We conducted two-dimensional numerical experiments of mantle convection with imposed kinematic motions of cold slabs, in order to study the mechanism for the generation of ascending flows in the “Big Mantle Wedge” (BMW), which has been recently proposed in order to relate the stagnant Pacific slab with the intraplate volcanism in northeast Asia. Our calculations demonstrated that the BMW is expanded oceanward in response to the retreating motion of trench and slab, which strongly affects the flows in the region. In particular, the subducting and retreating motion of slab induces a local but strong circulation near the oceanward end (or a hinge) of the stagnant slab in the BMW. Our findings suggest that ascending flows in the BMW can be triggered most easily near the hinge of the stagnant slab, which is in good agreement with the occurrence of several active intraplate volcanoes above the stagnant Pacific slab.
 There are several active intraplate volcanoes in northeast Asia, such as Wudalianchi and Changbai. Unlike typical hotspot volcanoes such as Hawaii [Turcotte and Schubert, 2002], these intraplate volcanoes are not rooted in the lower mantle. Instead, as has been revealed by recent progress of seismic survey [Zhao, 2004; Zhao and Ohtani, 2009], the origin of these volcanoes is closely linked to the presence of a subducted Pacific slab which is stagnated in the mantle transition zone beneath the region [Fukao et al., 2001; Li et al., 2008; Obayashi et al., 2009]. In particular, the eruption sites of both Wudalianchi and Changbai are, if projected downward to the transition zone, located near the Pacific plate reaching around 600 km depth [Gudmundsson and Sambridge, 1998]. These observations strongly suggest the connections between the intraplate volcanism in this region and the presence of stagnant Pacific slab.
 Recently, Zhao and coworkers [Zhao et al., 2009] proposed an idea termed “Big Mantle Wedge” (BMW), in order to discuss the active tectonic and volcanic processes in northeast Asia as a result of the stagnation of the Pacific slab. Here the BMW comes from an extension of the model of Tatsumi et al. , and includes both a (traditional) mantle wedge and the region of the upper mantle above the stagnant slab. According to this model, an emergence of ascending flows in the BMW region is of crucial importance for the deep origin of the intraplate volcanism above stagnant slabs. However, it is still left unclear what mechanisms are responsible for the origin of the ascending flows in the BMW.
 In this paper, we carry out two-dimensional numerical simulations of mantle convection in order to study how the stagnation of subducted slabs is related with ascending flows in the BMW. Some researchers attribute the ascending flows to a dehydration of hydrous minerals in subducting slabs [Zhao et al., 2009; Richard and Iwamori, 2010], while others argued a return flow induced by subducting slabs [Faccenna et al., 2010]. Here we will point out the potential importance of the stagnating and retreating motions of subducted slabs for the origin of ascending flows in the BMW.
2. Numerical Model
 We consider a thermal convection of a highly viscous fluid in a model of two-dimensional rectangular box ofd = 2000 km height and 6600 km width, which is driven by a subducting and retreating motion of a cold slab. We take into account the effects of phase transformation of mantle materials from olivine (Ol) to wadsleyite (Wad) at around 410 km depth, and that from ringwoodite (Rw) to perovskite (Pv) and magnesiowüstite (Mw) at around 660 km depth. The Clapeyron slopes of these phase transitions are taken to be 3 MPa/K and −3 MPa/K, respectively. The density jumps associated with these transitions are, on the other hand, assumed to be 8.3% and 7.8%, respectively. The viscosity η of mantle material is assumed to depend exponentially both on temperature T and pressure (or a depth) as η ≡ η0exp[(Tsurf − T)/a + (d − z)/b], where z is the height from the bottom surface. Note that the values of rheological parameters are chosen to yield a viscosity profile similar to that used in Torii and Yoshioka . In addition, a viscosity jump rη (≤30) between the upper and lower mantle is also taken into account. The meanings and values of parameters used in this study are given in Table 1.
Table 1. Meanings and Values of the Symbols Used in This Study
3.3 × 103 kg/m3
2 × 10−5 K−1
1.029 × 103 J/kg K
1 × 10−6 m2/s
1 × 1024 Pa s
temperature-dependence of viscosity
depth-dependence of viscosity
 In this model, we imposed the kinematic motion of a cold slab a priori including its subduction and retreat. The subduction of slab is modeled by a similar manner as in the works by Yoshioka and coworkers [Yoshioka and Sanshadokoro, 2002; Torii and Yoshioka, 2007; Yoshioka and Naganoda, 2010]. That is, we put a conduit (or a guide) of 80 km thickness along which a cold fluid flows from the top surface into the deep mantle at a constant velocity vp. The conduit bends downward with a dip angle θd = 30° at a “trench” located 500 km away from the left-hand side end of the top surface. In addition, we increased with time the length of the conduit (at most down to around 400 km depth) where the fluid motion is kinematically imposed, in order to model the descent of cold slab. The retreating motion of the slab, on the other hand, is modeled by a similar manner as in the work byvan Hunen et al. , where the effect of trench migration is taken into account by making good use of Galilean transformation. Here a oceanic plate is assumed to subduct and retreat below an overriding continental lithosphere which moves at a rate equal to that of trench retreat vt (positive oceanward). In this study, the value of vt is changed from 0 cm/yr to 4.73 cm/yr, while the sum vp + vt (≡ vc) is kept to be 9.46 cm/yr. The choices of vt and vc employed here are close to the nature of plate convergence at the Japan trench [Schellart, 2011].
