competing influences of plate width and far field boundary conditions on trench migration and morphology of subducted slabs in the upper mantle abstract seismic tomography of the mantle provides a snapshot view of the present day structure of subducted tectonic plates slabs in the mantle however a correct interpretation of how such features developed requires knowledge of both the history of plate motions in particular the locations of subduction zones over time as well as an understanding of how slabs deform and interact with the lower mantle the understanding of seismic tomography requires a detailed knowledge of the motion of the trench with time as well as the time evolution of subduction zones and their associated slabs we use 3 d numerical models to investigate two effects which can strongly influence the kinematics of subduction in particular the migration of the trench the width of the plate and the far field boundary conditions of the subducting plate these models study the full range of plate widths 300 6000 km and are subjected to the full range of boundary conditions fixed free and pushed representative of the tectonic settings found on earth additionally our results indicate that trailing edge boundary conditions dominate over the effect of plate width each boundary condition is identified to produce a particular trench migration behavior with an associated upper mantle slab morphology 1 fixed edges result in retreating trenches and retrograde motion of the slab which ends up lying flat atop the lower mantle 2 free trailing edges tend to exhibit quasi stationary trenches with slabs developing into folded piles atop the lower mantle and 3 pushed trailing edges generally result in advancing trenches that overrun previously subducted material to form forward draping slabs lying prone atop the lower mantle this range of behavior can be observed in seismic tomography and an example of each is provided within each suite of models with similar boundary conditions plate width has a subsidiary role in the observed slab morphology but three distinct regimes of plate width can be distinguished in regards to trench migration thus plate width is an important effect on trench migration and does result in notable differences in slab morphologies between narrow and wide plate widths

influence of lateral slab edge distance on plate velocity trench velocity and subduction partitioning 1 subduction of oceanic lithosphere occurs through both trenchward subducting plate motion and trench retreat we investigate how subducting plate velocity trench velocity and the partitioning of these two velocity components vary for individual subduction zone segments as a function of proximity to the closest lateral slab edge dse we present a global compilation for 207 trench segments from 17 active subduction zones on earth and three dimensional numerical models of progressive free subduction of a single oceanic plate that subducts into a stratified mantle the results show that the subducting plate velocity is always high 5 1 cm yr models and 4 2 cm yr nature and trench velocity is always low 2 5 cm yr models and 1 7 cm yr nature in the center of wide subduction zones dse 2200 km only in regions close to lateral slab edges dse 1000 km be it for narrow or wide subduction zones can the trench velocity exceed 4 cm yr models and 6 cm yr nature and can the subducting plate velocity go below 4 cm yr models and 2 cm yr nature in general plate velocities trench velocities and subduction partitioning are much more variable near slab edges than in the center of wide subduction zones owing to other parameters that affect subduction kinematics we conclude that subduction kinematics can vary considerably along individual subduction zones and that the upper bound values for trench velocity and lower bound values for subducting plate velocity and subduction partitioning at individual subduction zone segments depend critically on dse

buckling instabilities of subducted lithosphere beneath the transition zone a sheet of viscous fluid poured onto a surface buckles periodically to generate a pile of regular folds recent tomographic images beneath subduction zones together with quantitative fluid mechanical scaling laws suggest that a similar instability can occur when slabs of subducted oceanic lithosphere encounter enhanced resistance to penetration at 660 km depth beneath subduction zones such as central america and java the fast anomalies in elastic wavespeed are too broad 400 km to be explained by simple compressional thickening of subducted lithosphere that is initially 50 100 km thick by contrast a periodic buckling mechanism can account for both the characteristic wedge shapes of the anomalies and for their widths which agree closely with those predicted by the scaling laws in addition to providing a plausible physical interpretation of tomographic observations beneath some subduction zones buckling instabilities have important consequences for other aspects of global geodynamics such as tectonic plate reconstructions interpretation of geoid anomalies and modeling of secular changes in earth s moment of inertia

curvature of oceanic arcs oceanic arcs and deep sea trenches are the surface expressions of oceanic plates subducting into the earth s mantle we use a new numerical technique for simulating the dynamical evolution of the lithosphere mantle interaction in order to assess the causes of arc curvature we group the possible causes into two classes external feedback between the migrating lithosphere and the secondary induced mantle flow and internal heterogeneities within the lithosphere e g owing to differences in cooling ages of the plate at the trench we statistically assess that almost all arcs on the earth can be described by these hypotheses the method is also directly applied to the tonga and aleutian arcs bringing new insights on the origin of their shapes

effects of clay minerals on the aggregation and subsequent settling of marine synechococcus cyanobacteria are considered to play an important role in the oceanic biological carbon pump especially in oligotrophic regions but as single cells are too small to sink their carbon export has to be mediated by aggregate formation and possible consumption by zooplankton producing sinking fecal pellets here we study the aggregation and subsequent settling of the ubiquitous marine picocyanobacterium synechococcus as a model organism in roller tanks and investigate the effects of the clays kaolinite and bentonite in a series of concentrations we found that 1 synechococcus cells formed aggregates as large as 1 4 mm in diameter that sank at velocities of up to 440 m d 21 and 660 m d 21 with and without ballasting clays respectively 2 clay minerals increased the number and reduced the size of aggregates and their ballasting effects increased the excess density and sinking velocity of aggregates 3 kaolinite with its lower cation exchange capacity resulted in smaller and slower sinking aggregates compared to bentonite and 4 based on our experimental conditions synechococcus could potentially export carbon 2 3 times of that contained in their cells via aggregation likely due to the scavenging of transparent exopolymer particles and dissolved organic matter the presented results have relevance for our understanding of the role of cyanobacteria in the ecology and biogeochemistry in today s ocean and also elucidate mechanisms of carbon export in the early proterozoic ocean

variability in flow and temperatures within mantle subduction zones 1 a series of laboratory experiments is used to model three dimensional aspects of flow in subduction zones and the consequent temperature variations in the slab and overlying mantle wedge the effects of longitudinal rollback and slab steepening components of motions are considered along with different thicknesses of the over riding lithosphere the results show that the style of plate sinking influences the evolution of subduction zones both in terms of the speed orientation and temperature of flow in the overlying wedge and in terms of the temperatures at the surface of the descending slab in the simplest case of longitudinal sinking without rollback motion velocities in the mantle wedge are 30 40 of the downdip plate speed return flow paths in the shallow mantle wedge are nearly horizontal for slow slab speeds and steepen with higher slab speeds and there is no mass flux around the edges of a slab segment of finite width rollback subduction leads to flow both around and beneath the sinking slab with larger velocities in the wedge up to 150 of the slab speed and flow focused toward the center of the plate segment rollback subduction in which either the trench migrates or the plate steepens with time induces shallow and steep wedge return flow trajectories respectively the thermal evolution of the plate is strongly influenced by sinking style and rate highest temperatures are along the edges of the slab for longitudinal sinking but along the centerline of the slab segment for rollback motion slab surface temperatures when scaled to the mantle are higher than those given by previous two dimensional numerical models and are consistent with recent observational and experimental data on melt compositions

