1
Slab Dynamics in the Transition Zone
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Magali I. Billen∗
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Department of Geology, University of California. Davis, Davis, CA 95616, USA
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Abstract
Seismic images of horizontal slab segments in, across or below the transition zone invoke scenarios in which slabs
are laid down in the mantle through progressive trench retreat. However, observations of subduction characteristics
do not exhibit a clear correlation between trench retreat and slab dip in the transition zone. Instead analysis of a range
of subduction characteristics demonstrates that while transition-zone slabs include slabs of many ages and subduction
velocities, with both retreating and advancing trench motion, they also have several enigmatic characteristics such as
faster sinking rates and a larger range in slab dip than slabs that extend to either shallower or deeper depths. Comparison of subduction characteristics with several analytical and numerical models of subduction dynamics suggest that
many of the possible mechanisms for trapping slabs in the transition zone (e.g., positive buoyancy sources, viscous
resistance, slab weakening) are only viable if the slab is already shallow-dipping. Two scenarios for formation of
stagnant slabs are proposed: 1) trench retreat prior to slabs entering the transition zone or caused by the negative
buoyancy forces associated with the wadsleyite and ringwoodite phase transitions, and 2) slow, lateral migration of
slabs in stable subduction zones.
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Key words: slab dynamics, subduction, rheology, mantle composition, transition zone
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1. Introduction
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The Japanese subduction zone is characterized by long term subduction of old lithosphere (125–132 Ma) at rates
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of 86–93 mm/yr (Lallemand et al., 2005), suggesting that the sinking slab has more than enough negative buoyancy
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to pull the subducting plate and to sink deep into the mantle. Yet seismological observations show that the slab
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is subducting at a shallow dip of 19–26◦ extending more than 800 km laterally before reaching the transition zone
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and lies horizontally within the transition zone for another 600 km (Niu et al., 2005). While trench retreat is often
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suggested as a cause of stagnant slabs in the transition zone, the present day trench retreat rate in Japan is only 20
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mm/yr contributing less than 3◦ of slab shallowing per million years.
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The Japan slab is also characterized by scattered seismicity to depths of 670 km with down-dip compression axis at
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all depths (Isacks and Molnar, 1969) indicating that the slab remains stiff enough to transmit stresses up-dip. Seismic
∗ Corresponding
Author.
Email address: [email protected] (Magali I. Billen)
Preprint submitted to Physics of Earth and Planetary Interiors
May 4, 2010
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data indicate that the 410-km phase change is elevated in the slab contributing to the negative buoyancy of the slab,
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while the 660-km phase change is depressed over a broad region below the horizontal slab, which appears to rest on
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this boundary (Niu et al., 2005). However, there is also new evidence for a metastable olivine wedge extending from
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400 to 560 km at the core of the slab (Jiang et al., 2008).
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So why has the Japan slab failed to sink deeper into the lower mantle? Is the positive buoyancy of a meta-stable
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olivine wedge or delayed transformation to perovskite at 660-km to blame? Has intense deformation locally weakened
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the slab and prevented it from pushing into the higher viscosity lower mantle? Did transient trench roll-back in the
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past cause shallowing of the slab and therefore setting the stage later trapping of the slab in the transition zone?
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While the Japan slab is a particularly well-studied stagnant slab (Fukao et al., 2010), these questions can be asked
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of any of the present-day slabs that appear to be stagnant in the transition zone (e.g., Tonga, Java, Hebrides). Is the
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stagnation due to a lack of sufficient negative buoyancy, changes in slab strength, the background mantle viscosity
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structure, geometric effects, or all of these, possibly with each subduction zone exhibiting a unique combination?
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Are stagnant slabs a transient feature of all subduction zones (Fukao et al., 2001) or does a particular combination of
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conditions need to occur?
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Isolating the first order cause of stagnant slabs is a difficult task given the limited number of observations, and
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in particular the limited constraints on the evolution of many of these subduction zones. Instead, here I attempt to
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eliminate possible causes by combining analysis of subduction characteristics with comparisons to predictions from
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analytical models and the results of recent analog and numerical simulations of subduction.
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2. Enigmatic Subduction Characteristics
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The simplest models consider first order effects of the driving forces of subduction in combination with the effects
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of coupling a sinking slab with mantle flow, and provide basic intuition on the expected behavior of slabs. For
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example, we expect a slab with more negative buoyancy (e.g., older and/or longer) to sink more quickly, or a stiffer
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slab (e.g., colder, dryer, and/or less deformed) to have a more shallow dip. However, as many studies have shown
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before subduction zone characteristics do not appear to exhibit such straight-forward correlations (Jarrard, 1986;
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Lallemand et al., 2005; Heuret and Lallemand, 2005).
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In the following discussion slabs are divided into three groups: slabs with a maximum depth less than 410 km are
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shallow-mantle slabs (squares), slabs with a maximum depth between 410 km and 670 km are transition-zone slabs
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(triangles), and slabs with a maximum depth greater than 670 km are deep-mantle slabs (circles). The subduction
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characteristics data are from Lallemand et al. (2005) and include 159 transects across subduction zones that are not
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disturbed by nearby collision or ridge/plateau subduction. Transects near slab edges are more likely to be affected by
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three-dimensional geometry (open symbols), while other transects (filled symbols) are expected to be more sensitive
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to characteristics of the subducting plate such as the age of the plate (slab age). In this data set because individual
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subduction zones are represented by multiple transects the behavior of adjacent segments of the subduction zone are
2
Figure 1: Dependence of slab sinking rate on subduction zone characteristics (Lallemand et al., 2005). Slab sinking rate versus (a) slab-pull force
(F sp ), (b) slab age, and (c) slab depth. Symbols: slabs with a maximum depth of 0–410 km (squares), 410–660 km (triangles), 670–1300 km
(circles); data from near a slab-edge (open) and non-slab-edge (filled). Black dashed lines in (a) show expected increase in slab sinking rate with
increased buoyancy from Stokes’ flow for uniform and layered mantle viscosity. Thin-white lines in (b–c) indicate groups of data with an apparent
sinking-velocity versus slab-age trends: trends d2 and d4 have no depth dependence, while trends s1, s2, d1 and d3 could be due to slab depth, slab
age or both.
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coupled. Therefore, these transects should not be treated as statistically independent observations. However, the
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large number of transects allows for the identification of trends between characteristics, which do vary along strike in
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many subduction zones. These trends can be compared to predictions from models to identify the physical processes
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affecting subduction dynamics (e.g., Lallemand et al. (2005); Billen and Hirth (2007)).
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Slab Sinking Rate. Slab-pull depends primarily on the age of the slab (which determines the density anomaly) and
√
the length of the slab (which determines the volume of the slab) and is defined as F sp = k∆ρL A where k = 4.8 × g,
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g = 9.81 m/s2 , ∆ρ is the average density anomaly, L is the length of the slab, and A is the slab age (Carlson et al.,
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1983). Slab-pull is considered the main driving force for plate motions at the surface of the earth, therefore one would
57
expect that the sinking rate (Vr ) of slabs in the mantle would be correlated with the available slab-pull force. However,
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the data show that instead there appears to be a maximum speed limit on the sinking rate of slabs equal to about 60
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mm/yr, regardless of the available slab-pull force (Figure 1a).
