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

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Earth and Planetary Science Letters

www.elsevier.com/locate/epsl

Geodynamics of trench advance: Insights from a Philippine-Sea-style

geometry

Hana Cížková a,∗, Craig R. Bina b

a Charles University Prague, Faculty of Mathematics and Physics, V Holešovickách 2, 18000 Praha 8, Czech Republicb 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:Received 20 May 2015Received in revised form 29 June 2015Accepted 2 July 2015Available online xxxxEditor: J. Brodholt

Keywords:subductiontransition zonetrench migrationslab bucklingPhilippine SeaMarianas–Izu–Bonin

For terrestrial parameter sets, trench retreat is found to be nearly ubiquitous and trench advance quite rare, largely due to rheological and ridge-push effects. Recently updated analyses of global plate motions indicate that significant trench advance is also rare on Earth, being largely restricted to the Marianas–Izu–Bonin arc. Thus, we explore conditions necessary for terrestrial trench advance through dynamical models involving the unusual geometry of the Philippine Sea region. In this subduction system, a slab-pull force from distal subduction is transmitted to the overriding plate at the Pacific trench. Our 2D modeling demonstrates that trench advance can occur for terrestrial rheologies in such special geometries. We observe persistent trench advance punctuated by two episodes of back-arc extension. Characteristic features of the model, such as time interval between extensional episodes, high back-arc heat flow, and stress state of Philippine plate correspond to processes recorded in the region.

© 2015 Elsevier B.V. All rights reserved.

1. Introduction

Among the results of our recent study (Cížková and Bina, 2013), of the effects on slab stagnation and rollback of mantle and subduction-interface rheology and phase-transition buoyancy, was the striking observation that exploration of an extensive parameter space yielded only trench retreat. Even in cases of minimal trench retreat, involving high crustal viscosity and hence strong slab cou-pling, no persistent trench advance was observed. In retrospect, perhaps this should not be overly surprising. Previous models have suggested that, while a stiff overriding plate can moderate trench retreat (Yamato et al., 2009; Garel et al., 2014), parameters favoring trench-advance regimes typically fall at the extremes of or out-side the realm of Earth-like conditions – requiring, for example, very strong slabs (Billen, 2010; Stegman et al., 2010) or a very stiff lower mantle (Ribe, 2010), perhaps combined with extremely strong slab coupling (Baitsch-Ghirardello et al., 2012). Any contri-bution from slab elasticity also should favor retreat over advance (Fourel et al., 2014). Indeed, it has been suggested (Chertova et al., 2012) that a far-field lithospheric “pull” stress acting on the over-riding plate, countering the ridge-push force that enhances trench retreat, may be necessary to generate meaningful trench advance. Here we introduce a slab-pull force on the overriding plate to test

* Corresponding author.E-mail address: Hana.Cizkova@mff.cuni.cz (H. Cížková).

http://dx.doi.org/10.1016/j.epsl.2015.07.0040012-821X/© 2015 Elsevier B.V. All rights reserved.

the hypothesis that persistent trench advance can arise in such a scenario.

In seeking a suitable geometry for trench advance on Earth, it is important to note that estimates of trench motions vary sig-nificantly with choice of reference frame (Funicello et al., 2008). Using a reference frame optimized to minimize trench advance, a recent analysis (Schellart et al., 2008) nonetheless suggested the occurrence of trench advance at ∼25% of global subduction-zone segments. However, a new analysis of global plate-motion constraints (Mathews et al., 2013), combining corrections to the MORVEL model (DeMets et al., 2010) and statistical error prop-agation with a reference frame based on SKS seismic anisotropy (Zheng et al., 2014), indicates that most previous indications of terrestrial trench advance actually correspond to stationary or re-treating motion. Statistically significant trench advance is found to persist in only two regions: weakly in southern Kermadec and strongly in Marianas–Izu–Bonin. Given the relatively shallow ex-tent of subducting slab beneath southern Kermadec (Zhou, 1990;Chen et al., 2004), this region perhaps reflects transient advance associated with early subduction prior to the slab encountering re-sistance near 660 km depth (Yamato et al., 2009). We thus choose to focus upon the Marianas–Izu–Bonin region, where persistent trench advance is consistent with early analysis of Marianas ad-vance (Carlson and Melia, 1984) and with the observation that Marianas–Izu–Bonin advances in all reference frames (Funicello et al., 2008). We pursue the suggestion (Mathews et al., 2013)that the unique situation – in which the overriding Philippine Sea