effects of plate bending and fault strength at subduction zones on plate dynamics for subduction to occur plates must bend and slide past overriding plates along fault zones because the lithosphere is strong significant energy is required for this deformation to occur energy that could otherwise be spent deforming the mantle we have developed a finite element representation of a subduction zone in which we parameterize the bending plate and the fault zone using a viscous rheology by increasing the effective viscosity of either the plate or the fault zone we can increase the rates of energy dissipation within these regions and thus decrease the velocity of a plate driven by a given slab buoyancy we have developed a simple physical theory that predicts this slowing by estimating a convecting cell s total energy balance while taking into account the energy required by inelastic deformation of the bending slab and shearing of the fault zone the energy required to bend the slab is proportional to the slab s viscosity and to the cube of the ratio of its thickness to its radius of curvature the distribution of dissipation among the mantle lithosphere and fault zone causes the speed of a plate to depend on its horizontal length scale using the observation that earth s plate velocities are not correlated to plate size we can constrain the lithosphere viscosity to be between 50 and 200 times the mantle viscosity with higher values required if the fault zone can support shear tractions 50 mpa over 300 km these subduction zone strengths imply that the mantle fault zone and lithosphere dissipate about 30 10 and 60 of a descending slab s potential energy release if the slab is 100 km thick the lithospheric component is highly dependent on slab thickness it is smaller for thin plates but may be large enough to prevent bending in slabs that can grow thicker than 100 km ubduction zone strength should be more stable than mantle viscosity to changes in mantle temperature so the controlling influence of subduction zones could serve to stabilize plate velocities over time as the earth cools because the details of convergent plate boundaries are so important to the dynamics of plate motion numerical models of mantle flow should treat subduction zones in a realistic way

trench parallel flow beneath the nazca plate from seismic anisotropy shear wave splitting of s and sks phases reveals the anisotropy and strain field of the mantle beneath the subducting nazca plate cocos plate and the caribbean region these observations can be used to test models of mantle flow two dimensional entrained mantle flow beneath the subducting nazca slab is not consistent with the data rather there is evidence for horizontal trench parallel flow in the mantle beneath the nazca plate along much of the andean subduction zone trench parallel flow is attributale utable to retrograde motion of the slab the decoupling of the slab and underlying mantle and a partial barrier to flow at depth resulting in lateral mantle flow beneath the slab such flow facilitates the transfer of material from the shrinking mantle reservoir beneath the pacific basin to the growing mantle reservoir beneath the atlantic basin trenchparallel flow may explain the eastward motions of the caribbean and scotia sea plates the anomalously shallow bathymetry of the eastern nazca plate the long wavelength geoid high over western south america and it may contribute to the high elevation and intense deformation of the central andes

trench migration net rotation and slab mantle coupling article i nfo laboratory models have been conducted to improve our understanding of the role that the resistance of the slab to bending and its coupling to the ambient mantle play in subduction dynamics over geological time scales our models are set up with a viscous plate of silicone lithosphere subducting under negative buoyancy in a viscous layer of glucose syrup mantle for our study the lithosphere upper mantle viscosity contrast has been systematically varied from 10 to 10 5 in order to explore the parameter space between weak and strong slab dynamics we found that subduction is characterized by a retreating mode for viscosity ratios n10 4 by the coexistence of a retreating mode and an advancing mode for viscosity ratios between 10 4

mantle flow at a slab edge seismic anisotropy in the kamchatka region the junction of the aleutian island and the kamchatka peninsula defines a sharp turn in the boundary of the pacific and north american plates terminating the subduction zones of the northwest pacific the regional pattern of shear wave birefringence near the junction indicates that trench parallel strain follows the seismogenic benioff zone but rotates to trench normal beyond the slab edge asthenospheric mantle is inferred to flow around and beneath the disrupted slab edge and may influence the shallowing dip of the benioff zone at the aleutian junction

dynamics of free subduction from 3 d boundary element modeling 1 in order better to understand the physical mechanisms underlying free subduction we perform three dimensional boundary element numerical simulations of a dense fluid sheet with thickness h and viscosity 2 sinking in an ambient mantle with viscosity 1 the mantle layer is bounded above by a traction free surface and is either 1 infinitely deep or 2 underlain by a rigid boundary at a finite depth h d similar to the typical geometry used in laboratory experiments instantaneous solutions in configuration 1 show that the sheet s dimensionless stiffness s determines whether the slab s sinking speed is controlled by the viscosity of the ambient mantle s 10 time dependent solutions with tracers in configuration 2 demonstrate a partial return flow around the leading edge of a retreating slab and return flow around its sides the extra edge drag exerted by the flow around the sides causes transverse deformation of the slab and makes the sinking speed of a 3 d slab up to 40 less than that of a 2 d slab a systematic investigation of the slab s interaction with the bottom boundary as a function of 2 1 and h h delineates a rich regime diagram of different subduction modes trench retreating slab folding trench advancing and reveals a new advancing folding mode in which slab folding is preceded by advancing trench motion the solutions demonstrate that mode selection is controlled by the dip of the leading edge of the slab at the time when it first encounters the bottom boundary

toroidal mantle flow around the calabrian slab italy from sks splitting 1 sks wave birefringence is likely caused by ongoing and or fossil mantle flow splitting parameters in the southern tyrrhenian subduction zone define a quite complex pattern of fast directions with large delay times up to 2 7 s fast directions are prevalently trench parallel below the slab and rotate to trench normal at the western edge of the slab depicting a ring around it we interpret these anisotropic patterns also observed in laboratory experiment as toroidal mantle flow induced by rollback subduction

