Earth and Planetary Science Letters 403 (2014) 368–379

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Earth and Planetary Science Letters

www.elsevier.com/locate/epsl

Evolution of 3-D subduction-induced mantle flow around lateral slab

edges in analogue models of free subduction analysed by stereoscopic

particle image velocimetry technique

Vincent Strak ∗, Wouter P. Schellart

School of Earth, Atmosphere and Environment, Monash University, Melbourne, VIC 3800, Australia

a r t i c l e i n f o a b s t r a c t

Article history:Received 19 March 2014Received in revised form 30 June 2014Accepted 4 July 2014Available online xxxxEditor: J. Brodholt

Keywords:subductionmantle flowslab edgesanalogue modelsstereoscopic PIV

We present analogue models of free subduction in which we investigate the three-dimensional (3-D) subduction-induced mantle flow focusing around the slab edges. We use a stereoscopic Particle Image Velocimetry (sPIV) technique to map the 3-D mantle flow on 4 vertical cross-sections for one experiment and on 3 horizontal depth-sections for another experiment. On each section the in-plane components are mapped as well as the out-of-plane component for several experimental times. The results indicate that four types of maximum upwelling are produced by the subduction-induced mantle flow. The first two are associated with the poloidal circulation occurring in the mantle wedge and in the sub-slab domain. A third type is produced by horizontal motion and deformation of the frontal part of the slab lying on the 660 km discontinuity. The fourth type results from quasi-toroidal return flow around the lateral slab edges, which produces a maximum upwelling located slightly laterally away from the sub-slab domain and can have another maximum upwelling located laterally away from the mantle wedge. These upwellings occur during the whole subduction process. In contrast, the poloidal circulation in the mantle wedge produces a zone of upwelling that is vigorous during the free falling phase of the slab sinking but that decreases in intensity when reaching the steady-state phase. The position of the maximum upward component and horizontal components of the mantle flow velocity field has been tracked through time. Their time-evolving magnitude is well correlated to the trench retreat rate. The maximum upwelling velocity located laterally away from the subducting plate is ∼18–24% of the trench retreat rate during the steady-state subduction phase. It is observed in the mid upper mantle but upwellings are produced throughout the whole upper mantle thickness, potentially promoting decompression melting. It could thereby provide a source for intraplate volcanism, such as Mount Etna in the Mediterranean, the Chiveluch group of volcanoes in Kamchatka and the Samoan hotspot near Tonga.

© 2014 Elsevier B.V. All rights reserved.

1. Introduction

The subduction process is considered as being mainly driven by the negative buoyancy force through the diving of dense oceanic lithosphere into the mantle (Elsasser, 1971; Forsyth and Uyeda, 1975; Chapple and Tullis, 1977; Carlson et al., 1983; Davies and Richards, 1992; Conrad and Lithgow-Bertelloni, 2002; Bercovici, 2003; Schellart, 2004b; Funiciello et al., 2004; Capitanio et al., 2007; Goes et al., 2008). The sinking of slabs involves the mo-tion of subducting plates but it also induces mantle flow through the viscous drag and the pressure difference in the mantle, due to the down-dip and slab-normal component of slab motion, re-

* Corresponding author. Tel.: +61 (0) 399 054 317.E-mail address: vincent.strak@monash.edu (V. Strak).

http://dx.doi.org/10.1016/j.epsl.2014.07.0070012-821X/© 2014 Elsevier B.V. All rights reserved.

spectively. In turn the mantle flow is supposed to deform both the overriding plate (Sleep and Toksöv, 1971; Toksöz and Hsui, 1978; Duarte et al., 2013; Meyer and Schellart, 2013; Schellart and Moresi, 2013) and the slab, which can be curved in re-sponse to the quasi-toroidal return flow around the slab edges, thereby producing the trench curvature (Jacoby, 1973; Schellart, 2004a, 2010a; Morra et al., 2006, 2009; Stegman et al., 2006;Schellart et al., 2007; Loiselet et al., 2009). Furthermore mantle flow can produce upwelling that might result in decompression melting, thereby providing a source for volcanism. In particular, rollback-induced quasi-toroidal flow around the lateral slab edges has been proposed to be an alternative mechanism explaining the occurrence of intraplate volcanism near slab edges (e.g., Jadamec and Billen, 2010, 2012; Schellart, 2010b; Faccenna et al., 2010). Ex-amples of intraplate volcanoes or volcanics that could be explained by this mechanism include Mount Etna located near the southern

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edge of the Calabrian slab (e.g., Schellart, 2010b) and the Wrangell volcanics located east of the eastern edge of the Alaska subduction zone (e.g., Jadamec and Billen, 2010, 2012).

To better understand the interaction between the slab and am-bient mantle, seismic anisotropy and geochemical studies from the last two decades were dedicated to increase our knowledge of the mantle flow pattern in the vicinity of subduction zones. Some seis-mic anisotropy studies have documented a trench-parallel align-ment of the seismic shear wave splitting fast axis in the sub-slab domain, implying trench-parallel flow beneath the slab of various subduction zones (Russo and Silver, 1994; Gledhill and Gubbins, 1996; Marson-Pidgeon et al., 1999; Peyton et al., 2001;Anderson, 2004; Müller et al., 2008; Foley and Long, 2011). Other studies showed a more complicated pattern in the mantle wedge, with often trench-parallel flow close to the trench and trench-perpendicular flow farther away (Smith et al., 2001; Christensen et al., 2003; Levin et al., 2004; Morley et al., 2006; Léon Soto et al., 2009; Huang et al., 2011; and compilations by Long and Silver, 2008; Long and Wirth, 2013). Many other shear-wave split-ting analyses and geochemical studies moreover suggested rotat-ing return flow around one or both lateral slab edges as for the Alaska (e.g., Hanna and Long, 2012), Cascadia (Zandt and Humphreys, 2008; Eakin et al., 2010), Rivera–Cocos (Léon Soto et al., 2009), Sandwich (Pearce et al., 2001; Livermore, 2003;Leat et al., 2004; Müller et al., 2008), Calabria (Trua et al., 2003;Civello and Margheriti, 2004; Baccheschi et al., 2007), Kamchatka (Peyton et al., 2001; Yogodzinski et al., 2001), New Hebrides (Durance et al., 2012; Király et al., 2012) and Tonga (Turner and Hawkesworth, 1998; Smith et al., 2001) subduction zones. These studies highlighted a mantle flow pattern consistent with the idea of a return flow driven by slab motion, where slab rollback induces a quasi-toroidal flow around the lateral slab edges from the sub-slab region toward the mantle wedge (e.g., Russo and Silver, 1994;Long and Silver, 2008).

