Geophysical Journal International

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1 Geophysical Journal International Geophys. J. Int. (2013) 195, Advance Access publication 2013 July 25 doi: /gji/ggt257 Three-dimensional dynamic laboratory models of subduction with an overriding plate and variable interplate rheology João C. Duarte, Wouter P. Schellart and Alexander R. Cruden School of Geosciences, Monash University, Melbourne, VIC 3800, Australia. Accepted 2013 June 28. Received 2013 June 27; in original form 2013 January 3 1 INTRODUCTION Subduction is the process that takes place at convergent plate boundaries by which one tectonic plate (subducting plate, SP) sinks under another (overriding plate, OP) into the Earth s mantle. In some cases, the OP is characterized by extension and development of backarc basins, as in the Southwest Pacific and the Mediterranean, while in other cases the OP is characterized by shortening and growth of a mountain belt, as in the central Andes. SPs sink because they are negatively buoyant, which is a consequence of their higher density in relation to the ambient mantle. However, this sinking does not occur only along the slab dip direction; it also occurs perpendicular to the plane of the slab (Jacoby 1976; Schellart 2004, 2008a). Because of this, slabs have a horizontal component of motion through the upper mantle (UM), forcing the trench to migrate. Schellart (2008b) showed that there is a positive correlation between SUMMARY Subduction zones are complex 3-D features in which one tectonic plate sinks underneath another into the deep mantle. During subduction the overriding plate (OP) remains in physical contact with the subducting plate and stresses generated at the subduction zone interface and by mantle flow force the OP to deform. We present results of 3-D dynamic laboratory models of subduction that include an OP. We introduce new interplate materials comprising homogeneous mixtures of petrolatum and paraffin oil to achieve progressive subduction. The rheology of these mixtures is characterized by measurements using a strain rate controlled rheometer. The results show that the strength of the mixture increases with petrolatum content, which can be used as a proxy for the degree of mechanical coupling along the subduction interface. Results of subduction experiments are presented with different degrees of mechanical coupling and the influence this has on the dynamics and kinematics of subduction. The modelling results show that variations in the degree of mechanical coupling between the plates have a major impact on subduction velocities, slab geometry and the rate of OP deformation. In all experiments the OP is displaced following trench migration and experiences overall extension localized in the plate interior. This suggests that OP deformation is driven primarily by the toroidal component of subduction-related mantle return flow. The subduction rate is always very slow in experiments with medium mechanical coupling, and subduction stops prematurely in experiments with very high coupling. This implies that the shear forces along the plate interface in natural subduction zone systems must be relatively low and do not vary significantly. Otherwise a higher variability in natural subduction velocities should be observed for mature, nonperturbed subduction zones. The required low shear force is likely controlled by the rheology of highly hydrated sedimentary and basaltic rocks. Key words: Subduction zone processes; Dynamics of lithosphere and mantle; Mechanics, theory, and modelling. trench migration and OP deformation in which trench advance correlates with OP shortening and trench retreat correlates with OP extension. However, there are exceptions to this relationship, such as in the Marianna subduction zone where trench advance is accompanied by OP extension. A comprehensive conceptual and quantitative explanation for all these observations remains an outstanding requirement for understanding the kinematics and dynamics of subduction zone systems. Another fundamental characteristic of subduction zone systems is that the two participating plates must be somewhat mechanically coupled. During retreat of the trench and subduction zone hinge one could expect a potential void to form at the contact between the plates (Schellart & Lister 2004), but such voids are not observed in nature. This indicates that the OP must occupy this vacant region either by internal deformation and/or by bulk translation. When there is significant resistance to bulk translation of the OP, GJI Geodynamics and tectonics C The Authors Published by Oxford University Press on behalf of The Royal Astronomical Society. 47

2 48 J. C. Duarte, W. P. Schellart and A. R. Cruden the OP collapses towards the retreating hinge of the SP because it is not strong enough to permit a vacant region at the plate boundary (Elsasser 1971; Shemenda 1993; Lonergan & White 1997; Schellart & Lister 2004). Even though extension occurs in the backarc region, topographic elevation and shortening in the forearc is generally observed, suggesting significant frictional shear at the subduction zone interface (Malinverno & Ryan 1986; Shemenda 1993; Schellart & Lister 2004). However, as we will discuss elsewhere in this paper, high resistive forces at the interface may lock the subduction zone, causing subduction to stop. In the last three decades laboratory and numerical studies of subduction zones have flourished, exploring the interplay between geometry, kinematics and dynamics of subduction systems (e.g. Kincaid & Olson 1987; Faccenna et al. 1996; Buttles & Olson 1998; Funiciello et al. 2003, 2004; Kincaid & Griffiths 2003; Schellart 2004, 2008a; Morra et al. 2006; Stegman et al. 2006; Capitanio et al. 2007, 2010; Schellart et al. 2007; Boutelier & Cruden 2008; Stegman et al. 2010; Boutelier & Oncken 2011; Goes et al. 2011; Schellart et al. 2011; Gibert et al. 2012). It is common for 3-D subduction models to lack an OP, therefore not allowing the incorporation of shear stresses at the subduction interface, which is required to assess how the presence of an OP might affect the kinematics and dynamics of subduction. Conversely, when an OP is included, kinematical boundary conditions are often imposed using a constant-velocity piston, which conditions apriorithe evolution of the experiments (e.g. Heuret et al. 2007) and makes it difficult to ensure that the models are energetically consistent (Capitanio et al. 2007). Such experiments allow for detailed studies of the different styles of deformation associated with the process of subduction, but they are less suitable to build understanding of the origin of the velocities of subduction and the forces that drive subduction and OP deformation. On the other hand, fully dynamical experiments, here referred to as experiments without applied velocities, can interrogate the origin of those velocities and forces in a dynamical framework, which is important to assess and quantify the forces driving and resisting subduction as well as the resulting deformation of the overriding and SPs. One challenge in running fully dynamical experiments of progressive subduction that include both overriding and SPs is that the strength of the subduction zone interface has to lie between two end members. With a very weak interface the plates might separate leaving a gap filled with UM material. On the other hand, if the coupling is too high then subduction will stall and the slab will detach as a Raleigh Taylor instability. Therefore, a subduction fault parametrization is required to obtain the appropriate values of coupling between the plates and allow progressive subduction. This is usually achieved in both laboratory and numerical models by implementing a low viscosity or low friction lubricant on top of the SP. 2-D numerical models generally make use of a low friction layer on top of the SP (e.g. Hampel & Pfiffner 2006; Tagawa et al. 2007), a weak viscoplastic rheology (e.g. Capitanio et al. 2010) or a subduction channel with a weak plastic rheology (Sobolev & Babeyko 2005). A similar approach has also been taken in laboratory models of progressive subduction with applied kinematic boundary conditions (e.g. Heuret et al. 2007) and under partially gravity driven conditions (Boutelier & Cruden 2008). Inclusion of a subduction zone interface rheology in fully 3-D dynamic laboratory models of progressive subduction has so far not been accomplished. A first successful approach was presented recently by Meyer & Schellart (2013), involving a SP, an OP and a low-viscosity subduction channel. In their experiments, however, the low-viscosity subduction channel was progressively eroded, and therefore the channel had to be intermittently refilled at the trench with a low-viscosity fluid. Such a modelling procedure is rather impractical, particularly for use in more complex experiments. In this paper, we present the results of fully dynamic 3-D laboratory experiments of progressive subduction with a coupled OP without externally applied kinematic boundary conditions and without any interference during the evolution of the model. This was accomplished by introducing a new subduction fault material with a suitable and controllable rheology. The implementation of this approach required two steps: (i) investigation of new materials using a rheometer and (ii) evaluating the use of these materials in laboratory dynamic experiments of subduction. We ran a total of 14 experiments (Table 1) and present here the results of five experiments (with a particular focus on three representative experiments), in which progressive subduction developed with different degrees of mechanical coupling along the subduction interface (Table 2). We then analyse how the velocities of the SP, trench and OP, as well as the OP strain field vary as a result of the degree of coupling. The models provide new insights on the dynamics of subduction zones and on the mechanisms driving, controlling and resisting plate motion. This novel experimental approach has the potential to be refined and further applied to a broad range of geodynamic problems. 2 EXPERIMENTAL MATERIALS AND METHODS 2.1 Experimental apparatus and scaling Our modelling apparatus is made of two viscous layers contained in a rectangular tank simulating the lithosphere and the asthenospheric UM (Fig. 1). The upper layer consists of two plates, SP and OP, both made of a high-viscosity, linear-viscous silicone polymer (Rhodorsil Gum FB) mixed with fine iron powder. The SP is 1.6 cm thick, simulating a 80-km-thick oceanic plate, and has a density of 1520 kg m 3. The OP is 1.5 cm thick, simulating a 75- km-thick plate, and has a density of 1420 kg m 3. In the initial stage of the experiment, both plates rest on top of a lower layer, representing sublithospheric UM. The lower layer comprises transparent, low-viscosity, linear-viscous glucose syrup (see rheology of glucose syrups in Schellart 2011) with a density of 1420 kg m 3, which is the same as that of the OP. The OP is therefore neutrally buoyant and the SP is negatively buoyant due to a density contrast, ρ = 100 kg m 3 between the plate and ambient mantle, replicating oceanic lithosphere in nature whose basaltic crust has been entirely metamorphosed into eclogite (Cloos 1993). The viscosity of the glucose syrup (η UM ) varies between 140 and 151 Pa s (due to small, unwanted, variations in temperature during different experiments), while the viscosity of both the SP (η SP )andop(η OP ) is of the order Pa s. A viscosity ratio of η SP /η UM 165 is reached at a controlled room temperature of 21 C (Table 2), which is close to estimates of viscosity ratios in nature (e.g. Funiciello et al. 2008; Schellart 2008a; Loiselet et al. 2009; Ribe 2010; Stegman et al. 2010). The total modelling domain is 100 cm 60 cm in the horizontal directions and 13.3 cm in the vertical direction (Fig. 1). All sidewalls and the bottom boundary of the box are rigid no-slip boundaries, while the top surface of the model is a free surface. The bottom of the box simulates an impenetrable upper-lower mantle 660 km discontinuity. The upper layers are free at their trailing edges, as