 The initial distribution of temperature is given by the effects of the conductive cooling of half-space and the adiabatic compression, by assuming that the potential temperatureTpot = 1280°C and the “age” of subducting plate is around 100 My at the trench. The boundary conditions for temperature are (i) fixed temperature T = Tsurf = 0°C at the top surface, (ii) fixed temperature at the left-hand side wall, and (iii) adiabatic conditions at the bottom and right-hand side wall. The boundary condition for velocity is chosen so as to allow the mantle material to freely flow in and out of the boundaries of the model except at the top surface. In addition, we assumed that the net mass flux is zero across the right-hand side wall.
 We simultaneously solved the equations of conservation of mass, momentum and the thermal energy under the extended Boussinesq approximation [e.g., Christensen and Yuen, 1985], where the effects of adiabatic heating and latent heat due to phase transitions are explicitly included in the energy transport. However, we ignored the effect of viscous dissipation (or frictional heating), in order to avoid spurious dissipation occurring at the bends of the pre-assigned conduit. The equations for conservation of mass and momentum are solved for the streamfunctionψ instead of directly solving for the velocity and pressure.
 The basic equations are discretized by a finite volume scheme. In order to resolve the dynamic behaviors near and above the mantle transition zones, we employed different mesh divisions in the regions above and below 1320 km depth: The region above 1320 km depth is divided uniformly into square meshes with 128 vertical and 640 horizontal mesh points, while the region below the depth is divided uniformly into rectangular meshes with 32 vertical and 640 horizontal mesh points. The equations for temperature T and flow fields are solved by our thermal convection simulation code [Kameyama, 1998; Kameyama et al., 2005; King et al., 2010], whose numerical validity has been already verified.
 In Figure 1 we compare the behaviors of subducted cold slabs at around 40 My after the onset of subduction for various values of the rate of trench retreat vt and the viscosity jump rη at the 660 km discontinuity. Figure 1 clearly shows that the stagnation of subducted slabs is enhanced for larger values vt and rη. In particular, as has been discussed in Torii and Yoshioka , two types of slab stagnation can be observed in the figure depending on the values of vt and rη. Among them, large vt makes slabs lie horizontally over a long distance around the 660 km discontinuity, while large rη makes slabs be accumulated near the discontinuity.
Figure 1 also shows that, for the cases with slab stagnation, slabs of highly viscous cold fluid are thickened near the oceanward end (or a hinge) of stagnant slabs where they bend at around the 660 km discontinuity. In particular, the thickening occurs regardless the types of slab stagnation: it can be observed not only when the slabs are accumulated at the discontinuity (for large rη) but also when they are horizontally-lying at the discontinuity (for largevt). In addition, the thickening of cold slabs is significant for larger vt and rη. Indeed, the surfaces of the slabs are deflected upward almost up to the base of the top thermal boundary layer for the largest vt and rη in the figure.
 In order to see how the values of vt and rη affect the temporal evolution of stagnant slabs, we show in Figure 2the plots against time of the horizontal distances between the trench and the tip of stagnant slabs in the mantle transition zone. For clarity, shown in the figure are the plots only for the time instances of the cases where there exist horizontally-lying slabs in the mantle transition zones. Also shown by broken lines are the hypothetical ones estimated solely from the rates of two-plate convergencevc (with steeper slopes) and trench retreat vt (with gentler slopes). Considering that the rate vc determines the rate of supply of the cold fluid into the mantle transition zone, the plots in Figure 2 are expected to have the slopes close to vc if stagnant slabs are simply sliding above the 660 km discontinuity in response to the subduction of cold fluids at the trench. However, Figure 2 clearly shows that the rate of increases in the horizontal distances is significantly smaller than the rate of convergence of the two plates at the trench, reflecting a thickening of cold fluid during the slab stagnation. Rather, the slopes of the plots are almost equal to that of trench retreat vt, once the stagnant slabs are sufficiently developed (see the plots for t > 40 My). This means that the tips of the stagnant slabs are almost anchored in the mantle and, in other words, the “Big Mantle Wedge” (BMW) expands oceanward in response to the retreating motions of trench and slabs.