H. Cížková, 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, exhibiting complex bathymetry and plate shape (Yamazaki et al., 2010) and a complex patchwork of seafloor ages (Müller et al., 2008). The bounding subduction zones exhibit significant north–south variation in slab morphology and stagnation behavior. In 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 south-ern 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 ex-ample, 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-quences. Relative to our previous reference model (Cížková and Bina, 2013), we insert a third plate, yielding an overriding plate which is itself subducting, thereby changing the conceptual force-balance from one of ridge-push compression at the primary sub-duction interface to one of slab-pull extension (Fig. 1). (While the central overriding plate is clearly mobile, we can explore cases in which the third, marginal, overriding plate is either fixed or mo-bile.) Although these plates are 2D idealizations, we refer to them as the Philippine plate and Pacific plate for convenience. Our 2D rectangular model domain is 10 000 km wide and stretches from the surface to 2000 km deep. In the upper left and upper right corners, spreading ridges are positioned. (Both ridges are offset by ∼200 km from the corners to avoid complications at the vertical boundaries.)

Initial temperature distribution follows a halfspace cooling model in the uppermost part of the domain, with lithospheric age increasing from the left ridge to 140 Myr at the Pacific trench, from the right ridge to 40 Myr at the Philippine trench, and within the middle plate from 30 Myr at the Pacific trench to 40 Myr at the Philippine trench. Below the plates the temperature follows an adiabatic profile with a potential temperature of 1573 K. We set the initial inter-arc distance (i.e., the central plate width) at ∼1500 km, as a median value of the range seen in the Philippine Sea. Our model thus represents a simplified view of the Philip-

Fig. 1. Schematic force-balance diagrams for (a) a two-plate system in which one plate subducts beneath an overriding plate and (b) a three-plate system in which one plate subducts beneath an overriding plate which is itself subducting beneath an adjacent overriding plate. In the two-plate system, ridge-push exerted by the overriding plate inhibits trench advance. In the three-plate system, slab-pull exerted by the central plate may enhance advance of the leftmost trench.

Fig. 2. Model configuration (a) showing initial conditions, including full model space, focused study area (gray rectangle), plates (blue), crust (red), selected tracers (yel-low), and transition-zone boundaries (dashed). Starting configurations (b) after short initial runs with prescribed surface velocities to attain three initial temper-ature distributions (A, B, C) commensurate with differential times of subduction onset. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

pine Sea plate and its margins as viewed from the north looking southward (Fig. 2a).

At the top of both subducting plates a weak crustal layer of 15-km thickness is prescribed. The low viscosity ηcrust of this layer facilitates decoupling of the subducting and overriding plates. This crust is tracked using particle tracers, and it is not associated with any compositional density contrast. (Rather than try to capture the full complexity of a chemically layered crust, we abstract the es-sential property controlling coupling and represent it simply as a layer of reduced viscosity of sufficient thickness for numerical resolution.) At a depth of 200 km, where the decoupling effect is no longer needed, the crustal layer is replaced by mantle ma-terial for numerical convenience. As we previously demonstrated that higher crustal viscosities minimize trench retreat, we choose our initial crustal viscosity to be at the high end of the values ex-plored previously, at 1021 Pa s. In other respects the model follows the reference case from our prior study (Cížková and Bina, 2013).

