Physics of the Earth and Planetary Interiors

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1 Physics of the Earth and Planetary Interiors 170 (2008) Contents lists available at ScienceDirect Physics of the Earth and Planetary Interiors journal homepage: Subduction zone trench migration: Slab driven or overriding-plate-driven? W.P. Schellart a,b, a Research School of Earth Sciences, The Australian National University, Canberra, ACT 0200, Australia b School of Geosciences, Monash University, Melbourne, VIC 3800, Australia article info abstract Article history: Received 9 April 2008 Received in revised form 9 July 2008 Accepted 24 July 2008 Keywords: Subduction Trench migration Overriding plate Backarc Deformation Plate motion Slab Subduction zones on Earth, and their associated trenches and hinges, migrate with respect to the overriding plate, as indicated by overriding plate deformation (e.g. backarc extension or backarc shortening), and migrate with respect to hotspot and no-net-rotation reference frames (global or absolute reference frames). Three geodynamic models exist that attempt to explain how absolute trench migration velocity correlates with overriding plate deformation. In one model, trench and hinge migration result from lateral migration of the slab, with trench retreat causing overriding plate extension, and trench advance causing overriding plate shortening. In the second model, trench migration is forced by the overriding plate, with trenchward motion causing trench retreat and overriding plate shortening, and motion away from the trench causing trench advance and overriding plate extension. In the third model, the trench and subduction hinge are thought to be static, while overriding plate extension/shortening is accommodated by landward/trenchward overriding plate motion. In this paper, the conflicting geodynamic predictions made by these three models are tested by using global kinematic calculations of trench migration velocity ( T ), overriding plate velocity ( OP ) and overriding plate deformation in different global reference frames. The dependence between T and overriding plate deformation, as well as OP and overriding plate deformation was investigated. Correlation coefficients (R) and confidence limits were calculated using a quantitative approach with overriding plate deformation velocity ( OPD ), using a semi-quantitative approach with an overriding plate strain-classification approach, and using a Spearman rank correlation approach. For the quantitative approach the correlation between T and OPD is consistently positive (R = ), where trench retreat corresponds to extension, and statistically significant at 95% confidence level for all but one reference frame. For OP and OPD the correlation is consistently negative but much less significant (R = 0.29 to 0.17) and statistically not significant at 95% confidence level for all reference frames. These findings indicate that trench migration results predominantly from lateral migration of the slab rather than from overriding plate motion. Such lateral slab migration is most likely driven by the negative buoyancy force of the slab itself, as demonstrated by geodynamic models Elsevier B.V. All rights reserved. 1. Introduction It has long been recognized by geologists and geophysicists that many overriding plates bordering subduction zones experience permanent, non-elastic deformation. Overriding plate extension is commonly referred to as backarc extension or backarc spreading, but may also involve fore-arc or intra-arc extension. Well known examples of actively opening backarc basins include the Aegean Sea, Scotia Sea, Okinawa Trough, Mariana Trough, North Fiji Basin and Lau Basin, which experience extension or spreading at rates varying between 1 and 15 cm/year (Le Pichon, 1982; Malinverno and Ryan, 1986; Auzende et al., 1988; Fryer, 1996; McClusky et al., Correspondence address: School of Geosciences, Monash University, Melbourne, VIC 3800, Australia. Tel.: ; fax: address: wouter.schellart@sci.monash.edu.au. 2000; Zellmer and Taylor, 2001; Schellart et al., 2006). Overriding plate shortening is less common and can take place in the backarc, intra-arc or fore-arc region. The best know example is the Central Andes mountain belt, with active shortening up to 1.5 cm/year (Norabuena et al., 1998). There are three main classes of models concerning the driving mechanism of overriding plate deformation at subduction zones and the involvement of trench migration in such deformation (loosely based on the classification of Carlson and Melia, 1984). In the first class of models, trench migration is thought to be a key parameter with respect to overriding plate deformation and would thus show a correlation with such deformation (Fig. 1). The different models that belong to this class will be referred to as the migrating trench models. There are two sub-classes of migrating trench models, each with a different primary driving mechanism for trench migration. On one side of the spectrum of migrating trench models, overriding plate deformation, trench migration and /$ see front matter 2008 Elsevier B.V. All rights reserved. doi: /j.pepi

2 74 W.P. Schellart / Physics of the Earth and Planetary Interiors 170 (2008) Fig. 1. Schematic cross-sections of subduction illustrating the two end members of the migrating trench model and the static trench model. (A) Initial setting. (B E) The slab-driven migrating trench model, with (B) rollback of the slab inducing trench retreat and overriding plate extension, (C) roll-forward of the slab inducing trench advance and overriding plate shortening, (D and E) cross-plots for T and OPD and for OP and OPD in case the slab-driven model can perfectly explain all overriding plate deformation. (F I) The overriding-plate-driven migrating trench model, with (F) overriding plate motion away from the trench inducing trench advance and overriding plate extension, (G) trenchward overriding plate motion inducing trench retreat and overriding plate shortening, (H and I) cross-plots for T and OPD and for OP and OPD in case the overriding-plate-driven model can perfectly explain all overriding plate deformation. (J M) The static trench model, with (J) overriding plate motion away from the trench inducing overriding plate extension, (K) trenchward overriding plate motion inducing overriding plate shortening, (L and M) cross-plots for T and OPD and for OP and OPD in case the static trench model can perfectly explain all overriding plate deformation. Velocities: OP = trench-perpendicular overriding plate velocity; SP = trench-perpendicular subducting plate velocity; T = trench-perpendicular trench migration velocity (=hinge migration velocity); S = trench-perpendicular subduction velocity; C = trench-perpendicular convergence velocity; OPD = trench-perpendicular overriding plate deformation velocity. Note that all velocities are in an arbitrary hotspot reference frame. Convention is that extension, trench retreat and trench-directed motion for the plates are positive. subduction hinge migration are driven by lateral migration of the slab, i.e. a deep source (Elsasser, 1971; Havemann, 1972; Molnar and Atwater, 1978; Malinverno and Ryan, 1986; Hamilton, 1988; Lonergan and White, 1997; Schellart and Lister, 2004). This model will be referred to as the slab-driven model (Fig. 1B and C). Note that we are here not concerned with which physical parameter(s) actually promote/retard lateral slab migration. On the other side of the spectrum of migrating trench models, trench migration, subduction hinge migration and overriding plate deformation are driven by motion of the overriding plate, i.e. a shallow source (Jarrard, 1986; Heuret and Lallemand, 2005; Heuret et al., 2007). This model will be referred to as the overriding-plate-driven model (Fig. 1F and G). Note again that we are here not concerned with which physical parameter(s) actually promote/retard overriding plate motion.

