Download Effects of active crustal movements on thermal structure in

Geophys. J. Int. (2000) 141, 271–281
Effects of active crustal movements on thermal structure in
subduction zones
Yukitoshi Fukahata and Mitsuhiro Matsu’ura
Department of Earth and Planetary Physics, University of T okyo, T okyo 113–0033, Japan. E-mails: [email protected];
[email protected]
Accepted 1999 April 21. Received 1999 April 5; in original form 1998 July 24
SU M MA RY
In young suduction zones we observe steady uplift of island arcs. The steady uplift of
island arcs is always accompanied by surface erosion. The long duration of uplift
and erosion effectively transports heat at depth to shallower parts by advection. If the
rates of uplift and erosion are sufficiently large, such a process of heat transportation
will strongly affect thermal structure in subduction zones. First, we quantitatively
examine the effects of uplift and erosion on thermal structure by using a simple 1-D
heat conduction model, based on the assumption that the initial thermal state is in
equilibrium. The results show that temperature increase, DT , due to uplift and erosion
can be approximately evaluated by DT =n tb at depth, where n is the rate of uplift
e
e
(erosion), t is the duration of uplift (erosion), and b is the gradient of the geotherm in
the initial state. Next, considering the effects of vertical crustal movements such as
uplift and erosion in island arcs and subsidence and sedimentation in ocean trenches,
in addition to the effects of radioactive heat generation in the crust, frictional heating
at plate boundaries and accretion of oceanic sediments to overriding continental plates,
we numerically simulate the evolution process of the thermal structure in subduction
zones. The result shows that the temperature beneath the island arc gradually increases
as a result of uplift and erosion as plate subduction progresses. Near the ocean trench,
on the other hand, the low-temperature region gradually expands as a result of
sedimentation and accretion in addition to direct cooling by the cold descending slab.
The surface heat flow expected from this model is low in fore-arc basins, high in island
arcs and moderately high in back-arc regions.
Key words: advection, crustal uplift, subduction zone, surface erosion, thermal
structure.
1
I NT R O DU C TI O N
In subduction zones, very active crustal movements, characterized by uplift and erosion in island arcs and subsidence and
sedimentation in ocean trenches, proceed continuously for a
very long time. Uplift and erosion of the Earth’s crust inevitably
cause the upward movement of hot rocks from deeper parts.
The long duration of fast crustal uplift and erosion effectively
transports heat at depth to shallower parts by advection, and
significantly changes the thermal structure and surface heat
flow (England & Richardson 1977; England & Thompson
1984; Royden 1993).
So far, many studies have been made on the thermal
structure in subduction zones. Minear & Toksöz (1970)
have considered the effects of radioactive heat generation and
frictional heating at plate boundaries in addition to the cooling
of the descending oceanic slab. Andrew & Sleep (1974), Bodri
© 2000 RAS
& Bodri (1978) and Hsui & Toksöz (1979) have introduced
the mantle wedge flow that will be induced by the descending
oceanic slab into their models in order to solve a basic problem
of why island arcs are hot in spite of the subduction of the
cold oceanic slab. Honda (1985) and Furukawa (1993) have
also constructed induced-flow models of thermal structure in
subduction zones, under the constraints of observed surface
heat flow in the northeastern Japan arc and generation conditions of arc basaltic magmas given by Tatsumi et al. (1983).
In these models, however, the lithosphere in island arcs has
been implicitly assumed as an immobile lid overlying the
wedge mantle. That is, the effects of active crustal movements
on thermal structure in subduction zones have never been
taken into consideration.
In the present study, first we briefly summarize the observed
data of uplift and erosion rates in subduction zones, mainly in
Japan. Next, we quantitatively examine the effects of uplift and
271
272
Y. Fukahata and M. Matsu’ura
erosion on thermal structure with a simple 1-D model. Finally,
we construct an evolution model of thermal structure in subduction zones, introducing the effects of uplift and erosion in
island arcs and subsidence and sedimentation in ocean trenches.
2 A CT IVE CRU STAL MO VE MEN TS IN
SU BD UC TIO N ZO N ES
In subduction zones, as inferred from the existence of highrelief orogenic belts and deep ocean trenches, very active
crustal movements have continuously proceeded for a very
long time. In this section we briefly review observed crustal
movements in subduction zones, mainly in Japan, where we
can obtain plenty of data for crustal movement. In the following, we use the term ‘crustal uplift’ or just ‘uplift’ to describe
the vertical motion of material with respect to a reference
level, e.g. the geoid (Stüwe & Barr 1998), and the term ‘surface
erosion’ or ‘denudation’ to describe removal of the material at
the Earth’s surface.
Rates of crustal uplift and surface erosion for the last
100 years can be estimated from levelling data and solid and
solute load data in rivers. From sediment delivery rates into
reservoirs, Yoshikawa (1974) has obtained denudation rates
in many Japanese drainage basins. According to his report,
the denudation rates are greater than 1–2 mm yr−1 in the
central mountains, the Shikoku mountains and the Kyusyu
mountains in Japan. The fastest denudation rate reaches
6.3 mm yr−1 at the Kurobe river, north of the central mountains.