3 3-D dynamic laboratory models of subduction 49 Table 1. List of the performed analogue models. Experiment Subduction interface material Successful subduction Comment 1 Sorbolene lotion No 2 Sorbolene lotion No Opening of a gap at the subduction zone interface 3 Sorbolene lotion No per cent Petrolatum No 5 50 per cent Petrol. 50 per cent Par. oil. No 6 40 per cent Petrol. 60 per cent Par. oil. Partly 7 40 per cent Petrol. 60 per cent Par. oil. Partly Double-sided subduction Subduction terminated prematurely 8 30 per cent Petrol. 70 per cent Par. oil. Failed Failed 9 a 20 per cent Petrol. 80 per cent Par. oil. Yes 10 a 10 per cent Petrol. 90 per cent Par. oil. Yes Asymmetric single-sided subduction 11 a 30 per cent Petrol. 70 per cent Par. oil. Yes 12 a 40 per cent Petrol. 60 per cent Par. oil. Partly Subduction terminated prematurely per cent Petrol. 70 per cent Par. oil. Yes Asymmetric single-sided subduction 14 a 45 per cent Petrol. 55 per cent Par. oil. Partly Subduction terminated prematurely a Experiments discussed in this work. The results of Experiments 11 and 13 are qualitatively and quantitatively very similar (see the Appendix). Table 2. Experimental parameters. wt per cent of paraffin Yield Flow Experiment oil mixed with stress stress Mechanical T η UM η SP /η UM ρ petrolatum (Pa) (Pa) coupling ( C) (Pa s) (kg m 3 ) per cent 1 1 Low per cent 11 7 Medium per cent High per cent Very high per cent Extreme Note: Physical parameters for several experiments. Experiments 10, 9 and 12 are described and discussed in the text. T is the temperature of the glucose in the tank and η UM is its viscosity, both measured just before the start of each experiment; η SP /η UM is subducting plate glucose viscosity ratio; and ρ is the density contrast between the subducting plate and the glucose (note that the overriding plate is neutrally buoyant). might be expected in nature by a mid-oceanic ridge that offers negligible resistance to plate motion. Following Jacoby (1973), we scale our experiments using the general form of Stokes settling law, v ρ l2 g Const., (1) η where v is the velocity of the sinking slab, ρ is the density contrast between subducting lithosphere and asthenospheric mantle, l is a characteristic length, g is gravitational acceleration and η is the viscosity of the UM. Subduction experiments will be dynamically and kinematically similar to the natural prototype if the gravitational driving forces and resisting viscous forces are balanced, such that ρ m l 2 m g m η m v m = ρ p l 2 p g p η p v p, (2) where the subscripts m and p indicate values in the model and prototype, respectively (Jacoby 1973). Expressions (2) and (3) can be rewritten to define the velocity scale ratio v m v p = ρ m ρ p lm 2 lp 2 η p η m g m g p, (3) and because v m /v p = l m t p /l p t m we can define the scale ratio for viscosity as η m η p = ρ m ρ p l m g m l p g p t m t p. (4) For convenience, we chose a length-scale ratio of l m /l p = (1 cm in the experiment represents 50 km in nature) and a timescale ratio of t m /t p = (1 s to 8300 yr) and because experiments are carried out under Earth s field of gravity, g m /g p = 1. We also assume ρ m = 100 kg m 3 and ρ p = 80 kg m 3. The slightly higher value of the experimental density contrast ρ m compensates for the surface tension between silicone and glucose, which is a force that opposes the negative buoyancy of the SP (Jacoby 1976; Schellart 2010). The effect of surface tension, while unimportant on Earth, may compare to that of mechanical strength of the lithosphere (Walcott 1970; Jacoby 1976; Schellart 2010) and thus partially simulates the lateral constraint of absent side plates. From eq. (4), one obtains a viscosity scale ratio η m /η p = , such that glucose syrup represents a viscosity of Pa s in nature, which is in the range of estimates ( Pa s) for the UM (Ranalli 1995), and the model lithosphere scales to a viscosity

