95 makes shearing-off occur if
the leading edge subducts to a depth of 100 km. However,
for Qs <70 mW/m2, which is typical for continents
[Pollack and Chapman, 1977], shearing-off does not occur
unless l is smaller than 0.4. In other words, in the
environment with high l, all the continental crust would
subduct into the mantle without being sheared off, unless Qs
is very high.
[26] These results significantly differ from those of van
den Beukel [1992] in which l of 0.88– 0.97 are used, and
shearing-off still occurs for low to moderate heat flow
values of 6580 mW/m2. This distinction may arise from
different assumptions used in his models; they are inclusion
of the buoyancy of the crust as a driving force, hydrostatic
Pw within the crust of the subducting lithosphere, and usage
of the wet quartzite rheology for the upper crust. I make
sure that the latter two are not the factors that bring the
shallow depths of shearing-off in the work of van den
Beukel [1992]. I test the hydrostatic Pw (l = 1/3) in the
subducting crust and obtain the depths of shearing-off
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this effect, at the slower convergence rate such as 1.5 cm/a,
shearing-off occurs even at relatively higher values of l
such as 0.8– 0.6 at depths of 74 –87 km for Qs = 65-60 mW/
m2, yet having no solution for Qs < 55 mW/m2.
[28] Figure 5c shows the depths of shearing-off versus Qs
when d is varied between 15 and 45°. V is fixed at 3 cm/a.
The smaller the dip angle, the shallower shearing-off occurs.
The smaller dip angle makes the upper edge of F3 shallower
for the same thrust zone length and, thus, T3 smaller.
Because Tc is roughly proportional to the length of Fc
(Figure 4), the crossing point of Tc and Tall becomes
shallower. This explains why the smaller d, the shallower
shearing-off occurs. Conversely, the larger the dip angle, the
deeper shearing-off occurs. Because of this effect, when d is
15°, shearing-off occurs even at relatively higher values of
l such as 0.8– 0.6 at depths of 32– 34 km for Qs = 70–
60 mW/m2, yet having no solution for Qs < 50 mW/m2.
6. Discussion
Figure 4. Tractions Tc (solid line), T1 (chain line), T2
(chain line), T3 (broken line), and Tall (= T1 + T2 + T3,
dotted line) plotted versus distance from the trench in the
downdip direction. V = 3 cm/a, Qs = 70 mW/m2, and l = 0.
Tc and T2 increase as the lengths of faults Fc and F2
increase, respectively. When Tc becomes larger than Tall,
e.g., at a distance of 90 km in this case, shearing-off
occurs.
shallower only by a few km. The usage of the rheological
parameters of wet quartzite [Koch et al., 1980] for the upper
crust in the way I use in the present study makes the depths
of shearing-off rather deeper by 20 –30 km. This may be
caused by the reduction of Tc in the ductile part of the thrust
more significantly than at F1 and F3. Because details of the
calculation of Tc by van den Beukel [1992] are not known,
further investigation on this point is difficult. I further test
the cases including the buoyancy of the crust as a driving
force, with hydrostatic Pw and the rheological parameters as
used in this study, and obtain depths of shearing-off similar
to those of van den Beukel [1992] for l 0.93. The
magnitude of the buoyancy force is DrghucLsind, where
Dr is the density difference between the upper crust and the
mantle (500 Kg/m3), g is the gravity of acceleration, and
L is the length of the thrust zone. For the case shown in
Figure 4 where L 60 km, this amounts to be 2.7*1012 N/m,
about a half of Tc. This assures that even for a large l,
inclusion of the buoyancy makes shearing-off at shallow
depths possible. I therefore believe that the difference of the
results by van den Beukel [1992] from the present study
mainly come from the inclusion of the buoyancy force of the
crustal block.
