Geodynamics of Trench Advance: Insights from a Philippine-Sea-Style Geometry ∗ Hana Cížkováˇ A, , Craig R

Home , Philippine Sea, Philippine Sea Plate, Philippine Trench, Slab pull

Earth and Planetary Science Letters 430 (2015) 408–415

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Earth and Planetary Science Letters

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Geodynamics of trench advance: Insights from a Philippine-Sea-style geometry ∗ Hana Cížkováˇ a, , Craig R. Bina b a Charles University Prague, Faculty of Mathematics and Physics, V Holešoviˇckách 2, 18000 Praha 8, Czech Republic b Northwestern University, Department of Earth and Planetary Sciences, 2145 Sheridan Road, Evanston, IL 60208, USA a r t i c l e i n f o a b s t r a c t

Article history: For terrestrial parameter sets, trench retreat is found to be nearly ubiquitous and trench advance quite Received 20 May 2015 rare, largely due to rheological and ridge-push effects. Recently updated analyses of global plate motions Received in revised form 29 June 2015 indicate that significant trench advance is also rare on Earth, being largely restricted to the Marianas–Izu– Accepted 2 July 2015 Bonin arc. Thus, we explore conditions necessary for terrestrial trench advance through dynamical models Available online xxxx involving the unusual geometry of the Philippine Sea region. In this subduction system, a slab-pull force Editor: J. Brodholt from distal subduction is transmitted to the overriding plate at the Pacific trench. Our 2D modeling Keywords: demonstrates that trench advance can occur for terrestrial rheologies in such special geometries. We subduction observe persistent trench advance punctuated by two episodes of back-arc extension. Characteristic transition zone features of the model, such as time interval between extensional episodes, high back-arc heat flow, and trench migration stress state of Philippine plate correspond to processes recorded in the region. slab buckling © 2015 Elsevier B.V. All rights reserved. Philippine Sea Marianas–Izu–Bonin

1. Introduction the hypothesis that persistent trench advance can arise in such a scenario. Among the results of our recent study (Cížkováˇ and Bina, In seeking a suitable geometry for trench advance on Earth, it 2013), of the effects on slab stagnation and rollback of mantle and is important to note that estimates of trench motions vary sig- subduction-interface rheology and phase-transition buoyancy, was nificantly with choice of reference frame (Funicello et al., 2008). the striking observation that exploration of an extensive parameter Using a reference frame optimized to minimize trench advance, space yielded only trench retreat. Even in cases of minimal trench a recent analysis (Schellart et al., 2008)nonetheless suggested retreat, involving high crustal viscosity and hence strong slab cou- the occurrence of trench advance at ∼25% of global subduction- pling, no persistent trench advance was observed. In retrospect, zone segments. However, a new analysis of global plate-motion perhaps this should not be overly surprising. Previous models have constraints (Mathews et al., 2013), combining corrections to the suggested that, while a stiff overriding plate can moderate trench MORVEL model (DeMets et al., 2010) and statistical error prop- retreat (Yamato et al., 2009; Garel et al., 2014), parameters favoring agation with a reference frame based on SKS seismic anisotropy trench-advance regimes typically fall at the extremes of or out- (Zheng et al., 2014), indicates that most previous indications of side the realm of Earth-like conditions – requiring, for example, terrestrial trench advance actually correspond to stationary or re- very strong slabs (Billen, 2010; Stegman et al., 2010)or a very treating motion. Statistically significant trench advance is found stiff lower mantle (Ribe, 2010), perhaps combined with extremely to persist in only two regions: weakly in southern Kermadec and strong slab coupling (Baitsch-Ghirardello et al., 2012). Any contri- strongly in Marianas–Izu–Bonin. Given the relatively shallow ex- bution from slab elasticity also should favor retreat over advance tent of subducting slab beneath southern Kermadec (Zhou, 1990; (Fourel et al., 2014). Indeed, it has been suggested (Chertova et al., Chen et al., 2004), this region perhaps reflects transient advance 2012) that a far-field lithospheric “pull” stress acting on the over- associated with early subduction prior to the slab encountering re- riding plate, countering the ridge-push force that enhances trench sistance near 660 km depth (Yamato et al., 2009). We thus choose retreat, may be necessary to generate meaningful trench advance. to focus upon the Marianas–Izu–Bonin region, where persistent Here we introduce a slab-pull force on the overriding plate to test trench advance is consistent with early analysis of Marianas advance (Carlson and Melia, 1984)and with the observation that Marianas–Izu–Bonin advances in all reference frames (Funicello * Corresponding author. et al., 2008). We pursue the suggestion (Mathews et al., 2013) E-mail address: [email protected] (H. Cížková).ˇ that the unique situation – in which the overriding Philippine Sea http://dx.doi.org/10.1016/j.epsl.2015.07.004 0012-821X/© 2015 Elsevier B.V. All rights reserved. H. Cížková,ˇ C.R. Bina / Earth and Planetary Science Letters 430 (2015) 408–415 409 plate, beneath which the Pacific plate subducts along Marianas– Izu–Bonin, is itself subducting to the west – may account for the strong trench advance in this area, as this geometry imparts just such a slab-pull force to the overriding plate as hypothesized above.