cenozoic tectonics of western north america controlled by evolving width of farallon slab the basin and range province of western north america exemplified by the alternating mountain ridge and valley landscapes across nearly the entire u s state of nevada started to form 50 million years ago through a series of extensions of the continental crust prior to that massive mountain building collisions at the boundary between north america and the pacific ocean formed a subduction zone and compressed the continent by combining observations of global subduction zone velocities with numerical modeling schellart et al p 316 1 demonstrate that the thinning of the subducting portion of the oceanic plate controlled how and when the transition from compression to extension occurred even today where the much smaller remnant oceanic plate continues to slowly subduct below north america in the pacific northwest the width of the slab and not its age controls the velocity of subduction indeed this relation may explain the dynamics of other modern subduction zones from south america to japan 1 lookup doi 10 1126 science 1190366

dynamics of plate bending at the trench and slab plate coupling 1 the bending strength of subducting lithosphere plays a critical role in the earth s plate tectonics and mantle convection modulating the amount of slab pull transmitted to the surface and setting the boundary conditions under which plates move and deform however it is the subject of a lively debate how much of the potential energy of the downgoing plate is consumed in bending the plate and how the lithospheric strength is defined during this process we model the subduction of a viscoelastic lithosphere driven solely by the downgoing plate s buoyancy freely sinking in a passive mantle represented by drag forces to investigate the dynamics of bending 1 we vary the density and the viscosity profile within the plate from isoviscous where strength is distributed to strongly layered where strength is concentrated in a thin core and 2 we map the stress strain and dissipation along the downgoing plate the effective plate strength during bending is not a simple function of average plate viscosity but is affected by rheological layering and plate thinning earth like layered plates allow for the transmission of large fractions of slab pull 75 80 through the bend and yield a net slab pull of fspnet 1 to 6 1012 n m 1 which varies with the buoyancy of plates in all models only a minor portion of the energy is dissipated in the bending surprisingly bending dissipation hardly varies with lithospheric viscosity because in our dynamic system the plates minimize overall dissipation rate by adjusting their bending curvature as a result bending dissipation b is mainly controlled by the bending moment work rate exerted by slab pull we propose a new analytical formulation that includes a viscosity dependent bending radius which allows for assessment of the relative bending dissipation in the earth s subduction zones using parameters from a recent global compilation this yields estimates of b tot 20 these results suggest that plates on earth weakly resist bending yet are able to propagate a large amount of slab pull

effects of relative plate motion on the deep structure and penetration depth of slabs below the izu bonin and mariana island arcs an increasing number of seismological studies indicate that slabs of subducted lithosphere penetrate the earth s lower mantle below some island arcs but are deflected or rather laid down in the transition zone below others recent numerical simulations of mantle flow also advocate a hybrid form of mantle convection with intermittent layering we present a multi disciplinary analysis of slab morphology and mantle dynamics in which we account explicitly for the history of subduction below specific island arcs in an attempt to understand what controls lateral variations in slab morphology and penetration depth central in our discussion are the izu bonin and mariana subduction zones we argue that the differences in the tectonic evolution of these subduction zones in particular the amount and rate of trench migration can explain why the slab of subducted oceanic lithosphere seems to be at least temporarily stagnant in the earth s transition zone below the izu bonin arc but penetrates into the lower mantle below the mariana arc we briefly speculate on the applicability of our model of the temporal and spatial evolution of slab morphology to other subduction zones although further investigation is necessary our tentative model shows the potential for interpreting seismic images of slab structure by accounting for the plate tectonic history of the subduction zones involved we therefore hope that the ideas outlined here will stimulate and direct new research initiatives

evolution of subduction zone curvature and its dependence on the trench velocity and the slab to upper mantle viscosity ratio 1 three dimensional laboratory models of upper mantle subduction are presented investigating the effect of the trench velocity vt and the slab to upper mantle viscosity ratio sp um on trench curvature and slab curvature one set of experiments varies sp um from 66 to 1375 another set of experiments modifies vt through applying different velocities at the trailing plate the results show that the radius of trench curvature rtc progressively decreases with continuous trench retreat due to quasi toroidal mantle return flow from the subslab region around the lateral slab edges and toward the mantle wedge region but starts to increase when trench retreat changes to trench advance due to quasi toroidal return flow in the opposite direction furthermore rtc increases with increasing sp um i e progressively stronger slabs are progressively less curved following a cubic root function the force required to curve the slab and trench varies with progressive subduction but is only 0 1 2 5 of the total negative buoyancy force of the slab while the viscous dissipation rate due to progressive slab curvature is only 0 01 0 60 of the potential energy release rate comparison of trench curvature in the models scaled slab width w 750 km with that of the scotia subduction zone w 800 km indicates that for the scotia subduction zone the effective sp um is of the order 1 2 102 finally the elastic sphere indentation model for arc curvature is revisited demonstrating that four main predictions are not met by observations implying that the model should be rejected

plate force due to bending at subduction zones 1 bending of the lithosphere at subduction zones generates stresses that contribute to the force balance on plates we determine the net horizontal force on subducting plates by imposing a simple kinematic description of strain in the equations that govern the mechanical equilibrium of a thin viscous sheet the magnitude of the force depends on the velocity thickness and curvature of the subducting plate using representative values for old oceanic lithosphere we obtain an effective horizontal force that is nearly 40 of the buoyancy force due to slabs in the upper mantle

predicting trench and plate motion from the dynamics of a strong slab the motion of oceanic plates is commonly related to the subduction of cold and dense oceanic material into the mantle these models predict plate velocities from subduction velocities but the trench motion is not directly included in the computation here using a recent compilation of a global data set we found that the motion of trenches either advancing or retreating with respect to upper plates scales with their corresponding subducting plates motion based on simple experimental tests we found that subduction of strong slabs inside the upper mantle correctly predicts these kinematic relationships we deduce that the motion of the trenches represent the surface manifestation of the resistance encountered by the subducting lithosphere to bend and penetrate within the upper mantle

the bending mechanics in a dynamic subduction system constraints from numerical modelling and global compilation analysis abstract lithospheric plates bend at subduction zones where the vertical motions of the slabs are converted to surface plate motions to understand the mechanics of plate bending we derive scaling laws for the deflection at the margin i e radius and dip from numerical models of a subducting viscoelastic plate in such dynamic system we find that the buoyancy and the stiffness of the plates control the radius and the dip as well as the plate motions toward the trench this mechanical model successfully predicts the curvature of published three dimensional laboratory and numerical models for a thorough comparison with the observable we have also implemented forces additional to the slab pull such as the suction force and far field stresses by increasing or resisting the torque applied at the trench by the slab these forces can largely rearrange the dip and the radius of slabs and the inherent plate motions although they do not alter the observed anticorrelation between radius and dip similar inverse correlation relationship and dip radius ranges are shown by most of the subduction zones analysed from a global compilation radii in the range of 100 350 km and dips of 30 70 for slabs that extends to the bottom of the upper mantle are compatible with the models and allow estimating an average lithospheric viscosity contrast of 200 in the bending with respect to the ambient mantle radii and dips outside of this range are in good agreement with the trends and the magnitudes of models that include suction and far field forces in all these subduction zones the correlation between dip radius and plate velocity is found to be compatible with that of the models showing how relevant bending is for the dynamics of earth