[27] Figure 5b shows the depths of shearing-off versus Qs
when V is varied between 1.5 and 6 cm/a. Dip angle d is
fixed at 30°. The smaller the convergence rate, the shallower shearing-off occurs. This is because the plate is
warmed by the slower rate of convergence, being hotter,
resulting in reducing T1T3 and making shearing-off to
occur earlier. Conversely, larger V makes the slab colder,
and the shearing-off occurs at greater depths. Because of
[29] In the previous section, I have shown that Qs and l
are the main controlling factors to determine the depth
where shearing-off occurs. For typical continents with Qs <
70 mW/m2 [Pollack and Chapman, 1977], shearing-off
occurs for only l smaller than 0.4. Although this value
shifts to a larger one, when the dip angle or the convergence
Figure 5a. (a) Depths (solid circles) of the upper edge of
fault F3 when shearing-off occurs are plotted versus Qs for
various l. V = 3 cm/a and d is 30°. The calculation is made
for the range of Qs = 50– 90 mW/m2 and no solid circle
means that shearing-off did not occur at that point. For
higher Qs, shearing-off tends to occur at shallower depths
for the same l. For large l, it occurs at deeper depths for the
same Qs. For lower Qs, which are typical for continental
plates, shearing-off occurs only for small l.
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Figure 5b. (b) Effects of V on the depths of shearing-off.
Depths of the upper end of fault F3 when shearing-off
occurs are plotted versus Qs for l = 0 (solid circles) and for
l = 0.9 (open stars). Cases where V is 3 cm/a (large symbols),
and 1.5 and 6 cm/a (small symbols) are shown. d is 30°.
Shearing-off tends to occur at shallower depths for smaller V.
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depending on the phase relations of the hydrous minerals
[e.g., Ulmer and Trommsdorff, 1995; Schmidt and Poli,
1998; Okamoto and Maruyama, 1999]. This dehydration is
probably manifested by the intermediate-depth intraslab
seismic activities [Kirby et al., 1996; Seno and Yamanaka,
1996; Peacock and Wang, 1999; Hacker et al., 2003;
Yamasaki and Seno, 2003]. For example, dehydration from
the altered basaltic crust starts around 30 km depth for
young slabs and 70 km depth for old slabs [Hacker et al.,
2003; Yamasaki and Seno, 2003]. The fluids dehydrated
from the slab would migrate through the fractured conduit
in the thrust zone or escape upward into the wedge. This
would be a unique source for the high pore fluid pressure at
the thrust where an oceanic plate is subducting, because no
other metamorphic reaction is expected at such depths in the
subduction zone.
[31] Compared with the subduction of an oceanic plate,
there are pieces of evidence indicating that the extent of
dehydration is small for the subducting continental plate.
This was first noticed by Seno and Yamasaki [2003] in the
Nankai Trough, SW. Japan, on the basis of the fact that,
where island arc type crust is subducting, no low-frequency
tremor is observed [Obara, 2002]. They also showed that no
intraslab earthquakes are occurring in the subducting crust
in such places. These provide evidence for a small extent of
dehydration from the subducting island arc crust.
[32] Seno [2007] advanced the above speculation of Seno
and Yamasaki [2003] by studying intraslab seismicity and
crustal deformation in collision zones. Intermediate-depth
velocity is small, it is still much smaller than seen in
subduction zones (l0.95 [e.g., van den Beukel and Wortel,
1988; Tichelaar and Ruff, 1993; Peacock, 1996; Cattin et
al., 1997; Lamb, 2006]). It should be noted here that the
actual controlling factor for shearing-off is not l but m (1 l). If l is larger than the nominal value and close to those
seen in subduction zones, larger m is necessary to cause
shearing-off. On the other hand, if m becomes smaller than
the values used in this study by changes in composition or
foliation development, it makes easier the block to be
subducted without shearing-off, and even smaller l is
necessary to cause shearing-off. This may give us a way
to explain the variety of geological phenomena related to
shearing-off (Table 1) rather in terms of regional and
temporal variation of l, although possible change in m
may modify the value of l necessary for shearing-off.
Variation of l seems to be controlled by the availability of
fluids at the thrust where the continental lithosphere is
subducting. I will discuss these issues and some implications for ophiolite obduction in the following sub-sections.
6.1. Absence of Slab Dehydration and Collision
[30] Where the oceanic plate is subducting beneath the
overriding plate, dehydration from the subducted sediments/
clays and the porous basalt occurs at shallow depths (<10
km [e.g., Fyfe et al., 1978; Moore and Vrolijk, 1992]).
Dehydration from the metamorphic reactions in the altered
basalt and serpentinites in the slab starts at larger depths
Figure 5c. (c) Effects of d on the depths of shearing-off.