410 H. Cížková, C.R. Bina / Earth and Planetary Science Letters 430 (2015) 408–415

In order to attain an initial temperature distribution commen-surate with differential times of subduction onset, we first execute a short run with constant velocities prescribed at the tops of the modeled Pacific and Philippine plates, along with an imposed roll-back velocity on the Pacific plate to permit slab stagnation. When the tip of the Philippine slab reaches a depth of 400 km, this kinematic boundary condition is switched off, and the tempera-ture distribution with the developed slab positions is then used as an initial condition (Fig. 2b). Three initial model situations are assumed, in all of which the Pacific plate velocity is 5 cm/yr: model A with Philippine plate velocity 1 cm/yr, rollback velocity 4 cm/yr and initial run executed for 19 Ma; model B with Philip-pine plate velocity 3 cm/yr, rollback velocity 5.8 cm/yr executed for 9.5 Ma; and model C with Philippine plate velocity 1 cm/yr and rollback 5 cm/yr executed for 19 Myr. These three end-members were chosen to cover the range of plausible early behavior of slab. The plate and rollback velocities were chosen to produce different geometries and extent of Pacific plate near the base of transition zone when the Philippine plate tip reaches 410-km depth.

The evolution of both subducting slabs and migration of their trenches is demonstrated not only in snapshots of temperature and viscosity distribution but also by evaluating plate and trench velocities through the use of monitor tracers. Plate velocities of the Pacific and Philippine plates are evaluated using tracers num-bered 1 and 2 (see yellow dots in Fig. 2a), respectively. Trench velocity for the Philippine plate can be tracked using tracer num-ber 3 located in the overriding plate hinge, as the overriding plate is following the motion of the Philippine plate. A similar approach, however, cannot be used in case of the Pacific plate, because the motion of the hinge of the Philippine plate can be complicated by extension at the Pacific trench. Therefore, we use a chain of tracers located at the base of the Pacific plate crust to locate the point at which crust subducts below 25 km depth, and that point is then taken to be the position of the Pacific trench.

2.2. Numerical methods and model parameters

Subduction dynamics is described by a set of equations includ-ing continuity, momentum, thermal, constitutive, and state equa-tions. We use the extended Boussinesq approximation of the gov-erning equations without internal heating. The system of equa-tions is solved by the finite-element method using the package SEPRAN (Segal and Praagman, 2005). Free-slip boundary conditions are prescribed on all boundaries (except for the short initial run as mentioned above). Thermal boundary conditions are of constant temperature at the top and bottom boundaries, while zero heat flux is prescribed at vertical boundaries. Numerical resolution of the model varies across the model domain: the finest resolution of 4 km is used in the uppermost part, 8 km in the transition zone, and a coarse resolution of 60 km is sufficient in the lowermost mantle.

We use a composite rheological model (van den Berg et al., 1993) that combines diffusion creep, dislocation creep, and a power-law stress-limiter (van Hunen et al., 2002). The effective viscosity ηeff is calculated from the viscosities of individual creep mechanisms assuming unique stress:

ηeff =(

1

ηdiff+ 1

ηdisl+ 1

ηy

)−1

. (1)

Here ηdiff , ηdisl , and ηy are viscosities of diffusion creep, disloca-tion creep, and stress-limiter respectively:

ηdiff = 1

Aexp

(Ediff + pV diff

RT

), (2)

diff

ηdisl = 1

A1ndisl

e(1−n)/n exp

(Edisl + pV disl

nRT

), (3)

ηy = τye−1/nyy e1/ny−1. (4)

Upper mantle activation parameters are based on Hirth and Kohlst-edt (2003). As dislocation creep is generally believed to play a minor role in the lower mantle, we apply only diffusion creep in the lower mantle, with activation parameters based on slab sink-ing speed analysis (Cížková et al., 2012). For meanings of symbols and parameter values, see Table 1.

Our assumed thermal expansivity varies with depth from 3 ×10−5 K−1 at the surface to 1.2 × 10−5 K−1 at a depth of 2000 km (Chopelas and Boehler, 1992; Katsura et al., 2009). Thermal diffu-sivity is held constant. Major mantle phase transitions at 410-km and 660-km depths are included using harmonic parameterization of a phase function � (Cížková et al., 2007) with respective Clapey-ron slopes γ410 = 2 MPa/K and γ660 = −2.5 MPa/K.