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When sinking rate is compared to the two main factors in the slab-pull force equation some correlations emerge
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from the data (Figure 1b, c). First, slab sinking rate is not simply related to slab age, although separate trends with
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similar slopes exist for different aged shallow-mantle slabs (s1–s2) and deep-mantle slabs (d1–d4). Second, the
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maximum sinking rate increases from 10 mm/yr for slabs of only 100 km depth to 60 mm/yr for slabs with maximum
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depths of 300 km (trend s1 and s2; Figure 1c) as would be expected for a model in which the slab-pull force increases
65
as the volume of the slab increases. However, deeper than 660 km the sinking rate is only moderately correlated with
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either slab depth (trends d1 and d3) or slab age (trends d2 and d4).
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The upper limit on the sinking rate and the weak dependence of sinking rate on slab pull force for lower-mantle
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slabs suggests that beyond a certain depth, the increase in negative slab buoyancy is roughly balanced by an increase
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in viscous stresses on the slab perhaps caused by an increase in viscosity with depth (Jarvis and Lowman, 2007).
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Transition-zone slabs, however, do not fit any of these trends and clearly stand-out as being the only slabs with very
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fast sinking rates of up to 150 mm/yr (Figure 1c).
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Slab Dip. In the corner-flow model of subduction a rigid sinking slab drives flow in the mantle, which in turn induces
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pressure gradients that partially support the weight of slab (Batchelor, 1967). The corner-flow model is commonly
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used to predict slab thermal structure, but also makes the dynamical predictions that slab dip should: 1) decrease with
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increasing convergence velocity (subducting plate velocity plus overriding plate velocity) and 2) increase with slab
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age (i.e., density). This model correctly predicts the mean dip of slabs (Stevenson and Turner, 1977; Tovish et al.,
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1978) and is consistent with the weak trend of decreasing slab dip with convergence velocity in the data (Figure 2a).
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However, the data show three separate trends of increasing slab dip with slab age for slabs younger than 80 my and
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older than about 120 my, but a negative trend for slabs between 80 and 120 my old (Figure 2b). Previous analysis of
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these slab dip versus slab age data concluded that there was no correlation between these two characteristics (Heuret
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and Lallemand, 2005), whereas the complex pattern suggests that perhaps these apparent trends are instead an artifact
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of other non-physical correlations in the data. In particular, many of the data points making up the two trends for slabs
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less than 80 my also show a positive correlation between slab age and slab depth (s1, s2, d1; Figure 2c) and therefore
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slab dip may instead be dependent on slab depth.
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A plot of slab dip versus slab depth exhibits separate trends for upper-mantle slabs versus lower mantle slabs
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(Figure 2d). The dip of upper-mantle slabs increases with slab-depth, while the dip of lower-mantle slabs decreases
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with slab depth. Transition zone slabs shallower than 670 km fit the trend of upper-mantle slabs, while slabs that
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have reached 670 km do not follow either trend. This pattern of slab dip dependence on slab depth is not predicted
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by simple analytical models, but may be understood from viscous flow models simulating the interaction of relatively
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stiff slabs with a layered mantle viscosity structure.
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In models studying the behavior of slabs with varying age or convergence rate Billen and Hirth (2007) found that
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all models with relatively stiff slabs and a moderate increase of lower mantle viscosity had a distinctive evolution of
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slab dip with slab depth (Figure 3). In all these models the slabs start with a shallow dip of 30◦ , which then steepens
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to 60–90◦ as the slab lengthens in the upper mantle. This behavior has been observed in many models of subduction
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(Becker et al., 1999; Bellahsen et al., 2005; Funiciello et al., 2006). However, once the slab starts to sink into the more
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viscous lower mantle the difference in sinking rates between the upper and lower mantle forces the upper-mantle
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portion of the slab to migrate laterally away from the subduction zone (Figure 3). Because the slab is too stiff to
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thicken or buckle, it accommodates the difference in sinking rate by partitioning some of the slab-pull force into
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lateral motion of the slab. This lateral migration slowly leads to shallowing of the upper-mantle portion of the slab.
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The rate of migration depends on the slab age, convergence rate, and the mantle and slab viscosity structure (Figure
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Figure 2: Dependence of slab dip on subduction zone characteristics (Lallemand et al., 2005). Slab dip versus (a) convergence velocity (Vconv ), (b)
slab age, and (d) slab depth. Slab-age and slab-depth are correlated with each other (c): the apparent slab dip dependence on slab age is in fact a
dependence of slab dip on slab depth. Symbols: same as in Figure 1. Thin-white lines in (c) indicate groups of slab age and slab-depth correlations.
Black dashed lines in (d) indicate evolution of slab dip with slab depth in 2D numerical models of slab evolution (Figure 3).
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3). Partitioning of the gravitational (i.e., radially-directed) pull force of the slab into lateral motion is not possible for
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simple Stokes’ sinking of isoviscous or low viscosity slabs, but instead requires the strength of the slab to redirect this
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force.
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The pattern of increasing slab dip with slab depth for shallow-mantle slabs (and some transition-zone slabs) and
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decreasing slab dip with slab depth for deep mantle slabs in the observational data is in good agreement with the
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evolution of slabs found in the numerical models (dashed lines in Figure 2d). These models did not include any of
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the phase change anomalies associated with the transition zone or motion of the trench, so they indicate the behavior
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of slabs independent of most of the complications of the transition zone. Therefore it is no surprise that the transition
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zone slabs that have reached 660 km do not follow the trend predicted by these models and is another indication
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that the apparent anomalous behavior of slabs interacting with the transition zone. Interestingly, another group of
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anomalous slabs appears at a depth of 1200 km (Figure 2d) and may indicate yet another region of changing mantle
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structure that interferes with the descent of slabs through the lower mantle.
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Trench Motion. One commonly-proposed cause for the trapping of slabs in the transition zone is that trench roll-
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back lays the slab down at a shallow angle, distributing the negative buoyancy of the slab over a larger area and
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allowing viscous stresses to prevent further sinking of the slab into the lower mantle (e.g., Griffiths et al. (1995);
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Christensen (1996); Goes et al. (2008)). This type of model predicts a strong correlation between decreasing slab dip
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and increasing trench roll-back rate (positive Vt ) for transition zone slabs that is not observed in the data (Figure 4a).
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The lack of correlation of slab dip with trench velocity may therefore indicate that trench roll-back is not a primary
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cause of stagnation of slabs in the transition zone, or that the roll-back episodes are transient features that are difficult
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to correlate with present-day slab shapes.
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Trench velocity is correlated with subduction velocity and slab age (Lallemand et al., 2008). The data show that
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most subduction zones with old slabs (Figure 4b) and faster subducting plate velocities (Figure 4c) have advancing
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trenches (i.e., motion towards the overriding plate) with rates up to 50 mm/yr, and young slabs with slower subducting
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plate velocities have retreating trenches with rates up to 50 mm/yr for shallow-mantle and deep-mantle slabs. Only
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transition zone slabs have retreat rates up to 90 mm/yr, but these are not associated with shallow slab dip. These
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correlations of trench velocity with both subduction velocity and slab age may be understood from both laboratory and
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numerical viscous flow models of free subduction, which show that slab stiffness controls trench motion (Lallemand
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et al., 2008).