4 50 J. C. Duarte, W. P. Schellart and A. R. Cruden Figure 1. Schematic representation of the experimental apparatus used to model progressive subduction in 3-D space. Top view and side views of the initial stage of one of the experiments are also shown. Note that to initiate subduction the tip of the downgoing plate was manually bent at the same time that the overriding plate was moved towards it, leaving only a narrow gap ( 1 cm in a horizontal trench-normal direction) between the plates filled with glucose. The system was then allowed to develop freely (see Fig. 3). The glucose between the plates was progressively eroded and at the moment the subducting plate approached the bottom of the tank the plates became fully coupled and remained coupled for the remainder of the experiment. Note that subduction is driven only by buoyancy forces. of Pa s in nature. Finally, stresses (σ ) scale with the product of the length and density ratios, such that σ m σ p = ρ m ρ p l m l p. (5) Decoupling at the subduction fault interface was achieved by fully lubricating (brushing with a spatula) the top of the SP with a uniform thin weak layer (1 mm) of petrolatum paraffin mix. The lubrication layer remained static after application due to its (small) internal yield stress. This layer simulates a 5-km-thick upper oceanic crust comprising hydrated sediments and basalts, which acts as a lubricant in natural subduction systems (Moresi & Solomatov 1998; Tagawa et al. 2007). In our experiments we investigated the effect of five different degrees of coupling (Table 2) by using mixtures with varying proportions of paraffin oil and petrolatum (see next subsection for the rheological characterization of the mixtures). All experiments were conducted at a controlled room temperature of 21 C. Just prior to the start of each experiment the temperature and viscosity of the glucose were measured. At the start of each experiment, a subduction instability was produced by manually bending 2.5 cm of the leading edge of the SP downward at an angle of 30 and by moving the OP trenchward until the horizontal gap between the two plates was <1 cm (Fig. 1). The system was then allowed to evolve naturally. During an initial phase of 10 cm of subduction the plates were not in full contact because there was still a wedge of glucose between the plates. The thickness of this wedge decreased progressively until it was eventually eroded away. After this initial period the two plates remained in physical contact for the remainder of the experiment. Progress in the experiments was recorded with two digital cameras providing top-view and side-view perspectives. Some experiments were repeated in order to insure reproducibility of the results (see the Appendix). 2.2 Subduction interface rheology The materials used to reduce coupling between the silicone plates and allow progressive subduction in the experiments comprise homogeneous mixtures of commercial petrolatum and paraffin oil. Chemically, these compounds belong to a class of hydrocarbons with the general formula C n H 2n+2, generally known as paraffins (sensu lato) or alkanes. Petrolatum, also termed petroleum jelly or soft paraffin, consists of a semi-solid gel comprising solid and liquid hydrocarbons (normal, iso and ring paraffins) with carbon numbers (C n ) mostly higher than n = 25 (Longworth & French 1969; Chang et al. 2003; Pandey & Ewing 2008). Paraffin oil is a liquid mixture of saturated hydrocarbons in the range of C 10 to C 18 (Freund et al.

5 Table 3. Relation between the strength of the mixtures and the subduction velocity. 3-D dynamic laboratory models of subduction 51 Experiment Mechanical coupling Mix Flow stress (Pa) Scaled flow stress (MPa) v S (mm s 1 ) Scaled v S (cm yr 1 ) 10 Low 90 per cent Medium 80 per cent High 70 per cent Very high 60 per cent Extreme 55 per cent Notes: The values of flow stress were obtained using a strain-rate controlled rheometer (a strain-rate of 0.01 s 1 was imposed, mimicking laboratory conditions). These values correspond to the dynamical strength of the petrolatum paraffin oil mixtures. Mixtures with more than 50 per cent of paraffin are almost strain-rate independent for the values of experimental strain rates. Note the increase in the subduction velocity (v S ) with the increase paraffin oil content (percentages always refer to the weight per cent of paraffin oil in the mixture, see Table 1). Subduction velocities were averaged only for the period of progressive rollback after the plates were in full contact and subducting plate touched the bottom of the tank in order to avoid the interference of complex slab dynamics like the period of recumbent folding of the slab in Experiment 9 ( s for Experiment 10; s for Experiment 9, s for Experiment 11, s for Experiment 12; s for Experiment 14). The values scaled to nature are also presented. Error in v S is ± mm s 1.The standard deviations for v S are: ± 0.020, ± 0.006, ± 0.008, ± and ± 0.004, respectively. Figure 2. Shear stress shear strain curves obtained for pure petrolatum and several mixes of petrolatum and paraffin oil. The tests were carried out using a strain-rate-controlled rheometer with parallel geometry. A constant strain rate of 0.01 s 1 was applied while the stress was measure as function of progressive strain. Note that the mixtures are Bingham viscoplastic materials, that is, the samples start to flow only after a yield stress is exceeded. 1982). While pure paraffin oil is a liquid at room temperature, petrolatum maintains a solid-like state (Park & Song 2010). Petrolatum is chemically related to paraffin oil, and their combination results in a homogeneous mixture. The rheology of pure petrolatum and several mixtures with different wt per cent proportions of petrolatum and paraffin oil was measured using a low-friction Anton Paar Physica MCR-301 Rheometer. The rheometer has parallel plate geometry with a fixed lower plate and a rotating or oscillating upper plate geometry. The rheometer can carry out tests under controlled shear strain rate or controlled shear stress conditions. For the tests presented here, a constant shear strain rate was imposed and the shear stress was measured as a function of progressive strain. The tests were performed at 20 C and at a constant shear strain rate of 0.01 s 1, similar to conditions in our experiments, to a total shear strain γ = 10 (1000 per cent). A rotating upper plate geometry with a diameter of 50 mm and a gap of 2 mm between upper and lower plates were used in all the tests, with exception of mixtures with 90 per cent paraffin for which a gap of 1 mm was used due to the higher fluidity of the sample. In addition, a comprehensive set of tests under a broad spectrum of strain rates ( s 1 ) was preformed to complement our understanding of the rheology of the mixtures. However, due to their limited application to this work a detailed description of these results is outside the scope of this paper. The objective of the rheological tests reported here was, (i) to determine the value of the yield stress for each of the petrolatum paraffin mixes, which provides a value for the minimum stress required to initiate movement along the subducting interface and (ii) to assess the steady state flow stress under experimental conditions, which can be used to estimate the shear force and the shear stress along the subduction interface during progressive subduction (Table 3). High values of flow stress thus relate to conditions of high shear stress along the subduction interface in the experiments and, consequently, to strong coupling between the two silicone plates. Conversely, low values of flow stress correspond to a low degree of coupling between the plates due to lower stress conditions within the interplate zone. When the applied stress overcomes the inherent resistance of the sample, the material starts to flow (known as Bingham viscoplastic behaviour). The yield stress is then defined as the maximum stress on a stress strain plot (Fig. 2). It is immediately clear that the yield stress of the different mixes decreases with increasing content