 In order to see in detail the course of the thickening of slabs near the hinge of the stagnant slabs, we show in Figure 3 the snapshots of the distributions of (a) temperature T and (b) horizontal stress σxx and flow fields (velocity and streamlines) for the case with vt = 3.15 cm/yr and rη = 10 at the elapsed times indicated in the figures. (Note in Figure 3b that σxx = 0 in the slabs shallower than about 400 km depth, since no stress is acting in a fluid whose motion is kinematically imposed by the conduit.) Up to t ∼ 20 My where the subducting slab is about to stagnate around the 660 km discontinuity, there occurs an anticlockwise circulation in the upper mantle along with the descending motion of cold fluid. This circulation generates an ascending flow near the tip of the slab, which is similar to the finding by Faccenna et al. . During the same period, a strong horizontal compression is acting in the horizontally-lying portion of the slab (seeFigure 3b). However, for t > 30 My where the stagnant slab is well formed, a flow pattern significantly changes around the stagnant slab. Near the tip of the stagnant slab, for example, the fluid motion is negligibly small, as can be seen from a sparse distribution of streamlines. In addition, a slightly extensional (rather than compressional) stress is observed in the horizontal direction near the tip of the slab. This means that the horizontally-lying portion of stagnant slab is stretched in the horizontal direction in response to the trench retreat. Near the hinge of the stagnant slab, in contrast, a local but strong circulation takes place, which results in a strong horizontal compression in this region. Owing to the local ascending motion, a slab of cold fluid is driven upward in the region, which results in a thickening of the slab.
 In order to see the influence of the trench retreat on the local circulations described above, we compare in Figure 4 the behaviors of subducted cold slabs at around 40 My after the onset of subduction for rη = 10 and various values of the rate of trench retreat vt. The figure clearly demonstrates that the circulations become significant when vt is sufficiently large. Indeed, as can be seen from the flow fields, there are significant anticlockwise circulations near the hinge of stagnant slabs for vt ≥ 3.15 cm/yr, while there occurs only slightly for vt = 0 cm/yr. The comparison indicates that the local circulations are largely due to the oceanward expansion of the BMW associated with the subducting and retreating motion of slabs. In other words, the increase in the area of BMW is filled by the local circulation near the hinge of the stagnant slab.
4. Discussion and Concluding Remarks
 By conducting numerical experiments of mantle convection, we studied the mechanism for the generation of ascending flows in the “Big Mantle Wedge” (BMW), aiming at relating the stagnant Pacific slab with the intraplate volcanism in northeast Asia. Our calculations demonstrated that the retreating motion of trench is of the primary importance on the formation of horizontally-lying stagnant slabs at the 660 km discontinuity. In addition, we found that there occurs a local but strong circulation near the oceanward end (or a hinge) of the the stagnant slab in the BMW. This local circulation is driven by the subducting and retreating motion of slab, and induces an ascending flow which results in a thickening of cold fluids near the hinge of the stagnant slab. The ascending flow in the BMW presented here is in good agreement with the occurrence of active intraplate volcanoes in northeast Asia (such as Wudalianchi and Changbai) above the stagnant Pacific slab at around 600 km depth.
 Our results may have strong impacts on the significance of “wet plumes” proposed by several earlier studies [Richard and Iwamori, 2010; Richard and Bercovici, 2009]. A key assumption in their models is that a growth of convective instability is greatly enhanced by the release of water (or hydrogen ions) from stagnant slabs, since water lowers the density [Inoue et al., 1998] and/or viscosity [Karato, 2006] of minerals in the mantle transition zone. On the other hand, a strong local circulation obtained in our study (see Figure 3) is likely to act as a trigger of a convective instability in the BMW. Taking together with the effect of wet plumes, ascending flows are expected to form and grow most easily near the hinge of stagnant slabs. We thus speculate that wet ascending flows triggered by the local circulation near the hinge of stagnant Pacific slab are important agents for the deep origin of volcanism in northeast Asia.
 Although we believe that out model captures a fundamental nature of the slab stagnation and the flows in the BMW, our findings should be verified by further improving numerical models. Among the several assumptions in the present model, the prescribed kinematic motions of subducting plate and trench retreat were employed as key mechanisms in the development of stagnant slab [Torii and Yoshioka, 2007]. However, it is not clear if the surface motions imposed thus are truly consistent with the dynamics of the underlying mantle, even though it might not be necessarily the case in the actual subduction zones [Heuret and Lallemand, 2005]. In addition, our numerical results may also imply that the assumption of the constant rate of two-plate convergence (vc) throughout the calculations needs careful validation, since vcdetermines the rate of supply of cold fluid into the mantle and, in other words, is likely to affect the overall flow patterns in the BMW. It should be therefore quite important to study the development of horizontally-lying stagnant slabs by using models where the subducting and retreating motion of slabs are handled in a self-consistent manner (such asNakakuki et al. ), in order to fully address the dynamic nature of subducting and stagnant slabs, including its impacts on the BMW.
 We thank Shoichi Yoshioka for technical advice on the program development and Hiroki Ichikawa for fruitful discussion. We thank Dapeng Zhao and Cin-Ty Lee for their helpful comments which improved the paper. We greatly acknowledge thorough support from the Global COE program from the Ministry of Education, Culture, Sports, and Technology (MEXT) of Japan. MK acknowledges financial support from Grant-in-Aid for Scientific Research (B) from Japan Society for the Promotion of Science (22340127).
 The Editor thanks Dapeng Zhao and Cin-Ty Lee for assisting with the evaluation of this paper.