3 W.P. Schellart / Physics of the Earth and Planetary Interiors 170 (2008) In the second class of models, the subduction hinge and trench are considered to be static due to anchoring of the slab in the mantle (e.g. Hyndman, 1972; Uyeda and Kanamori, 1979). The models that belong to this class will be referred to as the static trench models. These models thus predict that the subduction hinge and trench are always static, irrespective of the overriding plate deformation rate. In the third class of models, trench migration is not taken into account as a potential parameter affecting overriding plate deformation (e.g. Karig, 1971; Sleep and Toksöz, 1971; Lamb and Davis, 2003). The models that belong to this class can be referred to as the non-kinematic models. From a kinematic perspective it is clear that overriding plate deformation next to a subduction zone requires relative motion between the subduction hinge and the far-field non-deforming overriding plate (Dewey, 1980). As the non-kinematic models do not provide any prediction regarding the potential correlation between trench migration and overriding plate deformation, they will not be discussed any further. This paper will discuss the key predictions that the two migrating trench models and the static trench model make with respect to trench migration, overriding plate motion and overriding plate deformation. It will be shown how these predictions fit with observations from active subduction zones around the world. It is found that the predictions from the slab-driven model best agree with the observations, arguing in favour of a deep mantle source as the dominant driving mechanism of trench migration, subduction hinge migration and overriding plate deformation. 2. Conceptual models 2.1. Migrating trench model 1: slab-driven model In the first type of migrating trench models, the slab-driven model, migration of the trench and subduction hinge are thought to be primarily caused by lateral migration of the slab through the mantle (Elsasser, 1971; Havemann, 1972; Molnar and Atwater, 1978; Malinverno and Ryan, 1986; Hamilton, 1988; Lonergan and White, 1997; Schellart and Lister, 2004). Trench retreat would result from slab rollback (retrograde, i.e. oceanward, slab motion), while trench advance would result from slab roll-forward (prograde, i.e. landward, slab motion). In such a model, slab rollback would induce overriding plate extension (Fig. 1B) (backarc/intraarc/fore-arc extension), while slab roll-forward would induce overriding plate shortening (Fig. 1C). In case the slab-driven model would perfectly explain all overriding plate deformation, then the correlation coefficient (R) between the trench-perpendicular trench migration velocity ( T, trench retreat is positive) and the trench-perpendicular overriding plate deformation velocity ( OPD, extension is positive) would be R = 1 and T = OPD (Fig. 1D). Also, for the trench-perpendicular overriding plate velocity ( OP ) and OPD there should be no correlation (R = 0) and OP = 0(Fig. 1E). The slab-driven model has been proposed in particular to explain backarc extension for a large number of backarc basins in the Northwest Pacific, Southwest Pacific, Mediterranean and Southern Atlantic (Molnar and Atwater, 1978; Le Pichon, 1982; Vaillon et al., 1986; Malinverno and Ryan, 1986; Lonergan and White, 1997; Schellart et al., 2002, 2003, 2006; Rosenbaum and Lister, 2004; Martin, 2006). These models appear conceptually plausible, and numerous dynamic models have indeed shown that: (1) trench migration induced by lateral slab migration is physically viable, in particular when subduction is driven by the negative buoyancy force of the slab (Jacoby, 1976; Kincaid and Olson, 1987; Zhong and Gurnis, 1995; Buiter et al., 2001; Funiciello et al., 2004; Schellart, 2004, 2005, 2008a; Bellahsen et al., 2005; Enns et al., 2005; Stegman et al., 2006; Morra et al., 2006; Schellart et al., 2007; Capitanio et al., 2007; Di Giuseppe et al., 2008); (2) trench retreat can result in overriding plate extension (Shemenda, 1993; Faccenna et al., 1999); (3) trench advance can result in overriding plate shortening (Heuret et al., 2007). Note, however, that purely dynamic models with plate motion and mantle flow driven by buoyancy forces only, which illustrate a coexistence of trench advance and overriding plate shortening, are still lacking. Also note that analogue and numerical models often lack a low-viscosity mantle wedge. Inclusion of a low-viscosity mantle wedge decreases the suction force, thereby facilitating slab rollback and thus enhancing extension in the overriding plate (e.g. Billen and Gurnis, 2003; Gurnis et al., 2004) Migrating trench model 2: overriding-plate-driven model In the other migrating trench model, the overriding-platedriven model, migration of the trench and subduction zone hinge are thought to result primarily from lateral motion of the overriding plate (Jarrard, 1986; Heuret and Lallemand, 2005; Heuret et al., 2007). Trenchward overriding plate motion would induce trench retreat and overriding plate shortening, as it is assumed that the subduction hinge and slab resist lateral migration (Fig. 1G). Overriding plate motion away from the trench would induce trench advance and overriding plate extension, as it is thought that overriding plate motion away from the trench would induce tensile deviatoric stresses or some form of suction at the trench, which would promote the trench and subduction hinge to advance (Fig. 1F). In case the overriding-plate-driven model would perfectly explain all overriding plate deformation, then the correlation coefficient between T and OPD would be R = 1, and T = a OPD, where a <0 (Fig. 1H). For example, if a = 1, then OP would be equally accommodated by trench migration and overriding plate deformation; for 1<a < 0 then OP would be predominantly accommodated by OPD ;fora< 1 then OP would be predominantly accommodated by T.For OP and OPD there should be a perfect correlation (R = 1), OP = b OPD and b < 1 (Fig. 1I). The overriding-plate-driven model has been proposed in particular to explain backarc opening of the Mariana Trough along the Mariana subduction zone, where the upper, Philippine, plate is moving westward, away from the Mariana subduction zone. The model has also been used to explain formation of the Andes mountains along the South American subduction zone, where the upper, South American, plate is moving westward (in most global reference frames) towards the South American subduction zone. The physical viability of this model has been tested with two-dimensional numerical simulations of subduction (Olbertz et al., 1997; Sobolev and Babeyko, 2005) and laboratory models of subduction (Heuret et al., 2007). The numerical simulations investigated the role of trenchward overriding plate motion (kinematically imposed), showing that such motion induces trench retreat (Olbertz et al., 1997) as well as overriding plate shortening (Sobolev and Babeyko, 2005). Heuret et al. (2007) reported on 19 subduction experiments, where overriding plate motion and subducting plate motion were kinematically controlled. Seven experiments had an overriding plate that was pulled away, three had a fixed overriding plate and nine had an overriding plate that was pushed trenchward. Out of these 19 experiments, only one showed overriding plate extension and only one had a neutralstrain overriding plate. These two experiments were for a retreating overriding plate setting. The other 17 experiments, including the remaining five with a retreating overriding plate setting, only showed overriding plate shortening. It is thus concluded that the analogue and numerical models only partly support the overridingplate-driven model, i.e. the part where trenchward overriding plate motion causes trench retreat and overriding plate shortening.