dynamics of retreating slabs 1 insights from two dimensional numerical experiments from the effects of mantle flux part 2 therefore in this paper we apply forces to the slab using simple analytical functions related to buoyancy and viscous forces in order to isolate the role of rheology on slab dynamics we analyze parameters for simplified elastic viscous and nonlinear viscoelastoplastic single layer models of slabs and compare them with a stratified thermomechanical viscoelastoplastic slab embedded in a thermal solution the near surface behavior of slabs is summarized by assessing the amplitude and wavelength of forebulge uplift for each rheology in the complete thermomechanical solutions vastly contrasting styles of slab dynamics and force balance are observed at top and bottom bends however we find that slab subduction can be modeled using simplified rheologies characterized by a narrow range of selected benchmark parameters the best fit linear viscosity ranges between 5 10 22 pa s and 5 10 23 pa s the closeness of the numerical solution to nature can be characterized by a deborah number 0 5 indicating that elasticity is an important ingredient in subduction index terms 8120 tectonophysics dynamics of lithosphere and mantle general 8159 tectonophysics rheology crust and lithosphere 8160 tectonophysics rheology general keywords subduction numerical models lithospheric rheology

bending mechanics and mode selection in free subduction a thin sheet analysis summary to elucidate the dynamics of free buoyancy driven subduction of oceanic lithosphere i study a model in which a 2 d sheet of viscous fluid with thickness h and viscosity 1 subducts in an infinitely deep ambient fluid with viscosity 1 numerical solutions for the sheet s evolution are obtained using the boundary element method bem starting from an initial configuration comprising a short protoslab attached to a longer horizontal plate that is free to move laterally beneath an impermeable traction free surface interpretation of the solutions using thin viscous sheet theory shows that the fundamental length scale controlling the subduction is the bending length lb defined at each instant as the length of the portion of the sheet s midsurface where the rate of change of curvature is significant geophysically speaking lb is the sum of the lengths of the slab and of the region seaward of the trench where flexural bulging occurs the bending length in turn enters into the definition of the sheet s dimensionless stiffness s h lb 3 which controls whether the sinking speed of the slab is determined by the viscosity of the sheet itself s 1 or by that of the ambient fluid s 1 motivated by laboratory observations of different modes of subduction retreating versus advancing trench folding versus no folding etc in fluid layers with finite depth i calculate numerically the dip d of the slab s leading end as a function of and the normalized depth d h to which it has penetrated the contours of the function d d h strongly resemble the intermode boundaries in the laboratory based regime diagram of schellart supporting the hypothesis that the mode of subduction observed at long times in experiments is controlled by the dip of the slab s leading end when it reaches the bottom of the layer in particular the bem solutions explain why trenches advance in the laboratory only when lies in an intermediate range and why they retreat when is either smaller or larger than this application of the bem model to wu et al s compilation of the minimum curvature radii of subducted slabs suggests 140 510 for the earth this is too small to permit the laboratory type trench advancing mode in agreement with the lack of tomographic evidence for slabs that are bent over backwards

segmentation of the farallon slab abstract recent tomography images reveal a complex 3d mantle structure beneath western united states with feature morphology varying rapidly with depth by assimilating plate motion history paleo age of sea floor and paleo geography of plate boundaries in a 3 d numerical model we simulate the farallon juan de fuca subduction during the past 40 ma we find that the highly segmented upper mantle structure of western u s is a direct result of the farallon subduction we show that the tilted horseshoe shaped fast seismic anomaly beneath nevada and utah at 300 600 km depth range is in fact a segment of curled slab subducted since 15 ma and the shallower linear slab beneath the cascades is younger than 5 ma the distinct morphology between these two parts of the subduction system indicates the strong influence of the fast trench rollback since 20 ma the northward migrating jf pa na triple junction and the toroidal flow around slab edges the observed mantle structures are used to constrain the rheology of the upper mantle through matching the shape depth and location of modeled subducted slab segments the inferred viscosity for the asthenosphere is 5 10 19 pa s and those for the transition zone and lower mantle are 1 5 10 21 pa s and 2 10 22 pa s respectively the slab is found to be about 2 orders of magnitude stronger than the ambient mantle above 410 km depth but of similar order of magnitude viscosity in the transition zone

the dynamics of subduction and trench migration for viscosity stratification summary although subduction plays a dominant role in plate tectonics related processes such as trench migration are not well understood we investigate the influence of viscosity stratification and different flow boundary conditions on the trench migration dynamics of a subducting lithosphere in a 2 d model using a finite difference code subduction and mantle flow are driven by a compositionally prescribed density contrast between the high viscosity slab and the ambient mantle no overriding plate is assumed the model rheology is viscoplastic at shallow and viscous at greater depth the mantle is stratified with a higher viscosity in the lower part of the computational domain the plastic rheology allows the plate to decouple from the top of the box and is described by a simplified friction law to mimic the brittle deformation of the shallow lithosphere the flow patterns and slab morphologies differ as a function of the velocity boundary conditions bcs for reflective bcs we model either a plate which is fixed on the box side or a plate that can freely move a slab with periodic bcs is always laterally free we find that when the slabs interact with the highly viscous lower mantle the slab with reflective bcs is more folded than the periodic one due to the confinement of mantle flow around the slab in general the trench is observed to roll back toward the oceanic plate for free slabs with reflective bcs the trench retreat velocity deceases after the interaction with the lower mantle in contrast for the free slab with periodic bcs it is nearly constant or even increases with time if described in a reference frame fixed to the lower mantle the free slab with periodic bcs exerts a force on the lower mantle which causes a net differential flow between the upper and lower mantle we also carried out additional experiments with different mechanical slab properties and thicknesses stiffer free slabs subduct more steeply and are able to penetrate straight into the lower mantle after penetration into the lower mantle the trench moves toward the continent thinner slabs deform more easily and are folded for all boundary conditions we can generalize the rollback systematics for free slabs by normalizing trench velocities by the plate speed free slabs being more representative of the west pacific subduction zones show large temporal variations of normalized trench velocities ranging between a retreat value of 1 0 to an advancing value of 0 3

