constraints on the lateral strength of slabs from three dimensional dynamic flow models if the viscosity of subducted lithosphere is described purely by temperature and pressure it should remain considerably more viscous than the surrounding material as it descends through the upper mantle many dynamic models of the long wavelength geoid associated with slabs require an increase in viscosity from the upper to the lower mantle but assume the perturbation to the lateral viscosity structure arising from the slabs themselves can be ignored previous studies indicate that strong and localized viscosity variations should have a dramatic influence on the geoid we present 3d finite element models of the regional geoid of the western pacific subduction zones slab buoyancies and viscosities are defined using the distribution of seismicity the geoid is very sensitive to the lateral strength of the slab very viscous slabs penetrating a low viscosity mantle generate significant 10 50 m long wavelength geoid lows opposite to the geoid high which is observed over slabs to obtain a geoid high comparable to that observed the lower mantle viscosity must be 60 200 times greater than the upper mantle viscosity and the slab must be in contact with the lower mantle these strict requirements suggest that slabs have been weakened and cannot act as stress guides from the deep mantle to the surface

the effect of rheological approximations in 3 d numerical simulations of subduction and collision abstract subduction and collision zones evolve differently from one another due to different rheological properties different amounts of regional isostatic compensation and the different mechanisms by which forces are applied to the convergent plates the rheology of mantle and lithosphere is known to have the largest influence on the dynamics of subduction and continental collision however previous 3 d geodynamic models of subduction collision processes have used various rheological approximations making their results difficult to compare since there is no clear understanding on the extent of these approximations on the dynamics here we test the effect of rheological approximations in a geometrically simplified 3 d model in which the dynamics of subduction and collision is entirely driven by slab pull i e free subduction the results exhibit a wide range of behaviors depending on the rheological law employed from linear viscous lv to temperature dependent visco elasto plastic vep rheology that takes into account both diffusion and dislocation creep rheological approximations exert a strong effect on slab morphology trench migration rates and topography in the upper plate for example we find that slab dynamics varies drastically between end member models in lv approximations slabs do not break off but instead buckle at the transition zone the dynamics is dominated by low strain rates and diffuse stresses and topography is controlled by lateral extrusion of material which homogenizes amplitudes in the upper plate in simulations with non linear vep rheology slab break off occurs at the corners of the indenting continent opening of a back arc basin is fast and topography has a laterally heterogenous distribution of amplitudes opening of a back arc basin is observed only in simulations with non linear vep rheology when the rheology is approximated with multiple discrete layers the dynamics also resembles more the non linear vep case

investigations of newly formed sea ice in the cape bathurst polynya 1 structural physical and optical properties 1 the physical structural and optical properties of newly formed ice types were studied in the cape bathurst polynya 71 n 127 w during fall freezeup in october to early november 2003 variable meteorological conditions with occasional snowfall resulted in the formation of numerous ice types and surface conditions ice samples were collected from horizontally homogeneous surfaces representative of the area crystallographic analysis on 33 ice cores revealed highly variable growth conditions and formation mechanisms in the area the mean fraction of granular ice was 33 while intermediate granular columnar and columnar ice contributed 37 and 30 respectively salinity profiles in the ice were c shaped and as the ice grew thicker bulk salinities decreased according to 4 582 13 358 hi cm these conditions resulted in brine volumes ranging from 4 to 46 bare ice surfaces commonly formed a high salinity brine skim layer due to brine expulsion salinities up to 40 were observed in this layer under suitable conditions frost flowers formed on the ice and their presence was related to characteristic ice microstructure with crystals that appeared disc like in shape fine grained snow ice was formed when snow merged with surface brine to create a complex hypersaline surface at the snow ice interface the spectral reflectance for the thin ice types was most strongly related to surface conditions the presence of frost flowers significantly increased the reflectance independent of snow precipitation any increase in ice thickness was found to have little effect on the reflectance once a 20 30 mm thick snow layer was present

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

numerical modeling of stress and topography coupling during subduction inferences on global vs regional observables interpretation abstract the mechanical strength of the oceanic lithospheres exerts a fundamental control on the dynamics and tectonics of convergent margins here we use numerical models of coupled subducting upper plates and mantle to investigate the impact of the subducting lithosphere properties on the parameters commonly measured at subduction zones the models predict a correlation among parameters such as subducting and convergence velocities slab dip and curvature and stress coupling with the upper plates such signature emerges in a dynamic system through the slab buoyancy similar trends are found when assessing the impact of laboratory constrained non linear rheologies uncertainties on the mechanical strength and mantle flow although some features are more affected when the role of upper plate thickness is tested we find a positive correlation of upper plate subsidence and fore arc topography with the buoyancy of the down going plate however plasticity in the crust limits the development of topography becoming increasingly relevant with thinner upper plates so that no correlation can be established similar control is found on the width of the long wavelength dynamic subsidence due to flexure which increases non linearly with the upper plate thickness the models constrain relations among parameters within the dynamic system driven that allow inferences on the observable parameters the comparisons supports the idea that the subduction dynamics emerges as a global phenomenon in plate motions bending and dynamic subsidence yet andean type margin tectonics is best addressed in a regional context