2. Model and methods

2.1. Model geometry

The Philippine Sea is a complicated three-dimensional region, Fig. 1. Schematic force-balance diagrams for (a) a two-plate system in which one exhibiting complex bathymetry and plate shape (Yamazaki et al., plate subducts beneath an overriding plate and (b) a three-plate system in which 2010) and a complex patchwork of seafloor ages (Müller et al., one plate subducts beneath an overriding plate which is itself subducting beneath 2008). The bounding subduction zones exhibit significant north– an adjacent overriding plate. In the two-plate system, ridge-push exerted by the south variation in slab morphology and stagnation behavior. In overriding plate inhibits trench advance. In the three-plate system, slab-pull exerted by the central plate may enhance advance of the leftmost trench. Izu–Bonin–Marianas, gently dipping slab stagnation in the north gives way to nearly vertical slab penetration in the south (Stern et al., 2003). For both the eastern and western subduction zones, north–south variations in dip angle can be observed in Wadati– Benioff zone seismicity (Chen et al., 2004; Smoczyk et al., 2013). Furthermore, seismicity exhibits a backwards bending of the deep slab (i.e., a change of sign in the dip angle at depth) in the southern Izu–Bonin and Marianas (zones Mar and Izu3 in Chen et al., 2004; profile F in Smoczyk et al., 2013), in apparent concord with a proposed relationship between slab curvature and advance/retreat mode (Bellahsen et al., 2005; Funicello et al., 2008). Moreover, such ◦ patterns can also be seen in seismic tomography (latitude 30 and ◦ 25 sections of Huang and Zhao, 2006; S. Bonin and N. Mariana sections of Fukao and Obayashi, 2013). Such spatial variability is further complicated by temporal variation, in that the age of onset of subduction along the Pacific trenches is estimated at ∼50 Ma (Cosca et al., 1998; Stern et al., 2003) while that along the Philip- pine trench may be much younger at ∼10 Ma (Ozawa et al., 2004). Overall, subduction exerts strong slab pull (Handayani, 2004)im- posing extension across the Philippine Sea plate, as evidenced by both relict and active back-arc rifts and related features. For example, Stern et al. (2003) report recurring episodes of extension at 20–30 Myr intervals. Of course, we cannot hope to capture such complexity in a simplified two-dimensional model, but here we abstract a repre- sentative geometry and explore the first-order dynamical conse- Fig. 2. Model configuration (a) showing initial conditions, including full model space, quences. Relative to our previous reference model (Cížkováˇ and focused study area (gray rectangle), plates (blue), crust (red), selected tracers (yel- Bina, 2013), we insert a third plate, yielding an overriding plate low), and transition-zone boundaries (dashed). Starting configurations (b) after which is itself subducting, thereby changing the conceptual force- short initial runs with prescribed surface velocities to attain three initial temper- balance from one of ridge-push compression at the primary sub- ature distributions (A, B, C) commensurate with differential times of subduction duction interface to one of slab-pull extension (Fig. 1). (While the onset. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) central overriding plate is clearly mobile, we can explore cases in which the third, marginal, overriding plate is either fixed or mobile.) Although these plates are 2D idealizations, we refer to them pine Sea plate and its margins as viewed from the north looking as the Philippine plate and Pacific plate for convenience. Our 2D southward (Fig. 2a). rectangular model domain is 10 000 km wide and stretches from At the top of both subducting plates a weak crustal layer of the surface to 2000 km deep. In the upper left and upper right 15-km thickness is prescribed. The low viscosity ηcrust of this layer corners, spreading ridges are positioned. (Both ridges are offset by facilitates decoupling of the subducting and overriding plates. This ∼200 km from the corners to avoid complications at the vertical crust is tracked using particle tracers, and it is not associated with boundaries.) any compositional density contrast. (Rather than try to capture the Initial temperature distribution follows a halfspace cooling full complexity of a chemically