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First, Schellart (2005) showed that advancing trench velocity is correlated with increasing subduction velocity in
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models with forced convergence. Advancing trench motion also occurs in models with higher viscosity slabs and is
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promoted by sinking of stiff slabs into a higher viscosity lower mantle (Enns et al., 2005). In addition, increasing
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along-strike width of the slab decreases the rate of retreating trench motion (Stegman et al., 2006; Schellart et al.,
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2007). A comprehensive numerical modeling study of trench motion considering plate age, stiffness, mantle structure
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and plate width found that plate stiffness is the primary control on trench motion (Di Giuseppe et al., 2008, 2009)
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Figure 3: Slab evolution without transition zone structure or trench motion. (a) reference model slab has initially shallow dip that steepens in the
upper mantle until the slab reaches the upper-lower mantle viscosity increase. Difference in sinking rates in upper and lower mantle cause slab to
migrate laterally in the upper mantle leading to more shallow dipping slabs. Both younger (b) and older (c) slabs have steeper dips because they
are less stiff or more dense, respectively. Decreasing the integrated strength of the slab by lowering the yield stress (d) or increasing the water
content (e) leads to steeper slabs. A larger increase in the lower mantle viscosity causes the slab to migrate laterally more quickly (f). Without an
increase in lower mantle viscosity (g) the slab sinks vertically. All models have a composite diffusion-dislocation viscosity in the upper mantle and
a diffusion creep viscosity in the lower mantle with plastic yielding. Other model parameters are listed in the figure.
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Figure 4: Dependence of trench velocity on subduction zone characteristics (Lallemand et al., 2005). Trench velocity versus (a) slab dip, (b)
subducting plate velocity (V sub ), (c) slab age, and (d) slab depth. Symbols: same as in Figure 1). Note two groups of transition zone slabs in
(a): shallowly-dipping with advancing trench motion and steeply-dipping with rapid retreating trench motion. The group of shallowly-dipping
transition-zone slabs with advancing trench motion are also the longest slabs in the data set. Symbols: same as in Figure 1
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For transition zone slabs, the enigma remains, in that slab shape (dip) does not appear to be simply correlated with
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slab age or trench velocity. However, comparison of the plot of slab-dip versus trench velocity (Figure 4a) with the
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plot of slab-dip versus slab length (Figure 4d) shows that the most shallow-dipping transition-zone slabs are advanc-
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ing and have very long slab lengths (longer than deeper mantle slabs). I will return to this observation in the discussion.
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From this comparison of observations with model predictions, it appears that the dynamics of shallow slabs is
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controlled mainly by increasing negative slab buoyancy with slab length and low viscous resistance to sinking. In
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contrast, the dynamics of deep-mantle slabs is controlled by increased viscous resistance to sinking of the slab and
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the ability of stiff slabs to partition the slab pull force into lateral motion of the slab or trench. Transition zone slabs
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clearly stand-out as having different subduction zone characteristics than other slabs, which are not easily explained
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by simple dynamical models that do not include special processes occurring in the transition zone. It appears that
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whatever process(es) leads to the stagnation of slabs, it affects all slabs similarly independent of slab age, convergence
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rate, or trench motion, and leads to fast sinking velocities under some conditions.
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3. Dynamics of Slab Descent
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The evolution of a slab as it descends through the mantle can be thought of as occurring through perturbations of
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the slab’s vertical descent by the evolution of the rheologic structure of the slab. In other words, without the strength
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of the slab, dense things sink vertically down through the mantle: changes in buoyancy (phase changes) or changes to
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the background viscosity can only slow down or speed up the descent. A stiff slab, however, can redirect the sinking
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motion into lateral motion of the slab, and of the plate or plate boundary at the surface, and in this case local changes
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in buoyancy can lead to changes not just in the sinking rate of a slab but also its direction.
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For the discussion of slab buoyancy forces below, I use the thermal structure of a slab from dynamic models of
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subduction in which the subducting plate has a fixed age of 80 Ma and subducts at a rate of 5 cm/yr (Figure 5) and
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other similar models with different plates ages and subduction rates from Billen and Hirth (2007). The shape of these
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slabs is the result of simulations without any phase changes, meta-stable olivine or grain-size dependent rheology.
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Therefore, the thermal structure is used to provide appropriate estimates of the various slab buoyancy forces. The
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analysis buoyancy forces in the transition zone presented here is similar in some respects to that of Bina et al. (2001)
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but uses different values for many of the phase transition parameters and, in particular, a different model of metastable
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olivine (Mosenfelder et al., 2001).
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3.1. Slab Buoyancy
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Thermal Buoyancy. The largest source of buoyancy in a subduction zone is the thermal buoyancy of the slab, because
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the volume of the slab is large in comparison to the volumes affected by phase changes. The density anomaly of a
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slab is ∆ρ = ρo α∆T , where ρo = 3300 kg/m3 is the background density of the mantle, α = 1–3 × 10−5 K−1 is the
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Figure 5: Slab thermal and rheologic structure from Billen and Hirth (2007) with predicted phase changes for an 80 my-old slab subducting at
50 mm/yr after (a) 20 my and (b) 40 my. High strain-rates cause viscous weakening surrounding the slab (η < 1020 Pa-s) while plastic yielding
limits the maximum viscosity of the cold slab interior. Profiles across the slab at 410, 540 and 660-km (c) show low strain-rate cold interior
and high-strain-rate surrounding mantle. Symbols: temperature (white contours every 300◦ C); viscosity (gray-scale image; note log-scale); phase
changes: thick dark-gray (olivine-wadsleyite; γ = 4.0%, ∆ρ = 5.0%), solid-gray (wadsleyite-ringwoodite; γ = 7.0%, ∆ρ = 3.0%), dashed gray
(calcium-perovskite, γ = 4.0%), dashed light-gray (garnet-ilmenite, γ = 4.0%), dashed white (ilmenite-perovskite, γ = −3.1%), dashed blackwhite (ringwoodite-perovskite+magnesiowustite, γ = −1.0%, ∆ρ = 7.0%), gray-shaded slab-interior (meta-stable olivine; grain size = 500 µm,
∆ρ = 5.0%, model 2 values from Mosenfelder et al. (2001): ∆G = −14.0 kJ/mol is the free energy of reaction, k = exp(13.421) µm/s-K is the
growth constant, ∆H = 369 kJ/mol is the activation enthalpy, V = 1.0 cm3 /mol is the activation volume, and S = 3.35/d is the grain size area).
10
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thermal expansion coefficient, and ∆T is the temperature difference between the slab and the surrounding mantle. The
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maximum possible density anomaly is on the order of 90 kg/m3 (about 2.7% for α = 2 × 10−5 K −1 ), but because
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the slab heats up as it descends the average density anomaly is usually not more than 30–45 kg/m3 (0.09–1.3%),
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corresponding to temperature differences of 500–700◦ C (Figure 5).