From levelling data for the period from 1895 to 1965, Dambara
(1971) has estimated crustal uplift rates in Japan. According
to his report, uplift motions greater than 2 mm yr−1 are
observed in the Pacific coast area of southwestern Japan and
in south of the central mountains.
From present heights of marine terraces we can estimate
average rates of crustal uplift for the last 10–100 ka. Ota (1975)
compiled the uplift rates of Holocene and Pleistocene marine
terraces developed along the coastlines of Japanese islands.
According to her report, uplift rates of Holocene marine
terraces reach about 4 mm yr−1 at Oiso hill and the Boso
peninsula, both in the south Kanto district. Uplift rates of
Pleistocene marine terraces are greater than 0.5 mm yr−1 at
many places in Japan and reach 2 mm yr−1 at the Muroto
promontory, southeastern Shikoku.
For New Zealand also we have many observations on
the rates of crustal uplift and surface erosion. The present
denudation rate estimated from sediment delivery rate is
2.8 mm yr−1 at the Waipaoa river, in the northeast of North
Island (Ohmori 1983). In North Island, well-developed marine
terraces are continuously distributed, indicating the long
duration of active uplift motion there. The present heights of
marine terraces formed in the last interglacial period are over
100 m at many places (Ota 1990), and reach 300 m at the
northeastern tip of North Island (Yoshikawa et al. 1980).
Pillans (1986) has made a late Quaternary uplift map of North
Island, mainly based on marine and fluvial terraces. According
to his map, the uplift rates are more than 1 mm yr−1 in the
eastern half of the Island.
On the basis of the field surveys of Holocene marine terraces,
rapid crustal uplift motions have also been reported in other
subduction zones; for example, 10 mm yr−1 at Middleton
Island, Alaska (Plafker & Rubin 1967), and 5.5 mm yr−1 at
Mocha Island, Chile (Kaizuka et al. 1973).
Although we do not have sufficient data for very longterm erosion rates, they must balance with the uplift rates on
long-term average. We also have little information on the
rate of sedimentation at ocean trenches. Eroded materials on
land are, however, finally transported to ocean trenches and
deposited there. Therefore, fast erosion on land must cause
fast sedimentation at ocean trenches.
3 TEM P ER ATU R E IN CR EA S E CA U S ED B Y
CR U S TA L U P LI FT A N D ER O S I O N
Crustal uplift and erosion, which produce the upward movement
of hot rocks from deeper parts, correspond to an advection
term in the thermal conduction equation. In this section, we
quantitatively examine the effects of uplift and erosion on
thermal structure. In the calculation we make the following
three assumptions for simplicity: (1) the initial thermal state
of the lithosphere is in equilibrium; (2) the rates of uplift and
erosion are equal and constant in time; and (3) heat flow at
the base of the lithosphere is constant. Using these assumptions,
first we consider an analytical solution of the 1-D thermal
conduction equation.
The 1-D thermal conduction equation with an advective
term can be written as
∂2T (z, t)
∂T (z, t) Q(z)
∂T (z, t)
=k
+n
+
e ∂z
∂t
∂z2
rC
(z≥0) ,
(1)
where T is the temperature of the medium, which is a function
of time t and depth z, Q is the rate of heat production by
radioactive elements, and n is the rate of uplift (erosion). The
e
time t is measured from the initiation of uplift (erosion),
and the depth z is measured downwards from the Earth’s
surface. The other parameters, r, k and C, denote the density,
the thermal diffusivity and the specific heat of the medium,
respectively. For simplicity, r, k and C are assumed to be
constants. The values of r, k and C used for the computation
are listed in Table 1. For the heat production rate we assume
the following functional form:
Q(z)=Q exp(−z/z ) ,
(2)
0
c
where Q is the heat production rate at the surface and z is a
0
c
characteristic depth. In the computation we take the values of
Q and z as 3.0 mW m−3 and 10 km, respectively, following
0
c
Jeanloz & Morris (1986).
In the steady state (∂T /∂t=0), the solution of eq. (1) without
erosion (n =0) is given by
e
z2
(3)
T (z)= c Q [1−exp(−z/z )]+bz ,
c
k 0
where k (=rCk) is the thermal conductivity and b denotes the
geothermal gradient at depth. The surface temperature is taken
to be 0 °C. We use this steady-state temperature profile as the
reference state for measuring the temperature increase due to
uplift and erosion.
Table 1. Material constants used for computation.
r
C
k
k
density
specific heat
thermal diffusivity
thermal conductivity
3.0×103 kg m−3
1.0×103 J K−1 kg−1
1.0×10−6 m2 s−1
3.0 W K−1 m−1
© 2000 RAS, GJI 141, 271–281
T hermal structure in subduction zones
Next, we consider a time-dependent solution of eq. (1) with
erosion. If the erosion rate n is sufficiently large,
e
∂2T
Q
∂T
&k
,
,
(4)
n
e ∂z
∂z2
rC
0
we can neglect the first and third terms on the right-hand side
of eq. (1), and then we obtain
10
0
300
600
900
T (z, t)=T (z+n t) .