layered crust, we abstract the es- model in the uppermost part of the domain, with lithospheric age sential property controlling coupling and represent it simply as increasing from the left ridge to 140 Myr at the Pacific trench, a layer of reduced viscosity of sufficient thickness for numerical from the right ridge to 40 Myr at the Philippine trench, and within resolution.) At a depth of 200 km, where the decoupling effect the middle plate from 30 Myr at the Pacific trench to 40 Myr at is no longer needed, the crustal layer is replaced by mantle ma- the Philippine trench. Below the plates the temperature follows terial for numerical convenience. As we previously demonstrated an adiabatic profile with a potential temperature of 1573 K. We that higher crustal viscosities minimize trench retreat, we choose set the initial inter-arc distance (i.e., the central plate width) at our initial crustal viscosity to be at the high end of the values ex- ∼1500 km, as a median value of the range seen in the Philippine plored previously, at 1021 Pa s. In other respects the model follows Sea. Our model thus represents a simplified view of the Philip- the reference case from our prior study (Cížkováˇ and Bina, 2013). 410 H. Cížková,ˇ C.R. Bina / Earth and Planetary Science Letters 430 (2015) 408–415 + In order to attain an initial temperature distribution commen- 1 (1−n)/n Edisl pVdisl ηdisl = e exp , (3) surate with differential times of subduction onset, we first execute 1 nRT A n a short run with constant velocities prescribed at the tops of the disl −1/n − modeled Pacific and Philippine plates, along with an imposed roll- = y 1/ny 1 ηy τye y e . (4) back velocity on the Pacific plate to permit slab stagnation. When the tip of the Philippine slab reaches a depth of 400 km, this Upper mantle activation parameters are based on Hirth and Kohlst- kinematic boundary condition is switched off, and the tempera- edt (2003). As dislocation creep is generally believed to play a ture distribution with the developed slab positions is then used minor role in the lower mantle, we apply only diffusion creep in as an initial condition (Fig. 2b). Three initial model situations are the lower mantle, with activation parameters based on slab sink- ˇ assumed, in all of which the Pacific plate velocity is 5cm/yr: ing speed analysis (Cížková et al., 2012). For meanings of symbols model A with Philippine plate velocity 1cm/yr, rollback velocity and parameter values, see Table 1. × 4cm/yr and initial run executed for 19 Ma; model B with Philip- Our assumed thermal expansivity varies with depth from 3 −5 −1 × −5 −1 pine plate velocity 3cm/yr, rollback velocity 5.8 cm/yr executed for 10 K at the surface to 1.2 10 K at a depth of 2000 km 9.5 Ma; and model C with Philippine plate velocity 1cm/yr and (Chopelas and Boehler, 1992; Katsura et al., 2009). Thermal diffu- rollback 5cm/yr executed for 19 Myr. These three end-members sivity is held constant. Major mantle phase transitions at 410-km were chosen to cover the range of plausible early behavior of slab. and 660-km depths are included using harmonic parameterization ˇ The plate and rollback velocities were chosen to produce different of a phase function (Cížková et al., 2007)with respective Clapey- = =− geometries and extent of Pacific plate near the base of transition ron slopes γ410 2MPa/K and γ660 2.5MPa/K. zone when the Philippine plate tip reaches 410-km depth. The evolution of both subducting slabs and migration of their 3. Results trenches is demonstrated not only in snapshots of temperature and viscosity distribution but also by evaluating plate and trench 3.1. Subduction in three-plate system velocities through the use of monitor tracers. Plate velocities of the Pacific and Philippine plates are evaluated using tracers num- The evolution of the subducting system in model A is shown in bered 1 and 2 (see yellow dots in Fig. 2a), respectively. Trench Fig. 3 (cf. also Supplementary video). Here, twelve snapshots of the ∼ velocity for the Philippine plate can be tracked using tracer num- temperature field, illustrating 70 Myr of evolution, are shown in ber 3 located in the overriding plate hinge, as the overriding plate a subregion of the model domain (cf. gray rectangle in Fig. 2a). At is following the motion of the Philippine plate. A similar approach, the beginning, the