3. Results

3.1. Subduction in three-plate system

The evolution of the subducting system in model A is shown in Fig. 3 (cf. also Supplementary video). Here, twelve snapshots of the temperature field, illustrating ∼70 Myr of evolution, are shown in a subregion of the model domain (cf. gray rectangle in Fig. 2a). At the beginning, the Pacific plate has already reached the bottom of the transition zone, and its tip is lying flat on the 660-km bound-ary; the Philippine plate is just approaching the 410-km boundary. White squares mark the initial positions of both trenches. Let us first follow the motion of the Philippine plate. The plate is acceler-ated by an exothermic phase transition at 410 km and reaches the 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 to subduct, a first buckle starts to form at ∼15 Myr. As a conse-quence, Philippine plate rollback ceases, and the plate advances during formation of the buckle. At ∼36 Myr, buckling is largely complete, and the buckled part of the Philippine slab is very slowly sinking vertically into the lower mantle while the shallow part resumes trench rollback. At ∼43 Myr, the slab begins to develop a second buckle. This process continues until ∼75 Myr, at which point subduction of the Philippine plate ceases because the mod-el’s initially prescribed crustal layer has been totally consumed, leading to a locked-slab situation. At ∼85 Myr, the Philippine slab detaches.

Now let us examine Pacific plate behavior. The initial morphol-ogy of this old and heavy plate – low dip angle at shallow depths – would be expected to lead to a rollback episode if the plate wassubducting under an overriding plate of the type shown in Fig. 1a. Here, however, the additional pull of the rapidly subducting Philip-pine plate causes immediate trench advance, while the velocity of the Pacific plate increases. The portion of the slab initially exhibit-ing a shallow dip angle across the upper mantle and transition zone now bends toward the vertical, while the flat-lying part at the 660-km boundary is extending. At ∼10 Myr, pull from the Philippine plate is decreasing, as this plate slows due to resistance encountered at the 660-km boundary. The advance of the Pacific plate continues, however, as the slab is just forming its first buckle. Such buckling favors trench advance – as the slab dip angle is at that moment already slightly beyond vertical and the base of the slab is mechanically coupled to the lower mantle at 660-km depth, the trench is forced to move forward. This mechanism reduces roll-back (Cížková and Bina, 2013) and eventually generates advance as observed here. After ∼20 Myr, while the Philippine plate velocity

H. Cížková, C.R. Bina / Earth and Planetary Science Letters 430 (2015) 408–415 411

Table 1Symbols and model parameters.

Symbol Meaning Value Units

Upper mantle and transition zone rheologyAdiff Pre-exponential parameter of diffusion creepa 1 × 10−9 Pa−1 s−1

Adisl Pre-exponential parameter of dislocation creepa 3.1 × 10−17 Pa−n s−1

Ediff Activation energy of diffusion creepa 3.35 × 105 J mol−1

Edisl Activation energy of dislocation creepa 4.8 × 105 J mol−1

V diff Activation volume of diffusion creepa 4.5 × 10−6 m3 mol−1

V disl Activation volume of dislocation creepa 11 × 10−6 m3 mol−1

n Power-law exponent 3.5 -ηcrust Viscosity of crust 1021 Pa sτy Yield stress 5 × 108 Pae y Reference strain rate 1 × 10−15 s−1

ny Stress limiter exponent 10 –p Hydrostatic pressure – PaR Gas constant 8.314 J K−1 mol−1

T Temperature – Ke Second invariant of the strain rate – s−1

Lower mantle rheologyAdiff Pre-exponential parameter of diffusion creep 1.3 × 10−16 Pa−1 s−1

Ediff Activation energy of diffusion creepb 2 × 105 J mol−1

V diff Activation volume of diffusion creepb 1.1 × 10−6 m3 mol−1

Other model parametersκ Diffusivity 10−6 m2 s−1

g Gravitational acceleration 9.8 m s−2

ρ0 Reference density 3416 kg m−3

cp Specific heat 1250 J kg−1 K−1

α0 Surface thermal expansivity 3 × 10−5 K−1

γ410 Clapeyron slope 410 km phase transitionc 1–2 × 106 Pa K−1

γ660 Clapeyron slope 660 km phase transitionc −2.5 × 106 Pa K−1

δρ410 Density contrast 410 km phase transitiond 273 kg m−3

δρ660 Density contrast 660 km phase transitiond 341 kg m−3

a Parameters of wet olivine after Hirth and Kohlstedt (2003).b Lower mantle activation parameters of family A models by Cížková et al. (2012).c Bina and Helffrich (1994).d Steinbach and Yuen (1995).