(6)
0
e
Therefore, the temperature increase, DT (z, t)=T (z, t)−T (z, 0),
due to the duration of erosion at the constant rate n is given
e
by
DT (z, t)=T (z+n t)−T (z) .
(7)
0
e
0
Furthermore, in sufficiently deep regions, where the effect of
radioactive heat generation is small and the geothermal gradient
is nearly constant, the above solution can be simplified to
DT =n tb .
(8)
e
This relation means that the temperature increase DT is
proportional to the erosion rate n , the duration of erosion t
e
and the initial geothermal gradient b. In other words, when
the erosion rate n is sufficiently large, rocks at depth are
e
uplifted while preserving the initial thermal state. Taking the
effect of adiabatic cooling into consideration, we obtain
DT =n t( b−a)
(9)
e
instead of eq. (8), where a denotes the adiabatic temperature
gradient. In the present study we do not consider the effect of
adiabatic cooling because the value of a ($1 °C km−1) is much
smaller than that of b ($20 °C km−1).
In order to demonstrate the validity of the approximate
relation in eq. (8) under realistic geophysical conditions, we solve
the original thermal conduction equation (1) directly by using
the finite difference method. In Fig. 1 we show changes in the
geotherm caused by uplift and surface erosion at a constant
rate of 1 mm yr−1 for three cases with different duration times,
t=5, 10 and 15 Myr. In the computation the initial geothermal
gradient b at depth is fixed to 20 °C km−1 and the radioactive
elements are assumed to move upwards together with the
rocks by crustal uplift and erosion. In Fig. 1 the broken line
indicates the initial temperature profile. In shallow regions the
temperature increase is restrained by conductive cooling from
the surface, but the temperature increase at depth is nearly
proportional to the duration of erosion. At t=15 Myr the
temperature increase reaches as much as 300 °C in regions
deeper than 20 km.
Fig. 2 shows the dependence of the temperature increase on
(a) the erosion rate n , ( b) the duration of erosion t and (c) the
e
initial geothermal gradient b. Here, the temperature increase
itself is plotted instead of the absolute value of temperature,
in order to emphasize the effect of each factor on the thermal
structure. The standard values of n , t and b are taken to be
e
1 mm yr−1, 10 Myr and 20 °C km−1, respectively, for all cases.
From Fig. 2 we can see that the approximate relation DT =n tb
e
holds at depth.
1200
t = 5 Myr
(5)
Denoting the initial temperature profile T (z, 0) by T (z), we
0
may write the solution of eq. (5) as
© 2000 RAS, GJI 141, 271–281
Temperature [˚C]
10
Depth [km]
∂T (z, t)
∂T (z, t)
=n
.
e ∂z
∂t
273
20
15
30
40
50
Figure 1. Change in geotherm due to uplift and erosion. The solid
lines indicate the vertical temperature profiles at 5, 10 and 15 Myr
after the initiation of uplift and erosion at a constant rate of 1 mm yr−1.
The broken line represents the initial temperature profile in thermal
equilibrium.
Surface heat flow is a very important observational quantity
in the investigation of underground thermal structure. In Fig. 3
we calculate changes in surface heat flow with time for given
erosion rates, where a negative erosion rate means sedimentation. As can be seen from Fig. 3, surface heat flow is
strongly affected by the erosion rate.
So far we have treated the problem within the framework
of the 1-D approximation on the assumption that the rates of
uplift and erosion are uniform in space, where heat transfer
occurs only in the vertical direction. In reality, since the rates
of uplift and erosion are not uniform in space, heat transfer
occurs not only in the vertical direction but also in the
horizontal direction.
With the 2-D thermal conduction equation given by
C
∂2T (x, z, t) ∂2T (x, z, t)
∂T (x, z, t)
=k
+
∂t
∂x2
∂z2
+n (x)
e
∂T (x, z, t) Q(z)
+
,
∂z
rC
D
(10)
we numerically evaluate the effects of lateral heat transfer. In
the computation we assume that the rates of uplift and erosion
n vary in space as
e
n (x)=nmax sin(2px/l) ,
(11)
e
e
where l is the wavelength characterizing the lateral variation
of uplift and erosion rates. Fig. 4 shows the vertical profiles of
temperature increase at the uplift axis (x=l/4) after a steady
uplift and erosion of 10 Myr duration with nmax =1 mm yr−1.
e
The broken line indicates the profile of temperature increase
274
Y. Fukahata and M. Matsu’ura
Temperature Increase
Temperature
Increase[˚C]
[dC]
0
0
100
200
300
0
100
200
300
0
100
200
300
20
30
20˚C/km
dC/km
βb==20
10
15
5
1.5
0.5
40
t = 10 Myr
30
v e = 1 mm/yr
Depth [km]
10
50
(a)
(b)
(c)
Figure 2. Diagrams showing the dependence of temperature increase on (a) the erosion rate n , ( b) the duration of erosion t and (c) the initial
e
geothermal gradient b. In each diagram the standard values of n , t and b are taken to be 1 mm yr−1, 10 Myr and 20 °C km−1, respectively.