6 52 J. C. Duarte, W. P. Schellart and A. R. Cruden of paraffin oil (Fig. 2 and Table 2). It is also observed that once the yield stress has been overcome, the shear stress drops due to strain softening and with increasing strain approaches a steady-state value, referred to here as the flow stress. Values of the flow stress clearly decrease with increasing paraffin oil content (Fig. 2). In all samples the yield stress is higher than the flow stress, except for the 90 per cent mixture, which shows no strain softening behaviour. In this paper, we report five experiments covering the range of mixtures from 55 to 90 per cent paraffin oil (Table 2), which was the range over which progressive subduction developed. Subduction stopped in a very early stage in all experiments that used mixtures with a paraffin oil content below 55 per cent. In some experiments with very strong mixtures (=55 per cent paraffin oil) and high coupling, a period of double-sided subduction occurred (i.e. simultaneous subduction of both subducting and OPs), with the development of Raleigh Taylor instabilities at the base of the plates. Conversely, when coupling was too low the plates separated, leaving a vacant region filled in with UM material. Even though some of the experiments failed to produce long-term subduction or were somewhat unrealistic (e.g. double-sided subduction), we have used them to understand, improve and adjust our apparatus. In the following sections we analyse in detail three representative experiments with low, medium and very high mechanical coupling along the interplate zone and evaluate the impact of the degree of coupling on subduction dynamics, kinematics and OP deformation. 3 RESULTS 3.1 Dynamics and kinematics of subduction Photos of progressive stages of Experiments 10, 9 and 12, with low, medium and very high mechanical coupling, respectively, are shown in Fig. 3 and the results of five experiments are given in Tables 3 and 4. The total time for the entire slab to be subducted for Experiments 9 11 increased with the increase of the interplate mechanical coupling (Table 3). In the two experiments with very high and extreme coupling (Experiments 12 and 14) subduction stalled after 6720 and s, respectively. The initial stages of all experiments were characterized by slab sinking and steepening (Fig. 3), as well as rapid increases in the trench retreat velocity (v T ) andinthesp(v SP )andop(v OP ) trenchward velocities (Fig. 4). The SP velocity reached a local or absolute maximum at a time just before the slab tip touched the bottom of the tank (blue arrows in Fig. 4), while the first maximum in the trench velocity corresponds to the time just before the plates came into full contact (red arrows in Fig. 4). Moreover, the period between the initial stage of each experiment and the moment when the slabs touched the bottom of the tank increased with increasing values of mechanical coupling in the interplate zone [ 500, 1500 and 2800 s, scaling to 4, 13 and 23 Ma, for low, medium and very high coupling, respectively; and with peak subduction velocities (v S ) of 0.2, 0.07 and mm s 1 scaling to 12, 4.2 and 3.5 cm yr 1 in nature]. In the low coupling Experiment 10, the slab steepening was less pronounced and once the slab touched the bottom of the tank it flattened and rolled back progressively (Fig. 3a), while the trench retreated at an approximately steady velocity of 0.08 mm s 1, scaling to 4.8 cm yr 1 (Fig. 4a and Table 4), to a total of 242 mm, scaling to 1212 km. Trench retreat in this experiment was accommodated by OP trenchward displacement (a total of 166 mm, scaling to 832 km) Figure 3. Sequential side-view photographs of the three-subduction experiments with different degrees of mechanical coupling at the subduction zone interface (Experiments 10, 9 and 12, with low (Mix 90 per cent), medium (Mix 80 per cent) and very high (Mix 60 per cent) mechanical coupling, respectively). Note that the percentages always refer to the relative amount (weight per cent) of paraffin oil in the mixtures of petrolatum and paraffin oil. The duration of each period is given in seconds (and scaled time). See text for detailed description of the experiments.

7 3-D dynamic laboratory models of subduction 53 Table 4. Experimental results (plate velocities and overriding plate deformation rate). Scaled Scaled Scaled Scaled Scaled Average average Average average Average average Average average Average average Experiment Mix v SP v SP v T v T v OP v OP v S v S v OPD v OPD v OP /v T (mm s 1 ) (cmyr 1 ) (mm s 1 ) (cmyr 1 ) (mm s 1 ) (cmyr 1 ) (mm s 1 ) (cmyr 1 ) (mm s 1 ) (cmyr 1 ) per cent per cent per cent per cent per cent Note: Average trench-normal velocities calculated for the period after the plates were in full contact and after the slab reached the bottom of the tank (see arrows in Fig. 4). v SP, subducting plate velocity; v T, trench velocity; v OP, overriding plate velocity; v S, subduction velocity; and v OPD, overriding plate deformation/extension rate. v OP /v T is the ratio between overriding plate velocity and trench velocity. Scaled values are also shown. Errors in measured velocities are ±0.002 mm s 1. at an average velocity of mm s 1 (3.17 cm yr 1 in nature) and OP internal deformation (a total of 76 mm of extension, scaling to 379 km; Table 4). In Experiment 9 with medium coupling, the slab also draped backward and rolled back after it touched the bottom of the tank (Fig. 3b). During this stage a small steady increase of trench retreat velocity (v T ) is observed (between 0.02 and 0.03 mm s 1, scaling to 1.2 and 1.8 cm yr 1, respectively; Fig. 4b). However, after 4800 s (scaling to 40 Ma in nature) the rollback stopped and the slab folded and rolled over itself. At this stage, the SP trenchward velocity (v SP ) increased to a peak of 0.06 mm s 1 (3.6 cm yr 1 ) and the trench retreat velocity dropped to zero. Eventually the trench advanced for a small period of time ( 500 s, scaling to 4 Ma) during the slab forward rollover phase. The OP simultaneously moved away from the trench at velocities up to 0.01 mm s 1 (0.6 cm yr 1 ). Then, after a short period of no movement, the trench retreat resumed with an increasing velocity while the SP velocity steadily decreased (see Fig. 4b). At this stage, while the trench retreated the lower segment of the slab was still folding forward. This caused a decrease in the slab dip before it folded back and rolled back over itself again (see Fig. 3b). In the very high coupling Experiment 12, after a short initial period of steady values, all the velocities increased but at lower rates than in the experiments described above (Fig. 4c). After the slab touched the bottom of the tank, at around 3000 s (scaling to 25 Ma) it rolled back for a short period during which all the velocities progressively decreased until subduction stopped prematurely at 6720 s (56 Ma; Figs 3c and 4c). At this point, the high mechanical coupling in the interplate zone inhibited further subduction. Consequently, the slab started to stretch and neck due to the pull exerted by the slab on the plate at the surface (Fig. 3c at s, scaling to 148 Ma). During the rollback period after the slab touched the bottom, it is conspicuous in all experiments that the average subduction velocity decreases with increasing interplate coupling (here given by the values of flow stress, Fig. 5a and Table 3). At this stage the subduction velocity in the very high coupling experiment was mm s 1, scaling to 1.4 cm yr 1, which is less than 15 per cent of the velocity in the experiment with low coupling (0.130 mm s 1, scaling to 7.8 cm yr 1 ). Consequently, the amount of subduction [i.e. the length of SP that is consumed in the mantle with progressive time, S in Fig. 5(b), S = (v T + v SP )/t] during a given time period also decreases with increasing mechanical coupling. In experiments with low and medium coupling (Experiments 10 and 9) the amount of subduction increased approximately linearly with time, while in the case of the very high coupling experiment (Experiment 12) the amount of subduction slowly approached a steady value before subduction stopped (Fig. 5b). 3.2 OP deformation The OP experienced significant deformation in the three experiments presented here. This deformation was mainly characterized by overall extension in the trench-normal direction, as measured by the average extension rate (v OPD ) in the OP (Fig. 4). A constant average extension rate (v OPD )of mm s 1, scaling to 1.47 cm yr 1 (Table 4), was maintained in the low coupling experiment to accommodate the mismatch between the trench retreat velocity (v T ) and the trenchward velocity of the trailing edge of the OP (v OP ; Fig. 4a). In the medium coupling experiment, the extension rate was slightly more variable around a mean value of 0.01 mm s 1, scaling to 0.6 cm yr 1 in nature (Fig. 4b), eventually dropping to approximately zero during the short phase of slow trench advance (see previous section). In the experiment with higher coupling, the extension rate oscillated around values 0.01 mm s 1 (Fig. 4c), with an average of mm s 1, scaling to 0.38 cm yr 1 (Table 4). The total trench-normal OP extensional strain was 17.5, 18.8 and 11.0 per cent for the experiments with low, medium and very high coupling, respectively. In all three cases, OP extension occurred along the entire length of the plate, but was most pronounced in the region within mm (scaling to km) from the trench (Figs 6 10). In the low coupling experiment, extension during the slab-sinking phase was distributed along the entire plate, being slightly higher in the frontal portion (Fig. 6a, 580 s curve). Indeed, when considering the total duration of the experiment it becomes clear that extension was concentrated in the frontal half of the plate, with a peak strain of 0.5 at 75 mm (scaling to 375 km) away from the trench (Figs 6a and 7a). In the strain map shown in Fig. 8 for the low coupling experiment, a diffuse circular region of maximum extensional strain is located in the interior of the plate. In the medium coupling experiment, localization of extensional deformation was more pronounced during the initial phase of slab sinking (Fig. 10a). This probably resulted from a suction force transmitted from the slab-lubrication layer across the subduction interface, which at this stage was still filled in with some glucose. According to lubrication theory, flow in this layer should induce large normal stresses that will resist the separation of the two plates, while allowing tangential movement between them. This may have led to the localization of extensional strain closer to the trench. During the following phases deformation remained noticeably more concentrated in the frontal third of the plate (Figs 6b and 10b and c). The area of maximum extension, with a total extensional strain of 0.8, was