4 76 W.P. Schellart / Physics of the Earth and Planetary Interiors 170 (2008) Static trench model In the static trench model, it is assumed that the trench and subduction hinge are fixed with respect to the underlying mantle, as it is assumed that the subducted slab itself is anchored in the mantle and can only move in a down-dip direction but not in a direction perpendicular to the plane of the slab. Overriding plate deformation is accommodated by overriding plate motion in the direction perpendicular to the trench (Hyndman, 1972), with overriding plate retreat causing extension (Fig. 1J) and overriding plate advance causing shortening (Fig. 1K). In case the static trench model would be perfectly applicable to all subduction zones, then there would be no correlation between T and OPD (R =0) and T = 0(Fig. 1L). In addition OP = OPD with a correlation R = 1(Fig. 1M). Uyeda and Kanamori (1979) proposed a somewhat modified version of this model, in which the trench and subduction hinge are thought to be static only for subduction systems with backarc extension. From a theoretical point of view, the conceptual model is kinematically viable. However, basic kinematic arguments can be put forward against the static trench model, since it cannot explain the lateral discontinuity of backarc basins, the complex variation in arc-perpendicular opening rate parallel to the trench, the irregular arc-shaped nature of many subduction interfaces, and the variation in paleomagnetic rotations along arc segments (Hsui, 1988; Schellart and Lister, 2004). To further counter the static trench model, global kinematic studies indicate that trenches predominantly migrate, irrespective of the adopted global reference frame, with variation of the trench velocity along individual subduction zones (e.g. Chase, 1978; Jarrard, 1986; Garfunkel et al., 1986; Heuret and Lallemand, 2005; Schellart et al., 2007, 2008). For example, in Schellart et al. (2007), only 18% of all the mature subduction zone segments (44 out of the total of 244 segments) have a slow trench-perpendicular trench migration velocity in the range of 0.5 to 0.5 cm/year. From the discussion above it thus appears that the static trench model is not supported by observations, as will be demonstrated more quantitatively below. 3. Kinematic calculations The procedure of the kinematic calculations for T, OP and OPD is described in detail in the online Appendix, and has also been described in Schellart et al. (2008). Here, only a summary of the procedure will be given. The velocities were calculated for a total of 24 mature subduction zones (see Fig. 2 for a list). Each subduction zone was divided into individual trench segments with a length of 200 km, resulting in a total of 244 subduction segments, for which the trench-perpendicular component of the velocity was calculated. The size of the trench segments was chosen as such to have segments that are larger than the maximum thickness of subducting oceanic lithosphere, so more than 100 km, but not larger than the narrowest subduction zone, so not more than 250 km. Furthermore, a number of narrow subduction zones with total trench-parallel widths (W) of km display a very tight trench curvature, such as the Scotia subduction zone (W 800 km) and Hellenic subduction zone (W 900 km). Because the trench-perpendicular component of the velocities is calculated, segmentation of these subduction zones into four or five 200 km segments captures the variation in T, OP and OPD along these trenches. For these reasons, segmentation was set at 200 km. The calculations were done in a number of global reference frames, including the Indo-Atlantic hotspot reference frame (O Neill et al., 2005), the Pacific hotspot reference frames from Gripp and Gordon (2002) and Wessel et al. (2006), the global hotspot model from Gordon and Jurdy (1986), a no-net-rotation reference frame based on a geophysical relative plate motion model (Argus and Gordon, 1991), a no-net-rotation reference frame based on a geodetic relative plate motion model (Kreemer et al., 2003) and the Antarctic plate reference frame (Hamilton, 2003). The Pacific and Indo-Atlantic hotspot reference frames and the Antarctic plate reference frame were combined with the relative plate motion model from DeMets et al. (1994) and the one from Kreemer et al. (2003). For the other reference frames, the rotation parameters for all the major plates were already provided. This resulted in a total of 11 reference frame models. The trench-perpendicular trench migration velocity ( T ) was calculated as such (trench retreat is taken as positive): T = OP + OPD + A (1) where OP is the trench-perpendicular overriding plate velocity (including potential microplate motion; trenchward motion is taken as positive), OPD is the trench-perpendicular overriding plate deformation rate (i.e. fore-arc/intra-arc/backarc deformation; extension is taken as positive), and A is the trench accretion/erosion rate (accretion is taken as positive). Calculations that made use of the geodetic relative plate motion model from Kreemer et al. (2003) were combined almost exclusively with geodetically derived OPD estimates (24 out of 28), whilst the others were combined primarily with geologically/geophysically derived OPD estimates (15 out of 28). As such, the calculated data sets are as homogeneous as currently possible. Full details can be found in the online Appendix. 