Depths of the upper end of fault F3 when shearing-off occurs
are plotted versus Qs for l = 0 (solid circles) and for l = 0.9
(open stars). Cases where d is 30° (large symbols), and 15
and 45° (small symbols) are shown. V is 3 cm/a. Shearingoff tends to occur at shallower depths for smaller d.
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intraslab seismicities are generally absent in collision zones,
such as the Himalayas and the Zagros. This suggests no or
scarce dehydration from the subducting slab in collision
zones. The crustal deformation associated with underthrusting in these places is described by the detachment model, in
which the shallow portion of the thrust is adhered. In
contrast, in subduction zones, the crustal deformation is
described by the back slip model [Savage, 1983]. This
implies that the adherence at the thrust is stronger in
collision zones than in subduction zones [Seno, 2007]. On
the basis of these facts, Seno [2007] proposed that the
continental or island arc crust, when it is subducted to
depths of tens of km, does not scarcely dehydrates. This is
probably due to the absence of dehydration reactions of
major hydrous minerals in the continental crust at these
depths. If white mica and biotite are contained, they
dehydrate at greater depths (>100 km [Ernst et al., 1998]).
[33] The small extent of dehydration from the slab with
continental crust would lead to small Pw and l at the thrust
zone, because there is no other effective source of fluids
filling the thrust zone at depth, as mentioned above. In
contrast, the metamorphic reactions in the oceanic slab
provide enough amount of fluids at the thrust, although
details of the mechanism of the fluid transport from the
source to the shallower portion of the thrust (10 – 60 km)
would be a subject of investigation in future studies. No
matter the transport mechanism is, however, the nearly
absence of dehydration will lead to small l at the thrust
zone, leading to shearing-off of the upper crust at shallow
depths from the underthrusting continental plate.
[34] The offscraping of the continental crust at shallow
depths has been believed to be one of the most typical
features of collision zones, as seen in the Himalayas
[Molnar, 1984; Butler, 1986; Mattauer, 1986] and the
Zagros [Synder and Barazangi, 1986; Bird et al., 1975].
The intense deformation in the hinterland of the collision
zone, like those in Tibet and C. Asia [Molnar and
Tapponnier, 1975] has been believed to be due to indentation of the buoyant colliding continent. It should be
noted, however, shearing-off may not occur, with large l,
even if the continental plate is underthrusting. In fact, it is
known that continental crust, by happen, can subduct into
the mantle of a depth >100 km in many collision zones
with UHP exhumation [Liou et al., 1994; Coleman and
Wang, 1995; Ernst and Liou, 1999; Chopin, 2003]. Molnar
and Gray [1979] also showed that the continental plate,
from the viewpoint of buoyancy, might subduct into such a
large depth, if the slab pull force is available. If l is large,
the shear stress at the thrust becomes small, resulting in
modest deformation in the hinterland. These imply that the
buoyancy of the subducted crust is not an essential factor
to cause features associated with collision, such as shallow
offscraping of a crustal sheet and intense deformation in
the hinterland, but rather the absence of dehydration and
small l might be the essential factor.
6.2. Two Types of Collision Zones
[35] Although the Himalayas and the W. Alps are both
type localities of collision zones, the features associated
with them are quite different. Offscraping of the Indian
continental crust has occurred in the foreland fold and thrust
belt of the Himalayan collision zone [e.g., Molnar, 1984;
B04414
Butler, 1986; Mattauer, 1986]. The overriding Asian continent has been extensively deformed by indentation of the
Indian continent as shown in the crustal thickening [Allegre
et al., 1984; England and Houseman, 1988] and in the
extrusion [Molnar and Tapponnier, 1975]. Although offscraping at shallow depths has been dominant in the
Himalayas, exhumation of the UHP terranes is known to
have occurred in the early stage of the collision (50 Ma) in
the Hindu Kush [Kaneko et al., 2003]. In contrast, in the W.
Alps, exhumation of HP/UHP terranes, forming numerous
nappes, has been dominant, and the offscraping of the
colliding continent is minor [e.g., Platt, 1986; Hsu, 1991;
Escher and Beaumont, 1997]. The deformation of the
overriding Adriatic plate has been also minor.