8 54 J. C. Duarte, W. P. Schellart and A. R. Cruden Figure 4. Diagrams illustrating the measured trench-normal velocities, across a longitudinal line passing through the trench middle point for each of the experiments with low, medium and very high coupling. v SP, subducting plate velocity, measured at the trailing edge of the subducting plate (trenchward motion is positive); v T, trench velocity, measured at the tip the overriding plate closest to the trench (trench retreat is positive); v OP, overriding plate velocity, measured at the trailing edge of the overriding plate (trenchward motion is positive); v OPD, overriding plate deformation rate, that is, the rate at which the overriding plate deforms, where extension is positive, calculated as the differential between trench velocity and overriding plate velocity (= v T v OP ); v S, subduction velocity, i.e. the rate at which the overriding plate is consumed in the mantle, calculated as the sum of trench velocity and subducting plate velocity (= v T + v SP ). v SP has been corrected for internal deformation. Since the subduction plate is negatively buoyant, with the passage of time it tends to shrink and thicken. This effect is negligible in short lasting experiments, such as in the case of the low mechanical coupling, but it is noticeable in the case of the experiments with higher coupling. Blue arrows indicate the moment when the subducting plate touches the bottom of the tank and red arrows indicate the moment when both plates become fully coupled. Errors in velocities are ± mm s 1 (0.1 cm yr 1 ).

9 3-D dynamic laboratory models of subduction 55 Figure 5. (a) Diagram illustrating the correlation between the average values of subduction velocity (v S ) and the values of flow stress for each corresponding mixture of petrolatum paraffin oil measured in the rheometer. The subduction velocities were averaged only for the first phase of steady rollback after the slab touched the bottom of the tank to avoid the interference of complex dynamical effects such as the refolding of the slab observed in the Experiment 9. Notethat the measured values of flow stress relate with the dynamical strength of the petrolatum paraffin oil mixtures. (b) Diagram illustrating the amount of subduction (S), that is, the length of subducting plate that is consumed in the mantle with progressive time, for the three experiments shown in Fig. 3 with low, medium and very high coupling. Errors in velocities are ±0.002 mm s 1 (0.1 cm yr 1 ). Errors in length are ±0.02 mm (0.1 km) more elongated in the trench-parallel direction and located closer to the trench ( 50 mm, scaling to 250 km) when compared to the low coupling experiment (Figs 6b, 7b and 10a c). OP extension was also localized closer to the trench during the sinking phase of the very high coupling experiment (Figs 6c, 7c and 8b). This remained the case until the end of the experiment, when total extensional strain reached a maximum value of 0.6, concentrated 40 mm away from the trench, scaling to 200 km in nature (Fig. 8b). An important observation in this experiment is that the central portion of the OP adjacent to the trench recorded noticeable shortening, indicated by a negative extensional strain value of 0.23 after the slab touched the bottom of the tank (Fig. 6c). This shortening can be observed adjacent to the trench in the strain map (Fig. 8b), which shows a rotation of the maximum horizontal extensional strain axis from a trench-perpendicular to a trench-parallel orientation, concomitant with a component of trench-parallel extension. Fig. 9 shows five top views of the low coupling experiment at different time steps (corresponding to Fig. 3a). While subduction developed during this experiment, the trench retreated and became progressively more arcuate. This was accompanied by growth of an accretionary wedge on top of the SP. Over time, trench-parallel passive strain-markers in the OP became more curved towards the trench, while the area of maximum extension localized at a distance of mm, scaling to km, from the trench (see also Figs 6a and 8a). 3.3 Plate kinematics and OP deformation Fig. 11 plots correlation charts for several measured experimental velocities. Figs 11(a) and (b), plot the trench velocity (v T ) and the SP velocity (v SP ) against the OP deformation rate (v OPD ) for the three experiments with different degrees of mechanical coupling and Figs 9(c) and (d) plot v T and v SP against the OP velocity (v OP )..Theaimof this analysis was to investigate how v T and v SP might correlate with OP internal deformation and translation. Trench velocity, v T has a consistent positive correlation with v OPD in all three experiments, with coefficients of determination R 2 higher than 0.2, and with v OP where R 2 is always higher than 0.9 (Figs 11a and c). The low correlation value of 0.2 in Fig. 11(a), Experiment 10, is probably a consequence of the relatively low range in the values of v T and v OPD. Another complementary explanation could be that despite the decrease in toroidal flow vigour associated with decrease in trench retreating rate, the progressive decrease of the OP thickness could sustain a higher than expected extensional rate, and thus explain the relatively poor correlation. On the other hand, v SP has inconsistent and variable correlations (positive and negative) with v OPD and v OP (Figs 11b and d). 4 DISCUSSION 4.1 Effect of mechanical coupling on the kinematics and dynamics of subduction Our results show that variations in the degree of mechanical coupling at the subduction zone plate interface have a significant impact on the subduction velocity (Figs 3 5; Table 3). Subduction velocities decrease exponentially with increasing mechanical coupling (Fig. 5a). This is a consequence of the increase in the strength of the petrolatum/paraffin mixtures (Table 3), which causes an increase in shear stress along the subduction interface. In Experiment 12, with very high coupling, subduction stalled due to a high resistive shear force at the plate interface (Table 5). These results are consistent with the properties of the investigated mixtures, whereby higher petrolatum contents result in higher flow stress values (Section 2.2). We conclude that the relative proportion of petrolatum and paraffin oil can be used as a proxy for the shear stress at the plate interface in subduction experiments. For the slab rollback phase that starts after the slab tip first touches the bottom we have calculated a slab negative buoyancy force of 0.33 N for the experiment with low coupling and 0.31 N for the medium and very high coupling experiments (Table 5). Note that this is the only available driving force in our subduction system. We have also estimated a resistive interplate shear force of 0.06, 0.17 and 0.21 N for the experiments with low, medium and very high coupling, respectively (Table 5), related to the increase in petrolatum content in the plate lubricating mixtures. In the very high mechanical coupling Experiment 12, the value of the shear force is approximately 68 per cent of the available slab negative buoyancy