4. Results of kinematic calculations The predictions for the slab-driven model, the overriding-platedriven model and the static trench model as discussed in Sections can be summarized as follows: (1) for the perfect slabdriven model one would expect that T = OPD and OP = 0 (Fig. 1D and E); (2) for the perfect overriding-plate-driven model one would expect that T = a OPD, with a < 0, and OP = b OPD, with b < 1 (Fig. 1H and I); (3) for the perfect static trench model one would expect that T = 0 and OP = OPD (Fig. 1L and M). Below, quantitative analyses and semi-quantitative analyses will be presented, which show the correlation between T and overriding plate deformation, and between OP and overriding plate deformation. In the quantitative analysis, overriding plate deformation is represented by OPD, the trench-perpendicular overriding plate deformation rate. In the semi-quantitative analysis, overriding plate deformation is classified into one of seven overriding plate deformation classes following the approach from Jarrard (1986). Here, 3 represents highly compressive, 2 intermediately compressive, 1 mildly compressive, 0 neutral, 1 mildly extensional, 2 moderately to highly extensional and 3 spreading Quantitative approach: T and OPD In Fig. 2 T is plotted against OPD in five different global reference frames. Fig. 2A shows a plot for the Indo-Atlantic hotspot reference frame, showing a positive correlation (R = 0.66), where an increase in T, i.e. an increase in trench retreat, corresponds to an increase in OPD, i.e. an increase in overriding plate extension. The diagram further shows a large number of points with OPD = 0 cm/year. These are the subduction segments with a non-deforming overriding plate. Overriding plate shortening occurs for T = 4.1 to5.1 cm/year, with 96% in the range T = 2.3 to3.2 cm/year, while overriding plate extension occurs for T = 3.5 to15.5 cm/year, with 90% in the range T = 2.0 to9.1 cm/year.

5 W.P. Schellart / Physics of the Earth and Planetary Interiors 170 (2008) Fig. 2. Diagrams illustrating the trench-perpendicular trench migration velocity ( T ) plotted against the trench-perpendicular overriding plate deformation velocity ( OPD ) for all mature subduction zones on Earth (24 in total). Each of the subduction zones has been segmented into 200 km segments (244 in total). Velocities were calculated in different global reference frames, with (A) the Indo-Atlantic hotspot reference frame (O Neill et al., 2005) combined with the relative plate motion model from DeMets et al. (1994); (B) the no-net-rotation reference frame from Kreemer et al. (2003); (C) the no-net-rotation reference frame from Argus and Gordon (1991); (D) the Antarctic plate reference frame (Hamilton, 2003) combined with the relative plate motion model from DeMets et al. (1994); (E) the Pacific hotspot reference frame (Gripp and Gordon, 2002) that makes use of the relative plate motion model from DeMets et al. (1994). (F) Frequency diagram of OPD for the 244 trench segments, using the geological deformation model. Bin sizes are 1 cm/year, except for one, which is defined by OPD = 0 cm/year (no deformation). NewB SanC NewH: New Britain San Cristobal New Hebrides; And-Sum-Java: Andaman Sumatra Java; Ka Ku Ja Iz Ma: Kamchatka Kuril Japan Izu-Bonin Mariana.

6 78 W.P. Schellart / Physics of the Earth and Planetary Interiors 170 (2008) Table 1 Correlations between overriding plate deformation and trench velocity Reference frame R 95% confidence interval, R (d.f. = 242) 95% confidence interval, R (d.f. = 22) a 95% confidence interval, a (d.f. = 242) 95% confidence interval, a (d.f. = 22) Geological OPD and OP G&J1986 Quantitative Strain class to Spearman rank to A&G1991 Quantitative Strain class Spearman rank G&G2002 Quantitative to Strain class to to to to 0.34 Spearman rank to to to to 0.25 H2003 Quantitative Strain class to Spearman rank to O2005 Quantitative Strain class to Spearman rank to W2006 Quantitative Strain class to Spearman rank to Geodetic OPD and OP G&G2002 Quantitative to Strain class to to to to 0.31 Spearman rank to to to to 0.23 H2003 Quantitative Strain class to Spearman rank to K2003 Quantitative Strain class to Spearman rank to O2005 Quantitative Strain class to Spearman rank to W2006 Quantitative Strain class to Spearman rank to Correlation coefficients (R) and slopes (a) for overriding plate deformation-trench migration velocity regression lines as calculated in 11 different global reference frame models. The 95% confidence intervals have been plotted for R using Fisher s z and for a using Student s t. For the 95% confidence limits an upper limit for the number of independent data (244, i.e. number of trench segments, so degrees of freedom d.f. = 242) and a lower limit (24, i.e. number of subduction zones, so d.f. = 22) were used. For each reference frame model, a quantitative correlation analysis was performed (quantitative, using OPD and T ), a semi-quantitative analysis was performed (strain class, using the strain classification and T ), and a Spearman rank correlation analysis was performed (Spearman rank, using ranked OPD and ranked T ). Six models use a geological/geophysical relative plate motion model (e.g. DeMets et al., 1994) for OP and mostly geologically derived OPD rates (15 out of 28). Five models use a geodetic relative plate motion model (i.e. Kreemer et al., 2003)for OP and OPD values that are nearly all geodetically determined (24 out of 28). Reference frames: A&G1991: Argus and Gordon (1991); G&G2002: Gripp and Gordon (2002); G&J1986: Gordon and Jurdy (1986); H2003: Hamilton (2003); K2003: Kreemer et al. (2003); O2005: O Neill et al. (2005); W2006: Wessel et al. (2006). The same positive correlation is found in other global reference frames, including the no-net-rotation reference frame from Kreemer et al. (2003) with R = 0.66 (Fig. 2B), the no-net-rotation reference frame from Argus and Gordon (1991) with R = 0.68 (Fig. 2C), the Antarctic plate reference frame from Hamilton (2003) with R = 0.53 (Fig. 2D), and the Pacific hotspot reference frame from Gripp and Gordon (2002) with a weaker, but still positive correlation (R = 0.33) (Fig. 2E). Table 1 provides a summary of the correlation coefficients for the 11 different reference frame models, with R = Table 1 also summarizes the values for the slope of the regression line (a), with a = Finally, Fig. 2F shows a frequency plot for OPD. From a total of 244 subduction zone segments ( 48,800 km), 89 experience extension (36.5%), 45 experience shortening (18.4%), while the remaining 110 have a neutral overriding plate strain field (45.1%) with OPD = 0 cm/year.