e
200
Temperature Increase [˚C]
0
180
50
100
150
200
250
ve = 2 mm/yr
160
10
140
Depth [km]
1
120
0.5
100
20
30
80
40
60
-1
40
400
200
- 0.5
λ = 100 km
Surface Heat Flow [mW/m2]
0
-2
50
20
0
2
4
6
8
10
12
14
Duration of erosion [Myr]
Figure 3. Changes in surface heat flow with time after the initiation
of steady uplift and erosion. The negative sign of the erosion rate n
e
represents subsidence and sedimentation.
computed with the 1-D model, which corresponds to the case
of l=2 in the 2-D model. From Fig. 4 we can see that the
effects of lateral heat transfer are negligible if the characteristic
wavelength l is greater than 400 km. On the other hand, if the
characteristic wavelength is less than 200 km we cannot neglect
the effect of lateral heat transfer. In the case l=100 km,
for example, the temperature increase goes down to about
two-thirds of that in the case of no lateral heat transfer.
Figure 4. Effects of lateral variation in uplift and erosion rates on the
profile of temperature increase. The solid lines indicate the vertical
profiles of temperature increase at the uplift axis for three cases with
different characteristic wavelengths, l=100, 200 and 400 km. The
broken line represents the profile of temperature increase in the case
l=2. The duration of steady uplift and erosion is taken to be 10 Myr
and its maximum rate at the uplift axis to be 1 mm yr−1.
4 EVO LU TI O N O F T HE R MA L S T R UCT UR E
I N S UB DU CTI O N Z ON ES
On a long timescale, subduction zones are subjected to
steady uplift and erosion in island arcs and subsidence and
sedimentation in ocean trenches. Considering these advective
effects in addition to the effects of radioactive heat generation
in the crust, frictional heating at plate boundaries and accretion
© 2000 RAS, GJI 141, 271–281
T hermal structure in subduction zones
of oceanic sediments to overriding continental plates, we
numerically simulate the evolution process of the thermal
structure in subduction zones.
4.1 Vertical crustal movements caused by steady plate
subduction
Matsu’ura & Sato (1989) and Sato & Matsu’ura (1988, 1992,
1993) have constructed a kinematic plate subduction model
representing interaction between a descending oceanic plate
and an overriding continental plate by a steady increase in
tangential displacement discontinuity across the plate interface.
This model can consistently explain gross features of cyclic
crustal movements related to the periodic occurrence of interplate earthquakes, steady uplift of marine terraces formed by
eustatic sea-level changes, and gravity anomalies observed in
subduction zones. According to these studies, the pattern of
vertical crustal movements by plate subduction, which depends
on thickness of the lithosphere and geometry of the plate
interface, is characterized by steady uplift in island arcs and
steady subsidence in ocean trenches. To describe such a characteristic pattern of crustal movements, we take the following
Uplift Rate [mm/yr]
2
1
0
-1
-2
300
250
200
150
100
50
0
Distance from Trench [km]
Figure 5. The curve of the uplift rate (erosion rate) function in eq. (12)
with nmax =2 mm yr−1 and x =150 km.
e
p
T=0
x
z=0
uplift-rate function:
G
−2 cos(px/x )
0<x≤x
1
p
p ,
n (x)= nmax
e
e
2
1+cos(p(x−x )/x ) x <x≤2x
p p
p
p
(12)
where x denotes the distance measured from the trench axis.
The erosion rate is in general not equal to the uplift rate,
but it must balance the uplift rate on long-term average.
Therefore, we take the erosion-rate function with the same
form as the uplift-rate function, assuming that a steady state
of surface topography is quickly realized. In the following
numerical simulations we take the uplift rate (erosion rate)
function n (x) in eq. (12) with nmax=2 mm yr−1 and x =150 km
e
e
p
(Fig. 5), based on the results of Sato & Matsu’ura (1988, 1993).
Here the negative uplift (erosion) rate means subsidence
(sedimentation).
4.2
Model for numerical simulation
Now we construct a numerical simulation model for the
evolution of thermal structure in subduction zones. The model
used for the simulation is illustrated in Fig. 6. Fig. 6(a) represents the situation before the initiation of plate subduction.
The horizontal planes at z=0 and z=z correspond to the
L
Earth’s surface and the lithosphere–asthenosphere boundary,
respectively. We assume that the lithosphere (0≤z<z ) is
L
initially in thermal equilibrium under the conditions T =0 °C
at the Earth’s surface (z=0) and T =T at and below the
m
base of the lithosphere (z≤z ). In the computation we take
L
the values of z and T to be 60 km and 1200 °C, respectively.