Pacific plate has already reached the bottom of however, cannot be used in case of the Pacific plate, because the the transition zone, and its tip is lying flat on the 660-km bound- motion of the hinge of the Philippine plate can be complicated by ary; the Philippine plate is just approaching the 410-km boundary. extension at the Pacific trench. Therefore, we use a chain of tracers White squares mark the initial positions of both trenches. Let us located at the base of the Pacific plate crust to locate the point at first follow the motion of the Philippine plate. The plate is acceler- which crust subducts below 25 km depth, and that point is then ated by an exothermic phase transition at 410 km and reaches the ∼ taken to be the position of the Pacific trench. bottom of the transition zone in 10 Myr as its trench rolls back. When its tip arrives at the 660-km interface, the plate is decelerat- ing, and the slab tip lies flat at the boundary. As the slab continues 2.2. Numerical methods and model parameters to subduct, a first buckle starts to form at ∼15 Myr. As a consequence, Philippine plate rollback ceases, and the plate advances Subduction dynamics is described by a set of equations includ- during formation of the buckle. At ∼36 Myr, buckling is largely ing continuity, momentum, thermal, constitutive, and state equa- complete, and the buckled part of the Philippine slab is very slowly tions. We use the extended Boussinesq approximation of the gov- sinking vertically into the lower mantle while the shallow part erning equations without internal heating. The system of equa- resumes trench rollback. At ∼43 Myr, the slab begins to develop tions is solved by the finite-element method using the package a second buckle. This process continues until ∼75 Myr, at which SEPRAN (Segal and Praagman, 2005). Free-slip boundary conditions point subduction of the Philippine plate ceases because the mod- are prescribed on all boundaries (except for the short initial run as el’s initially prescribed crustal layer has been totally consumed, mentioned above). Thermal boundary conditions are of constant leading to a locked-slab situation. At ∼85 Myr, the Philippine slab temperature at the top and bottom boundaries, while zero heat detaches. flux is prescribed at vertical boundaries. Numerical resolution of Now let us examine Pacific plate behavior. The initial morphol- the model varies across the model domain: the finest resolution of ogy of this old and heavy plate – low dip angle at shallow depths 4km is used in the uppermost part, 8km in the transition zone, – would be expected to lead to a rollback episode if the plate was and a coarse resolution of 60 km is sufficient in the lowermost subducting under an overriding plate of the type shown in Fig. 1a. mantle. Here, however, the additional pull of the rapidly subducting Philip- We use a composite rheological model (van den Berg et al., pine plate causes immediate trench advance, while the velocity of 1993) that combines diffusion creep, dislocation creep, and a the Pacific plate increases. The portion of the slab initially exhibit- power-law stress-limiter (van Hunen et al., 2002). The effective ing a shallow dip angle across the upper mantle and transition viscosity ηeff is calculated from the viscosities of individual creep zone now bends toward the vertical, while the flat-lying part at mechanisms assuming unique stress: the 660-km boundary is extending. At ∼10 Myr, pull from the Philippine plate is decreasing, as this plate slows due to resistance −1 1 1 1 encountered at the 660-km boundary. The advance of the Pacific = + + (1) ηeff . plate continues, however, as the slab is just forming its first buckle. ηdiff ηdisl ηy Such buckling favors trench advance – as the slab dip angle is at Here ηdiff , ηdisl, and ηy are viscosities of diffusion creep, disloca- that moment already slightly beyond vertical and the base of the tion creep, and stress-limiter respectively: slab is mechanically coupled to the lower mantle at 660-km depth, the trench is forced to move forward. This mechanism reduces roll- 1 Ediff + pVdiff back (Cížkováˇ and Bina, 2013) and eventually generates advance as η = exp , (2) diff observed here. After ∼20 Myr, while the Philippine plate velocity Adiff RT H. Cížková,ˇ C.R. Bina / Earth and Planetary Science Letters 430 (2015) 408–415 411