spherical dynamic models of top down tectonics 1 we use the multipole boundary element method mp bem to simulate regional and global geodynamics in a spherical 3 d setting we first simulate an isolated subducting rectangular plate with length llitho and width wlitho varying between 0 5 and 2 times the radius of the earth rearth and with viscosity litho varying between 100 and 500 times the upper mantle um sinking in a layered mantle characterized by lower upper mantle viscosity ratio lm um varying between 1 and 80 in a mantle with small upper lower viscosity contrast 1 trench and plate motions are weakly dependent on wlitho plate motion is controlled by slab pull if llitho rearth while for longer plates plate speed strongly decreases because of the plate basal friction and flow reorganization an increasing viscosity ratio gradually breaks this pattern and for 10 combined with wlitho rearth and greater trench advance and retreat are simultaneously observed these results offer a first order explanation of the origin of the size llitho wlitho rearth of the largest plates observed over the past 150 myr finally two global plate tectonic simulations are performed from reconstructed plates and slabs at 25 ma before present and before 100 ma respectively it is shown that mp bem predicts present plate kinematics if plate mantle decoupling is adopted for the longest plates llitho rearth models for 100 ma show that the slab slab interaction between india and izanagi plates at 100 ma can explain the propagation of the plate reorganization from the indian to the pacific plate

quantifying the energy dissipation of overriding plate deformation in three dimensional subduction models in a subduction system the force and the energy required to deform the overriding plate are generally thought to come from the negative buoyancy of the subducted slab and its potential energy respectively such deformation might involve extension and back arc basin formation or shortening and mountain building how much of the slab s potential energy is consumed during overriding plate deformation remains unknown in this work we present dynamic three dimensional laboratory experiments of progressive subduction with an overriding plate to quantify the force fopd that drives overriding plate deformation and the associated energy dissipation rate opd and we compare them with the negative buoyancy fbu of the subducted slab and its total potential energy release rate bu respectively we varied the viscosity ratio between the plates and the sublithospheric upper mantle with sp um 157 560 and the thickness of the overriding plate with top 0 5 2 5 cm scaling to 25 125 km in nature the results show that fopd fbu has average values of 0 5 2 0 with a maximum of 5 3 and opd bu has average values of 0 05 0 30 with a maximum of 0 41 the results indicate that only a small portion of the negative buoyancy of the slab and its potential energy are used to deform the overriding plate our models also suggest that the force required to deform the overriding plate is of comparable magnitude as the ridge push force furthermore we show that in subduction models with an overriding plate bending dissipation at the subduction zone hinge remains low 3 15 during steady state subduction

influence of trench width on subduction hinge retreat rates in 3 d models of slab rollback subduction of tectonic plates limited in lateral extent and with a free trailing tail i e free subduction is modeled in a three dimensional 3 d geometry the models use a nonlinear viscoplastic rheology for the subducting plate and exhibit a wide range of behaviors depending on such plate characteristics as strength width and thickness we investigate the time evolution of this progressive rollback subduction measure the accompanying return flow in the upper mantle and quantify the plate kinematics due to the 3 d geometry flow is allowed to accompany slab rollback around the lateral edges of the slab the toroidal component as opposed to 2 d geometry where material is forced to flow underneath the slab tip the poloidal component a simple force balance is provided which relates the speed of backward trench migration to the resistive forces of generating flow and weakening the plate our results indicate most of the gravitational energy of the system i e the negative buoyancy of the subducting slab is converted into a toroidal flow 69 a much smaller amount goes into weakening the plate 18 and the remaining amount goes into driving flow parallel to displacement of the slab 13 for the trench widths w we investigate 1500 km a maximum trench retreat rate occurs for trenches 600 km wide which is attributed to the interaction between a plate of finite width and the induced flow which has a lengthscale in the horizontal direction these numerical results quantitatively agree with comparable 3 d laboratory experiments using analogue models with a purely viscous plate material schellart 2004a 2004b including correlations between increasing retreat rate with increasing plate thickness trench width for maximum retreat rate 500 km and estimated amount of slab buoyancy used to drive rollback induced flow 70 several implications for plate tectonics on earth result from these models such as rollback subduction providing a physical mechanism for ephemeral slab graveyards situated above the more viscous lower mantle and endothermic phase transition prior to a flushing event into the lower mantle mantle avalanche

subduction zone evolution and low viscosity wedges and channels dehydration of subducting lithosphere likely transports fluid into the mantle wedge where the viscosity is decreased such a decrease in viscosity could form a low viscosity wedge lvw or a low viscosity channel lvc on top of the subducting slab using numerical models we investigate the influence of low viscosity wedges and channels on subduction zone structure slab dip changes substantially with the viscosity reduction within the lvws and lvcs for models with or without trench rollback overthickening of slabs is greatly reduced bylvws or lvcs two divergent evolutionary pathways have been found depending on the maximum depth extentofthelvwandwedgeviscosity assumingaviscositycontrastof0 1withbackgroundasthenosphere modelswithalvwthat extendsdown to 400km depthshow asteeply dipping slab while models with anlvw that extends to muchshallower depth such as 200 km can produce slabs that are flat lying beneath the overriding plate there is a narrow range of mantle viscosities that produces flatslabs 5to10 10 19 pas andthe slab flatteningprocessisenhanced bytrenchrollback slabcanbedecoupled fromthe overriding platewithalvcifthe thicknessisatleastafew10s ofkm the viscosityreduction isatleastafactor oftwoandthedepthextentofthe lvc is several hundred km these models have important implications for the geochemical and spatial evolution of volcanic arcs and the state of stress within the overriding plate the models explain the poor correlation between traditional geodynamic controls subductingplateageandconvergencerates onslabdip wepredictthatwhenvolcanicarcschangetheirdistancefromthetrench they could be preceded by changes in arc chemistry we predict that there could be a larger volatile input into the wedge when arcs migrate toward the trench and visa versa the transition of a subduction zone into the flat lying regime could be preceded by changes in the volatile budget such that the dehydration front moves to shallower depths our flat slab models shed some light on puzzling flat subductionsystems likeincentralmexico wherethereisnodeformationwithintheoverridingplateabovetheflatsegment thelack