L
m
At a time t=0 the oceanic plate (x≤0) starts descending
at a rate n with a dip angle of h, as shown in Fig. 6( b). After
pl
the initiation of plate subduction, we set the temperature
conditions as T =0 °C at the Earth’s surface and T =T at
m
the base of the descending oceanic slab. Under these conditions
we compute temperature changes after the initiation of plate
subduction by numerically solving the following 2-D thermal
conduction equations; for the continental block above the
x
θ
Overriding Plate
z = zL
T = Tm
275
z=0
z = zL
T
v pl
=
Tm
Sl
ab
Mantle Wedge
z
(a)
z
(b)
Figure 6. Schematic representation of the structural models and boundary conditions used for numerical computation. (a) shows the situation
before the initiation of plate subduction. The horizontal planes at z=0 and z=z correspond to the Earth’s surface and the lithosphere–
L
asthenosphere boundary, respectively. ( b) shows the situation after the initiation of plate subduction. At a time t=0, the oceanic plate (x≤0)
starts descending at a rate of n with a dip angle h.
pl
© 2000 RAS, GJI 141, 271–281
276
Y. Fukahata and M. Matsu’ura
upper surface of the descending slab (z≤x tan h),
C
∂2T (x, z, t) ∂2T (x, z, t)
∂T (x, z, t)
=k
+
∂t
∂x2
∂z2
+
h as 50 mm yr−1 and 45°, respectively. The values of model
parameters used for the computation are summarized in
Table 2.
D
∂T (x, z, t)
Q(z) F(z)
+
d(z−x tan h)+n (z)
a
rC
rC
∂x
∂T (x, z, t)
,
+n (x)
e
∂z
4.3
(13)
and for the descending slab and its extension (x tan h≤z≤
z +x tan h),
L
C
D
Q(z−x tan h)
∂2T (x, z, t) ∂2T (x, z, t)
∂T (x, z, t)
=k
+
+
∂t
∂x2
∂z2
rC
+
∂T (x, z, t)
F(z)
d(z−x tan h)+n cos h
pl
rC
∂x
+n sin h
pl
∂T (x, z, t)
.
∂z
(14)
On the upper surface of the descending slab and its extension
(z=x tan h) we require continuity of temperature through the
computation.
In eq. (13) the second and third terms on the right-hand
side represent the effects of radioactive heat generation in the
upper crust and frictional heating at the plate boundary. We
assume the rate of radioactive heat production Q per unit
volume to be
Q(z)=Q exp(−z/z ) ,
0
c
(15)
with Q =3 mW m−3 and z =10 km, and the rate of frictional
0
c
heating F per unit area to be
G
z/z
0≤z≤z
T
T ,
F(z)=n t (z)=n tmax
pl f
pl f
(z −z)/(z −z ) z ≤z≤z
L
L
T
T
L
(16)
with the maximum frictional stress tmax =50 MPa at the
f
brittle–ductile transition depth z =30 km. The fourth term
T
represents the effect of accretion of oceanic sediments to the
underside of the overriding continental plate. Although the
actual process of accretion is complex and very varied, in our
model, for simplicity, we represent the effect of accretion as a
landward migration of the continental plate at a constant rate
n , i.e.
a
n (z)=n [H(z)−H(z−z )] ,
a
a
L
(17)
with n =5 mm yr−1. Here, H(z) denotes the unit step function.
a
The fifth term represents the effect of vertical crustal movements, namely, uplift and erosion in island arcs and subsidence
and sedimentation in ocean trenches. In the computation
we take the uplift-rate function n (x) in eq. (12) with
e
nmax =2 mm yr−1 and x =150 km (Fig. 5).
e
p
In eq. (14) the second term on the right-hand side represents
the effect of radioactive heat generation in the descending
oceanic slab. The third term, which represents the effect of
frictional heating at the plate boundary, is the same as that in
eq. (13). The fourth and fifth terms represent the effects of
steady subduction of the cold oceanic slab. In the computation
we take the values of the subduction rate n and the dip angle
pl
Results of numerical simulation
In the following part of this section we show the results of
numerical simulation. We direct our attention to temperature
changes for the first 5 Myr after the initiation of plate subduction, because the uplift and erosion in island arcs and the
subsidence and sedimentation in ocean trenches are expected
to be very active in this period (Sato & Matsu’ura 1993). After
this period the rates of uplift and subsidence due to plate
subduction will decrease with time because of the viscoelastic
stress relaxation of the lithosphere.
The most essential factor controlling the evolution of thermal
structure in subduction zones is, of course, cooling by the
descending oceanic slab. In order to see only this effect, first
we carried out a numerical simulation neglecting all the other
effects. The results are shown in Fig. 7, where the intervals
of isotherms are taken to be 200 °C and the vertical scale is
exaggerated twice in every diagram. From Fig. 7 we can see
that the temperature field in and around the descending slab
changes rapidly with time. The inland temperature field is,
however, not affected by the subduction of the cold slab itself,
even after 5 Myr. It should be noted that the effective distance
L $2√kt of thermal conduction in the Earth’s lithosphere
is only about 25 km for t=5 Myr, which is much shorter
than the characteristic width ($400 km) of island arc–trench
systems.