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When slabs reach the transition zone they have a total negative buoyancy in the range of -20 to -50×1012 N/m
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(only the slab volume deeper than 200 km is included). Differences in the initial age of the slab or convergence rate,
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as well the duration of subduction, can lead to differences of up to a factor of two in the thermal buoyancy (Figure
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6a). Similarly, for strong dipping slabs the slab-pull force is partitioned into vertical and horizontal components, with
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only about half the slab-pull force contributing to sinking for shallow-dipping slabs (< 30◦ dip).
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Phase Changes. The density anomaly associated with the phase change of ringwoodite to perovskite and magne-
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siowüstite at 660 km depth is consider a primary candidate for slab stagnation because the negative clapeyron slope
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for the phase change leads to a delay of this reaction within the cold slab, and therefore forms a positive density
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anomaly that can counteract the negative thermal buoyancy of the slab. Early dynamic models using values of the
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clapeyron slope in the range of γ = 5–7 MPa/K (Christensen and Yuen, 1984; Christensen, 1996) showed that this
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density anomaly can effectively trap a slab in the transition by creating a localized buoyancy anomaly on the order
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45×1012 N/m (for a density difference of 7%; Figure 6b). This buoyancy force is greater than or equal to that of the
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negative thermal buoyancy, and in particular, if a slab is non-vertical, only part of the thermal buoyancy is directed
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down-dip. Therefore, the buoyancy anomaly of the phase change can temporarily remove the net driving force of the
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slab.
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Advances in the methods used to measure the clapeyron slope of ringwoodite phase change at 660 km have
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resulted in smaller values for the clapeyron slope ranging from γ = −0.4 to −2.0 MPa/K (Fei et al., 2004; Katsura
188
et al., 2004), and therefore a smaller buoyancy anomaly of only 7 to 20 ×1012 N/m (Figure 6b). In this case, for a slab
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more than 50–150 km long above the region going through the phase change, the thermal bouyancy will continue to
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drive sinking of the slab (I will consider the effect of non-buoyancy related forces below). However, if prior dynamics
191
have significantly shallowed the slab dip, the local negative buoyancy of the slab may not be sufficient to overcome
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this density anomaly. There are also other phase changes occurring around 660-km (garnet to perovskite γ = +1.3
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MPa/K (Hirose, 2002), ilmenite to perovskite γ = −3.1 MPa/K (Fei et al., 2004)) which can also contribute to the net
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buoyancy of the slab. In doing the calculation above, I consider that the full volume underwent the olivine system
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phase change, so this value in effect takes into account the density anomalies from the other minerals in the slab. Note,
196
that the current laboratory-derived values for the Clapeyron slopes are also consistent with seismological observations
197
of the discontinuity in subduction zones (Bina and Helffrich, 1994; Lebedev et al., 2002b,a; Thomas and Billen, 2009),
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however, these observations are not yet capable of further narrowing the range of acceptable values.
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The phase transitions at the top of the transition zone also contribute to the net buoyancy of the slab, although these
200
phase changes have received less attention in consideration of transition zone dynamics. The olivine to wadsleyite
11
201
transition at 410-km has a clapeyron slope of 3.4 to 4.0 MPa/K and a density difference of 5% (Katsura et al., 2004).
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The wadsleyite to ringwoodite transition at 540-km has a clapeyron slope of 4.0 to 6.9 MPa/K and a density difference
203
of 3% (Suzuki et al., 2000; Inoue et al., 2006). Because of the larger magnitude clapeyron slope of these phase changes
204
compared to the phase change at 660 km, the volume of slab contributing to the density anomaly is also larger (Figure
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5). Therefore, each of these phase changes, with buoyancy values of −8 to −25 × 1012 N/m and −10 to −28 × 1012
206
N/m, can locally double the negative buoyancy of the slab (Figure 6b, d). If the slab is free to respond to this extra
207
source of slab-pull force, then the slab sinking rate should increase proportionally as the slab passes through each of
208
these phase transitions.
209
The additional negative buoyancy from these two shallow transition zone phase changes provides a simple expla-
210
nation for the observed group of fast sinking transition-zone slabs (Figure 1a–c). These are slabs that have undergone
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the olivine to wadsleyite to ringwoodite transitions, but are not yet subject to the increased buoyancy at the base of the
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transition zone, or increased viscous resistance to sinking in the lower mantle.
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Metastable Olivine. The affect of the olivine to wadsleyite transition on slab dynamics in the transition zone has re-
214
ceived much more attention in terms of the potential effect of metastable olivine (Schmeling et al., 1999; Mosenfelder
215
et al., 2001; Tetzlaff and Schmeling, 2009). If olivine at the cold core of the slab is kinetically hindered from trans-
216
forming to wadsleyite (and then ringwoodite) this provides a positive buoyancy that can resist subduction of the slab
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at the top of the transition zone. Recent seismic studies may have detected metastable olivine within the Japan slab
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(Jiang et al., 2008) but the volume of material involved is unclear. Schmeling et al. (1999) concluded that the volume
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of metastable olivine expected in young (70 my) slabs was too small to cause considerable slowing of the slab, but the
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effect on older slabs (> 100 my) may be significant Schmeling et al. (1999); Bina et al. (2001). Recent simulations
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also suggest that a feedback occurs between the formation of metastable olivine and the rate of subduction (Tetzlaff
222
and Schmeling, 2009). In these models, for old (cold slabs) the formation of metastable olivine slows the sinking
223
rate of the slab. This in turn allows the slab to warm, which produces less metastable olivine and allows the slab to
224
speed-up again.
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Applying the model for formation of metastability of olivine from Mosenfelder et al. (2001) to the thermal models
226
from Billen and Hirth (2007) (Figure 5) predicts that buoyancy of the metastable olivine wedge is more than an order
227
of magnitude smaller than each of the other slab buoyancy sources for grain sizes of 500–1000 µm (Figure 6b). We
228
note that the slab age is younger (80 my) and therefore the slabs are warmer (∼ 100◦ C) than the models used by
229
Tetzlaff and Schmeling (2009) (130 my) and Bina et al. (2001) (140 my) and the volume of metastable olivine is very
230
sensitive to the thermal structure. In the models presented here, the small metastable olivine buoyancy is primarily
231
due to the narrow width (< 25 km) of the cold core region of the slab. Therefore, metastable olivine may cause time-
232
dependent variations in the sinking rate of very old slabs (Bina et al., 2001; Tetzlaff and Schmeling, 2009), but is not
233
likely to have an effect on younger slabs.
234
12
235
From this analysis of the positive and negative sources of buoyancy related to the slab, I conclude that 1) the
236
positive buoyancy associated with the phase changes at 660-km is not a good candidate for slab stagnation, although
237
it may cause a minor slowing of the slab descent rate, 2) the positive buoyancy of metastable olivine is unlikely to
238
cause even a minor slowing of the slab descent except for very old slabs, and 3) the negative buoyancy of the olivine
239
to wadsleyite to ringwoodite transitions at 410-km and 540-km could temporarily double the descent rate of the slab.