[36] I show that these differences can be explained by the
evolution of Pw and l in the thrust zone through the history
of collision. Several collision zones that accompany intermediate-depth seismic activities, such as Vlancia, Hindu
Kush, Timor, and Taiwan, give us a hint for investigating
this problem. In these zones, dehydration from the leading
oceanic slabs is manifested by the intermediate-depth seismic activities [Seno, 2007]. These can be regarded as
transient or intermediate cases between subduction of an
oceanic plate and underthrusting of the continental plate. It
is expected that Pw and l at the thrust zone of these places
would be moderately large by the fluids released from the
attached oceanic slab, making l higher than typical collision zones. In such a case, the continental crust could
subduct deep into the mantle due to the higher l, as
observed in the collision zones cited above [Seno, 2007].
[37] Prior to the collision of the Indian continent, the
Tethys Sea had been subducting beneath the Asian continental fragments [e.g., Sengor, 1992]. In the early stage of
the collision, the dehydration of the leading oceanic plate
would have made the subduction of the continental crust to
a large depth possible, having made it suffer the UHP
metamorphism. As the collision proceeded, the ocean-continent boundary would have subducted deep into the mantle,
having, in turn, made the thrust zone starved of fluids. Tc
would have gradually become large as l decreased. When it
satisfied the condition Tc > Tall, part of the subducted
continental plate would have been sheared off, having
provided a source of the exhumed UHP terranes at the
initial stage of the collision. Afterward, the continental plate
continued to underthrust, and the upper crust would have
been offscraped at shallow depths because the thrust zone
has been devoid of fluids. This scenario explains why only
the offscraping at shallow depths, along with the exhumation of the low-grade metamorphic rocks [Le Fort, 1986],
occurred in the Himalayas during the succeeding stages.
The level of t c of the thrust would have been kept high
during these stages, on the order of 100 MPa (Figure 2b),
having resulted in the intense deformation of Asia by the
indentation of India.
[38] In the case of the W. Alps, in contrast, a series of
continents and oceans have been subducting beneath the
Adriatic plate since Late Cretaceous [Platt, 1986; Escher
and Beaumont, 1997]. When the continental plate was first
subducted, similarly to the initial stage of the Himalayas,
dehydration from the leading oceanic plate would have
made l large along the thrust, and the continental crust
would have subducted into a great depth. After the oceanic
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slab went deeper, part of the subducted continental crust
was sheared off and was exhumed as the UHP rocks, such
as the Dora Maira Massif [Chopin, 1987]. In contrast to the
Himalayas, however, subduction of another oceanic plate
succeeded [e.g., Platt, 1986], and the cycle of oceanic plate
subduction - continental plate subduction - exhumation oceanic plate subduction has been repeated. Offscraping at
shallow depths, therefore, did not occur, except for the
recent one of the European continental crust, for which a
succeeding oceanic plate does not exist. Pw and l are likely
to have been kept at a relatively high level throughout the
collision history in the W. Alps, leading to small t c at the
thrust zone. This would have made a small extent of
indentation and deformation of the hinterland in the upper
Adriatic plate.
6.3. Ophiolite Obduction
[39] Some types of ophiolite obduction [Coleman, 1971;
Dewey and Bird, 1971; Dewey, 1976] and exhumation of
HP/UHP rocks in subduction zones [Aoya et al., 2003; Ota
et al., 2004] indicate that sheet-like bodies are possibly
sheared off also from the subducted oceanic plate, not only
from the continental one. To discuss these phenomena
quantitatively, we need to model the temperature of the
subducting oceanic slab, and calculate driving and resistive
forces for shearing-off, in a similar manner to the present
study. Leaving such work in the future, I discuss the
problem only qualitatively using the results obtained in
the previous sections.
[40] I note here that shearing-off them from the oceanic
plate is generally difficult. First, in the scheme of Figure 1,
T2 is generally very large because the oceanic crust is as
thin as 6 km, which prevents the development of the
ductile shear zone at the base of the crust. Secondly, Pw and
l are usually very large in subduction zones [e.g., van den
Beukel and Wortel, 1988; Tichelaar and Ruff, 1993; Peacock,
1996; Cattin et al., 1997; Lamb, 2006], which reduces the
level of Tc.