The mantle flow pattern induced by subduction has also been studied in analogue and numerical models. When geometrically two-dimensional (e.g., Garfunkel et al., 1986; Becker et al., 1999;Enns et al., 2005), the models logically predicted the existence of two poloidal flow cells: one occurring underneath the sub-ducting plate and the other in the mantle wedge. However, such 2-D models do not take into consideration the three-dimensional nature of subduction zones. Indeed, 3-D models with a limited trench-parallel slab extent show the existence and the impor-tance of the quasi-toroidal return flow around the slab edges (Dvorkin et al., 1993; Buttles and Olson, 1998; Kincaid and Grif-fiths, 2003, 2004; Schellart, 2004a, 2008, 2010b; Funiciello et al., 2004, 2006; Morra et al., 2006; Piromallo et al., 2006; Stegman et al., 2006, 2010; Schellart et al., 2007; Di Giuseppe et al., 2008;Honda, 2009; Jadamec and Billen, 2010, 2012; Druken et al., 2011;Husson et al., 2012; Li and Ribe, 2012; Kincaid et al., 2013;Lin and Kuo, 2013; Schellart and Moresi, 2013) as first suggested by Jacoby (1973).

Most previous models focused on the general horizontal flow pattern in map view, or the cross-sectional mantle flow pattern in the centre of the subduction zone and did not investigate the flow pattern in the vicinity of the slab edges, the recent studies of Jadamec and Billen (2010, 2012), Schellart (2010b) and Faccenna et al. (2010) excepted. In this paper, we study the evolution of the 3-D subduction-induced mantle flow from the initial (tran-sient) stage until the mature (steady-state) stage of subduction both close to the slab edges and at depth using analogue models of free subduction. We use a stereoscopic Particle Image Velocime-try (sPIV) technique to map the three-dimensional velocity field in the upper mantle. We present here the results of two similar models from a set of 8 experiments, where the mantle flow has been mapped on four vertical cross-sections for one and on three

horizontal depth-sections for the other model. The main goal is to provide predictions for the location of maxima of upwelling and to track their evolution through time in relation with the location of the lateral slab edges.

2. Method

The experimental approach is similar to that of previous works considering the buoyancy force as the main driver for subduction and assuming the rheological response of lithosphere to be domi-nantly viscous over geological timescales (e.g., Jacoby, 1973, 1976; Kincaid and Olson, 1987; Funiciello et al., 2004, 2006; Schellart, 2004a, 2004b, 2008, 2010b; Bellahsen et al., 2005). The fluid dy-namic models involve two linear-viscous layers contained in a rectangular tank of 100 cm length and 60 cm width (Fig. 1). The top layer rests on top of the lower layer at the initial stage of the experiments and is prevented from sinking entirely into the lower layer by surface tension acting around its edges. It is made of a Newtonian silicone (Wacker silicone, from Dow corning com-pany) mixed with fine iron powder and is 2 cm thick, simulating a 100-km-thick subducting oceanic plate. The lower layer is made of transparent glucose syrup, which has a viscosity that is strain and strain rate independent (Newtonian) but strongly dependent on temperature (Schellart, 2011), and simulates the upper mantle. The mixture of silicone and iron powder has a density of 1517 kg/m3

and a viscosity of 6.32 ±0.1 ×104 Pa s while the glucose syrup has a density of 1422 kg/m3 and a viscosity of 2.25 ± 0.05 × 102 Pa sat 20 ◦C. The subducting plate-upper mantle density contrast of 95 kg/m3 reflects natural conditions of 100 km thick 80 Ma old oceanic lithosphere (Cloos, 1993), although it is slightly higher in the models to negate surface tension effects that are negligible in nature (Schellart, 2008), and makes the subducting plate negatively buoyant. Thus, by initiating a sinking instability (up to 2–3 cm long) the mixture of silicone and iron powder (i.e., the subduct-ing plate) dives into the glucose syrup (i.e., the upper mantle) due to the negative buoyancy force only. Thereafter the models con-tinue to evolve without any external influences.

The models were conducted at very low Reynolds number

Re = ρUM V L/ηUM (1)

(Re estimated between 6.3 × 10−7 and 4.72 × 10−5) where ρUM

is the upper mantle density, V the characteristic flow velocity (V = 0.5–5 × 10−5 m/s), L the characteristic length scale (L =0.02–0.15 m) and ηUM the sub-lithospheric upper mantle viscosity. Thus the viscous forces dominate and inertial forces are negligi-ble, indicating that the experiments are in the laminar symmet-rical flow regime. We scale the models following Jacoby (1973), Schellart (2008) and Duarte et al. (2013). We use a length scale ratio Lm/Lp of 2.0 × 10−7 (1 cm in the models, subscript m, rep-resents 50 km in nature, subscript p), a time scale ratio tm/tp of 3.81 × 10−12 (1 min in the models scales to 0.5 Ma), and a sub-ducting plate to upper mantle viscosity ratio of ∼280.