240
Each of these conclusions assumes that the majority of the negative thermal buoyancy of the slab is transmitted down
241
dip: if the dip is already shallow or the slab weakens locally, then the positive buoyancy sources can inhibit further
242
sinking of the slab. In either case, it appears that slab stagnation in the transition zone is caused by changes in slab
243
and/or mantle rheology and/or transient changes in trench motion, rather than changes in buoyancy.
244
3.2. Mantle Rheology
245
The speed at which slabs descend into the mantle is, to first order, determined by the Stokes sinking velocity:
246
that is, by the balance of the net negative slab buoyancy against the shear stresses on the side and tip of the slab.
247
Therefore, changes in the viscosity (and rheology) in the transition zone and the lower mantle can change the viscous
248
shear stresses and can modify slab descent. However, there are far fewer constraints on the rheology of the transition
249
zone and lower mantle, compared to what is known about the rheology of olivine in the upper mantle.
250
Radial Viscosity. The average absolute viscosity of the upper 1400 km of the mantle is 1021 Pa-s as constrained by
251
models of post-glacial rebound (Mitrovica, 1996). Models of the observed long wavelength geoid require an increase
252
in viscosity between the upper and lower mantle by about a factor of 10–100 (Hager, 1984; Forte and Mitrovica, 2001),
253
but whether this is a sharp or gradual increase and the depth at which it occurs is not well-constrained (Panasyuk and
254
Hager, 2000). Other observations of post-seismic deformation rates and other non-tectonic unloading events (rebound
255
of drying lakes or rebound following recent retreat of glaciers) also constrain the shallow upper-mantle viscosity to
256
be in the range of 1018 –1019 Pa-s and are often better fit by models using non-linear viscosity (Bürgmann and Dresen,
257
2008). Therefore, the upper-most mantle viscosity is probably on the order of 1018 –1020 Pa-s, while the upper-most
258
lower-mantle viscosity is 1021 –1022 Pa-s.
259
Deformation Mechanisms. Laboratory constraints on the rheology of olivine are consistent with dynamical con-
260
straints on the upper-mantle viscosity structure (Hirth and Kohlstedt, 2003; Bürgmann and Dresen, 2008). Olivine
261
deforms by a combination of diffusion creep (linear stress-strain-rate flow law) and dislocation creep (power-law
262
stress-strain-rate flow law) (Hirth, 2003; Karato et al., 2008). For reasonable estimates of the average grain size (10
263
mm), water content (1000 H/106 Si), and strain-rate on the order of 1 × 10−15 s−1 , the predicted viscosity is 1020
264
Pa-s and the deformation is roughly equally accommodated by the diffusion and dislocation mechanisms (Hirth and
265
Kohlstedt, 2003). In regions of higher strain-rate (directly beneath plates or surrounding slabs), deformation is primar-
266
ily accommodated by dislocation creep and leads to a reduction in viscosity to values of 1018 –1019 Pa-s (see viscosity
267
image and strain-rate profiles in Figures 5a–c). Deformation of olivine dominated by dislocation creep, which leads
13
Figure 6: Comparison of slab buoyancy sources and viscous shear forces. (a) Slab (negative) thermal buoyancy is the largest magnitude force due
to the large volume of the slab thermal anomaly. (b) Buoyancy due to phase changes depends on the slab temperature, clapeyron slope and the
density difference between the phases. Symbols: large circles indicate preferred values; small circles indicate range of previously-used values in
the literature. (c) Shear force resisting sinking of the slab. Symbols: upper mantle absolute viscosity (UM), transition zone viscosity factor (TZ),
lower mantle viscosity factor (LM). (d) Total force available to drive sinking of the slab as a function of the maximum slab depth for three different
sets of phase change parameters and mantle viscosity structures. Symbols: P.C.: 1– γol−wa = 4.0 MPa/K, γwa−ri = 6.9 MPa/K, γ sp−pv = −1.3
MPa/K; 2–γol−wa = 2.0 MPa/K, γwa−ri = 4.0 MPa/K, γ sp−pv = −2.9 MPa/K; 3–metastable olivine with a grain-size of 500 µm and sinking rate of
5.0 cm/yr, γ sp−pv = −1.3 MPa/K; N–no phase changes. F shear : viscous shear models shown in (c).
14
Figure 7: Mantle mineralogy and rheology structure. Average radial mantle viscosity structure is constrained by geophysical observations, while
dominant deformation mechanism is constrained by observation (or lack of) seismic anisotropy. The rheology of olivine is well-constrained by
laboratory measurements, whereas viscous behavior of other minerals is estimated based on diffusion rates of major elements and theoretical
considerations. Pv – perovskite; mw – magnesiowüstite.
268
to lattice-preferred orientation of crystals, is consistent with the widespread observation of shear wave splitting in
269
the shallow upper mantle and in subduction zones (Karato et al., 2008; Jadamec and Billen, 2010). In addition, the
270
pressure-dependence of the flow law predicts a gradual increase in viscosity with depth.
271
Much less is known about the rheology of wadsleyite, ringwoodite or perovskite. Seismic observations of shear-
272
wave splitting within the transition zone (Trampert and van Heijst, 2002) suggests that wadsleyite and ringwoodite
273
also deform by a combination of dislocation creep (i.e., a composite Newtonian and non-Newtonian viscosity), while
274
the lack of widespread shear-wave splitting in the lower mantle (Karato et al., 1995) suggests that deformation of
275
perovskite is dominated by diffusion creep (i.e., a Newtonian viscosity).
276
There are currently no direct measurements of the stress-strain-rate flow-laws, which determine the magnitude of
277
the viscosity and the conditions under which each deformation mechanism is active for wadsleyite, ringwoodite, per-
278
ovskite or magnesiowustite. However, estimates of these flow-laws and the viscosity magnitude have been based on
279
a combination of experimental results on the diffusion coefficients of major elements (Karato et al., 2001; Yamazaki
280
and Karato, 2001; Shimojuku et al., 2009), the plastic strength of these minerals (Weidner et al., 2001; Yamazaki
281
et al., 2009), and deformation theory (Karato et al., 2001; Shimojuku et al., 2009). These estimates predict that wad-
282
sleyite and ringwoodite have similar flow law parameters (similar diffusion coefficients) to olivine, while perovskite
283
deforming by diffusion creep would have a viscosity of 1022 Pa-s for a grain size of 2–3 mm. For all these minerals,
284
variations in the water content also affect the average viscosity: therefore a dry transition zone (Bercovici and Karato,
15
285
2005; Yoshino et al., 2008) may be 10–100 times more viscous than the upper-mantle.
286
Given the current state of observational and laboratory constraints, the best estimate of the mantle rheologic
287
structure (Figure 7) is one in which the upper-mantle and transition zone deform by similar flow-laws (composite
288
diffusion and dislocation creep) to that given by laboratory constraints on olivine. The transition zone may be drier
289
than the upper mantle and therefore more viscous by a factor of 10–100. The lower-mantle is likely dominated
290
by deformation by diffusion creep with a viscosity on the order of 1022 Pa-s. Therefore, in the absence of better
291
constraints, it is reasonable for current dynamical models to use the olivine flow laws in the transition zone, and a
292
modification of the olivine diffusion creep flow-law in the lower mantle (e.g., Schmeling et al. (1999); Cı́žková et al.