10 56 J. C. Duarte, W. P. Schellart and A. R. Cruden Figure 6. Diagrams showing the distribution of overriding plate deformation as function of trench distance along the (trench-normal) centreline. Strain was measured using the change in distance between adjacent passive markers on the top of the overriding plate. Values of extension are positive and values of shortening are negative The left column shows the cumulative strain over the given periods of time, while the right column shows the incremental strain in each of the given time steps. Note that during the first period (dark blue curves) the plates were not in full contact because there was still a wedge of glucose between the plates. After this period the two plates were always in physical contact (see text). Errors in strain are ±0.01. force (Table 5). This only leaves a small part ( 32 per cent) of the slab negative buoyancy force to drive flow and deformation elsewhere in the system (e.g. flow in the mantle, deformation of the slab at the subduction zone hinge), causing the subduction and slab sinking rates to slow down. As the slab slows down, it will start to deform internally by stretching and necking close to the surface, causing both the total negative buoyancy force and the effective slab pull to the surface plate to decrease, leading in turn to a further decrease in the subduction and slab sinking rates. Such a slowdown in subduction rate and associated slab necking is observed

11 3-D dynamic laboratory models of subduction 57 Figure 7. Top-view photographs and line drawings of the three experiments shown in Fig. 3 with low, medium and very high coupling. The photos correspond to stages with the same amount of subduction (S in Fig. 5b) of 160 mm, scaling to 800 km in nature (corresponding to 1040, 3200 and 4800 s, scaling to 9, 27 and 40 Ma, respectively). Note that most of the lubricating material on the top of the subducting plate is subducted, except for an accretionary wedge that developed in the lower coupling experiment. Nevertheless, after a first period of fast growth the width of the accretionary wedge stabilizes (see Fig. 9), indicating that most of the lubrication material enters the subduction channel. in Experiment 12 (Figs 3c and 4c). Eventually the slab will detach and subduction will cease. Lateral and perspective views of the final stages of the three investigated experiments are shown in Fig. 12. Figs 12(a) and (b) show that the tip of the OP that was in contact with the top of the SP (lubricated with the mixtures) was slightly thickened and dragged down as consequence of friction on the subduction interface. This is clearly marked by linear down dip striations (Figs 12a and b). Experiment 9, with medium coupling, showed evidence of significantly more drag than Experiment 10 with lower coupling. In very high coupling Experiment 12 (Fig. 12c) a portion of the OP was also dragged down into the mantle before the subduction stalled and the slab started to stretch. Progressive drag of the tip of the OP has the effect of increasing the contact area between the plates, which eventually stabilizes in the low coupling experiment, but not in the higher coupling experiments. Consequently, the shear force (given by the shear stress multiplied by the surface area) increases until it reaches a threshold value. At this point the slab pull force can no longer overcome the shear force at the interface, causing the subduction to cease. This explains why subduction did not stop immediately in the very high coupling experiment. Even though the stresses were relatively high in the first stages of the experiment, the contact area between the plates was probably sufficiently small to allow for some slow subduction. With progressive subduction the surface area between the plates increased, causing the subduction velocity to decrease in order to maintain the shear force at the subduction interface, eventually causing subduction to stop. Mechanical coupling at the subduction interface also has a major impact on the dynamics of the subduction experiments. While the slab always retreated in the low coupling experiment (Fig. 3a), the evolution was significantly more complex in the medium coupling experiment. After a first phase of trench retreat and slab rollback, the trench halted and was forced to advance as a consequence of slab roll over. This roll over was a consequence of the first rollback phase (approximately from 2000 to 4000 s; see Fig. 3b) when the base of the slab rolled back faster than the trench retreated. Roll over resulted from a subvertical orientation of the slab as its tip was draping the base of the tank between 2000 and 4000 s (Fig. 3b, third panel from the top). This behaviour is attributed to relatively slow trench retreat due to medium coupling at the interface and is consistent with previous subduction modelling, which found that slab dip angle increases with decreasing trench retreat velocity (Schellart 2004). The subvertical slab dip angle in the medium coupling experiment, combined with slow trench retreat, continued trenchward motion of the SP and resistance to further sinking at the base of the tank caused the slab to fold forward, accommodating newly arriving slab material at depth.

12 58 J. C. Duarte, W. P. Schellart and A. R. Cruden Figure 8. Overriding plate displacement vectors (left-hand side) and horizontal extensional strain-field maps (right-hand side) of experiments with low and very high mechanical coupling, computed for the period after the plates were in full contact. Red lines on right hand side indicate directions of maximum horizontal extensional strain. Note that the region of maximum extension is located a considerable distance from the trench (far right). Note also the trench-parallel orientation of extension in the centre near the trench in Experiment 12, which coincides with local minor trench-normal shortening. The maps were produce by tracking the position of all the passive markers in a 2-D Cartesian space using the software Image J ( and by computing the displacement and the strain fields with the software SSPX (Cardozo & Allmendinger 2009). The grid was produced using the grid-distance weighted function, which uses all the markers to calculate and interpolate the strain. The Newtonian nature of our overriding plate allows for a higher resolution (regrinding) interpolation since only smooth variations in strain are expected. 4.2 Effect of mechanical coupling on OP deformation The OP always showed overall trench-normal extension in our experiments (Figs 4, 6, 8 and 10). The extension was mostly accommodated by trench retreat and an increase in trench curvature (Figs 7 and 9). This is particularly true in the low mechanical coupling experiment in which the maximum extension was accommodated mm (scaling to km) away from the trench (Fig. 8a). This suggests that extension in the OP is driven mainly by shear tractions at the base of the plate generated by a gradient in mantle flow-induced drag, which decreases from the frontal to the rearward parts of the plate (Fig. 13, see next section for discussion). The experiment with medium coupling also experienced overall OP extension. However, the area of maximum extension was localized closer to the trench (at 50 mm; scaling to 250 km) with a more elongated, trench-parallel orientation (Fig. 10), which formed in the first, free sinking, phase of the experiments when there was still a low-viscosity glucose layer at the subduction zone interface. This suggests the action of an additional force affecting deformation of the OP. This force could be related to an increase in the tensile stress normal to the subduction interface for experiments with a higher coupling material on the SP, causing an increase in the slab suction force. This suction force would have been small in the case of the low coupling experiment but more significant in the medium coupling experiment. Also, in the medium coupling experiment there was a period of trench advance (Figs 4b and 10b) when there was almost no extension in the OP, which also moved away from the trench. This backward movement of the OP was a consequence of our experimental setup, in which the OP had a free trailing edge. If the trailing edge were to be fixed some shortening would be expected as a consequence of the trench advance. The OP in the very high coupling experiment also showed overall extension during the subduction period, but two noteworthy differences are evident with respect to the low coupling experiments. First, during the free sinking phase before the slab tip touched the bottom of the tank the maximum extension was located very close to the trench (at 10 mm; scaling to 50 km). Secondly, shortening was observed in the frontal-most portion of the OP during the period of progressive subduction rollback after the slab touched the bottom of the tank and the plates were in actual physical contact (Figs 6c and 8b). Both the localization of extension closer to the trench and shortening in the OP close to the plate contact are also likely related to comparatively higher stress at the subduction interface. As in the case of the medium coupling experiment, the proximity of the extension to the trench may be related to an increase in tensile stress normal to the subduction interface and the consequent increase in slab suction force. On the other hand, the shortening may be related to a horizontal component of compressive stress associated with slab-parallel shear. During the initial period dominated by slab suction (until 3840 s; Fig. 6c) the plates were not yet in full contact and shear stresses were relatively low, whereas after this stage the shear stresses became dominant. 4.3 Control of slab rollback and mantle flow on OP deformation The localization of maximum extensional strain in the interior of the OP indicates that deformation must have been propagated from below. Because our plate behaves as a Newtonian fluid under experimental strain rates, a horizontal stress acting on the trenchward side of the OP should result in the highest strain at the leading