[41] There might be two possible cases that overcome the
first difficulty. If the oceanic plate is extremely young, the
oceanic crust could still be hot enough to develop a ductile
shear zone at its base, or within it. The temperature at a
depth of 6 km from the surface of an oceanic plate becomes
greater than 300°C for ages younger than 5 Ma, if the
temperature is calculated by the plate model with the
asthenosphere temperature of 1300 °C [Parsons and Sclater,
1977]. Next, if the mantle part of the subducting plate is
serpentinized, dehydration in the slab mantle occur as it
subducts deeper and warmed by conduction [Nishiyama,
1992; Seno and Yamanaka, 1996; Peacock, 2001; Hacker et
al., 2003; Yamasaki and Seno, 2003]. The dehydration front
of serpentinite in the subducting slab is expected to be
located a few tens km below the slab surface based on the
phase diagram [Yamasaki and Seno, 2003]. Since the
strength along this dehydration front in the slab would be
small [Fyfe, 1985], this could be used as a lower boundary
of a block to be sheared off.
[42] However, even if the 1st difficulty is remedied by
these situations, the 2nd one remains; Tc in subduction
zones is generally small because Pw and l are large due to
dehydration from the altered basalt. I note here that there are
some exceptional cases, however, in which l might be very
B04414
small. For example, where the Kinan Seamounts, the extinct
spreading centers affected by the volcanism during 10 m.y.
after the cessation of the spreading of the Shikoku Basin
[Sato et al., 2002], are subducting beneath SW. Japan,
intraslab seismicity does not occur in the subducted crust
[Kodaira et al., 2002; Kurashimo et al., 2002], or no lowfrequency tremor is observed [Obara, 2002]. Seno and
Yamasaki [2003] suggested the absence of dehydration of
the crust in this place, which might lead to small l. Another
case is the subduction of the Izu-Bonin forearc beneath
Kanto, central Honshu. The absence of intraslab seismicity
in the crust [Hori, 2006] and low-frequency tremor [Obara,
2002] here also suggests that dehydration might be absent in
the crust [Seno et al., 2001; Seno and Yamasaki, 2003].
These are possible places where shearing-off of part of the
crust or the mantle from the oceanic lithosphere could
occur, due to small l, if a weak zone is developed in the
slab. The exhumation of the Sanbagawa HP/UHP terrane
occurred at the end of Cretaceous in the SW. Japan forearc.
The subducting slab was very young in this case [Isozaki,
1996; Aoya et al., 2003], and Terabayashi et al. [2005]
reconstructed seamount sequences from the geological
sections of the exhumed UHP terrane. Therefore the exhumation of this terrane might have occurred in a favorable
situation, satisfying both the conditions depicted above.
Ben-Avraham et al. [1982] once proposed that ophiolites
are emplaced in association with collision of buoyant
features such as the continental fragments and plateaus/
seamounts. This might be, in the context of this study,
interpreted as small l and large Tc due to insufficient
dehydration from these features upon subduction facilitate
shallow offscraping of such features, when a ductile shear
zone is developed inside the slab.
6.4. Future Scopes
[43] There are several directions that might be explored in
the future. The model in this study can be extended to the
cases of shearing-off of the oceanic plate, as mentioned
above, once the temperature of subducting oceanic lithosphere is calculated. The obduction of ophiolites and
exhumation of HP/UHP terranes would be able to be
discussed in a more quantitative manner. There are also
many buoyant features having thicker crust with low
densities on the oceanic plate, such as remnant ridges,
plateaus, and seamounts [Ben-Avraham et al., 1981]. The
fate of these buoyant features could be discussed in terms of
l, their spatial dimensions, and crustal thickness. Discussion of their fate in terms of buoyancy only [e.g., Cloos,
1993] would not be adequate.
[44] I infer that a low value of l is caused by a small
extent of dehydration of the subducting continental plate.
The connection between the dehydration process from the
crust and l is still obscured, and this should be more
substantiated through high-pressure experimental and theoretical work. Simultaneously, the fate of fluids derived from
metamorphic reactions of altered basalt/serpentinites should
be investigated more through theoretical work. This is not
only applicable to the subducting oceanic plate generally,
but also important for collision zones where subduction of
the oceanic plate leading the trailing continent may gradually shifts to subduction of the continental plate.