The total depth of the models is 13 cm, with the bottom of the tank representing an impenetrable 660 km discontinuity. The mod-elled subducting plate is 15 cm wide, simulating a narrow 750 km wide subduction zone, comparable with the Scotia and Hellenic subduction zones. The distance between the lateral edges of the subducting plate and the sidewalls of the tank is 22.5 cm, which allows us to minimise boundary effects that could be produced by the interaction between mantle circulation and the sidewalls. Both the trailing edge and the lateral edges of the subducting plate are free, representing a mid-oceanic ridge and strike-slip faults, respec-tively, that offer negligible resistance to plate motion.

The monitoring system consists of four high-resolution cameras (2000 × 2000 pixels), a laser, and two step motors, all managed by

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Fig. 1. (a) 3-D sketch and (b) front-view sketch of the laboratory set-up with the subducting plate at an early stage of the subduction process. Cameras 1 and 2 were fixed and dedicated to study the subducting plate kinematics. Cameras sPIV3 and sPIV4 were placed in stereoscopic arrangement and recorded pictures during intermittent laser sheet emission, which illuminated fluorescent particles randomly distributed inside the glucose syrup. The 3-D mantle flow pattern could be calculated for a given laser sheet position using a stereo cross-correlation technique. Cameras sPIV3 and sPIV4 were moved simultaneously with the laser beam to visualise the 3-D mantle flow pattern on 4 vertical (experiment 1 with optical arrangement in green) or 3 horizontal (experiment 2 with optical arrangement in blue) planes. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

software (Fig. 1). Cameras 1 and 2 were fixed in space and ded-icated to record pictures from side view and top view at regular time intervals. Passive markers were equidistantly placed both on top of and at the sides of the subducting plate to track plate and slab motion, and to measure the subducting plate velocity (V SP ) and the trench retreat velocity (V T ). An additional set of passive tracers of fluorescent polymer particles (PMMA-RhB) with a size of 20–50 μm was randomly placed within the glucose syrup to track the mantle flow. Cameras 3 and 4 were stereoscopic PIV, sPIV, cameras and recorded pictures simultaneously during a quick (5 μs) 2 mm thick laser sheet emission (wavelength of 532 nm) illuminating the fluorescent particles. The two sPIV cameras were positioned obliquely to the laser sheet with an angle of ∼40◦ be-tween them in stereoscopic arrangement. Several pairs of images were recorded through time and then compared between each other using a stereo cross-correlation technique, allowing the cal-culation of the 3-D mantle flow velocity field in individual planes (e.g., Raffel et al., 2007). The out of plane velocity vector was reconstructed from the two in-plane projections of the 3-D veloc-ity vector calculated independently with each stereoscopic camera. The sPIV technique has been widely used in studies linked to the physics of flow (e.g., Raffel et al., 2007) but rarely in geoscience ex-periments except to compute 3-D sub-surface displacement fields of dry sandbox experiments (Adam et al., 2005). The PIV tech-nique has been more often used to compute 2-D displacement, strain and strain rate maps of sandbox and subduction experiments (Adam et al., 2005; Funiciello et al., 2006; Guillaume et al., 2010;Boutelier and Cruden, 2013).

We carried out a total of 8 experiments under the same initial and boundary conditions in order to examine the three-dimensional flow field through time. For each experiment, the laser sheet and the two sPIV cameras were simultaneously moved from one position to another, allowing us to record pictures of sev-eral equidistant parallel planes containing a random distribution of illuminated particles. Here we report on two experiments having different parallel-plane laser sheet orientations (Fig. 1). For experi-ment 1, we used 4 vertical laser sheet positions, yielding xz planes (vertical cross sections) spaced at 3 cm intervals around one lat-eral edge of the subducting plate. For experiment 2, we used 3 horizontal laser sheet positions, yielding xy planes (depth sections) spaced at 3 cm intervals and starting at 3 cm depth. The 3-D man-tle flow velocity field was computed with a spatial resolution of 3.92 pixels/mm in experiment 1 and 3.58 pixels/mm in experi-ment 2, a seeding density of ∼40 particles/cm2, a multi-pass inter-rogation window decreasing from 64 × 64 pixels to 48 × 48 pixelswith an overlap of 50%, and a time lapse between two images used for the stereo cross-correlation of 9 s in experiment 1 and 30 s in experiment 2. Both the time lapse and the size of the interro-gation window were optimised to reach the best signal to noise ratio. Pictures of a 3-D-textured calibration board aligned to each laser sheet position allowed us to scale and correct the stereo-scopic images used for the calculation. As a filtering process, we sorted out not-consistent vectors based on their correlation value and we used a median filter. We also applied a 3 × 3 smoothing algorithm, which is justified since we use only Newtonian rheolo-gies.

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3. Results

3.1. General kinematics of the subduction experiments

Figs. 2 to 7 illustrate the slab geometry acquired at 3 differ-ent stages with the 3-D mantle velocity field mapped for the 4 vertical cross-sections of experiment 1 (Figs. 2, 4 and 6) and for the 3 horizontal depth-sections of experiment 2 (Figs. 3, 5 and 7).

Despite some minor differences between them (steady-state slab dip angle of ∼66–69◦ in experiment 1 versus ∼63–65◦ in exper-iment 2, difference of ∼10% in trench retreat velocity), the two experiments show a similar evolution of subducting plate kine-matics with trench retreat, slab rollback and trenchward plate mo-tion occurring during the whole experiment (Fig. 8a), as expected for experiments carried out with a narrow slab and a subduct-ing plate/upper mantle viscosity ratio of ∼280 (Schellart, 2010a). They exhibit 3 main evolutionary phases as classically described in previous analogue models of free subduction (Funiciello et al., 2004; Schellart, 2004a, 2008), with a first phase of acceleration of subduction and slab steepening as it descents freely in the up-per mantle (free sinking phase; Figs. 2–5), a second phase show-ing slowdown of subduction followed by acceleration during slab tip-660 km discontinuity interaction, and finally a third steady-state phase (Figs. 6 and 7) with constant subducting plate and trench retreat velocities, and backward slab draping on top of the 660 km discontinuity (Fig. 6).