Table 1 Symbols and model parameters. Symbol Meaning Value Units Upper mantle and transition zone rheology a −9 −1 −1 Adiff Pre-exponential parameter of diffusion creep 1 × 10 Pa s a −17 −n −1 Adisl Pre-exponential parameter of dislocation creep 3.1 × 10 Pa s a 5 −1 Ediff Activation energy of diffusion creep 3.35 × 10 Jmol a 5 −1 Edisl Activation energy of dislocation creep 4.8 × 10 Jmol a −6 3 −1 V diff Activation volume of diffusion creep 4.5 × 10 m mol a −6 3 −1 V disl Activation volume of dislocation creep 11 × 10 m mol n Power-lawexponent 3.5 - 21 ηcrust Viscosity of crust 10 Pa s 8 τy Yield stress 5 × 10 Pa −15 −1 e y Reference strain rate 1 × 10 s ny Stress limiter exponent 10 – p Hydrostatic pressure – Pa − − R Gas constant 8.314 JK 1 mol 1 T Temperature – K − e Second invariant of the strain rate – s 1

Lower mantle rheology −16 −1 −1 Adiff Pre-exponential parameter of diffusion creep 1.3 × 10 Pa s b 5 −1 Ediff Activation energy of diffusion creep 2 × 10 Jmol b −6 3 −1 V diff Activation volume of diffusion creep 1.1 × 10 m mol

Other model parameters − − κ Diffusivity 10 6 m2 s 1 − g Gravitational acceleration 9.8 m s 2 −3 ρ0 Reference density 3416 kg m −1 −1 cp Specific heat 1250 J kg K −5 −1 α0 Surface thermal expansivity 3 × 10 K c 6 −1 γ410 Clapeyron slope 410 km phase transition 1–2 × 10 Pa K c 6 −1 γ660 Clapeyron slope 660 km phase transition −2.5 × 10 Pa K d −3 δρ410 Density contrast 410 km phase transition 273 kg m d −3 δρ660 Density contrast 660 km phase transition 341 kg m a Parameters of wet olivine after Hirth and Kohlstedt (2003). b Lower mantle activation parameters of family A models by Cížkováˇ et al. (2012). c Bina and Helffrich (1994). d Steinbach and Yuen (1995). increases during formation of its first buckle, we observe extension a buckle, and consequently its trench advances (positive trench at the Pacific trench as a response to increased pull from Philippine velocity, dashed red curve). Its pull becomes so strong as to in- plate. Although such extension should weaken coupling between duce extension at ∼20 Myr. Weakened, extended lithosphere is the plates and thus perhaps inhibit Pacific plate advance, such ad- not strong enough to transmit the pull; thus, Pacific trench advance still continues, partly as a consequence of the Pacific plate vance decreases despite acceleration of the Philippine plate while buckle that is just forming in the transition zone. The extended its buckle is forming. At ∼34 Myr, we observe maximal extension, lithosphere, however, cools and strengthens relatively quickly, and as Philippine trench advance reaches its maximum while Pacific the trench-advance period for the Pacific plate thus continues un- trench advance is at a minimum. After ∼30 Myr, when the first til ∼65 Myr. At that time, a second extension in the Philippine buckle is formed, advance of the Philippine plate slows, and roll- plate occurs due to extended pull of the Philippine plate during its back eventually resumes at ∼40 Myr. At ∼50 Myr, the Philippine second buckling period. This extension and associated weak ridge plate accelerates while forming a second buckle, resulting in a sec- formation then suppresses transmission of slab pull to the Pacific ond extensional period which culminates during 65–70 Myr. In this trench, and Pacific advance ceases. period, extended lithosphere is again too weak to transmit the pull Plate- and trench-motion relationships are illustrated in more of the Philippine plate, and consequently the Pacific trench rolls detail in Fig. 4a. Persistent Pacific trench advance is clearly visi- back as the Pacific plate forms another buckle. Qualitatively sim- ble: throughout the first 65 Myr, Pacific trench velocity is posi- ilar behavior is observed in models B and C, with differences in tive (dashed blue line). At the beginning of model evolution, the initial setup yielding varying details of slab deformation, but the Philippine plate has a very small plate velocity and is rolling back Pacific trench always experiences advance. (trench velocity ∼−2cm/yr, dashed red line). It almost imme- The episodes of “extension” noted above can be viewed from a diately passes the 410-km interface and accelerates due to the couple of perspectives. From the point of view of relative velocities, additional negative buoyancy arising from thermal uplift of the the gray regions in Fig. 4 denote episodes of “extension” defined exothermic phase transition (cf. Fig. 4a, solid red line). Conse- according to two measures: a broad measure indicating that the Ph Pa quently, Philippine plate pull generates Pacific trench advance, and Philippine plate is moving away from the Pacific trench (vpl > vtr ), Pacific trench velocity also increases (dashed blue line). Philippine and a narrow measure indicating that the Philippine trench is mov- plate velocity reaches its maximum at ∼10 Myr, and thereafter it ing away from the Pacific trench which results in lateral extension Ph Pa decelerates due to buoyant and viscous resistance at the 660-km of the Philippine plate (vtr > vtr ). However, rather than simply mineralogical and rheological interface. This decreased pull is then tracking tracers, one may also examine the evolution of the instan- reflected in decreasing Pacific trench advance. Pacific plate velocity taneous principal deviatoric stress fields, as shown in Fig. 5. From (blue solid line), however, continues to increase while the sub- this latter perspective, the shallow portion of the Philippine plate ducted Pacific slab is consumed in the transition zone forming a (initially in slight horizontal compression) experiences large hor- vertical buckle. At ∼18 Myr, the Philippine plate starts to form izontal extensional stresses as the subducting portion accelerates 412 H. Cížková,ˇ C.R. Bina / Earth and Planetary Science Letters 430 (2015) 408–415