293
(2002); Billen and Hirth (2007)).
294
Viscous Shear Force on the Slab. The effect of viscous shear stress on slab descent can be estimated using a simple
295
model in which the shear stress is proportional to the viscosity immediately surrounding the slab and the effective
296
strain-rate at the slab surface (σ shear = 2ηe f ˙e f . The effective strain-rate can be estimated as the sinking-rate divided
297
by a length-scale (˙e f = 2v sink /w slab is the strain-rate, v sink is the sinking rate of the slab, w slab is the slab width),
298
here taken as the half-width of the slab (50 km). The net shear force on a slab is given as the shear stress times the
299
area (per unit length) of the top and bottom surfaces (F shear = σ shear L slab ). With this simple model the viscous shear
300
force increases with slab length and descent rate, but is most sensitive to changes in the surrounding mantle viscosity
301
(Figure 6c).
302
For an upper mantle viscosity of 1019 –1020 Pa-s the viscous shear force is less than 5 × 1012 N/m for a vertical slab
303
extending from 200 to 600 km and is therefore always less than half, or even less than 10% of the negative buoyancy
304
of the slab. Slabs with shallow dip in the upper mantle will experience slightly larger viscous shear force because the
305
length of the slab is longer, but this is likely to only make a difference for very young and slowly subducting slabs.
306
However, increasing the viscosity of the lower mantle by a factor of 100 causes the viscous shear force to become
307
comparable to the driving force by a depth of around 1000 km. With an increase in lower-mantle viscosity by a factor
308
of 300 to 3 × 1021 –3 × 1022 Pa-s, the viscous shear forces outpace the negative buoyancy forces as the slab reaches
309
1000–1200 km depth (Figure 6c,d).
310
A viscosity increase in the lower mantle has been shown to effect the dynamics of slab evolution in the transition
311
zone in combination with the phase change buoyancy sources, both with and without trench roll-back. With trench
312
roll-back an increase in the lower-mantle viscosity helps to trap the slab across or just below the 660-km boundary,
313
however roll-back rates of greater than 4 cm/yr are generally needed to cause flattening of relatively weak (Chris-
314
tensen, 1996; Torii and Yoshioka, 2007) or stiff slabs (Cı́žková et al., 2002). In the absence of trench roll-back, stiff
315
slabs subduct easily into the lower mantle (Billen and Hirth, 2007), with or without the transition zone buoyancy
316
sources. However, weak slabs (a yield stress of 100 MPa) buckle before sinking into the lower mantle, creating very
317
broad thermal anomalies below the transition zone in the lower mantle (Běhounková and Cı́žková, 2008). Also, slabs
318
that are completely weakened by grain-size reduction due to the phase transitions do become trapped in the transition
16
319
zone (Tagawa et al., 2007).
320
321
Constraints on the mantle rheology and its affect on slab descent suggest that: 1) viscous resistance to sinking is
322
minor in the upper mantle, consistent with the observed increase in maximum sinking rate with slab depth in the upper
323
mantle (Figure 1c), and 2) increases in viscosity and the change in rheology in the lower mantle creates significant
324
resistance to sinking of the slab and can even cause the slab to stop sinking and perhaps buckle and pile-up within
325
the upper-most lower mantle (660–1200 km). This suggest that the observed speed-limit on slab descent rates (Figure
326
1a–c) is the result of a net zero balance between the growing viscous resistance on, and negative buoyancy of, the
327
lower-mantle portion of the slab. Therefore, only the upper-mantle portion of the slab is available to drive plate
328
motion through slab-pull, consistent with previous models of plate motion rates and directions (Conrad and Lithgow-
329
Bertelloni, 2002). However, these results do not explain how slabs become trapped within the transition zone in the
330
absence of trench roll-back.
331
3.3. Slab Strength
332
Variations in the slab strength remain the most promising mechanism for explain the trapping of slabs in the
333
transition zone in cases without rapid trench rollback. Within the subduction zone the tectonic plate undergoes such
334
strong deformation that essentially all of the elastic strength of the slab is lost and the plate deforms visco-plastically
335
(Goetze and Evans, 1979; Billen and Gurnis, 2005). Because of the strong temperature dependence of the viscosity,
336
the viscous stresses in the cold slab interior predicted for deformation by diffusion or dislocation creep exceed the
337
yield stress. Therefore, the cold interior of the slab probably deforms by a stress-dependent mechanism (Peierls
338
mechanism; Goetze (1978)) or plastic yielding.
339
Experimental constraints on the yield strength as a function of temperature predict the minimum yield strength (for
340
temperatures ∼900◦ ) to increase from 0.5–1.0 GPa for olivine to 2.0 GPa for wadsleyite and ringwoodite and 3.5 GPa
341
for perovskite (Weidner et al., 2001). In the absence of other processes the slab should become stronger with depth
342
and therefore be more effective at transmitting the negative buoyancy of the upper-mantle slab to deeper portions of
343
the slab.
344
The integrated strength of a slab depends on both the effective viscosity for the cold plastically deforming interior
345
and the viscously deforming outer portions of the slab, the rate of deformation of the slab and stress applied to the slab.
346
The effective strength is always lower than the maximum yield stress (Figure 8): for example, the average effective
347
strength of slab with a maximum yield stress of 1000 MPa is about 450–650 MPa (model 1) depending on its age,
348
while a slab with a yield stress of 500 MPa has an average effective strength of 300 MPa (model 4).
349
Perhaps unexpectedly, younger slabs may have a higher effective strength than older slabs simply because a
350
younger slab is less negatively buoyant and therefore is subject to a smaller applied stress (models 1–3; Figure 8).
351
Similarly, the effective stress is affected by the amount of viscous support from the lower mantle: less viscous re-
352
sistance in the lower mantle decreases the net stress acting on the slab, which results in a higher effective strength
17
Figure 8: Comparison of average integrated slab strength for Models 1–7 shown in Figure 3. Slab strength increases moderately for younger (1)
and older slabs (3) due to lower driving stress or broader thermal anomaly, respectively. Slab strength drops significantly for lower yield strength
or wet slabs (4–5). Increasing viscous support from the lower mantle (6) decreases the stress in the slab (because it deforms less), while decreasing
viscous support from the lower mantle (7) increases stress in the slab (as it deforms at a faster rate).
353
(models 6, 7; Figure 8). The lithosphere is expected to be dry due to melting processes at the ridge, however, faulting
354
and subsequent serpentinization of the lithosphere during bending at the trench (Ranero et al., 2003) could decrease
355
slab strength by increasing the water content. This effect causes only minor increases in the dip of wet slabs compared
356
to dry slabs (model 5; Figure 3e).