3.2. Mantle flow geometries and location of maximum velocities

The experiments show a general pattern of quasi toroidal-type return flow with material flowing away from the sub-slab region around the lateral slab edges and returning towards the mantle wedge region (Figs. 2–7). The projection of the 3-D mantle flow in horizontal planes gives two toroidal flow cells each spatially linked to a lateral slab edge. These are most evident in advance stages of subduction and relatively close to the surface (e.g., Figs. 5a and 7a, b). In vertical cross sections, there are two poloidal flow cells apparent through the subduction zone with one flow cell in the mantle wedge and one in the sub-slab domain. These are best de-veloped during the free sinking phase (e.g., Figs. 2a, b and 4a, b). Although the toroidal flow is more pronounced in the advanced stages of subduction evolution, even in the free sinking phase, there is toroidal flow with mantle material escaping the sub-slab domain with velocities of up to 3 cm/yr at 3 cm inboard (scaling to 150 km in nature) (Figs. 4a and 6a). The Y component of the mantle flow velocity field (V Y ), showing the motion into and out of the cross section plane, is maximum in two regions depend-ing on depth. One region of maximum amplitude is observed at great depth for mantle escaping the sub-slab domain. The other is observed closer to the surface (at ∼0–30 mm depth scaling to 0–150 km in nature) for mantle material converging toward the mantle wedge (e.g., Figs. 4a and 6a), suggesting that the return flow around the lateral slab edges has a component of upwelling.

The experiments exhibit four principal upwelling domains. One is located in the mantle wedge at ∼70–90 mm (scaling to 350–450 km in nature) from the trench and can in some cases

Fig. 2. The 3-D mantle flow velocity field mapped at an early stage of the free sink-ing phase (slab tip at ∼5.5 cm depth scaling to ∼275 km depth) for the 4 vertical cross-sections (a, b, c, d) of experiment 1. (a) Cross-section AA′ located inside the subducting plate at 3 cm from the lateral edge (3 cm inboard). (b) Cross-section BB′located close to the lateral edge (at the edge). (c) Cross-section CC′ located away from the subducting plate at 3 cm from the lateral edge (3 cm outboard). (d) Cross-section DD′ located away from the subducting plate at 6 cm from the lateral edge (6 cm outboard). For each couple of cross-sections (a, b, c, d), the top cross-section displays the in plane components (V X , V Z ; black vectors) and the out of plane com-ponent (V Y ; colour scale, with out of plane motion in green and into plane motion in brown) of the 3-D velocity field. Note that reference for the vector length changes between (a), (b) and (c), (d) and that 1 mm/min in the models scales to 1 cm/yrin nature. The bottom cross-section represents the vertical component (V Z ; colour scale, with out of plane motion in green and into plane motion in brown) of the 3-D velocity field with upwellings in red, downwellings in blue and with black con-tour lines every 0.2 mm/min. The geometry of the subducting plate edge is shown in full grey for (a) and (b) and in grey contour line for (c) and (d). The locations of the 3 horizontal depth-sections of experiment 2 are indicated with grey arrows. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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be slightly wider than the length of the trench (e.g., Figs. 2a, 3, 4a and 5). A second is weak and situated in the sub-slab do-main (Fig. 4a). These two upwelling domains form during the free falling phase of subduction and are produced by dominantly poloidal mantle circulation, due to the down-dip component of slab motion. Their amplitude thereafter strongly decreases during the steady-state phase when subduction occurs mainly by rollback

(Figs. 6a and 7). A third upwelling domain is recognised in the far-field back-arc during the steady-state phase and it is due to slow motion and deformation of the antiformal slab fold that ad-vances sub-horizontally with time (Figs. 6a, 6b and 7). A fourth upwelling domain is located on the outboard side of each lateral slab edge. It is characterised by either a single but broad upwelling area (Figs. 2d, 4d, and 7a) or by several more narrow upwelling ar-eas that form a collectively broad region (Figs. 2c, 3b, 4c, and 7c). This type of upwelling occurs for the entire duration of the exper-iment, from subduction initiation with a very short and shallow slab, until the final stage of subduction. We can distinguish two main zones of relatively fast upward motion both located in the slab edge domain. The first occurs outboard of the sub-slab do-main (Figs. 4c and 5b) and the second outboard of the mantle wedge (Figs. 4c and 7c). In experiment 1, at the early stage of the free falling phase, upwellings in the slab edge domain are of the same amplitude both outboard of the mantle wedge and outboard of the sub-slab domain (Figs. 2c and 2d). In contrast, from the end of the free falling phase the upwellings in the slab edge domain that are outboard of the sub-slab domain become more vigorous (Figs. 4c, 6c, and 6d). In experiment 2, at the early stage of the free falling phase, upwellings in the slab edge domain are faster outboard of the sub-slab domain at 6 and 9 cm depth (Figs. 3b and 3c). They thereafter become of similar amplitude both out-board of the mantle wedge and outboard of the sub-slab domain from the end of the free falling phase (Figs. 5b, 5c and 7).