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[45] The result that l controls the depth of shearing-off
may lead to the basic idea that the tectonic style of the Earth
is controlled by l. Although this idea was explored by the
earlier paper of the same author [Seno, 2007] and the effects
of l in collision zones are discussed in a quantitative
manner in this study, effects of l and dehydration should
be pursued in various tectonic, volcanic, and seismic
activities on and within the Earth, and a general model
might be explored to explain the different tectonic styles of
the Earth on the basis of l in a unified manner.
7. Conclusions
[46] I study the conditions for a crustal block to be
sheared off from a subducting continental lithosphere. I
show that the buoyancy does not operate selectively to the
crustal block. I suppose that shearing-off occurs when the
shear traction at the thrust, whose maximum value is
calculated from the strength along the thrust, overcomes
the strength of the boundary faults of the detached block,
and determine the depths of the leading edge of the block
when shearing-off occurs. The temperatures of the slab and
of its surface are calculated by the steady state formula of
Molnar and England [1990] as a function of the surface
heat flow, the dip angle, and the convergence velocity. The
shear stress and temperature at the ductile part of the thrust
zone are determined to satisfy both the ductile flow law and
the temperature due to shear heating. The shear stress at the
brittle part is represented by the Byerlee’s friction law using
the pore fluid pressure ratio l. I show that shearing-off of an
upper crustal block is possible only for small l if the surface
heat flow is below 70 mW/m2 unless the convergence rate is
very small.
[47] These results imply that temporal and/or regional
variation of l might help us to understand various features
associated with shearing-off, such as exhumation of HP/
UHP terranes, offscraping of continental crust at shallow
depths, and obduction of part of the oceanic lithosphere.
Taking into account the possibility that the continental or
island arc crust does no dehydrate when it is subducted
[Seno, 2007; Seno and Yamasaki, 2003], the above condition for shearing-off implies that the essential factor to cause
features characteristic of collision might not be the buoyancy of the subducting crust, but is the absence of dehydration from it. In the early stage of collision, dehydration
from the subducted oceanic plate leading the continent
would lubricate the thrust zone, making l to be large. The
continental plate is then able to subduct to great depths. As
the collision proceeds, the thrust zone becomes less lubricated. l becomes smaller, resulting in shearing-off and
providing a source of exhumation of the UHP terranes in
the early stage of collision. In later stages, absence of
dehydration from the slab causes offscraping of the continental crust at shallow depths, producing a stack of sliced
sheets often seen in the fold and thrust belts. The shear
stress at the thrust zone becomes as high as 100 MPa,
leading to the intense deformation of the hinterland. This
could be the case of the Himalayas.
[48] If the subduction of an oceanic plate succeeds in later
stages, the dehydration of the oceanic plate makes l larger
again, subduction of another trailed continental plate
becomes possible, and the shear stress level of the thrust
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zone remains low on the average. The W. Alps, where
exhumation of HP/UHP terranes have occurred extensively
and repeatedly, with a small amount of both offscraping and
deformation in the hinterland, could be this case.
[49] For a typical oceanic plate, it is generally difficult to
cause shearing-off, i.e., obduction of ophiolite or exhumation of HP/UHP terranes, because of the absence of
conditions of developing ductile shear zones within the
subducting crust, except for the case of the very young
plate. Shearing-off is also difficult because of large l due
to dehydration from the subducted altered crust. For
shearing-off to occur, two conditions seem to be satisfied.
(1) Weakening along a dehydration front bordering a region
of serpentinized slab mantle, or at the base of the crust in
the plate younger than 5 Ma, and (2) small l at the thrust
zone caused by the absence of dehydration from the
subducted crust. Some places of the subduction zones near
Japan show that these conditions are partly satisfied.
Exhumation of HP/UHP terranes or ophiolite obduction
might have occurred in the situation where these conditions
were met.