7 W.P. Schellart / Physics of the Earth and Planetary Interiors 170 (2008) Fig. 3. Diagrams illustrating the trench-perpendicular trench migration velocity ( T ) plotted against overriding plate deformation as classified into one of seven strain classes for all mature subduction zones on Earth (24 in total). Each of the subduction zones has been segmented into 200 km segments (244 in total). Velocities were calculated in different global reference frames, with (A) the Indo-Atlantic hotspot reference frame (O Neill et al., 2005) combined with the relative plate motion model from DeMets et al. (1994); (B) the no-net-rotation reference frame from Kreemer et al. (2003); (C) the no-net-rotation reference frame from Argus and Gordon (1991); (D) the Antarctic plate reference frame (Hamilton, 2003) combined with the relative plate motion model from DeMets et al. (1994), and (E) the Pacific hotspot reference frame (Gripp and Gordon, 2002) that makes use of the relative plate motion model from DeMets et al. (1994). Strain classification scheme (based on Jarrard, 1986): 3 = highly compressional; 2 = intermediately compressional; 1 = mildly compressional; 0 = neutral; 1 = mildly extensional; 2 = moderately to highly extensional; 3 = spreading. (F) Frequency diagram of the seven strain classes for the 244 trench segments. NewB SanC NewH: New Britain San Cristobal New Hebrides; And Sum Java: Andaman Sumatra Java; Ka Ku Ja Iz Ma = Kamchatka Kuril Japan Izu-Bonin Mariana.

8 80 W.P. Schellart / Physics of the Earth and Planetary Interiors 170 (2008) Semi-quantitative approach: T and strain classes In Fig. 3, T is plotted against overriding plate deformation class, where overriding plate deformation is characterized following the strain classification approach from Jarrard (1986). The classification of the individual subduction zone segments is in large part identical to the classifications from Jarrard (1986) and Heuret and Lallemand (2005), but a number of additional subduction zones Fig. 4. Diagrams illustrating the trench-perpendicular overriding plate velocity ( OP ) plotted against the trench-perpendicular overriding plate deformation velocity ( OPD ) for all mature subduction zones on Earth (A, C, and E) and frequency plots for OP (B, D, F). Each of the subduction zones has been segmented into 200 km segments (244 in total). Velocities were calculated in different global reference frames, with (A and B) the Indo-Atlantic hotspot reference frame (O Neill et al., 2005) combined with the relative plate motion model from DeMets et al. (1994); (C and D) the no-net-rotation reference frame from Argus and Gordon (1991); (E and F) the Pacific hotspot reference frame (Gripp and Gordon, 2002) that makes use of the relative plate motion model from DeMets et al. (1994). Bin sizes in frequency diagrams are 1 cm/year.

9 W.P. Schellart / Physics of the Earth and Planetary Interiors 170 (2008) were incorporated in this study not incorporated in the previous studies. Note, however, that there are two limitations with this semi-quantitative approach, as acknowledged and discussed in Jarrard (1986). First, there will always remain some uncertainty in classifying a number of subduction zones, as the boundaries between several strain classes are not well quantified. Second, it is impossible to demonstrate that the seven strain classes constitute equally spaced points along a strain continuum. The results for the semi-quantitative approach are presented here primarily for comparison with the fully quantitative analysis and for comparison with previous works (e.g. Jarrard, 1986; Heuret and Lallemand, 2005; Heuret et al., 2007), but it should be emphasized that the results from this semi-quantitative analysis are less objective and less accurate than those of the quantitative analysis. Also the calculated slopes do not provide the meaning that those for the quantitative analysis provide. Table 2 Correlations between overriding plate deformation and overriding plate velocity Reference frame R 95% confidence interval, R (d.f. = 242) 95% confidence interval, R (d.f. = 7) b 95% confidence interval, b (d.f. = 242) 95% confidence interval, b (d.f. = 7) Geological OPD and OP G&J1986 Quantitative to to to to 0.10 Strain class to to to to 0.24 Spearman rank to to to to 0.24 A&G1991 Quantitative to to to to 0.03 Strain class to to to to 0.09 Spearman rank to to to to 0.07 G&G2002 Quantitative to to to to 0.21 Strain class to to to to 0.59 Spearman rank to to to to 0.24 H2003 Quantitative to to to to 0.15 Strain class to to to to 0.40 Spearman rank to to to to 0.31 O2005 Quantitative to to to to 0.08 Strain class to to to to 0.24 Spearman rank to to to to 0.21 W2006 Quantitative to to to to 0.13 Strain class to to to to 0.39 Spearman rank to to to to 0.27 Geodetic OPD and OP G&G2002 Quantitative to to to to 0.21 Strain class to to to to 0.61 Spearman rank to to to to 0.25 H2003 Quantitative to to to to 0.15 Strain class to to to to 0.42 Spearman rank to to to to 0.32 K2003 Quantitative to to to to 0.02 Strain class to to to to 0.10 Spearman rank to to to to 0.06 O2005 Quantitative to to to to 0.08 Strain class to to to to 0.26 Spearman rank to to to to 0.22 W2006 Quantitative to to to to 0.13 Strain class to to to to 0.39 Spearman rank to to to to 0.28 Correlation coefficients (R) and slopes (b) for overriding plate deformation-overriding plate velocity regression lines as calculated in 11 different global reference frame models. The 95% confidence intervals have been plotted for R using Fisher s z and for b using Student s t. For the 95% confidence limits an upper limit for the number of independent data (244, i.e. number of trench segments, so degrees of freedom d.f. = 242) and a lower limit (9, i.e. number of overriding plates, so d.f. = 7) were used. For each reference frame model, a quantitative correlation analysis was performed (quantitative, using OPD and OP ), a semi-quantitative analysis was performed (strain class, using the strain classification and OP ), and a Spearman rank correlation analysis was performed (Spearman rank, using ranked OPD and ranked OP ). Six models use a geological/geophysical relative plate motion model (e.g. DeMets et al., 1994) for OP and mostly geologically derived OPD rates (15 out of 28). Five models use a geodetic relative plate motion model (i.e. Kreemer et al., 2003)for OP and OPD values that are nearly all geodetically determined (24 out of 28). Reference frames: A&G1991: Argus and Gordon (1991); G&G2002: Gripp and Gordon (2002); G&J1986: Gordon and Jurdy (1986); H2003: Hamilton (2003); K2003: Kreemer et al. (2003); O2005: O Neill et al. (2005); W2006: Wessel et al. (2006).