357
Grain-size Weakening. Large variations in slab strength (by more than a factor of 10–1000) are possible through
358
localized changes in grain-size (Rubie, 1984; Rubie and Ross II, 1994). When grain size is very small (100–1000
359
microns) deformation by diffusion creep will occur at cold temperatures at a stress lower than the yield stress or
360
Peierls stress (Karato et al., 2001). At phase transition boundaries, the new phase nucleates as sub-micron-size grains
361
that slowly grow into larger grains. However, at cold temperatures, grain growth rates can keep grain sizes very small
362
(less than 100 microns) (Karato, 1989; Yamazaki et al., 1996, 2005; Nishihara et al., 2006). Because the diffusion
363
creep flow law has a power-law dependence on grain-size (power-law exponent of 3) a reduction in the average grain
364
size by a factor of 10 leads to a viscosity decrease by a factor of 1000.
365
Laboratory constraints on grain-growth kinetics are still limited and the volume of slab material under-going a
366
net grain-size reduction depends on the assumed growth-rate, presence of water, and temperature (Karato, 1989).
367
To test the effect of grain-size induced weakening of the slab following the olivine to wadsleyite transition Cı́žková
18
368
et al. (2002) systematically varied the grain-size and timing of grain-growth within a slab in 2D numerical subduction
369
models. They found that even with a grain-size reduction by a factor of 100 (viscosity decrease of 106 ) in the cold
370
slab interior the slab was still able to subduct into the lower mantle unless slab roll-back rates exceeded 4 cm/yr. The
371
grain-size weakened slabs continued to transmit the thermal buoyancy force of the slab to deeper portions of the slab
372
because the outer (warmer) regions of the slab remain viscously strong (Cı́žková et al., 2002). Only if the entire slab
373
permanently loses all of its strength in the transition zone, does this type of processes lead to trapping of the slab
374
(Tagawa et al., 2007).
375
However, grain-size reduction weakening of the slab may still be a viable mechanism for causing localized defor-
376
mation of the slab at 660-km, as this is the only depth at which all the minerals in the slab undergo a phase transition at
377
nearly the same depths. Grain-growth rates for combined perovskite and periclase samples suggest very slow growth
378
and small grain size (Yamazaki et al., 1996). Therefore, grain-size weakening of the slab at 660-km depth could affect
379
slab deformation at this boundary, but there are presently no models testing this possible mechanism.
380
4. Two Scenarios for Stagnant Slabs
381
The analysis of the slab buoyancy forces, viscous resistance to sinking and slab strength demonstrate that in the
382
absence of trench motion it is difficult for these processes to modify the behavior of an initially steeply-dipping slab. In
383
addition, the observations of slab-dip show that slabs tend to steepen as they lengthen in the upper mantle. Therefore,
384
in order to trap slabs in the transition zone, it is necessary to shallow the slab by other means either before or after it
385
reaches the transition zone. However, because the observations show no clear correlation between trench motion and
386
slab dip, it is necessary to propose two different mechanism for slab stagnation, depending on the stage of subduction
387
(new versus long-term) and stability of the overriding plate (Figure 9). The first mechanism, which applies to new
388
or unstable subduction zone, is trench roll-back (Funiciello et al., 2003; Bellahsen et al., 2005; Schellart, 2005) that
389
occurs before the slab reaches the base of the transition zone. The second mechanism, which applies to long-term,
390
stable subduction zones, is a decrease in slab dip by lateral migration of the deeper slab relative to the position of the
391
trench (Billen and Hirth, 2007).
392
Scenario 1: Transient Trench Retreat. Trench motion in 2D and 3D numerical models is primarily dependent on the
393
strength of the slab: strong slabs have advancing trench motion once they reach the bottom of the model domain, while
394
weaker slabs have retreating trench motion (Di Giuseppe et al., 2008). This behavior is interpreted as being controlled
395
by the increased resistance to bending (or unbending) with increased slab strength (or age), and is consistent with the
396
observation that trench motion is correlated with age (Figure 4b; Lallemand et al. (2008)). However, retreating motion
397
occurs for both strong and weak slabs before reaching the bottom of the model domain (i.e., base of the transition
398
zone), although the rate of retreat is faster for younger slabs (Figure 9a; t3 to t5 ). Models of subduction initiation also
399
exhibit a stage of rapid trench retreat as subduction becomes self-sustaining (Hall et al., 2003).
19
400
Kinematically, trench retreat as the slab sinks freely through the upper mantle occurs because the sinking rate of the
401
slab is higher than the rate at which the plate is being pulled into the mantle. Dynamically the partitioning of motion at
402
the trench occurs because energy dissipation caused by bending of the slab at the trench decreases the amount of slab-
403
pull force transferred from the sinking slab to the plate (e.g., Appendix A, Billen and Hirth (2007); Conrad and Hager
404
(2001)). To accommodate the difference in the rates of motion without stretching the slab, the trench motion must
405
balance the difference in the rate of motion of the slab and the rate of motion of the plate: Vt = V slab −V plate . Therefore,
406
unlike models with a fixed trench position (Billen and Hirth, 2007), if the trench is free to move, steepening of the
407
slab as it lengthens in the upper mantle will be partly balanced by trench retreat resulting in more shallow dipping
408
slabs entering the transition zone.
409
Shallowing of the slab as it enters the transition zone may also occur in response to acceleration of the slab caused
410
by the additional negative buoyancy from the olivine to wadsleyite to ringwoodite phase transitions (Figure 9a; t5 to
411
t8 ). This acceleration could increase the discrepancy between the slab velocity and plate velocity and lead to more
412
rapid trench roll-back or effective roll-back of the slab around 410-km: both causing further shallowing of the slab
413
above the transition zone. However, once the slab starts to interact with the increased viscous resistance of the lower
414
mantle and the phase transition at 660-km, the decrease in slab velocity could lead to a rapid decrease trench retreat
415
rate, and may even switch into trench advance for stronger, older slabs (Figure 9a; t8 to t9 ).
416
This time-dependent scenario is consistent with the observation that in general, young (weaker) slabs in the upper
417
mantle and transition zone exhibit trench retreat rates up to 50 mm/yr, while there is no clear correlation between the
418
retreat rate and the dip of each slab for the present-day (Figure 4a). In other words, the present-day slab shape in the
419
transition zone, is the result of transient trench motion while the slab was sinking into the transition zone, and not a
420
result of the trench motion once the slab has reached the base of the transition zone. Because this scenario depends
421
on changes in trench motion in response to the changing dynamics of the slab, it also requires that the overriding
422
plate can respond to this changing force by accommodating trench retreat via deformation or back-arc spreading in
423
the overriding plate.
424
This first scenario may be valid in places like the Marianas, where the trench is currently advancing, but was
425
recently rolling back and appears to have a flat slab portion just below the transition zone, Java where the trench is
426
currently stationary, but rapid retreat occurred at 30 Ma, or in Tonga, where rapid roll-back starting in 5–10 Ma, may
427
be responsible for the more shallow dip of the slab above 400 km (Fukao et al., 2001; Sdrolia and Müller, 2006).