tethyan subducted slabs under india abstract tomographic imaging of the mantle under tibet india and the adjacent indian ocean reveals several zones of relatively high p wave velocities at various depths under the hindu kush region in northeastern afghanistan and southern tajikistan a regional northward dipping slab is seen in the entire upper 600 km of the mantle and is apparently still attached to the lithosphere of the indian plate under northern pakistan this same slab shows a roll over structure with the deeper portion overturned and dipping southward as can also be seen in the distribution of earthquake hypocenters farther east southeast e g in the vicinity of nepal a well resolved anomaly below 450 km depth is connected to the slab under the hindu kush but seems to be separated from the lithosphere above 350 km these upper mantle anomalies are interpreted as the remnants of delaminated sub continental lithosphere that went down when greater india continued to converge northward with asia after 45 ma the deeper high velocity anomalies under the indian sub continent appear clearly separated from the shallower ones as well as from each other and are inferred to represent remnants of oceanic lithospheric slabs that have sunk into the lower mantle and were subsequently overridden by the indian plate they occur at depths between 1000 and 2300 km and occasionally descend down to the core mantle boundary the anomalies form three parallel wnw ese striking zones we interpret the two southern zones as remnants of oceanic lithosphere that was subducted when the neo tethys ocean closed between india and tibet in the cretaceous and earliest tertiary the northern deep mantle zone under northern afghanistan the himalayas and the lhasa block in southern tibet may represent the last subducted remnant of the paleo tethys ocean which is thought to have closed before the hauterivian stage of the early cretaceous the middle zone continues southeastward as a rather straight high velocity zone towards sumatra where it becomes convex southward and parallel to the subduction zone under the sunda arc comparison of this straight middle zone near india with the shallower upper 600 1000 km northern zone which displays a cusp like shape near the yunnan sw china syntaxis of the eastern himalayas supports the notion that the shallow northern zone represents later subduction than the deeper middle zone the suggestion of a counterclockwise rotation 20 of the indian plate during tertiary indentation of asia is supported by these features the present day latitudes of 5 35 n of the deep slabs under india and adjacent areas correspond to the approximate paleolatitudes of the cretaceous subduction zones the slab remnants in the middle mantle occur therefore near the ancient locations where they started their downward journey which implies that lateral movements in the deeper mantle were not large

slab stiffness control of trench motion insights from numerical models 1 subduction zones are not static features but trenches retreat roll back or advance here we investigate the dominant dynamic controls on trench migration by means of two and three dimensional numerical modeling of subduction this investigation has been carried out by systematically varying the geometrical and rheological model parameters our viscoplastic models illustrate that advancing style subduction is promoted by a thick plate a large viscosity ratio between plate and mantle and a small density contrast between plate and mantle or an intermediate width w 1300 km advancing slabs dissipate 45 to 50 of the energy in the system thin plates with relatively low viscosity or relatively high density or wide slabs w 2300 km on the other hand promote subduction in the retreating style i e slab roll back the energy dissipated by a retreating slab is 35 to 40 of the total dissipated energy most of the energy dissipation occurs in the mantle to accommodate the slab motion whereas the lithosphere dissipates the remaining part to bend and unbend with a simple scaling law we illustrate that this complex combination of model parameters influencing trench migration can be reduced to a single one plate stiffness stiffer slabs cause the trench to advance whereas more flexible slabs lead to trench retreat the reason for this is that all slabs will bend into the subduction zone because of their low plastic strength near the surface but stiff slabs have more difficulty unbending at depth when arriving at the 660 km discontinuity those bent slabs tend to cause the trench to advance in a similar way variation of the viscoplasticity parameters in the plate may change the style of subduction a low value of friction coefficient weakens the plate and results in a retreating style while higher values strengthen the plate and promote the advancing subduction style given the fact that also on earth the oldest and therefore probably stiffest plates have the fastest advancing trenches we hypothesize that the ability of slabs to unbend after subduction forms the dominant control on trench migration

a regime diagram for subduction styles from 3 d numerical models of free subduction abstract previous models of subduction both analogue and numerical have observed a number of distinct styles of subduction each with particular subduction motions partitioned between slab rollback and forward plate advance and associated slab morphologies we use 3 d numerical models to investigate subduction dynamics by varying the strength of slabs as well as the buoyancy and propose a new classification based on these parameters the slab strength is specified both through the ratio of viscosities between the subducting plate and upper mantle plate um as well as the plate thickness h plate only a very restrictive range of plates strong plates with smaller buoyancy tend to favor modes of subduction which are exclusively advancing plates which have greater negative buoyancy will eventually transition into a retreating style we find that the flexural strength and the buoyancy determine the subduction style as distinguished by a characteristic slab morphology and control several subduction characteristics including the partitioning between slab rollback and plate advance the trench curvature and the slab s radius of curvature plates that are 80 100 km thick with plate um 100 300 are classified here as weak and are the only plates to exhibit slab geometry with several recumbent folds atop the more viscous lower mantle this regime of weak plates with their associated slab morphologies predominant folding is argued to be most similar to slabs on earth based on the presence of folded slab piles in earth s upper mantle as interpreted from seismic tomography

reconciling strong slab pull and weak plate bending the plate motion constraint on the strength of mantle slabs although subducting slabs undergo a bending deformation that resists tectonic plate motions the magnitude of this resistance is not known because of poor constraints on slab strength however because slab bending slows the relatively rapid motions of oceanic plates observed plate motions constrain the importance of bending we estimated the slab pull force and the bending resistance globally for 207 subduction zone transects using new measurements of the bending curvature determined from slab seismicity predicting plate motions using a global mantle flow model we constrain the viscosity of the bending slab to be at most similar to 300 times more viscous than the upper mantle stronger slabs are intolerably slowed by the bending deformation weaker slabs however cannot transmit a pull force sufficient to explain rapid trenchward plate motions unless slabs stretch faster than seismically observed rates of similar to 10 15 s 1 the constrained bending viscosity similar to 2 x 10 23 pa s is larger than previous estimates that yielded similar or larger bending resistance here similar to 25 of forces this apparent discrepancy occurs because slabs bend more gently than previously thought with an average radius of curvature of 390 km that permits subduction of strong slabs this gentle bending may ultimately permit plate tectonics on earth c 2008 elsevier b v all rights reserved