Fig. 3. Snapshots of temperature fields showing temporal evolution of starting configuration A. White boxes denote initial trench positions; white lines mark position of the major mantle phase transitions. Only part of the model domain is shown (cf. gray rectangle in Fig. 2a). upon encountering the uplifted 410-km phase transition. Subse- ble advance, with two brief extensional periods (of ∼30 Myr quent buckling of subducted Philippine plate induces sufficient slab periodicity) before Philippine plate detachment. Strong crust re- pull to weaken the shallow plate in the “extension” regime, with sults in stable but very slow advance without any extensional a result that resembles fore-arc upwelling of mantle wedge (and episode. Another crucial parameter that affects subduction veloc- consequent high heat flow) in the thermal field. Later, some of the ities, buckling, and trench migration is the effective Clapeyron extension-induced weakening thermally heals just outboard of the slope of 410-km phase transition (Behounkováˇ and Cížková,ˇ 2008; Pacific trench, but overall extension continues and localizes in a Cížkováˇ and Bina, 2013). Models discussed above assume a mod- manner similar in appearance to incipient back-arc rifting in the erate value of γ410 = 2MPa/K. Let us now examine the effect thermal field (with onset of such quasi-rifting occurring earlier for of a lower Clapeyron slope of γ410 = 1MPa/K. Fig. 6 shows one weaker crust). temperature snapshot for higher (6a) and lower (6b) Clapeyron slopes. The model with lower Clapeyron slope also results in Pa- 3.2. Sensitivity to crustal viscosity and Clapeyron slope cific trench advance, but its amplitude is smaller than in the case with higher Clapeyron slope (cf. Fig. 4a, b, blue dashed lines). This As crustal strength is a primary controlling parameter that af- is not surprising, as lower Clapeyron slope results in lower negative fects subduction velocities (Androvicováˇ et al., 2013), we further buoyancy associated with the phase transition and thus in smaller investigated its effects on the regime of our double-subduction pull exerted by the Philippine plate. Overall, Philippine plate be- setup. A lower crustal viscosity (5 · 1020 Pa s) produces higher plate velocities, and the associated larger pull from the Philip- havior is much simpler in this case, as no buckling is observed pine plate generates faster initial trench advance for the Pacific in first 60 Myr. This is clearly visible in Fig. 4b, where Philip- plate. Such weaker crust, however, also facilitates extension in pine plate velocity (solid red curve) first increases due to the extra the Pacific trench region. The extension period thus starts very pull of 410-km phase transition and, after reaching maximum at ∼ early (at less than 10 Myr) and continues without interruption 15 Myr, then decreases due to resistance at the 660-km inter- until the fast Philippine plate is fully subducted and breaks off face. Thereafter, velocity remains small as the plate continues sub- at ∼40 Myr. Higher viscosity crust (5 · 1021 Pa s), on the other ducting while its trench is rolling back (negative Philippine trench hand, results in very small subduction velocities for both plates velocity, dashed red curve). Pacific trench advance essentially fol- (less than 2cm/yr); it is, however, strong enough to prevent ex- lows the trend of Philippine plate velocity, and both of them drop tension at the Pacific trench. In this model, we therefore observe to zero at ∼60 Myr, when the Philippine plate is purely rolling steady but very slow advance of the Pacific trench (∼0.5 cm/yr). back. Shortly after 60 Myr, strain-rate weakening of the Philip- Weak crust thus produces unstable initial advance followed by pine plate at around 410 km depth induces formation of a weak swift extension and detachment. Intermediate crust results in sta- horizontal buckle. Acceleration of the Philippine plate due to this H. Cížková,ˇ C.R. Bina / Earth and Planetary Science Letters 430 (2015) 408–415 413