10 82 W.P. Schellart / Physics of the Earth and Planetary Interiors 170 (2008) In Fig. 3, the data are plotted for the same five global reference frames as plotted in Fig. 2. The data show a positive correlation in all the reference frames, i.e. an increase in trench retreat velocity corresponds to a more extensional strain pattern. The correlation coefficients for this semi-quantitative approach are systematically lower than for the quantitative approach. For 9 out of 11 models, R = and a = (Table 1). Only in the Pacific hotspot reference frame from Gripp and Gordon (2002) is the correlation coefficient negligible (R = 0.03 and 0.01), while the best-fit line is nearly flat (a = 0.06 and 0.03) Quantitative approach: OP and OPD In Fig. 4 OP is plotted against OPD in three different global reference frames. Fig. 4A shows a plot for the Indo-Atlantic hotspot reference frame, showing a weak negative correlation (R = 0.25), where trenchward overriding plate motion corresponds to overriding plate shortening. Overriding plate shortening occurs for OP = 3.9 to5.5 cm/year, while overriding plate extension occurs for OP = 5.3 to6.0 cm/year. Similar weak negative correlations are found in other global reference frames Fig. 5. Diagrams illustrating the trench-perpendicular overriding plate velocity ( OP ) plotted against overriding plate deformation as classified into one of seven strain classes for all mature subduction zones on Earth. Each of the subduction zones has been segmented into 200 km segments (244 in total). Velocities were calculated in different global reference frames, with (A) the Indo-Atlantic hotspot reference frame from O Neill et al. (2005) combined with the relative plate motion model from DeMets et al. (1994); (B) the no-net-rotation reference frame from Argus and Gordon (1991); (C) the Pacific hotspot reference frame from Gripp and Gordon (2002) that makes use of the relative plate motion model from DeMets et al. (1994). Strain classification scheme (based on Jarrard, 1986): 3 = highly compressional; 2 = intermediately compressional; 1 = mildly compressional; 0 = neutral; 1 = mildly extensional; 2 = moderately to highly extensional; 3 = spreading.

11 W.P. Schellart / Physics of the Earth and Planetary Interiors 170 (2008) with R = 0.29 to 0.17 (Fig. 4C and E, and Table 2). The values for the slope of the regression line (b) are all within the range of 0.42 to 0.15 (Table 2). The frequency plots for OP in Fig. 4B, D and F show different distributions from skewed (Fig. 4B and F) to roughly normal (Fig. 4D). In the Indo-Atlantic hotspot reference frame 71.3% has OP > 0 (trenchward motion) (Fig. 4B), while it is 65.2% in the no-net-rotation reference frame (Fig. 4D), and only 51.2% in the Pacific hotspot reference frame (Fig. 4F). These differences are primarily related to the large global westward drift of the lithosphere in the Pacific hotspot reference frame of Gripp and Gordon (2002) compared to minor westward drift in the Indo-Atlantic hotspot reference frame of O Neill et al. (2005) and no drift in the no-netrotation reference frame of Argus and Gordon (1991) Semi-quantitative approach: OP and strain classes In Fig. 5, OP is plotted against the strain classes for the same three global reference frames as plotted in Fig. 4. The data show a negative correlation in all the reference frames where trenchward overriding plate motion corresponds to shortening. The correlation coefficients for this semi-quantitative approach are systematically slightly more significant ( 0.42 to 0.22) compared to the quantitative approach ( 0.29 to 0.17) (Table 2) Statistical significance Statistical tests have been conducted to investigate if the correlations are statistically significant at 95% confidence level. These tests have all been conducted using the raw data ( OPD, T and OP ) and under the assumption that the data have a normal (Gaussian) distribution. From the frequency plots for T in Fig. 2 from Schellart et al. (2008) it is indeed found that the data have a distribution that is approximately normal. The frequency plot for OPD in Fig. 2F and the frequency plots for OP in Fig. 4B, D and F show a distribution that is roughly normal, although some datasets are skewed. Two tests were conducted: first, 95% confidence intervals were calculated for R using Fisher s z. Second, 95% confidence intervals were calculated for a and b using the Student s t-test. The two tests have also been conducted for the semiquantitative analysis, again under the assumption that the data have a normal distribution. Note however, that the frequency plot for the strain classes in Fig. 3F shows that the data have a distribution that is not normal. The frequency plots for both OPD and T show a small outlier on the right-hand side, implying a minor deviation from normality, while the frequency plots for OP show in some cases a skewed distribution. In addition, the frequency plot for the strain classes shows significant deviation from normality. Therefore, additional regression lines and correlation coefficients were calculated using the Spearman rank correlation test, which does not require a normal distribution. For this Spearman test the 95% confidence intervals were also calculated for R, a, and b. The number of data (n) as plotted in the scatter plots in Figs. 2 5 is 244. The number of independent data might be less, because many subduction zone segments are connected to one another along individual subduction zones. The number of independent data needs to be established to be able to determine the degrees of freedom (d.f.), which are required to establish the confidence limits of R, a and b. The upper limit of independent data for T and OP, which will provide the