an experimental study of subduction and slab migration results of fluid dynamical experiments on the behavior of subducted slabs are presented that address two important characteristics of subduction slab penetration through the transition zone and horizontal slab migration cold negatively buoyant molded slabs of concentrated sucrose solution with viscosities of 3 5 106 p were introduced into a more dilute two layered sucrose solution representing the upper and lower mantle the transition zone was modeled by a step increase in both density and viscosity ratios of slab thickness to upper layer depth the relative viscosities in each layer and the effective rayleigh number were close to mantle values the initial configuration consisted of two plates separated by a trench gap with one plate attached to a dipping slab simulating a developing subduction zone with an overriding plate two different boundary conditions were used at the trailing ridge end of the subducting plate 1 fixed end corresponding to zero ridge motion and 2 free end corresponding to zero ridge resistance based on results from 15 experiments with various combinations of upper layer lower layer and slab densities u l s and viscosities we find that slab penetration depth is sensitive to both the normalized slab density anomaly r s l s u and the dip angle three penetration regimes are recognized r 0 5 in which the slab sinks into the lower layer without distortion 0 2 r 0 5 which permits limited penetration the amount dependent on dip angle in this regime the slab develops a thick root just beneath the transition zone and r 0 2 in which the slab is deflected by the transition and little or no penetration occurs retrograde slab motion and trench migration occurred in nearly every case with the overriding plate moving parallel to but faster than the trench causing the gap between subducting and overriding plates to close with time prograde trench motion was never observed and the trench remained stationary only in the extreme case free ridge condition with equal upper and lower layer densities these results suggest that the transient extension found in many back arc basins may be a direct consequence of the tendency for retrograde subduction and the amount of extension may be governed in part by the degree of slab penetration through the transition zone

multiscale dynamics of the tonga kermadec subduction zone our understanding of mantle convection and the motion of plates depends intimately on our understanding of the viscosity structure of the mantle while geoid and gravity observations have provided fundamental constraints on the radial viscosity structure of the mantle the influence of short wavelength variations in viscosity is still poorly understood we present 2 d and 3 d finite element models of mantle flow including strong lateral viscosity variations and local sources of buoyancy owing to both thermal and compositional effects we first use generic 2 d models of a subduction zone to investigate how different observations depend on various aspects of the viscosity structure in particular the slab and lower mantle viscosity and the presence of a low viscosity region in the mantle wedge above the slab we find that 1 the strain rate provides a strong constraint on the absolute viscosity of the slab 10 23 pa s 2 stress orientation within the slab is sensitive to the relative viscosity of the slab lower mantle and the wedge and 3 the stress state and topography of the overriding plate depend on the wedge viscosity and local sources of buoyancy in particular the state of stress in the overriding plate changes from compression to extension with the addition of a low viscosity wedge we then use observations of strain rate stress orientation dynamic topography and the geoid for the tonga kermadec subduction zone as simultaneous constraints on the viscosity and buoyancy in a 3 d regional dynamic model together these observations are used to develop a self consistent model of the viscosity and buoyancy by taking advantage of the sensitivity of each observation to different aspects of the dynamics over a broad range of length scales the presence of a low viscosity wedge makes it possible to match observations of shallow dynamic topography and horizontal extension within the backarc and down dip compression in the shallow portion of the slab these results suggest that a low viscosity wedge plays an important role in controlling the presence of backarc spreading however for a model with a low viscosity and low density region that provides a good fit to the observed topography we find that a reduction of the slab density by a factor of 1 3 relative to the reference density model is required to match the observed geoid these results suggest that compensation of the slab by dynamic topography may be a much smaller effect at short to intermediate wavelengths than predicted by long wavelength modelling of the geoid

a laboratory model of subduction zone anisotropy abstract measurements of split seismic shear waves near pacific subduction zones show that fast polarization directions are primarily trench parallel in the seaward side mantle beneath a subducting slab and variable in the mantle wedge beneath back arc basins it is generally accepted that the azimuth of the fast polarization direction defines the average orientation of the crystallographic a axis in olivine here we use laboratory experiments to determine the orientation of the olivine a axis in the upper mantle in the vicinity of a subducting slab a laboratory analog for olivine a axis motion during creep deformation is developed using small cylinders whiskers suspended in a viscous fluid subduction beneath a stationary overriding plate variable dip angles and realistic rollback and down dip plate kinematics are examined plate rollback produces strong plate parallel whisker alignments for all dip angles examined alignment in the wedge occurs in three layers a layer of dip parallel alignment above the downgoing plate a layer of subhorizontal alignment beneath the overriding plate and a core of intermediate orientations the amount of alignment beneath the overriding plate and the wedge core decreases with increasing dip angle our results indicate that olivine a axis orientation in the seaward side mantle is controlled by the amount of slab rollback and that orientations in the mantle wedge depend upon slab dip angle

kinematics of subduction and subduction induced flow in the upper mantle 1 results of fluid dynamical experiments are presented to model the kinematics of lithospheric subduction in the upper mantle the experiments model a dense high viscosity plate subducting lithosphere overlying a less dense low viscosity layer upper mantle the overriding lithosphere is not incorporated several important features of slab behavior were investigated including the temporal variability of hinge line migration the kinematic behavior of the slab and the subduction induced upper mantle flow both fixed and free trailing edge boundary conditions of the subducting plate were investigated results show that hinge line retreat is a natural consequence of subduction of a negatively buoyant slab the migration rate increases until the slab approaches the upper lower mantle discontinuity resulting in a decrease in migration rate followed by a renewed increase and finally approaching a steady state slab retreat results in mantle flow with material initially located underneath the slab flowing around the lateral slab edges toward the mantle wedge experimental results indicate that all rollback induced flow occurs around the lateral slab edges forcing the hinge line to attain a convex shape toward the direction of retreat no signs for poloidal flow underneath the slab tip have been detected only a small component of toroidal type flow was observed underneath slanting slab tips for a fixed trailing edge the slab does not sink vertically downward but sinks at an angle in a regressive manner for a free trailing edge slab sinking is oriented more vertically while the surface part of the subducting plate is pulled into the subduction zone

role of lateral mantle flow in the evolution of subduction systems insights from laboratory experiments summary we present 3 d laboratory experiments constructed to investigate the pattern of mantle flow around a subducting slab under different boundary conditions in particular we present a set of experiments characterized by different conditions imposed at the trailing edge of the subducting plate that is plate fixed in the far field plate detached in the far field imposed plate motion experiments have been performed using a silicone slab floating inside a honey tank to simulate a thin viscous lithosphere subducting in a viscous mantle for each set we show differences between models that do or do not include the possibility of out of plane lateral flow in the mantle by varying the lateral boundary conditions our results illustrate how a subducting slab vertically confined over a 660 km equivalent depth can be influenced in its geometry and in its kinematics by the presence or absence of possible lateral pathways on the basis of these results we show implications for natural subduction systems and we highlight the importance of suitable simulations of lateral viscosity variations to obtain a realistic simulation of the history of subduction

