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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. 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