Fig. 6. Contemporaneous snapshots of temperature ﬁeld for models with 410-km Clapeyron slope of normal (a) value γ410 = 2MPa/Kand low (b) value γ410 = 1MPa/K, illustrating differences in total trench offsets (relative to white boxes) and slab-tip geometry near 660 km depth.

simpler Paciﬁc trench behavior, characterized by an initial period of relatively fast advance followed by a single extensional episode and ﬁnally a short period of rather slow advance.

4. Links with Philippine-Sea region observations

In summary, modeling of subduction dynamics in a Philippine- Sea-style geometry indicates that trench advance can, indeed, occur for terrestrial rheological regimes, but (as suggested previ- Fig. 4. Graphs of evolving plate (solid) and trench (dashed) velocities for Pacific ously) it appears to require a force balance in which a second slab (blue) and Philippine (red) plates for 410-km Clapeyron slope with normal (a) value pulls on the overriding plate. Our 2D modeling of such a three- = = γ410 2MPa/Kand low (b) value γ410 1MPa/K. Grey regions denote episodes of plate geometry yields persistent trench advance, interrupted by “extension” defined according to two measures: broad measure (light gray) indi- Ph Pa episodes of back-arc-like extension. Complex oscillatory behavior cates Philippine plate velocity exceeds Pacific trench velocity (vpl > vtr ); narrow measure (dark gray) indicates Philippine trench velocity exceeds Pacific trench ve- of the system is a direct consequence of buckling, without which Ph Pa locity (vtr > vtr ). (For interpretation of the references to color in this figure legend, switching between different modes of the process would not oc- the reader is referred to the web version of this article.) cur. The time interval between extensional episodes reflects the characteristic period of buckling of the Philippine plate. Some ex- buckling is visible as a rise in plate velocity at ∼65 Myr (Fig. 4b, ploration of the parameter space reveals behavioral dependence solid red curve). Consequently, we observe weak Pacific trench ad- upon the same two petrological properties found to dominate con- vance during the same period. This advance period is complete by trol of trench motion in our previous two-plate study (Cížkováˇ and ∼85 Myr, when the Philippine plate crustal layer has been fully Bina, 2013): namely the strength of the crustal (e.g., serpentinized consumed, yielding a locked-slab situation followed by Philippine basalt) layer and the effective Clapeyron slope of the 410-km (e.g., break-off. Thus, a lower Clapeyron slope that results in reduced wadsleyite-forming) phase transition. For the former parameter, strain-rate weakening of the Philippine plate and a flat-lying slab while weak crust gives rise to unstable initial advance followed at the 660-km interface (rather than a buckled structure) produces by swift extension and detachment, intermediate crust results in