Next, in order to examine the individual effects of the
radioactive heat generation, the frictional heating, the erosion
and sedimentation and the accretion, we carried out numerical
simulation by incorporating each process into the simple plate
subduction model. The results of the numerical simulations
are summarized in Fig. 8, where every diagram indicates the
temperature field at t=5 Myr. For reference, the result of
the simple plate subduction model is shown in (a), which is
identical to Fig. 7(f ). ( b) and (c) show the effects of radioactive
heat generation and frictional heating, respectively. Radioactive
heat generation raises the temperature in the shallow part of
the continental lithosphere. The frictional heating causes temperature increases at and around the plate boundary. These
effects are, however, not very remarkable. (d) and (e) show,
respectively, the effects of erosion and sedimentation on the
Earth’s surface and accretion at the plate boundary. The
steady uplift and erosion in the island arc causes a remarkable
temperature increase over the broad region of the continental
lithosphere. The temperature increase reaches about 200 °C at
the uplift axis (x=150 km). The steady subsidence and sedimentation in the ocean trench causes a temperature decrease,
but its effect is not so prominent. The effect of subsidence and
sedimentation cannot be clearly distinguished from the effect of
cooling by the cold slab. The process of accretion continuously
Table 2. Model parameters used for numerical simulations.
z
L
T
m
n
pl
h
lithospheric thickness
asthenospheric temperature
relative plate velocity
subduction angle
60 km
1200 °C
50 mm yr−1
45°
© 2000 RAS, GJI 141, 271–281
T hermal structure in subduction zones
277
Distance from Trench [km]
Depth [km]
300
0
200
100
0
300
0
200
100
0
300
0
50
50
50
100
100
100
t = 0 Myr
1 Myr
150
(b)
100
0
300
0
200
100
0
300
0
50
50
100
100
100
3 Myr
100
0
(c)
50
4 Myr
150
0
150
(a)
200
100
2 Myr
150
300
0
200
200
5 Myr
150
150
(d)
(e)
(f)
Figure 7. The evolution of thermal structure in subduction zones computed with the simple plate subduction model. The time t is measured from
the initiation of plate subduction. In this computation only the effect of cooling by a descending oceanic slab is considered. The surface temperature
is fixed to 0 °C and the intervals of isotherms are taken to be 200 °C. The vertical scale is exaggerated twice.
Distance from Trench [km]
Depth [km]
300
0
200
100
0
300
0
200
100
0
300
0
50
50
50
100
100
100
150
150
200
(b)
100
0
300
0
200
100
0
300
0
50
50
100
100
100
150
(d)
0
100
0
(c)
50
150
100
150
(a)
300
0
200
200
150
(e)
(f)
Figure 8. Comparison of the effects of (b) radioactive heat generation, (c) the frictional heating, (d) the erosion and sedimentation and (e) the
accretion. (a) is the case of simple plate subduction, which is identical to Fig. 7(f ). ( b)–(e) are computed by incorporating the corresponding process
into the simple plate subduction model. The temperature field computed with the full model including all of the effects is shown in (f ). All diagrams
show the temperature field at t=5 Myr.
creates a new continental region with a low temperature
at the plate boundary. In the present case (n =5 mm yr−1)
a
the horizontal extent of this cold region reaches 25 km at
t=5 Myr. Another important effect of accretion is to move
© 2000 RAS, GJI 141, 271–281
the old continental plate away from the trench axis. This effect
is not noticeable in (e) because the temperature field in the old
continental plate has no lateral variation. In (f ) we show the
temperature field computed from the full model including all
278
Y. Fukahata and M. Matsu’ura
of the effects. From this diagram we can recognize the landward
migration of the high-temperature region beneath the island
arc, which can be interpreted as the results of the additive
effects of the erosion and the accretion.
Finally, with the full model including all of the effects we
carried out a numerical simulation of the thermal evolution
process in the subduction zone. In this numerical simulation
we considered the change in distribution of radioactive elements
associated with the uplift and erosion, the subsidence and sedimentation, and the accretion. In practice we assumed that the
radioactive elements in the upper crust move together with
the surrounding material and that the radioactive elements
in the eroded or accreted sediments are uniformly distributed
with the average value of the upper crust. The results of the
numerical simulation are shown in Fig. 9. (a) shows the initial
temperature field in thermal equilibrium. After the initiation
of plate subduction, the cooling of the continental plate and
the mantle wedge by the cold descending slab proceeds near
the plate boundary as shown in ( b) and (c). With further progress of plate subduction, the temperature beneath the island
arc gradually increases as a result of uplift and erosion, and the
low-temperature region near the ocean trench gradually
expands as a result of sedimentation and accretion, as shown
in (e) and (f ). After t=5 Myr, the rate of crustal uplift and
subsidence motion due to steady plate subduction is considered
to decay with time because of viscoelastic stress relaxation in
the Earth’s lithosphere.
The most important observable quantity in investigating the
thermal state in the Earth’s interior may be surface heat flow.
In Fig. 10 we show the patterns of the spatio-temporal variation
of surface heat flow calculated from three different plate
subduction models: (a) with radioactive heat generation and
frictional heating; ( b) with erosion and sedimentation in
addition to radioactive heat generation and frictional heating;
and (c) the full model with all of the effects including accretion.