increases during formation of its first buckle, we observe extension at the Pacific trench as a response to increased pull from Philippine plate. Although such extension should weaken coupling between the plates and thus perhaps inhibit Pacific plate advance, such ad-vance still continues, partly as a consequence of the Pacific plate buckle that is just forming in the transition zone. The extended lithosphere, however, cools and strengthens relatively quickly, and the trench-advance period for the Pacific plate thus continues un-til ∼65 Myr. At that time, a second extension in the Philippine plate occurs due to extended pull of the Philippine plate during its second buckling period. This extension and associated weak ridge formation then suppresses transmission of slab pull to the Pacific trench, and Pacific advance ceases.

Plate- and trench-motion relationships are illustrated in more detail in Fig. 4a. Persistent Pacific trench advance is clearly visi-ble: throughout the first 65 Myr, Pacific trench velocity is posi-tive (dashed blue line). At the beginning of model evolution, the Philippine plate has a very small plate velocity and is rolling back (trench velocity ∼−2 cm/yr, dashed red line). It almost imme-diately passes the 410-km interface and accelerates due to the additional negative buoyancy arising from thermal uplift of the exothermic phase transition (cf. Fig. 4a, solid red line). Conse-quently, Philippine plate pull generates Pacific trench advance, and Pacific trench velocity also increases (dashed blue line). Philippine plate velocity reaches its maximum at ∼10 Myr, and thereafter it decelerates due to buoyant and viscous resistance at the 660-km mineralogical and rheological interface. This decreased pull is then reflected in decreasing Pacific trench advance. Pacific plate velocity (blue solid line), however, continues to increase while the sub-ducted Pacific slab is consumed in the transition zone forming a vertical buckle. At ∼18 Myr, the Philippine plate starts to form

a buckle, and consequently its trench advances (positive trench velocity, dashed red curve). Its pull becomes so strong as to in-duce extension at ∼20 Myr. Weakened, extended lithosphere is not strong enough to transmit the pull; thus, Pacific trench ad-vance decreases despite acceleration of the Philippine plate while its buckle is forming. At ∼34 Myr, we observe maximal extension, as Philippine trench advance reaches its maximum while Pacific trench advance is at a minimum. After ∼30 Myr, when the first buckle is formed, advance of the Philippine plate slows, and roll-back eventually resumes at ∼40 Myr. At ∼50 Myr, the Philippine plate accelerates while forming a second buckle, resulting in a sec-ond extensional period which culminates during 65–70 Myr. In this period, extended lithosphere is again too weak to transmit the pull of the Philippine plate, and consequently the Pacific trench rolls back as the Pacific plate forms another buckle. Qualitatively sim-ilar behavior is observed in models B and C, with differences in initial setup yielding varying details of slab deformation, but the Pacific trench always experiences advance.

The episodes of “extension” noted above can be viewed from a couple of perspectives. From the point of view of relative velocities, the gray regions in Fig. 4 denote episodes of “extension” defined according to two measures: a broad measure indicating that the Philippine plate is moving away from the Pacific trench (vPh

pl > vPatr ),

and a narrow measure indicating that the Philippine trench is mov-ing away from the Pacific trench which results in lateral extension of the Philippine plate (vPh

tr > vPatr ). However, rather than simply

tracking tracers, one may also examine the evolution of the instan-taneous principal deviatoric stress fields, as shown in Fig. 5. From this latter perspective, the shallow portion of the Philippine plate (initially in slight horizontal compression) experiences large hor-izontal extensional stresses as the subducting portion accelerates

412 H. Cížková, 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-quent buckling of subducted Philippine plate induces sufficient slab pull to weaken the shallow plate in the “extension” regime, with a result that resembles fore-arc upwelling of mantle wedge (and consequent high heat flow) in the thermal field. Later, some of the extension-induced weakening thermally heals just outboard of the Pacific trench, but overall extension continues and localizes in a manner similar in appearance to incipient back-arc rifting in the thermal field (with onset of such quasi-rifting occurring earlier for weaker crust).