Fig. 5. Three snapshots of evolution of viscosity field (left), showing corresponding principal deviatoric stresses (right) for subregion within black rectangle. Stress axes are represented by oriented orthogonal segments for which length is scaled to magnitude and color is scaled to both magnitude and sign. Note how transmission of subhorizontal extensional stresses from Philippine subduction to Pacific trench is modified by onset of “extension” episode from Fig. 4. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) 414 H. Cížková,ˇ C.R. Bina / Earth and Planetary Science Letters 430 (2015) 408–415

Fig. 7. Tomographic images (left) from panels D (top) and J (bottom) of Fig. 4 (south Bonin) from Fukao and Obayashi (2013); seismicity distribution (lower left) from profile F (south Bonin/north Mariana) of Smoczyk et al. (2013). Note general morphological similarities to temperature-field snapshots from this study (right-column panels). Also note that perspective of these plots is from the south looking northward, following convention of the seismological plots. stable advance with successive extensional periods before plate de- Pacific plate in the northern region and the backward-bending tachment, and strong crust yields stable but slow advance without curvature of the Pacific plate at depth in the southern region, as extensional episodes. As for the latter parameter, a lower effec- observed in seismic tomography (Fukao and Obayashi, 2013) and tive Clapeyron slope (e.g., perhaps reflecting metastability) results Wadati–Benioff zone seismicity (Smoczyk et al., 2013), appear to in reduced strain-rate weakening of the plate and a flat-lying slab have counterparts at various stages of evolution of our model slabs (rather than a buckled structure) at the 660-km interface, yielding (Fig. 7). simpler trench behavior characterized by initially fast advance followed by a single extensional episode and a short period of slow Author contributions advance. While such double-subduction-induced trench advance may H.C. designed numerical experiments, performed calculations be limited to the eastern boundary of the Philippine Sea on and post-processing of the results. C.R.B. developed the ideas un- the present-day Earth, similar double-subduction geometries have derlying the research and performed post-processing of principal been implicated in the northward migration of India in the early stresses. Both authors co-wrote the paper. Cretaceous prior to Eurasian collision (Jagoutz et al., 2015) and more generally during prior intraoceanic subduction of regions of Acknowledgements the Neo-Tethys (van Hunen and Miller, 2015). Our results suggest that such geometries may also have been loci of trench advance. We are grateful to R. Gordon and D. Mathews for discussions Finally, while we have absolutely no expectation of capturing of plate-motion models and to Y. Fukao and M. Obayashi for the full spatial and temporal complexity of Philippine-Sea tecton- providing reformatted tomographic images. We thank Neil Ribe ics in our simplified model, it is nonetheless striking that several and Jeroen van Hunen for comments that helped to improve the phenomena arising in our model appear to bear some correspon- manuscript. dence to reported properties of the region. Such phenomena in- clude: Pacific trench advance (Otsuki, 1990), maintenance of the Philippine plate under strong extensional stress (Stern et al., 2003), Appendix A. Supplementary video episodes of back-arc extension including two at ∼30 Ma intervals (Stern et al., 2003), intermittent back-arc spreading (Taylor, 1992; Supplementary material related to this article can be found on- Stern et al., 2003), high forearc heat flow during rollback-induced line at http://dx.doi.org/10.1016/j.epsl.2015.07.004. episodes of extension (Deschamps and Lallemand, 2003), and high back-arc heat flow in eastern Philippine basin (Watanabe et al., References 1970; Wang et al., 2013) perhaps related to eponymous boninitic magmatism (Deschamps and Lallemand, 2003). At a fundamen- Androvicová,ˇ A., Cížková,ˇ H., van den Berg, A., 2013. The effects of rheological decou- tally simpler level, however, it is at least intriguing to observe pling on slab deformation in the Earth’s upper mantle. Stud. Geophys. Geod. 57, 460–481. http://dx.doi.org/10.1007/s11200-012-0259-7. certain geometrical similarities between the behavior exhibited in Baitsch-Ghirardello, B., Gerya, T.V., Burg, J.-P., 2012. Geodynamic regimes of intra- our simple models and geophysically illuminated regional subduc- oceanic subduction: implications forearc extension vs. shortening processes. tion structures. In particular, both the apparent stagnation of the Gondwana Res. 25, 546–560. http://dx.doi.org/10.1016/j.gr.2012.11.003. H. Cížková,ˇ C.R. Bina / Earth and Planetary Science Letters 430 (2015) 408–415 415

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