narrowest (least certain) confidence limits, is the total number of data (244). The lower limit of independent data for T, which will provide the widest (most certain) confidence limits, is likely the number of subduction zones, which is 24. The lower limit of independent data for OP is likely the number of overriding plates bordering the 24 subduction zones, which is 9. These upper-limit and lower-limit values were used to determine the least robust and most robust 95% confidence limits as shown in Tables 1 and 2. The results of all the 95% confidence limit calculations are plotted in Tables 1 and 2 for all the global reference frame models. For the correlation between T and OPD in Table 1 the narrowest 95% confidence intervals (d.f. = 242) for both R and slope a are in all (11 out of 11) reference frame models significantly above 0. For the widest 95% confidence intervals (d.f. = 22) all reference frame models have a intervals significantly above 0 and 9 out of 11 reference frame models have R intervals significantly above 0. The only exception here is the Pacific hotspot reference frame from Gripp and Gordon (2002). Thus, ignoring the exception, it can be said that at 95% confidence level T and OPD have a positive correlation, where trench retreat corresponds to extension. For the semi-quantitative analysis and the Spearman rank analysis, all reference frame models except the Pacific hotspot model from Gripp and Gordon (2002) have R and a intervals significantly above 0 for the narrowest 95% confidence interval. For the widest 95% confidence interval, however, all except the no-net-rotation reference frame from Argus and Gordon (1991) have R intervals that go significantly below 0. For the correlation between OP and OPD in Table 2 the narrowest 95% confidence intervals (d.f. = 242) for both R and slope b are in all (11 out of 11) reference frame models below 0. For the widest 95% confidence intervals (d.f. = 7), however, all reference frame models have R intervals that go significantly above zero. Thus, it cannot be said that at 95% confidence level OP and OPD have a negative correlation; it cannot be said that at 95% confidence level trenchward overriding plate motion corresponds to shortening and vice versa. For the semi-quantitative analysis and the Spearman rank analysis, all reference frame models have R and b intervals significantly below zero for the narrowest 95% confidence interval. For the widest 95% confidence interval, however, all have R intervals that go significantly above 0. In summary, for the quantitative approach a clear positive correlation is established between T and OPD using the most strict 95% confidence level test. Thus, the positive correlations as shown in the scatter plots in Fig. 2A D, with trench retreat corresponding to extension and trench advance or slow trench motion corresponding to shortening, are statistically significant at 95% confidence level. Correlation tests for OP and OPD fail to meet the most strict 95% confidence level test, and thus the weak negative correlations that are apparent in the scatter plots in Fig. 4 are statistically not significant at 95% confidence level Dependence on subduction zone segmentation In this study 24 subduction zones were segmented into a total of 244 trench-parallel 200-km segments. To test the influence of this segmentation on the statistical findings, scatter plots have also been constructed for larger, geologically defined, subduction zone segments (43 in total). Short subduction zones (e.g. Scotia) are represented by one data-point. Longer subduction zones are segmented into two up to maximally six segments, where segmentation is mainly based on arc cusps. The segmentation is based on the subduction zone subdivision as shown in Table A1 in the Appendix with the only exception that the Chile segment was subdivided into three segments (north, centre and south). This results in a total of 43 subduction segments, for which the mean T, OPD and OP were calculated. In Fig. 6 scatter plots for T and OPD, and for OP and OPD are shown for three global reference frames: Indo-Atlantic

12 84 W.P. Schellart / Physics of the Earth and Planetary Interiors 170 (2008) Fig. 6. Cross-plots for T and OPD (A, C, and E) and for OP and OPD (B, D, and F) for all mature subduction zones on Earth. Subduction zone segments have been geologically defined (total of 43 segments). Short subduction zones (e.g. Scotia) are represented by one data-point, while longer subduction zones are segmented into two to maximally six segments, where segmentation is mainly based on arc cusps. Velocities were calculated in different global reference frames and were averaged for each segment, with (A and B) the Indo-Atlantic hotspot reference frame from O Neill et al. (2005) combined with the relative plate motion model from DeMets et al. (1994); (C and D) the no-net-rotation reference frame from Argus and Gordon (1991); (E and F) the Pacific hotspot reference frame from Gripp and Gordon (2002) that makes use of the relative plate motion model from DeMets et al. (1994). Numbers in between brackets behind subduction zone names indicate number of data points. hotspot (O Neill et al., 2005), no-net-rotation (Argus and Gordon, 1991) and Pacific hotspot (Gripp and Gordon, 2002). From comparison of the best-fit lines and correlation coefficients in Fig. 6 with those of the same reference frames in Figs. 2 and 4 it is clear that results are numerically very similar: maximum variation in R is only 0.05, maximum variation in slope a is only 0.04, and maximum variation in slope b is only This implies that the statistical findings are robust and are not significantly dependent on the choice of subduction zone segmentation.