3.2. Sensitivity to crustal viscosity and Clapeyron slope

As crustal strength is a primary controlling parameter that af-fects subduction velocities (Androvicová et al., 2013), we further investigated its effects on the regime of our double-subduction setup. A lower crustal viscosity (5 · 1020 Pa s) produces higher plate velocities, and the associated larger pull from the Philip-pine plate generates faster initial trench advance for the Pacific plate. Such weaker crust, however, also facilitates extension in the Pacific trench region. The extension period thus starts very early (at less than 10 Myr) and continues without interruption until the fast Philippine plate is fully subducted and breaks off at ∼40 Myr. Higher viscosity crust (5 · 1021 Pa s), on the other hand, results in very small subduction velocities for both plates (less than 2 cm/yr); it is, however, strong enough to prevent ex-tension at the Pacific trench. In this model, we therefore observe steady but very slow advance of the Pacific trench (∼0.5 cm/yr). Weak crust thus produces unstable initial advance followed by swift extension and detachment. Intermediate crust results in sta-

ble advance, with two brief extensional periods (of ∼30 Myr periodicity) before Philippine plate detachment. Strong crust re-sults in stable but very slow advance without any extensional episode. Another crucial parameter that affects subduction veloc-ities, buckling, and trench migration is the effective Clapeyron slope of 410-km phase transition (Behounková and Cížková, 2008;Cížková and Bina, 2013). Models discussed above assume a mod-erate value of γ410 = 2 MPa/K. Let us now examine the effect of a lower Clapeyron slope of γ410 = 1 MPa/K. Fig. 6 shows one temperature snapshot for higher (6a) and lower (6b) Clapeyron slopes. The model with lower Clapeyron slope also results in Pa-cific trench advance, but its amplitude is smaller than in the case with higher Clapeyron slope (cf. Fig. 4a, b, blue dashed lines). This is not surprising, as lower Clapeyron slope results in lower negative buoyancy associated with the phase transition and thus in smaller pull exerted by the Philippine plate. Overall, Philippine plate be-havior is much simpler in this case, as no buckling is observed in first 60 Myr. This is clearly visible in Fig. 4b, where Philip-pine plate velocity (solid red curve) first increases due to the extra pull of 410-km phase transition and, after reaching maximum at ∼15 Myr, then decreases due to resistance at the 660-km inter-face. Thereafter, velocity remains small as the plate continues sub-ducting while its trench is rolling back (negative Philippine trench velocity, dashed red curve). Pacific trench advance essentially fol-lows the trend of Philippine plate velocity, and both of them drop to zero at ∼60 Myr, when the Philippine plate is purely rolling back. Shortly after 60 Myr, strain-rate weakening of the Philip-pine plate at around 410 km depth induces formation of a weak horizontal buckle. Acceleration of the Philippine plate due to this

H. Cížková, C.R. Bina / Earth and Planetary Science Letters 430 (2015) 408–415 413

Fig. 4. Graphs of evolving plate (solid) and trench (dashed) velocities for Pacific (blue) and Philippine (red) plates for 410-km Clapeyron slope with normal (a) value γ410 = 2 MPa/K and low (b) value γ410 = 1 MPa/K. Grey regions denote episodes of “extension” defined according to two measures: broad measure (light gray) indi-cates Philippine plate velocity exceeds Pacific trench velocity (vPh

pl > vPatr ); narrow

measure (dark gray) indicates Philippine trench velocity exceeds Pacific trench ve-locity (vPh

tr > vPatr ). (For interpretation of the references to color in this figure legend,

the reader is referred to the web version of this article.)