[50] In the future, shearing-off from the subducting oceanic plates should be treated in a more quantitative manner,
by calculating the temperature of the slab. Further studies
are needed to elucidate the connection between the extent of
dehydration of the slab and the value of l. The results in
this study lead to a general view that the tectonic style on
the Earth, like subduction and collision, is controlled by
l. Pursuing this view through various tectonic, seismic
and volcanic activities may provide a new paradigm
beyond plate tectonics.
Appendix A: Normal Stress Operating at the
Thrust
[51] In this appendix, I show that normal stress sn
operating at thrust zone Fc is given by the lithostatic
pressure based on the force balances in the shallow portion
of the subducting plate and the lithospheric wedge of the
upper plate. A schematic cross-section of the shallow
portion of the subduction zone is depicted in Figure A1.
The downgoing plate is in contact with the upper plate at the
thrust zone AC with average shear stress t*, length L, and
dip angle d. BC is the location of the aseismic front, where
interplate coupling is terminated [Yoshii, 1979].
[52] I first try to obtain relations between the slab pull Tsp,
ridge push Tr, and t*. I ignore in the following discussion
all the forces operating at the interfaces with the asthenosphere, regarding them small compared with Tsp and other
tectonic forces. Tsp is the negative buoyancy multiplied by
sind integrated over the slab deeper than point C [McKenzie,
1969]. It could be a force on the order of 1013 N/m, if the
slab has a length of 300 km [Molnar and Gray, 1979].
[53] I first consider the force balance in rectangle ACEF. I
assume that Tsp is directing downdip because forces perpendicular to the slab surface are likely to be balanced
with the fluid dynamic forces associated with subduction
[Stevenson and Turner, 1977]. Tsp should then be balanced
with the downdip component of Tr and the shear traction at
the thrust, and I obtain
11 of 15
Tsp þ Tr cos d ¼ t*L:
ðA1Þ
SENO: SHEARING-OFF OF THE CRUSTAL BLOCK
B04414
B04414
Figure A1. A schematic cross-section showing the force balances in a subduction zone T.A. and A.F.
denote the trench axis and the aseismic front, respectively. d is the dip angle of the subducting plate, and
Tr, Tsp, and Tc are the ridge push, slab pull, and collision forces, respectively. Tv0 and Tv are the shear
forces operating at GF and BC, respectively. At the thrust interface between the upper and lower plates,
shear stress t* is operating.
Next, I consider the force balance in trapezoid GBDF. The
horizontal component of Tsp is balanced with Tr and
collision force Tc operating at the aseismic front of the
upper plate, then I obtain
follows. Let us write the generalized constitutive equation
as
Tsp cos d þ Tr ¼ Tc :
where A0, n, E* and v* are material constants, eij is the
strain rate tensor, sij0 is the deviatoric stress tensor, and s is
the 2nd invariant of the stress tensor, as s2 = sij0 sij0 /2. In the
triaxial compression test, let s10 be the axial principal
deviatoric stress, and s20 and s30 are the other principal
deviatoric stresses in the orthogonal directions. Then, s20 =
s30 = s10 /2, and we obtain s2 = 3s10 2/4. The constitutive
equation for the triaxial compression test in the form of (B1)
is
ðA2Þ
The vertical forces at the aseismic front Tv and at the trench
Tv0 are balanced with the vertical component of Tsp, then I
obtain
Tsp sin d ¼ Tv þ Tv0 :
ðA3Þ
Normal traction at the thrust zone Tn, in excess of the
lithostatic pressure, is
Tn ¼ Tc sin d Tv cos d:
ðA4Þ
Substituting Tc and Tv using (A2) and (A3) in (A4), I obtain
eij ¼ A0 sn1 sij 0 exp½ðE* þ v*PÞ=RT;
ðn1Þ=2 0
e1 ¼ A0 3s02
s1 exp½ðE* þ v*PÞ=RT
1 =4
0
n
0 ðnþ1Þ=2
¼ 2A 3
s1 s3 exp½ðE* þ v*PÞ=RT:
ðA5Þ
We thus obtain
Because the ridge push force is on the order of 1012 N/m
[Parsons and Richter, 1980] and gives a stress of a few
MPa, it is negligibly small compared with the lithostatic
pressure, which amounts to 1 GPa at a depth of 30 km.