The results moreover indicate that the extent at which the mantle flow occurs is large, spanning more than two times the trench width in horizontal plane around each lateral slab edge, and the entire upper mantle in terms of depth. We defined the perime-ter of the poloidal and toroidal flow cells using velocity magnitude close to zero. The trench-parallel extent of the around-slab mantle flow is ∼300 mm (scaling to 1500 km in nature), while its trench-perpendicular extent is ∼400 mm (scaling to 2000 km in nature) from the late phase of the free sinking phase (Figs. 5 and 7). In terms of vertical extent, both the poloidal flow cell in the man-tle wedge (e.g., Figs. 2a and 4a) and the around-slab return flow (e.g., Figs. 4c, d and 6c, d) occur over the whole sub-lithospheric upper mantle thickness. In contrast, the poloidal cell occurring in the sub-slab domain is less wide and lies directly underneath the subducting plate (e.g., Figs. 4a and 6a). Furthermore, the experi-ments indicate that the zones of maximum upwelling velocities are produced in the mid-upper mantle. The upwelling in the mantle wedge has 60% of its maximum velocity (0.6 V Zmax ) comprised be-tween ∼40 mm and ∼90 mm depth (scaling to 200–450 km depth in nature) at an early stage (Fig. 2a) and between ∼35 mm and ∼110 mm depth (scaling to 175–550 km) at a late stage (Fig. 4a) of the free sinking phase. Similarly, for the part of the upwelling in slab edge domain located outboard of the sub-slab domain, 0.6 V Zmax occurs between ∼25 mm and ∼95 mm depth (scaling to 125–475 km) from the late stage of the free sinking phase.

Fig. 3. The 3-D mantle flow velocity field mapped at an early stage of the free sink-ing phase (slab tip at ∼5.5 cm depth scaling to ∼275 km depth) for the 3 depth-sections of experiment 2. (a) Depth-section located at 3 cm depth (scaling to 150 km depth in nature). (b) Depth-section located at 6 cm depth (scaling to 300 km depth in nature). (c) Depth-section located at 9 cm depth (scaling to 450 km depth in nature). The in plane components (V X , V Y ) are shown with black vectors and the out of plane component (V Z ) is displayed with the colour scale. Note that 1 mm/min in the models scales to 1 cm/yr in nature. Also note the location of upwellings in red and downwellings in blue. The position of the sub-ducting plate is shown in full grey with the part being not subducted yet in light grey and the slab in dark grey. The position of the trench is also specified with a very light grey line and with triangle symbols. The locations of the 4 vertical cross-sections of experiment 1 are indicated with grey arrows. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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Fig. 4. The 3-D mantle flow velocity field mapped at a late stage of the free sink-ing phase (slab tip at ∼9–10 cm depth scaling to ∼450–500 km depth) for the 4 vertical cross-sections (a, b, c, d) of experiment 1. Please refer to Fig. 2 for legend details.

3.3. Evolution of mantle flow velocities

To study the evolution of mantle flow velocities, we tracked three main maximum velocities for both experiments: the maxi-mum amplitude of the horizontal components (XY) of the quasi-

Fig. 5. The 3-D mantle flow velocity field mapped at a late stage of the free sink-ing phase (slab tip at ∼9–10 cm depth scaling to ∼450–500 km depth) for the 3 depth-sections of experiment 2. Please refer to Fig. 3 for legend details.

toroidal flow for mantle escaping the sub-slab domain (V XYmax), the maximum upwelling velocity occurring in the mantle wedge (V Zmax-MW ), and the maximum upwelling velocity occurring in the slab edge domain (V Zmax-Edge) (Fig. 8b and c). They all show

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Fig. 6. The 3-D mantle flow velocity field mapped at an intermediate stage of the steady-state phase for the 4 vertical cross-sections (a, b, c, d) of experiment 1. Please refer to Fig. 2 for legend details.

a polyphase evolution that is consistent with the three evolu-tionary phases of the experiments. All velocities increase dur-ing the free falling phase and then decrease during the slow-down of subduction. They thereafter increase again and follow an evolution that slightly differs from one to another. V XYmax

increases and decreases again before reaching a steady-state value

Fig. 7. The 3-D mantle flow velocity field mapped at an intermediate stage of the steady-state phase for the 3 depth-sections of experiment 2. The position of the subducting plate is shown in full grey with the part being not subducted yet in light grey. The slab portion located above the laser sheet is in dark grey and the slab portion located below the laser sheet is in white with a black dashed contour line. Please refer to Fig. 3 for legend details.

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Fig. 8. Time evolution of velocities occurring in the 2 models. V T is the trench velocity (retreat is positive). V SP is the subducting plate velocity (trenchward mo-tion is positive). V Zmax is the maximum upwelling velocity that has been tracked in 2 different upwelling domains: laterally away from the lateral edges of the sub-ducting plate (outboard; V Zmax-Edge), and in the mantle wedge (V Zmax-MW ). V XYmax

is the maximum toroidal velocity produced by mantle material escaping the sub-slab domain. (a) Time plot of V T and V SP showing the subducting plate kinematics in both analogue models. Note the kinematic similarity between the experiments. (b), (c) Subducting plate kinematics and evolution of the maxima of upwelling (V Zmax-Edge and V Zmax-MW ) and toroidal flow in (b) experiment 1 and (c) experi-ment 2.

of 4.01 mm/min (scaling to 4.01 cm/yr in nature) for experi-ment 1 and 3.1 mm/min (scaling to 3.1 cm/yr) for experiment 2. V XYmax measured in experiment 1 is higher than V XYmax mea-sured in experiment 2 because the toroidal components of the mantle flow velocity are stronger inside or laterally very close to the sub-slab domain (e.g., Figs. 4b, 6a and 6b), which is a zone that is better documented in experiment 1 than in experiment 2. Thus, we infer that V XYmax is close to the value of V T during the whole subduction process (as in Fig. 8b). V Zmax-MW decreases slowly and progressively with time during the steady-state phase

as the poloidal flow cell in the mantle wedge produces only very weak upwellings. Conversely V Zmax-Edge remains constant during the steady-state phase with a value of 0.7 mm/min (scaling to 0.7 cm/yr) for experiment 1 and 1 mm/min (scaling to 1 cm/yr) for experiment 2. Thus, we can infer from the experiments and for their particular set-up that V Zmax-Edge is ∼18.5–24% of V T .