428
Scenario 2: Stable Long-Term Subduction. Lateral migration of the slab away from the trench occurs in dynamical
429
models of subduction with a fixed trench, composite viscosity structure, stiff slabs and a more viscous lower mantle
430
(Figure 3; Billen and Hirth (2007)). The migration occurs because the difference in sinking rate of the slab in the
431
upper mantle (fast) compared to the lower mantle (slow) can not be accommodated by shortening or buckling of the
432
strong slab (Běhounková and Cı́žková, 2008). Shallowing of the slab via lateral migration requires stable, long-term
433
subduction because the rates of lateral migration are on the order of 10 to 20 mm/yr (Billen and Hirth, 2007). A slab
20
Figure 9: Two scenarios for the formation of stagnant slabs. a) Trench retreat before, and as, the slab reaches the transition zone, followed by fixed
or advancing trench motion leads to shallow-dipping slabs with no correlation to present-day retreating trench motion. This scenario requires that
the overriding plate can deform or move to accommodate trench retreat. b) For stable overriding plates, long-term subduction can lead to slow
lateral migration and shallowing of the slab. For very shallow slab dips, the inability to transmit sufficient slab forces down-dip may allow the
transition-zone portion of the slab to become stagnant and detach from the deeper slab.
21
434
that reaches the base of the transition zone with a vertical dip (Figure 9b; t1 to t3 ) and then continues to subduct into
435
the lower mantle, will take on the order of 50 to 100 million years to reach a dip of 20–30◦ (Figure 9b; t4 to t7 ).
436
As the slab approaches more shallow dipping geometry, it relies on the strength of the slab to transmit the overall
437
negative buoyancy of the slab to the slab-tip to overcome the local buoyancy anomaly associated with the 660-km
438
phase change (Figure 9b; t4 to t7 ). Local variation in the slab strength could prevent the negative slab-buoyancy
439
force from being fully transmitted to the transition-zone portion of the slab causing this portion of the slab to become
440
stagnant (Figure 9b; t8 to t9 ). This process can be viewed as a kind of instability, where above a certain dip, the slab-
441
transmitted stresses are sufficient to overcome resistance to sinking, but once a threshold dip is crossed, insufficient
442
stresses are transmitted to the slab-tip. The random orientation of moment tensor solution in very shallow-dipping
443
(< 20◦ ) portions of slabs compared to the down-dip alignment of moment tensor solution in all other slabs (Brudzinski
444
and Chen, 2005) supports this conclusion that stagnation of the slab is the result of a loss of down-dip transmitted
445
stresses.
446
For this scenario, stagnant slabs evolving from long-term shallow subduction are characterized by a very long slab
447
with shallow dip throughout the upper mantle, flattening of the slab tip within the transition zone, and evidence of
448
earlier (long-term) subduction in the form of a deeper slab segment in the lower mantle. This predicted evolution is
449
consistent with the observation that slab dip is directly correlated with slab length, in particular for shallow-dipping
450
transition-zone slabs (Figure 4d). This suggest that these stagnant slabs, started out as deep-mantle slabs that progres-
451
sively shallowed during long-term stable subduction, but have crossed the stability threshold leading to slab stagnation,
452
and in some cases, to detachment of the deeper portion of the slab.
453
This second scenario may be valid in places like Japan, where there has been little or no trench retreat and long term
454
subduction, the former Farallon slab, where there had been long-term stable subduction and a stagnant slab remains in
455
the transition zone (van der Lee and Nolet, 1997), or the central Aleutians, which has had stable subduction for more
456
than 60 my, little or no trench retreat, but also has a stagnant slab in the transition zone (Fukao et al., 2001; Sdrolia
457
and Müller, 2006).
458
5. Conclusions
459
Observations of subduction zone characteristics provide many important insights on slab dynamics both outside
460
and inside the transition zone, by illustrating the ways in which slab behavior deviates from simple model predictions,
461
and by making it possible to isolate combinations of parameters contributing to observed behavior. By comparing
462
these observations to a range of model predictions, two scenarios for the formation of stagnant slabs are proposed:
463
episodic trench retreat of young slabs with unstable overriding plates, and slow lateral migration of older slabs with
464
stable overriding plates. These two scenarios are consistent with the inferred behavior of shallow-mantle and deep-
465
mantle slabs, and with the behavior of slabs in numerical and laboratory models of subduction.
466
First, the observations show that slabs which have not yet reached the transition zone or have subducted beyond
22
467
it, appear to behave as existing physical models predict: 1) upper-mantle slabs steepen and sink more quickly with
468
increasing slab depth consistent with models with stiff slabs and a composite rheology, 2) lower-mantle slabs shallow
469
with increased slab depth and advancing trench roll-back rate, and show no dependence of sinking rate on slab-pull,
470
indicating that a high viscosity lower mantle supports and anchors the slab; and 3) both upper and lower mantle slabs
471
exhibit a moderate dependence of slab dip on slab age and a maximum sinking rate of 60 mm/yr, consistent with
472
models with stiff slabs, a composite upper mantle rheology and a higher viscosity lower mantle.
473
Second, observations of transition zone slabs show that: 1) the transition zone is currently occupied by slabs
474
with the full range of observed subducting plate ages, convergence velocities and trench roll-back rates, and therefore
475
the modification of the descent of slabs through the transition zone may be independent of these characteristics; 2)
476
these are the only slabs with a sinking rates of greater than 60 mm/yr and up to 150 mm/yr indicating that there is a
477
significant local increase in the negative buoyancy of the slab, consistent with current phase change data for the 410-
478
km and 540-km phase transitions, and no increase in viscous shear stresses; and 3) these slabs exhibit no correlation
479
of slab dip with trench retreat rate, as is predicted by models with a freely-sinking slab and no overriding plate.
480
Consideration of the buoyancy forces in the slab using current constraints on phase changes shows that 1) the
481
thermal bouyancy of the slab is many times larger than all other sources of buoyancy due to its larger volume; 2) the
482
increase in negative buoyancy of the slab as it converts from olivine to wadsleyite and ringwoodite can more than
483
double the local slab-pull force; 3) due to the very small volume of slab that may be affected by metastable olivine the
484
associated positive buoyancy is not likely to impede sinking of the slab, but would instead be associated with a non-
485
accelerated sinking rate; and 4) due to the small clapeyron slope of the major phase change at 660-km, the associated
486
small positive buoyancy is not expected to impede subduction of a stiff steeply-dipping slab. Therefore, while the
487
buoyancy sources due to phase changes above 660-km may aid in subduction, the buoyancy sources at 660-km are
488
insufficient to impede subduction into the lower mantle unless the slab already has a shallow dip.
489
Formation of a shallow-dipping slab, either due to transient trench retreat or slow lateral migration of the slab at
490
depth, is necessary for any of the other physical processes (buoyancy, increased viscous resistance, reduction in slab
491
strength) to trap a slab in the transition zone. Transient trench retreat is driven by the difference between the slab
492
velocity and the plate velocity, and should increase as the slab crosses the phase transitions at 410-km and 540-km.
493
Lateral migration of slabs accommodates the difference in sinking rate between the slab that has entered the more
494
viscous lower mantle and the faster sinking slab in the upper mantle. Both of these scenarios depend on having a stiff
495
slab capable of transmitting stress along the slab to cause the initial shallowing of the slab.
496
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