Similarly, because the shear force Tv0 at the trench is on the
order of 1012 N/m [Caldwell et al., 1976], it can also be
neglected. Therefore we can regard that normal traction Tn
acting at the thrust is independent on Tsp and negligible
compared to the lithostatic pressure. This is used in the
estimation of the brittle strength at AC based on the
Byerlee’s friction law in section 3 and in the force balance
between Tc and Tall in section 4. The smallness of Tr also
implies that the average shear stress at the thrust zone is
balanced by Tsp through equation (A1).
A ¼ 2A0 3ðnþ1Þ=2
Tn ¼ Tr sin d þ Tv0 cos d:
Appendix B
0
ðnþ1Þ=2
A ¼3
ðB1Þ
ðB2Þ
or
ðB3Þ
A=2
In the 2-dimensional simple shear strain problem, which is
suitable for Fc and F2, taking x1 along the thrust plane, and
x3 orthogonal to it, other components than s130 = s310 and
02
. Inserting these into
e13 = e13 are zero. We obtain s2 = s13
(B1),
e13 ¼ A0 s0n
13 exp½ðE* þ v*PÞ=RT or
s013 ¼ t c ¼ ½e=A0 1=n
exp½ðE* þ v*PÞ=nRTs :
ðB4Þ
This indicates that the constant for the simple shear problem
is A0.
Rewriting equation (B1) in the form using E2 = eijeij/2,
[54] Constants A0 and A00 in equations (3) and (9) in the
text are converted from A in the triaxial compression test as
12 of 15
sij ¼ A01=n Eðn1Þ=n e0ij exp½ðE* þ v*PÞ=nRT:
ðB5Þ
SENO: SHEARING-OFF OF THE CRUSTAL BLOCK
B04414
In the 2-dimensional plain strain problem, applied to the
strength of F1 and F3, e1 = e3 and e2 = 0. We obtain E2 =
e21 and e1 – e3 = 2e1. Inserting these into (B5),
ðn1Þ=n
s1 s3 ¼ A01=n e1
¼
1=n
2A01=n e1
ðB6Þ
Rewriting this, we obtain
e1 ¼ 2n A0 ðs1 s3 Þn exp½ðE* þ v*PÞ=RT:
ðB7Þ
Therefore the constant for the 2-d plain strain problem is
A00 ¼ 2n A0 ¼ ð3=4Þðnþ1Þ=2 A:
ðB8Þ
Appendix C
[55] Temperature at the thrust zone Ts is composed of the
three terms due to (1) advection Ts1, (2) internal radiogenic
heating Ts2, and (3) frictional heating Ts3. From Molnar and
England [1990, pp. 4838– 4839], the expression for advection is
Ts1 ¼ Qs zf =k=S;
ðC1Þ
where Qs is the surface heat flow, zf is the depth of the point
of the thrust plane, k is the thermal conductivity. S is the
divisor, which is common to all the terms, and written as
S ¼ 1 þ b sin d
pffiffiffiffiffiffiffiffiffiffiffiffiffi
uf V=k;
ðC2Þ
where b is the constant close to 1, which depends on the
exponent of the temperature increase with time [Molnar and
England, 1990, p. 4837], d is the dip angle of the thrust, uf
is the distance from the trench axis along the thrust in the
downdip direction, V is the convergence rate, and k is the
thermal diffusivity.
The expression for radiogenic heating is
Ts2 ¼ A0 D2 ½1 expðzf =DÞ½1 þ zf =DA0 D expða=DÞ =ðkSÞ;
ðC3Þ
where A0 is the radiogenic heat generation at the surface, D
is the scaling depth of the radiogenic heat generation
assuming the exponential decay, a is the plate thickness.
The expression for shear heating is
Ts3 ¼ ðt c V=kÞ=S;
ðC4Þ
where t c is the shear stress at the thrust.The temprature
within the subducting plate is determined by the temerature
gradient given by
qffiffiffiffiffiffiffiffiffiffiffiffiffi
@T =@y ¼ bTs ðuf Þ= kuf =V ;
[56] Acknowledgments. I thank Steve Kirby, Dave Stegman and
Susanne Buiter for critically reviewing of the manuscript, and I also thank
the staffs at Oxford University, Kyushu, Kumamoto, and Kagoshima
Universities for discussion.
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