4. Discussion

4.1. Geometry, amplitude and evolution of the 3-D mantle flow

Despite some minor differences in slab dip angle and trench retreat velocity, the two analogue models show similar results and allow for a good inference about the geometry, the amplitude and the evolution of the 3-D subduction-induced mantle flow. From the late stage of the free falling phase, V XYmax for mantle escaping the sub-slab domain is always observed in the deep upper man-tle. In this zone, the overpressure effect is more important than in the uppermost part because of the presence of the 660 km discontinuity and the specific kinematics of the slab sinking. The kinematics of the slab sinking has been studied in detail by Schel-lart (2004a, 2008) and explains the sub-vertical orientation of the velocity vectors for mantle located close to the lateral slab edges in the sub-slab domain (compare Fig. 6a, b with Fig. 4 of Schellart, 2004a and Fig. 10 of Schellart, 2008).

In addition to the upwelling formed in the mantle wedge, up-wellings are produced adjacent to each lateral slab edge, outboard of both the sub-slab domain and the mantle wedge. A minor dif-ference in the slab dip angle (∼66–69◦ in experiment 1 versus ∼63–65◦ in experiment 2) leads to a difference in the pattern of upwellings. Indeed, for a slab dip angle higher than ∼65◦ dur-ing the steady-state phase, the upwelling in the slab edge do-main occurs outboard of the sub-slab domain, whereas at a dip angle lower than ∼65◦ , it occurs outboard of both the sub-slab domain and the mantle wedge. From this observation we expect a strong control of the slab dip angle on the geometry of the return flow around the lateral slab edges. Upwellings occurring outboard next to the sub-slab domain are located laterally close to the lateral edges of the subducting plate while those occur-ring outboard away from the mantle wedge can extend further away (up to ∼12.5–17.5 cm scaling to 625–875 km in nature). This result emphasises the large horizontal dimension at which the subduction-induced mantle flow around the slab edges occurs.

The toroidal cells are elongated in the X direction, suggest-ing a potential boundary influence due to the presence of rigid walls at 22.5 cm on either side of the lateral slab edges. Subduc-tion models with similar setup and boundary conditions display similar elongated toroidal-component cells (Funiciello et al., 2006;Piromallo et al., 2006). We suspect that this boundary effect is small but it is difficult to quantify. It has been shown, though, that the elongation is amplified with increasing slab/box width ratio (Piromallo et al., 2006). Furthermore, previous upper man-tle subduction models show, similarly to this study, that the poloidal-component cells are of small dimension compared with the size of the toroidal-component cells (Funiciello et al., 2006;Piromallo et al., 2006; Stegman et al., 2006). Moreover, the am-plitude of the toroidal component of mantle flow in our models is globally higher than the amplitude of upwellings. We infer that box depth strongly constrains the geometry of the 3-D subduction-induced mantle flow by enhancing slab rollback and toroidal flow and limiting subducting plate motion and poloidal flow. Indeed, experiments with the same set-up except for a deep mantle reser-voir show that subduction is dominated by trenchward subducting plate motion and poloidal flow (Schellart, 2008).

The return flow around the lateral slab edges is already present early during the free falling phase, suggesting that subduction

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Fig. 9. Sketch of the 4 upwelling types associated with the subduction-induced mantle flow as inferred from the analogue models presented in this study, at (a) a late stage of the free falling phase and (b) during the steady-state phase where part of the slab is resting on the 660 km discontinuity. Orange arrows represent upwellings associated with the poloidal circulation induced by the downdip component of slab motion (type 1 upwelling with continuous line and type 2 upwelling with dotted line; see text in Section 3.2). The yellow arrow represents upwelling due to slow motion and deformation of the antiformal slab fold that advances sub-horizontally with time over the 660 km discontinuity (type 3 upwelling). Red arrows represent upwellings associated with the quasi-toroidal flow occurring around the lateral slab edges (type 4 upwellings). Arrow size is relative to the magnitude of upwelling. Also shown is the lateral surface extent of these zones of upwelling, and thus the areas where one could expect intraplate volcanism due to upwelling promoting decompression melting. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

zones in nature with the slab tip at ∼150–200 km depth can in-duce 3-D quasi-toroidal return flow with mantle upwelling in the vicinity of lateral slab edges (Figs. 2c, d and 3b, c). The evolution of mantle flow velocities shows a good correlation to the trench retreat rate. Stegman et al. (2006) drew the same conclusion from their numerical models. This suggests that, knowing V T and the slab geometry (i.e., slab dip angle and depth extent) in nature, we can infer the maximum velocities of upwellings and toroidal flow induced by subduction for similar slab width (750 km) and kine-matics.

Upwellings located in the slab edge domain are persistent dur-ing the whole process of subduction. They occur over a large volume of the upper mantle and initiate close to the 660 km dis-continuity with upwelling maxima in the mid-upper mantle. Such long-lived upwellings can potentially induce decompression melt-ing and thereby be a source of intraplate volcanism over a large areal extent next to the lateral slab edges. This area extends away from the lateral slab edge up to a distance roughly equivalent to the width of the slab, which is 15 cm (scaling to 750 km) in our experiments (Fig. 9). The poloidal upwelling in the mantle wedge is strong only during the transient subduction phase and occurs in the far-field back-arc over a width extent equivalent to the slab width and between ∼450 km and ∼1100 km from the trench. Such upwelling could also produce decompression melting and intraplate volcanism, but it would be mostly expected in the transient stage of subduction (Fig. 9a). Intra-plate volcanism asso-ciated with upwelling near the slab front due to horizontal motion over the 660 km discontinuity could be found in an advanced stage of subduction very far from the trench (e.g., ∼1250 km in Fig. 7), depending on the length of slab already subducted (Fig. 9b).

4.2. Advantages and limitations of the models

Our modelling approach has the advantage to allow the explo-ration of the models in a fully dynamic way, where subduction is driven entirely by the negative buoyancy of the slab and kinematic boundary conditions are absent. Therefore, the only available en-ergy to drive flow and deformation in the system (the potential energy of the subducting plate) is properly scaled with respect to the energy dissipation in the system (Meyer and Schellart, 2013). Another advantage of our modelling is the visualisation of the 3-D mantle flow on several horizontal or vertical planes. The sPIV tech-nique employed in this study allows for accurate determination of the mantle flow velocity field upon experimental conditions: the mantle reservoir (glucose syrup) needs to be transparent and the

fluorescent particles need to be seeded with a random distribution and relatively high density (∼40 particles/cm2).