13 W.P. Schellart / Physics of the Earth and Planetary Interiors 170 (2008) Discussion 5.1. Discussion of data and correlation coefficients It is clear from Figs. 2 6 that the correlation coefficients are dependent on the reference frame model. This is primarily because the plate velocities are different in the different global reference frames, and therefore the trench velocities also differ (see Eq. (1)). The influence of relative plate motion model and overriding plate deformation model (i.e. geological or geodetic) is minor (see Tables 1 and 2). The variation in plate velocities in different global reference frames is primarily a result of the degree of west-directed net rotation of the lithosphere with respect to the underlying mantle. The net rotation varies from zero (nonet-rotation reference frames) to minor (Indo-Atlantic hotspot reference frame) to intermediate (Pacific hotspot reference frame from Wessel et al., 2006) to major (Pacific hotspot reference frame from Gripp and Gordon, 2002). From the different reference frames with different rates of net rotation it appears that the Indo-Atlantic hotspot reference frame with minor net rotation best complies with a number of predictions from geodynamic models of subduction and plate motion, such as trenchward subducting plate motion, predominance of trench retreat, small total upper mantle toroidal volume flux and slow trench migration in the centre of wide subduction zones (Schellart et al., 2008). The Pacific hotspot reference frame from Gripp and Gordon (2002) with large net rotation is least compliant with the above-mentioned predictions, suggesting it is unfit to serve as a global reference frame. In addition, the large net global westward rotation of the lithosphere in this Pacific hotspot reference frame and the mantle shearing that is induced by such rotation are at odds with observations from azimuthal seismic anisotropy (Becker, 2008). Modelling indicates that in order to fit predicted anisotropy with observed anisotropy the net rotation should be less than 50% of the net rotation as implied by the Gripp and Gordon Pacific hotspot reference frame (Becker, 2008). The correlation coefficients between T and overriding plate deformation are systematically significantly lower for the semiquantitative approach than for the quantitative approach (see Table 1). This is due to the linear scaling of the strain classes and the classification of the trench segments into only seven strain classes. This has a large effect on the data points, in particular for those in the extensional domain. For example, data for the Tonga subduction zone with trench-perpendicular backarc spreading up to 15 cm/year are classified in the same group as data for the Mariana subduction zone with trench-perpendicular backarc spreading up to only 3 cm/year. The data plotted in Figs. 2 and 3 contain a lot of scatter. Nonetheless, correlation coefficients are consistently positive and statistically significantly different from 0 at 95% confidence level for all quantitative plots except the Pacific hotspot reference frame from Gripp and Gordon (2002) (see Fig. 2 and Table 1). This is also true for all the semi-quantitative analyses and all the Spearman rank correlation analyses using the least strict 95% confidence level test, except those in the Gripp and Gordon reference frame (see Fig. 3 and Table 1). It might be difficult to get an appreciation of how good the correlation coefficients in Fig. 2 actually are without a proper comparison. Schellart (2008b) tested numerous physical parameters that have been proposed to affect the overriding plate deformation rate, such as slab age, overriding plate velocity, convergence velocity, subducting plate velocity and slab dip angle. For 10 of these parameters the correlation coefficients are significantly less, with R Thus, one can say at least that correlation coefficients of R = as shown in Figs. 2A C stand out significantly. In simple linear regression, the coefficient of determination, R 2,gives the ratio of variance explained by the regression relative to the total variance. The largest correlation coefficient obtained for the parameters OPD and T is R = 0.68, and so R This indicates that the best-fit regression line can explain slightly less than half (46%) of the variance, while slightly more than half of the variance (54%) remains unexplained. The most significant correlation coefficient obtained for the parameters OPD and OP plotted in Fig. 4 is R = 0.29, and so R This indicates that the best-fit regression line can explain only a negligible percentage (9%) of the variance. For the other physical parameters reported in Schellart (2008b) with R 0.39, then R Comparison between data and model predictions The results provide support for the slab-driven model, in which trench migration and subduction hinge migration are primarily driven by lateral migration of the slab through the mantle (e.g. Elsasser, 1971). The results do not support the overriding-platedriven model (e.g. Jarrard, 1986; Heuret and Lallemand, 2005; Heuret et al., 2007) where trench migration is thought to be passive and primarily driven by overriding plate motion. Indeed, none of the correlation coefficients between OPD and T show 1 R <0, and none of the slopes show a < 0. Also, all the 95% confidence intervals of R and a are significantly above 0 for the quantitative approach, except in the Pacific hotspot reference frame of Gripp and Gordon (2002). Furthermore, the correlation coefficients and slopes for OPD and T are more significant (R = , a = ) than for OPD and OP (R = 0.29 to 0.17, b = 0.42 to 0.15). However, the slab-driven model is not foolproof, as a minority of slowly retreating trenches undergoes overriding plate shortening and a minority of advancing trenches undergoes overriding plate extension (Fig. 2). It also becomes clear from comparing Fig. 1D and E with Figs. 2 and 4: The most significant correlation that is found for OPD and T is R = 0.68 (rather than R = 1), the steepest slope a = 0.73 (rather than a = 1.00), the least significant correlation between OPD and OP is R = 0.17 (rather than R = 0), and the gentlest slope b = 0.15 (rather than b = 0). But note again that the overriding-plate-driven model is very far from foolproof as becomes clear from comparing Fig. 1H and I with Figs. 2 and 4:For OPD and T the lowest correlation is R = 0.33 (rather than R = 1), the gentlest slope a = 0.45 (rather than a < 0), the most significant correlation for OPD and OP is R = 0.29 (rather than R = 1) and the steepest slope b = 0.42 (rather than b < 1.00). For a few subduction zones the overriding-plate-driven model might (partly) apply. One example is the Izu-Bonin Mariana subduction zone, which is advancing westward in a variety of global reference frames (e.g. Heuret and Lallemand, 2005; Schellart et al., 2007, 2008), and experiences very slow extension in the Izu-Bonin arc and backarc spreading in the Mariana Trough. Segments of the South American subduction zone could be potential candidates, with significant overriding plate shortening, but the direction of trench migration and overriding plate motion are very much dependent on the adopted global reference frame (Schellart et al., 2008) (Figs. 2 and 4). The two above mentioned examples are wide subduction zones, and some role for the overriding plate in determining overriding plate deformation and trench migration could be expected in these regions, as dynamic models of subduction show that the central parts of wide subduction zones (W > 4000 km) migrate very slowly, with T = 2 to 1 cm/year (Schellart et al., 2007). Because the central segments of these wide subduction zones resist rapid migration due to large mantle resistance to toroidal return flow around the lateral slab edges, one would expect overriding plate motion to play a more important role in determining overriding