13 3-D dynamic laboratory models of subduction 59 Figure 9. Top-view photographs and line drawings of low mechanical coupling Experiment 10. Time steps correspond to those shown in Fig. 3(a). Note that while the experiment evolves the trench retreats and its curvature increases. This is accompanied by build up of an accretionary wedge on top of the subducting plate. edge with a progressive decrease towards the plate interior. Therefore, we propose that extensional deformation of the OP was driven mainly by a gradient in shear traction at its base (Fig. 13). Meyer & Schellart (2013) reached a similar conclusion based on subduction experiments using a very low viscosity interplate lubrication material (with values of about 5 per cent of the UM viscosity). As mentioned previously, the gradient in shear traction acting on the base of the OP is caused by differential mantle flow that drags the frontal portion of the plate faster than its rear portion. Although it is not known whether the toroidal or the poloidal components of mantle flow, or both, are responsible for such basal drag, the correlation charts in Fig. 9 provide additional insight. Before analysing the charts in detail a few general observations from previous subduction models should be discussed. The lateral movement of a slab

14 60 J. C. Duarte, W. P. Schellart and A. R. Cruden Figure 10. Overriding plate displacement vectors (left-hand side) and horizontal extensional strain-field map (right-hand side) of the model with medium mechanical coupling, computed for three different periods after the plates were in full contact: (a) initial roll back phase; (b) slab re-folding and trench advance phase; (c) second slab roll back phase. Red vectors on right hand side indicate directions of maximum horizontal extensional strain. Note that the region of maximum extension is located a considerable distance from the trench (far right). The negligible extensional deformation in (b) corresponds to a period of slow trench advance/very slow trench migration. The trench-parallel orientation of extension in the centre near the trench in (b) and (c) coincides with local minor trench-normal shortening. through a viscous mantle causes the trench to migrate and induces mainly toroidal flow around the slab (Russo & Silver 1994; Buttles & Olson 1998; Funiciello et al. 2003, 2004; Kincaid & Griffiths 2003; Schellart 2004, 2008a; Stegman et al. 2006). On the other hand, the down dip movement of the slab is transmitted continuously to the segment of SP still at the surface, and such movement induces poloidal flow in the mantle wedge above the subducting slab (Kincaid & Griffiths 2003; Schellart 2008a). Consequently, an increase in the trench velocity should correlate with an increase in mantle toroidal flow, while an increase in the subduction plate velocity should relate to an increase in mantle poloidal flow. Having this in mind, the relatively high and consistent correlations between trench velocity (v T ) and OP extensional deformation rate (v OPD ; Fig. 11a), which contrast with the poorer and inconsistent correlations between SP velocity (v SP ) and OP deformation (Fig. 11b), suggests that toroidal flow is the primary driver of OP extension in our experiments. This is in agreement with recent numerical models of subduction that include OP deformation, which demonstrate the strong correlation between the presence or absence of backarc extension in the OP and the presence or absence of slab rollbackinduced toroidal mantle flow (Schellart & Moresi 2013). The best correlations are found between the values of trench retreat (v T )and OP velocity (v OP ; Fig. 11e), suggesting that the mantle toroidal flow is also the main driver of OP displacement. In the case of an imposed fixed trailing edge (i.e. a fixed OP) the mantle toroidal flow would mainly cause internal deformation of the OP, not translation as observed in our experiments. 4.4 Experimental advantages and limitations The main improvement in our subduction experiments has been the implementation of an OP in a fully dynamical 3-D setting, in which the only available force in the system was the negative buoyancy of the SP. While subduction experiments with kinematic boundary conditions, that is, with imposed external forces and velocities (e.g. Heuret et al. 2007), allow for the study of deformation, fully dynamic experiments allow us to assess the origin of those forces and velocities. Nevertheless, we acknowledge that our experiments do not simulate a hypothetical ridge push force, which is considered to be one order of magnitude smaller than the slab negative buoyancy force (Turcotte & Schubert 2002). However, as discussed below the very low resistance of the lateral boundaries of our plates compensates in part for this omission. Another development reported here is the inclusion of a new material to model the interplate zone with a rheology that allows for realistic mechanical coupling at the subduction interface. The challenge of such an implementation was that a very weak material

15 3-D dynamic laboratory models of subduction 61 Figure 11. Diagrams showing correlations between several measured experimental velocities (for the period after the plates were coupled) for Experiments 10, 9 and 12 (low, medium and very high mechanical coupling). Continuous coloured lines are linear best-fitting lines and R 2 is the coefficient of determination. Note in (a) and (e) the good and consistent correlations of v T versus v OPD and v T versus v OP. Errors in velocities are ± mm s 1. Table 5. Relation between the interplate frictional force and the slab negative buoyancy force. Experiment Mix Mechanical coupling F BU (N) Shear rate (s 1 ) F SH (N) F SH /F BU (per cent) per cent Low per cent Medium per cent Very high Notes: The slab negative buoyancy (F BU ) was calculated using the formula F Bu = ρ gv, in which ρ is the density contrast between the subducting plate and the upper mantle, g is the acceleration of gravity and V is the volume of the slab extending between the bottom of the tank and the surface. Note that we do not incorporate the horizontal slab segment resting on the bottom boundary, as it does not contribute to the negative buoyancy force. The interplate shear force (F SH ) was calculated using the formula: F SH = σ A, in which σ is the shear stress at the subduction interface and A is the surface area of the subduction interface (Note that this surface area increased with progressive subduction and with the increase of the mechanical coupling; see text for explanation). The shear stress (σ ) was calculated by multiplying the dynamic viscosity of the mixtures measured in the rheometer by the strain rates estimated for each experiment (using the subduction velocities in Table 2). Note that our largest uncertainty in the calculations is in the thickness of the subduction channel. To assess it we have separated the plates manually in the end of some experiments. A thickness of around 1 mm was estimated. However, we estimate that it may have a variation of the order of ±50 per cent (which is reflected as an error of ±0.1, ±0.02 and ±0.01 s 1 in the values of strain rate); nevertheless, it does not substantially affect the trend in the values of shear force. The errors in F SH are ±0.02, ±0.05 and ±0.06 N, respectively. Errors for F BU are ±0.05 N for Experiments 10 and 9 and ± 0.1 N for Experiment 12. The higher value of negative buoyancy in Experiment 10 is due to the lower angle of the slab and the higher error in Experiment 12 is consequence of some slab stretching in the z dimension and shrinking in x and y dimensions. would have fully decoupled the plates, creating an unrealistic gap between and separating the plates, while the use of a strong material (or no material at all) would have caused the subduction to stall (as in our experiments with very high mechanical coupling). The introduction of a material of suitable rheology facilitated a study of the effect of the variation in the degree of the mechanical coupling in subduction zone models, including quantitative estimates of the shear force at the subduction interface and a qualitative