In each diagram the profiles of surface heat flow are calculated
every 1 Myr after the initiation of plate subduction. In the case
of model (a), the cooling by the descending slab gradually
decreases the surface heat flow near the ocean trench with
time, but the surface heat flow in the island arc does not
change from the initial state even after 5 Myr. In model (b),
on the other hand, the surface heat flow in the island arc
increases rapidly after the initiation of plate subduction. This
dramatic change in the profile of surface heat flow is clearly
due to the steady uplift and erosion in the island arc. The
steady subsidence and sedimentation near the oceanic trench
further depress the surface heat flow there. In model (c), the
accretion of cold oceanic sediments to the continental plate
steadily expands the low heat flow region near the ocean
trench and moves the high heat flow region away from the
trench axis. At t=5 Myr after the initiation of plate subduction,
the maximum value of surface heat flow in the island arc
reaches 150 mW m−2, which is about twice as large as that in
model (a).
5 CO M PA R IS O N W I TH O B S ER V ED DATA
I N S HI K OK U , SO U TH W ES TE R N JA PA N
In order to examine the validity of our model, we compare
the results of numerical simulations with observed data in
Shikoku, southwestern Japan. This region is one of the few
young subduction zones where detailed observations of both
surface heat flow and crustal movement have been made.
In southwestern Japan, the Philippine Sea plate is descending beneath the Eurasian plate at the Nankai trough with a
convergence rate of 40 mm yr−1 (Seno et al. 1993). From
Distance from Trench [km]
Depth [km]
300
0
200
100
0
300
0
200
100
0
300
0
50
50
50
100
100
100
t = 0 Myr
1 Myr
150
200
0
300
0
200
100
0
300
0
50
50
100
100
100
3 Myr
4 Myr
200
0
5 Myr
150
(d)
100
(c)
50
150
0
150
(b)
100
100
2 Myr
150
(a)
300
0
200
150
(e)
(f)
Figure 9. The evolution of thermal structure in subduction zones computed with the full model including all of the effects. The time t is measured
from the initiation of plate subduction.
© 2000 RAS, GJI 141, 271–281
T hermal structure in subduction zones
3
150
Uplift Rate [mm/yr]
(a)
100
1 Myr
5 Myr
50
250
200
150
100
50
0
(a)
2
1
0
-1
-2
-3
-4
5 Myr
150
200
150
100
(b)
150
100
1 Myr
50
0
300
250
200
150
150
100
50
5 Myr
100
0
(c)
Surface Heat Flow [mW/m2]
Surface Heat Flow [mW/m2]
0
300
279
(b)
100
50
0
1 Myr
250
200
150
100
50
0
Distance from Nankai Trough [km]
50
0
300
250
200
150
100
50
0
Distance from Trench [km]
Figure 10. Changes in the profile of surface heat flow with time calculated from three different plate subduction models: (a) the model with
radioactive heat generation and frictional heating; ( b) the model with
erosion and sedimentation in addition to radioactive heat generation
and frictional heating; and (c) the full model with all of the effects
including accretion. The heat flow profiles are calculated every 1 Myr
after the initiation of plate subduction. For reference, the heat flow
profile at t=5 Myr in (a) is shown by the broken lines in ( b) and (c).
geological data, Niitsuma (1985) has estimated that the plate
subduction at the Nankai trough started about 6 Myr ago.
Along the western coast of the Muroto Promontory, the
southernmost part of Shikoku, well-developed Pleistocene
marine terraces are observed (Yoshikawa et al. 1964). In
Shikoku, geodetic surveys started in the 1890s and have been
repeated at intervals of 20–30 years.
With the kinematic plate subduction model, Sato &
Matsu’ura (1992) have calculated the uplift rate due to steady
plate subduction in southwestern Japan. In Fig. 11(a) we show
the profile of calculated uplift rates as a thick solid line, which
reaches a maximum just south of Shikoku Island. We also
show the uplift rate inferred from the present heights of marine
terraces (Yoshikawa et al. 1964) and that estimated from the
inversion analysis of levelling data (Fukahata et al. 1996). The
theoretically calculated uplift rate is consistent with these
observed uplift rates.
Surface heat flow data in this region have been compiled by
Yamano (1995). Recently, Furukawa et al. (1998) have added
new data to Yamano’s data set. We have plotted these heat
© 2000 RAS, GJI 141, 271–281
Figure 11. (a) The uplift rates in Shikoku, southwestern Japan. Thick
solid line: calculated from the plate subduction model (after Sato &
Matsu’ura 1992); thin solid line: estimated from the inversion analysis
of levelling data (after Fukahata et al. 1996); diamonds: inferred from
the present heights of Pleistocene marine terraces (after Yoshikawa
et al. 1964). ( b) Profiles of surface heat flow obtained from observed
data (Yamano 1995; Furukawa et al. 1998) by taking a five-point
running average. The vertical and horizontal bars indicate standard
deviations. It should be noted that the horizontal scales in the two
diagrams are different.
flow data as a function of the distance from the trench axis,
and then taken a five-point running average in order to see
the general trend of spatial variation in surface heat flow. The
results are shown in Fig. 11( b), where the vertical and horizontal bars indicate standard deviations. From this diagram it
is seen that the profile of surface heat flow has a significant
peak at the southernmost part of Shikoku, where the profiles
of uplift rates, estimated from the levelling data, the present
heights of marine terraces and the plate subduction model,
reach a maximum. Furukawa et al. (1998) have also pointed
out that the high heat flow in southern Shikoku could be
attributed to the uplift of accreted materials. According to
their estimation, an uplift rate of about 1 mm yr−1 is required
to explain the high heat flow in this region.