effects of mantle and subduction interface rheologies on slab stagnation and trench rollback abstract trench rollback has been a widely discussed phenomenon in recent years and multiple studies have concentrated on various parameters that may influence trench migration and related aspects of slab deformation in the upper mantle here we concentrate on the effects of rheological description yield stress lower mantle viscosity viscosity of crust in controlling the rollback and associated stagnation of slabs in the transition zone 410 660 km depth we perform numerical simulations of slab evolution in a 2d cartesian model with strongly nonlinear rheology combining diffusion creep dislocation creep and a power law stress limiter we demonstrate that trench retreat develops in most models considered regardless of the subducting plate age or prescribed strength rollback then mostly produces slabs that are horizontally deflected at the 660 km phase boundary and remain subhorizontal at the bottom of the transition zone slab morphologies are in agreement with stagnant horizontally deflected structures reported in the transition zone by seismic tomography furthermore if the strength of the slab is limited to less than 0 5 gpa the slab experiences a significant amount of horizontal buckling the amplitude of the rollback velocity is sensitive to several model parameters as one might expect it increases with the age of the subducting plate thus reflecting its increasingly negative buoyancy on the other hand rollback velocity decreases if we increase the viscosity of the crust and thereby strengthen the coupling between the subducting and overriding plates high friction on the contact between the subducting and overriding plates may even result in slabs penetrating into the lower mantle after a period of temporary stagnation also reducing the additional negative buoyancy imparted by the 410 km exothermic phase transition suppresses trench rollback interpretation of the controls on slab rollback and stagnation may be rather complex in strongly nonlinear rheological models where for example buoyancy effects may be counteracted by associated yield stress weakening

dynamics of subduction and plate motion in laboratory experiments insights into the plate tectonics behavior of the earth 1 three dimensional laboratory experiments have been designed to investigate the way slab bearing plates move during subduction inside the mantle in our experiments a viscous plate of silicone lithosphere subducts under its negative buoyancy in a viscous layer of pure honey mantle varying thickness width viscosity and density of the plate and mantle three characteristic modes of subduction are observed a retreating trench mode mode i a retreating trench mode following a transient period of advancing trench mode ii and an advancing trench mode mode iii these modes are characterized by different partitioning of the amount of subduction into plate and trench motion our experiments show that the velocity of subduction can be modeled by the dynamic interaction between acting and resisting forces where lithospheric bending represents 75 95 of the total resisting forces however our experimental results also show the impossibility to predict a priori the plate velocity only from the velocity of subduction without considering trench migrations we find experimentally that the lithospheric radius of curvature which depends upon plate characteristics stiffness and thickness and the mantle thickness exerts a primary control on the trench behavior our results suggest that the complexity of the style of subduction could be controlled by geometrical rules of a plate bending inside a stratified mantle the earth system is in the crucial range for the interplay between the rigidity of the plate and the mantle stratification this setting may be the responsible for the complexity of the past and present tectonic styles

chilean flat slab subduction controlled by overriding plate thickness and trench rollback how flat slab geometries are generated has been long debated it has been suggested that trenchward motion of thick cratons in some areas of south america and cenozoic north america progressively closed the asthenospheric wedge and induced flat subduction here we develop time dependent numerical experiments to explore how trenchward motion of thick cratons may result in flat subduction we find that as the craton approaches the trench and the wedge closes two opposite phenomena control slab geometry the suction between ocean and continent increases favoring slab flattening while the mantle confined within the closing wedge dynamically pushes the slab backward and steepens it when the slab retreats as in the peru and chile flat slabs the wedge closure rate and dynamic push are small and suction forces generate in some cases flat subduction we model the past 30 m y of subduction in the chilean flat slab area and demonstrate that trenchward motion of thick lithosphere 200 300 km currently 700 800 km away from the peru chile trench reproduces a slab geometry that fits the stress pattern seismicity distribution and temporal and spatial evolution of deformation and volcanism in the region we also suggest that varying trench kinematics may explain some differing slab geometries along south america when the trench is stationary or advances the mantle flow within the closing wedge strongly pushes the slab backward and steepens it possibly explaining the absence of flat subduction in the bolivian orocline

kinematics and flow patterns in deep mantle and upper mantle subduction models influence of the mantle depth and slab to mantle viscosity ratio 1 three dimensional fluid dynamic laboratory simulations are presented that investigate the subduction process in two mantle models an upper mantle model and a deep mantle model and for various subducting plate mantle viscosity ratios sp m 59 1375 the models investigate the mantle flow field geometrical evolution of the slab sinking kinematics and relative contributions of subducting plate motion and trench migration to the total rate of subduction all models show that the subducting plate is always moving trenchward resulting from slab pull furthermore all deep mantle models show trench retreat as do upper mantle models in the initial stage of subduction before slab tip transition zone interaction upper mantle models with a low sp m 66 217 continue to show trench retreat after interaction upper mantle models with a high sp m 378 709 show a period of trench advance after interaction followed by trench retreat upper mantle models with a very high sp m 1375 show continued trench advance after interaction the difference in trench migration behavior and associated slab geometries is attributed to both sp m and the mantle depth to plate thickness ratio tm tsp which both affect the slab bending radius to mantle thickness ratio rb tm four subduction regimes can be defined regime i with rb tm 0 3 trench retreat slab draping and a concave trench regime ii with 0 3 rb tm 0 5 episodic trench migration slab folding and a concave trench regime iii with rb tm 0 5 trench advance slab rollover geometries and minor trench curvature and regime iv with rb tm 0 8 trench retreat slab draping and a rectilinear trench in all models slab parallel downdip motion induces poloidal mantle flow structures in addition trench retreat and rollback motion of the slab induce quasi toroidal return flow around the lateral slab edges toward the mantle wedge rollback induced poloidal flow around the slab tip is not observed in any of the experiments finally comparison between the slab geometries observed in the upper mantle models and slab geometries observed in nature imply that the effective viscosity ratio between slab and ambient upper mantle in nature is less than 103 and of the order 1 7 102 with a best estimate of 1 3 102