buckling is visible as a rise in plate velocity at ∼65 Myr (Fig. 4b, solid red curve). Consequently, we observe weak Pacific trench ad-vance during the same period. This advance period is complete by ∼85 Myr, when the Philippine plate crustal layer has been fully consumed, yielding a locked-slab situation followed by Philippine break-off. Thus, a lower Clapeyron slope that results in reduced strain-rate weakening of the Philippine plate and a flat-lying slab at the 660-km interface (rather than a buckled structure) produces

Fig. 6. Contemporaneous snapshots of temperature field for models with 410-km Clapeyron slope of normal (a) value γ410 = 2 MPa/K and low (b) value γ410 =1 MPa/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, oc-cur for terrestrial rheological regimes, but (as suggested previ-ously) it appears to require a force balance in which a second slab pulls on the overriding plate. Our 2D modeling of such a three-plate geometry yields persistent trench advance, interrupted by episodes of back-arc-like extension. Complex oscillatory behavior of the system is a direct consequence of buckling, without which switching between different modes of the process would not oc-cur. The time interval between extensional episodes reflects the characteristic period of buckling of the Philippine plate. Some ex-ploration of the parameter space reveals behavioral dependence upon the same two petrological properties found to dominate con-trol of trench motion in our previous two-plate study (Cížková and Bina, 2013): namely the strength of the crustal (e.g., serpentinized basalt) layer and the effective Clapeyron slope of the 410-km (e.g., wadsleyite-forming) phase transition. For the former parameter, while weak crust gives rise to unstable initial advance followed 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, 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-tachment, and strong crust yields stable but slow advance without extensional episodes. As for the latter parameter, a lower effec-tive Clapeyron slope (e.g., perhaps reflecting metastability) results in reduced strain-rate weakening of the plate and a flat-lying slab (rather than a buckled structure) at the 660-km interface, yielding simpler trench behavior characterized by initially fast advance fol-lowed by a single extensional episode and a short period of slow advance.

While such double-subduction-induced trench advance may be limited to the eastern boundary of the Philippine Sea on the present-day Earth, similar double-subduction geometries have been implicated in the northward migration of India in the early Cretaceous prior to Eurasian collision (Jagoutz et al., 2015) and more generally during prior intraoceanic subduction of regions of the Neo-Tethys (van Hunen and Miller, 2015). Our results suggest that such geometries may also have been loci of trench advance.

Finally, while we have absolutely no expectation of capturing the full spatial and temporal complexity of Philippine-Sea tecton-ics in our simplified model, it is nonetheless striking that several phenomena arising in our model appear to bear some correspon-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), episodes of back-arc extension including two at ∼30 Ma intervals (Stern et al., 2003), intermittent back-arc spreading (Taylor, 1992;Stern et al., 2003), high forearc heat flow during rollback-induced episodes of extension (Deschamps and Lallemand, 2003), and high back-arc heat flow in eastern Philippine basin (Watanabe et al., 1970; Wang et al., 2013) perhaps related to eponymous boninitic magmatism (Deschamps and Lallemand, 2003). At a fundamen-tally simpler level, however, it is at least intriguing to observe certain geometrical similarities between the behavior exhibited in our simple models and geophysically illuminated regional subduc-tion structures. In particular, both the apparent stagnation of the

Pacific plate in the northern region and the backward-bending curvature of the Pacific plate at depth in the southern region, as observed in seismic tomography (Fukao and Obayashi, 2013) and Wadati–Benioff zone seismicity (Smoczyk et al., 2013), appear to have counterparts at various stages of evolution of our model slabs (Fig. 7).

Author contributions

H.C. designed numerical experiments, performed calculations and post-processing of the results. C.R.B. developed the ideas un-derlying the research and performed post-processing of principal stresses. Both authors co-wrote the paper.

Acknowledgements

We are grateful to R. Gordon and D. Mathews for discussions of plate-motion models and to Y. Fukao and M. Obayashi for providing reformatted tomographic images. We thank Neil Ribe and Jeroen van Hunen for comments that helped to improve the manuscript.

Appendix A. Supplementary video

Supplementary material related to this article can be found on-line at http://dx.doi.org/10.1016/j.epsl.2015.07.004.

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