The high heat flow around the Nankai trough is basically
due to the subduction of the young and hot oceanic plate
(Wang et al. 1995), but the extraordinarily high heat flow
observed at several points is considered to be due to hydrothermal circulation (Yamano et al. 1992). Fluid flow causes a
strongly scattered pattern of heat flow like that seen here
because upward fluid flow leads to high surface heat flow and
downward fluid flow leads to low surface heat flow.
280
6
Y. Fukahata and M. Matsu’ura
D IS CU SSI O N A N D CON CLU SION S
In plate tectonics a basic question is why island arcs are hot
in spite of the long duration of cooling by cold descending
oceanic slabs. In the present study we proposed a possible
answer to this question.
In subduction zones, steady subduction of oceanic plates
kinematically causes steady uplift of island arcs. The steady
uplift of island arcs is always accompanied by surface erosion.
The long duration of uplift and erosion effectively transports
heat at depth to shallower parts by advection. In the present
study, considering the effects of vertical crustal movements
such as uplift and erosion in island arcs and subsidence and
sedimentation in ocean trenches, in addition to the effects of
radioactive heat generation in the crust, frictional heating at
plate boundaries and accretion of oceanic sediments to overriding continental plates, we have numerically simulated the
evolution process of thermal structure in subduction zones.
The results show that the temperature beneath the island arc
gradually increases as a result of uplift and erosion as plate
subduction progresses. Near the ocean trench, on the other
hand, the low-temperature region gradually expands as a result
of sedimentation and accretion in addition to direct cooling
by the cold descending slab.
Radiogenic heating increases the geotherm, especially in
shallow regions, but this effect is not unique to subduction
zones and cannot produce a lateral variation of the thermal
structure in the arc lithosphere by itself. Frictional heat is
generated at the plate interface. Its effect on thermal structure
in the whole subduction zone is considered to be small, because
the rate of thermal conduction is very slow. On the other
hand, uplift and subsidence, which transport heat by advection,
have large effects on thermal structure if they continue for
several million years at a rate of 1 mm yr−1 or more. In
addition, the horizontal scale of uplift and subsidence caused
by plate subduction is comparable to the width of subduction
zones. Thus, the uplift and subsidence can produce lateral
variation in thermal structure on the island-arc scale. Accretion
is also considered as a process of heat transport by advection,
and its effect on the thermal structure in subduction zones is
not small.
Fluid flow and magma migration also transport heat by
advection. They will drastically change the thermal state,
especially in shallower parts, and cause a strongly scattered
heat flow distribution (Lewis et al. 1988; Yamano et al. 1992).
In the present study, we did not take these effects into account,
because they are local effects (Blackwell et al. 1982; Henry
et al. 1989; Foucher et al. 1990).
So far, in most cases the thermal structure in subduction
zones has been treated as a steady-state problem (e.g. Honda
1985; Royden 1993). However, as Wang et al. (1995) have pointed
out, the thermal structure in subduction zones intrinsically
evolves with time, and it will take several tens of millions of
years to reach a steady state under given boundary conditions
(Honda 1985; Royden 1993). During this period various changes
in tectonic environment may occur. For example, in the
Japanese islands back-arc spreading occurred 15–25 Myr ago
(Jolivet et al. 1994), and the subduction of the Philippine Sea
plate at the Nankai trough started about 6 Myr ago (Niitsuma
1985). Therefore, most subduction zones in the world may be
considered to be in some stage of thermal evolution. In the
present study we focused on the first 5 Myr after the initiation
of plate subduction, for which the most active crustal movements and thus the most drastic changes in thermal structure
will occur.
With the thermal evolution model we calculated changes in
the profile of surface heat flow across the island arc–trench
system with time after the initiation of plate subduction. The
results show the gradual development of a characteristic heat
flow pattern; that is, low heat flow in the fore-arc basin, high
heat flow in the island arc and moderately high heat flow in
the back-arc region. So far, observations of surface heat flow
have been considered to give us direct information about the
thermal state of the Earth’s interior. Therefore, observed heat
flow patterns have been used as primary constraints in constructing thermal structure models of subduction zones (Honda
1985; Furukawa 1993). In these models the lithosphere overlying the wedge mantle is assumed to be stable, and so the
effect of advection on heat transfer in the lithosphere is
neglected. As demonstrated in the present study, however, the
arc lithosphere is not stable, and the advection has essential
effects on heat transfer and the pattern of surface heat flow.
The validity of the thermal structure models constructed under
the constraints of observed heat flow patterns should be
re-examined by considering the effect of advection in the arc
lithosphere.
A C K NO W LE DG M EN TS
We wish to thank Makoto Yamano for his valuable comments
and helpful discussion. We thank also the anonymous referees
for their useful comments.
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