Our models do adopt simplifications including the absence of side plates and an overriding plate, the use of Newtonian rhe-ologies, and the simulation of the 660 km discontinuity as an impenetrable barrier. These limitations have been investigated and are discussed in detail elsewhere (Funiciello et al., 2004; Schel-lart, 2004a, 2008; Duarte et al., 2013; Meyer and Schellart, 2013;Schellart and Moresi, 2013), indicating that the geometric and kinematic evolution of subduction are not significantly affected un-der the assumptions of a weak subduction zone interface and weak transform plate boundaries along the sides of the plates, as well as a rigid 660 km discontinuity. In our models we use only two vis-cous layers and Newtonian rheologies, but we expect that a viscos-ity layering or a non-Newtonian viscosity would affect the dynam-ics of subduction and consequent mantle flow. A viscosity layering can decrease the slab dip angle (Royden and Husson, 2006), which would affect the mantle flow geometry and potentially the loca-tion and amplitude of upwellings occurring next to the sub-slab domain (see Section 4.3). A non-Newtonian upper-mantle viscos-ity can localise and increase the rate of the subduction-induced mantle flow in regions of high strain rate (Jadamec and Billen, 2010, 2012).

4.3. Comparison with previous models

The general pattern of mantle flow presented in this study is generally in agreement with previous analogue and numeri-cal subduction models without velocity boundary conditions sim-ulating upper mantle flow (Schellart, 2004a, 2008, 2010b; Funi-ciello et al., 2004, 2006; Piromallo et al., 2006; Stegman et al., 2006, 2010; Faccenna et al., 2010; Jadamec and Billen, 2010, 2012; Husson et al., 2012; Li and Ribe, 2012; Schellart and Moresi, 2013). Indeed, we similarly observe the occurrence of a poloidal flow cell both in the mantle wedge and in the sub-slab domain, and strong quasi-toroidal patterns associated with return flow around the lateral slab edges during slab rollback. In more detail, we find in agreement with previous works that poloidal flow circu-lation in the mantle wedge is very active during the free falling phase and decreases in intensity after (Faccenna et al., 2010;Li and Ribe, 2012), mantle flow velocities are very well correlated to the trench retreat velocity (Stegman et al., 2006), and upwellings produced outboard of the slab edge reach their maximum ampli-tude in the mid-upper mantle (Schellart, 2010b).

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Several previous studies are particularly interesting for purpose of comparison (Piromallo et al., 2006; Schellart, 2004a, 2010b; Jadamec and Billen, 2010; Faccenna et al., 2010) because they all suggest the occurrence of upwellings associated to the quasi-toroidal flow around the lateral slab edges. Schellart (2010b), in analogue models of free subduction, observed maximum upwelling close to the sub-slab domain at 220–300 km from the trench on the subducting plate side for a slab dip angle α of ∼75–80◦ . In our models these upwellings are located at ∼150–250 km (ex-periment 1, α ≈ 66–69◦) and ∼50–150 km (experiment 2, α ≈63–65◦) from the trench on the subducting plate side, suggest-ing that the distance between the trench and the maximum up-welling increases with increasing α. Jadamec and Billen (2010), in an instantaneous numerical model of subduction and mantle flow applied to the Alaska subduction-transform system, observed up-wellings close to the north-eastern slab edge during the free falling phase. Using a Newtonian viscosity upper mantle, they computed maximum upwelling velocities smaller than or equivalent to the Pacific plate motion, which corresponds to V SP in this paper. In our models these velocities are ∼0.5–0.68 V SP . Jadamec and Billen(2010) also computed maximum absolute velocities of ∼2.5 V SP

close to the slab and they are similar in this study, with values of ∼2.7–3 V SP . Using a non-Newtonian viscosity for the upper man-tle, the authors found that both the maximum upwelling velocities and absolute velocities close to the slab were drastically increased, with values of ∼2 V SP and ∼17 V SP , respectively, suggesting a strong influence of upper mantle rheology on mantle flow veloc-ities. Finally, Piromallo et al. (2006) and Faccenna et al. (2010), using a generic instantaneous and time-evolving numerical model of free subduction, respectively, evidenced the occurrence of up-wellings in the slab edge domain. Faccenna et al. (2010) found that upwellings in the mantle wedge are very active during the free falling phase only. In contrast, upwelling velocities in the slab edge domain increased progressively during the free falling phase till reaching a constant value during the steady-state phase, simi-larly to this study.

4.4. Implications for subduction-induced mantle flow in nature

The two analogue models presented in this study are in par-ticular comparable with natural subduction zones such as Scotia and Hellenic, having similar trench length (∼750 km) and mode of subduction (mostly through slab rollback). An important result is the presence of broad upwelling regions that are located outboard of the sub-slab domain and, for cases with shallow slab dip, also outboard from the mantle wedge (Fig. 9). This type of upwelling occurs during the whole subduction process while upwelling due to the poloidal circulation in the mantle wedge is present only during the free falling phase. We suspect that for all retreating subduction zones, the quasi-toroidal mantle flow around the lat-eral slab edges and the associated component of upwelling are present. In some cases a mantle plume can also produce upwelling in the vicinity of subduction zones, and it is very likely to inter-act with the slab and the subduction-induced mantle flow (e.g., Liu and Stegman, 2012; Long et al., 2012). For instance, vigorous quasi-toroidal mantle flow has a high potentiality of deflecting the path of a mantle plume, as shown in experiments by Kincaid et al.(2013).