16 62 J. C. Duarte, W. P. Schellart and A. R. Cruden Figure 12. Lateral and perspective view photographs taken after the end of the experiments with low, medium and very high coupling. Note in (a) and (b) the slightly thicker edge of the overriding plate and the surface that was in contact with the top of the subducting plate marked by down dip striations. In (c) it is possible to observe the stretching of the slab that had occurred after the subduction stalled. Note that a significant portion of the overriding plate was dragged down as well. understanding of the slab suction force. Since our experiments are 3-D they also incorporate both the poloidal and toroidal components of the mantle flow induced by a sinking subducting slab. It is worth noting that 2-D and quasi-2-d models fail to produce a toroidal return flow, which we expect to have a significant effect on OP deformation, in particular on the localization of extension and the curvature of the trench (Fig. 13; see also Schellart & Moresi 2013). Nevertheless, several simplifications have been adopted in our experiments. Our models are iso-thermal and iso-viscous and thus our plates always deform in a uniform viscous manner, which promotes the widespread deformation of the OP. The presence of a brittleviscous stratification in the OP would certainly enhance strain localization, which is essential for the generation of faulting. Hence, even though a region of maximum extension is observed in the OP of our experiments (Figs 7 10) the rheology of our models prohibits the formation of features such as well-delimited back arc basins. Another limitation of our models is that side plates are not included. Our set-up therefore simulates a system with very low resistance at transform boundaries. A stronger resistance on these plate boundaries would have an impact on both the plate and trench retreat velocities, meaning that in our experiments these velocities may be slightly overestimated when compared to natural examples (Yamato et al. 2009). Nevertheless, transform plate boundaries can be very weak (e.g. Lockner et al. 2011), and previous subduction modelling has shown that the inclusion of both side plates and very

17 Figure 13. Schematic model illustrating the mechanism for the localization of deformation in the interior of the overriding plate. Slab rollback creates toroidal mantle flow. The velocity variation within the flow below the overriding plate induces a difference in the amount of basal drag, causing the frontal portion of the plate to migrate faster than the rearward portion. This in turn results in localization of extensional strain within the plate were the difference in basal drag is greatest. weak transform plate boundaries does not have a significant influence on the subduction kinematics and dynamics (Schellart & Moresi 2013). Furthermore, the effect of the absence of side plates may compensate for the lack of a ridge push force. The lack of lateral plates, together with the buoyancy of the SP, has an additional side effect. Since the SP is negatively buoyant, with the passage of time it tends to thicken, which is compensated by reduction in its trench-parallel horizontal dimension. While this effect is minimal in short-lasting experiments, as in the case of low mechanical coupling (Fig. 3a), it is noticeable in the higher coupling experiments (Fig. 3c). For this reason, experiments with higher overall velocities are more plate like and hence should be favoured when using the current experimental set-up to study other variables. Moreover, our experimental tank has a rigid base simulating an impenetrable upper- and lower-mantle discontinuity. This may cause an amplification of the effects of the slab-discontinuity interaction and it also means that our experiments are limited to subduction in the UM only. Furthermore, the isothermal nature of our experiments means that they do not allow simulation of the effects of temperature gradients on the dynamics of the subduction. Nevertheless, seismic tomographic images suggest that slabs remain relatively cold over many tens of millions of years, in agreement with the scaled time of our low-coupling experiment (Fig. 3a). Finally, it should be noted that the models presented are simplifications of natural prototypes and our scaling is valid only if several assumptions inherent in eq. (2) are met, namely that the main driving force of the subduction system in nature and in our models is the negative buoyancy force of the slab, and that the main resisting force is the viscous resistance of the mantle. The first assumption is generally accepted (e.g. Elsasser 1971; Forsyth & Uyeda 1975) and recent models of subduction support the second assumption (e.g. Capitanio et al. 2007; Krien & Fleitout 2008; Schellart 2009, 2010, Irvine & Schellart 2012). 4.5 Comparison with previous experiments Previous experiments with both a subducting and an OP made use of hydrocarbon compounds to lubricate the subduction interface, in particular Petrolatum (e.g. Heuret et al. 2007), or apparently no lubricant at all (Espurt et al. 2008; Guillaume et al. 2009). However, these authors used plates with higher viscosity values than the ones used in our experiments and applied stepping motors to drive their models, thus providing an additional external force to their subduction systems. This may explain why subduction developed even in the presence of high shear forces at the interface. Without such an external force subduction would have probably 3-D dynamic laboratory models of subduction 63 stalled. Boutelier & Oncken (2011) used Paraffin Oil to lubricate the subduction channel under the assumption of zero shear friction at the subduction interface but also applied velocities to their plates. Boutelier & Cruden (2008) used low viscosity PDMS on top of the subduction plate in a quasi-2-d set-up, which had the same viscosity of the asthenospheric mantle. Progressive subduction was driven by combinations of imposed SP velocity, induced mantle flow and slab negative buoyancy. However, because these experiments are not fully 3-D it is difficulty to establish a direct comparison with the models presented in this paper. Finally, our models reproduce well some of the results of experiments presented by Meyer & Schellart (2013), such as trench curvature and localization of OP deformation. Nevertheless, in this work we have significantly improved the experimental procedure, which allowed the investigation of not only the OP deformation in a dynamic framework but also other parameters such as the degree of mechanical coupling and shear forces at the subduction interface. 4.6 Comparison with natural examples Our experiments successfully reproduce several features of natural subduction zones. In the experiments subduction was always asymmetric and the OPs always remained in physical contact with the underthrust SP (Fig. 3). The trench was curved and convex towards the SP, as is the case for narrow subduction systems like the Scotia, Lesser Antilles, Gibraltar, Hellenic and Calabria arcs (Figs 7 and 9; Schellart et al. 2007). However, it should be noted that these relatively small subduction zones are embedded within larger, slowly moving tectonic plates (e.g. South America for the Scotia and Lesser Antilles arcs; Africa for the Gibraltar, Hellenic and Calabria arcs). In our models the free trailing edge of the SP therefore probably leads to a moderate overestimation of v SP. Another agreement between our experiments and nature is that an area of maximum extension was observed in a location where back arc basins would be expected to form, mm from the trench, scaling to km in nature (Figs 7 10). Our analysis also suggests that translation and internal deformation of the OP is mainly driven by mantle toroidal flow around the slab (Fig. 13). Even though subduction systems have often been treated as 2-D phenomena, several authors have recognized the importance of the toroidal flow for the dynamics of both natural and model subduction systems (e.g. Russo & Silver 1994; Buttles & Olson 1998; Kincaid & Griffiths 2003; Funiciello et al. 2004; Schellart 2004, 2008a; Stegman et al. 2006; Schellart et al. 2007; Guillaume et al. 2010; Faccenna et al. 2011). Using UM SKS splitting measurements, Diaz et al. (2010) recently showed that fast polarization directions (FPD) clearly rotate along and follow the curvature of the Gibraltar arc, interpreted as the imprint of horizontal asthenospheric flow around the retreating slab. Civello & Margheriti (2004) have identified a similar pattern in the Calabria subduction zone. These authors describe the toroidal flow accommodating the horizontal movement of the slab through the UM. Our models show that in addition to accommodating slab rollback, the mantle flow also has a strong feedback into the plate kinematics, in particular in driving and deforming the OP. Of our experiments only the low coupling case produced realistic average subduction velocities ( 7cmyr 1 ; Table 3) and interplate shear forces ( 16 per cent of the available driving force; Table 5). All other experiments had very low subduction velocities (ranging from 0.5 to 2.3 cm yr 1 ) and very high interplate shear forces (more than 50 per cent of the driving force). This suggests that in natural