Directions of seismic shear wave splitting fast-axis are compat-ible with the 3-D flow occurring around the lateral slab edges. They also indicate a trench-perpendicular mantle flow in the man-tle wedge far away from the trench, as observed in this study. However, our models don’t match the trench-parallel alignments of seismic shear wave splitting fast-axis commonly observed in the warm regions of the mantle wedge away from the cold wedge nose. They only locally explain a sub-parallel orientation around

the slab edges, as in Druken et al. (2011). A change in the vis-cous properties of the upper mantle (from Newtonian to non-Newtonian) could enhance the production of trench-parallel flow by decreasing the viscosity in zones of high strain rate (if toroidal flow is important) (Jadamec and Billen, 2010). Lateral variations in slab shape/dip have also been mentioned as a potential factor to produce trench-parallel flow in the mantle wedge close to the slab due to strong trench-parallel stretching (Kneller and van Keken, 2007; Long and Wirth, 2013; MacDougall et al., 2014).

In the experiments presented here, the maximum upwelling velocities produced laterally away from the subducting plate are ∼0.5–0.68 V SP and ∼0.18–0.24 V T . These upwellings initiate deep in the upper mantle and therefore bring mantle material nearly from the 660 km discontinuity to the upper part of the sub-lithospheric upper mantle. Moreover they are long-lived and active from the transient phase of the free slab sinking, sug-gesting that they are capable of inducing decompression melting and, therefore, could be a source for intraplate volcanism dur-ing the whole process of subduction. Whether they actually in-duce decompression melting or not may depend on several fac-tors, such as upwelling velocity and water content. In experi-ment 1, we observe an acceleration of upwelling from ∼600 km depth to ∼250 km depth (Figs. 4c and 6c). This acceleration might potentially trigger decompression melting. Previous stud-ies suggest that Mount Etna is caused by upwelling associated with subduction-induced mantle flow around the southern edge of the Calabrian slab (Schellart, 2010b; Faccenna et al., 2010). Up-wellings in this case seem to have a deep source origin as in-dicated by tomography studies, which show a thick low-velocity anomaly close to the lateral slab edge (Lucente et al., 1999;Chiarabba et al., 2008). The Wrangell volcanics, in Alaska, have also been suggested as related to upwellings occurring close to the lateral slab edge (Jadamec and Billen, 2010). These upwellings could be enhanced in the case of a non-Newtonian upper mantle viscosity. In any case, our models suggest that even with a New-tonian upper mantle, upwellings close to the lateral slab edges can form deeply in the upper mantle and accelerate to reach maximum velocities of ∼0.18–0.24 V T in the mid upper man-tle. Other volcanics are possibly related to upwellings associated with the subduction-induced flow around the slab edges. Lam-proites in the eastern Betic-Rif orogen (Pérez-Valera et al., 2013)and Trois Fourches in Morocco (Faccenna et al., 2004, 2010) are possibly associated with return flow induced by the retreating Gibraltar slab. The Samoan hotspot volcanoes could potentially be associated with strong upwellings induced by fast slab rollback at the northern edge of the Tonga subduction zone. Here, east-directed rollback velocities reach up to 16 cm/yr (Schellart et al., 2007) and seismic anisotropy and geochemistry suggest toroidal return flow around the slab edge (Turner and Hawkesworth, 1998;Smith et al., 2001). Finally, the Shiveluch group of volcanoes and close Aleutian adakites are potentially associated with return flow around the northern edge of the Kamtchatka slab with partial melting of the slab edge producing an adakite signature in the geo-chemistry of volcanic rocks (Yogodzinski et al., 2001).

5. Conclusion

From our experimental results, which are most relevant to nar-row slabs with a trench retreat mode, we draw the following main conclusions:

(1) Subduction induces a quasi-toroidal mantle flow around the lateral slab edges, with mantle material escaping the sub-slab do-main, then going around the slab edges, and finally returning in the mantle wedge.

(2) Maximum toroidal velocities for mantle material escaping the sub-slab domain are observed deep in the upper mantle and

378 V. Strak, W.P. Schellart / Earth and Planetary Science Letters 403 (2014) 368–379

they are shallower for mantle material returning toward the man-tle wedge.

(3) Four types of upwelling are produced, of which two are re-lated to poloidal circulation due to downdip slab sinking (one in the mantle wedge and one in the sub-slab region), one is related to horizontal motion of the slab front over the 660 km disconti-nuity and one is associated with quasi-toroidal circulation around each lateral slab edge.

(4) Strong upwellings are produced outboard from the sub-slab domain and, for slab dip smaller than ∼65◦ , also outboard from the mantle wedge. They span a wide area that is roughly com-parable with the slab width of 750 km. They occur throughout the whole upper mantle thickness with maximum upward velocity ob-served in the mid upper mantle.

(5) Another strong upwelling is produced in the mantle wedge due to the down-dip component of slab motion during the free falling phase. It dominates during the free falling phase but its magnitude decreases substantially during the steady-state phase whereas upwellings associated to each lateral slab edge are long-lived.

(6) The maximum horizontal component (V XYmax) and upward component (V Zmax-Edge) of the mantle flow velocity field in the slab edge domain are correlated to the trench retreat velocity (V T ). They are constant during the steady-state phase with V XYmax ∼= V T

and V Zmax-Edge ≈ 0.18–0.24 V T .

Acknowledgements

We thank David Boutelier for his expert technical assistance handling the PIV system during the first test experiments. Joao Duarte and Zhihao Chen are also acknowledged for their assistance in the lab. Fruitful discussions with Sandy Cruden, David Boutelier, Joao Duarte and Manuele Faccenda on subduction-induced man-tle flow and upwellings are greatly appreciated. We also thank Margarete Jadamec and an anonymous reviewer for their thought-ful reviews and constructive comments that helped improving the manuscript. This research was supported by the Discovery grant DP120102983 from the Australian Research Council. WPS was sup-ported by a Future Fellowship (FT110100560) from the Australian Research Council.

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