haskell 1935 revisited the haskell 1935 value of 1021 pa s for mantle viscosity is a classic and enduring constraint on the rheology of the earth s interior we revisit this inference using spherically symmetric self gravitating maxwell viscoelastic earth models our inference is based on both forward and inverse analyses of decay times associated with uplift at two sites considered by haskell angerman river sweden and oslo norway rather than the raw relative sea level rsl data at these sites we demonstrate that predictions of the decay time associated with the angerman river data are insensitive to variations in both the late pleistocene ice load history and the lithospheric thickness of the earth model the predictions at oslo are sensitive to both these inputs and hence decay times at this site provide a remarkably robust constraint on mantle viscosity we derive a constraint on the average viscosity of the mantle of 0 65 1 10 1021 pa s where the average resolved by the data encompasses a region which extends from the base of the lithosphere to a depth of near 1400 km this indicates that many previous analyses which have invoked the haskell value of 1021 pa s as a constraint on the average upper mantle i e above 670 km depth viscosity alone have misinterpreted the resolving power of the inference furthermore our analysis indicates that a number of apparently contradictory inferences of viscosity based on fennoscandian data satisfy the new rigorous interpretation of the haskell constraint finally we demonstrate how the ambiguity in the upper mantle lower mantle viscosity contrast associated with the haskell average may be reduced by invoking decay time constraints estimated from rsl curves in hudson bay a preliminary inversion of decay times at angerman river and richmond gulf in hudson bay suggests a contrast of approximately an order of magnitude between the average viscosities of the upper mantle and the top 1000 km of the lower mantle however a conclusive analysis in this regard must await the determination of consistent decay time estimates for the hudson bay region

field observations and model calculations of dielectric properties of arctic sea ice in the microwave c band the complex dielectric constant of first year and multiyear sea ice was measured during the seasonal ice monitoring and modeling simms field experiments conducted in the arctic in the spring of 1992 1993 and 1995 the dielectric constant was also computed based on an established dielectric mixing model by using different assumptions about inclusion shape computations were based on detailed measurements and observations of ice physical properties and crystalline structure comparison between measurements and model results was conducted to identify working models for first year and multiyear ice for first year ice models that employ the assumption of vertically oriented brine pockets are applicable to columnar ice and those with the assumption of randomly oriented brine pockets are applicable to frazil ice the validity of the models are established only for ice temperatures less than 8 spl deg c for multiyear ice there is no need to account for air bubble shape the coexistence of brine and air inclusions in multiyear pond ice makes it characteristically different from hummock ice best results for pond ice were obtained from a simple model that accounts only for volume fractions of inclusions rather than their shape physical parameters that can be retrieved directly from the dielectric constant are salinity of first year ice at temperatures below 15 spl deg c and density of multiyear hummock ice detailed measurements of permittivity and loss of first year and multiyear ice are presented along with some insight into interactions between the dielectric constant and physical parameters

remote sensing of sea ice thickness and salinity with 0 5 2 ghz microwave radiometry an ultrawideband radiometer was used to measure microwave brightness temperature spectra over arctic sea ice in the lincoln sea near the north coast of greenland spectra over the range of 0 5 2 ghz were compared to thermal infrared images collected during the airborne campaign and also compared to nearly concurrent sentinel 1 c band synthetic aperture radar sar data based on those comparisons spectral signatures were associated with thick multiyear ice and thin ice a radiative transfer rt model consisting of a homogeneous slab of sea ice bounded by sea water and air was then used to invert the spectra for sea ice thickness and salinity inferred thicknesses were consistent with ice thickness climatology for ice floes in the lincoln sea salinities are higher than expected which may be a consequence of neglecting surface and volume scattering contributions in the models

trench curvature and deformation of the subducting lithosphere summary the subduction of oceanic lithosphere is generally accompanied by downdip and lateral deformation the downdip component of strain is associated with external forces that are applied to the slab during its sinking namely the gravitational force and the mantle resistance to penetration here we present theoretical arguments showing that a tectonic plate is also subject to a predictable amount of lateral deformation as a consequence of its bending along an arcuate trench zone independently from the long term physical processes that have determined the actual curvature of the subduction zone in particular we show that the state of lateral strain and the lateral strain rate of a subducting slab depend from geometric and kinematic parameters such as trench curvature dip function and subduction velocity we also demonstrate that the relationship between the state of lateral strain in a subducting slab and the geometry of bending at the corresponding active margin implies a small component of lateral shortening at shallow depths and may include large extensional lateral deformation at intermediate depths whereas a state of lateral mechanical equilibrium can only represent a localized exception our formulation overcomes the flaws of the classic ping pong ball model for the bending of the lithosphere at subduction zones which lead to severe discrepancies with the observed geometry and style of deformation of the modern subducting slabs a study of the geometry and seismicity of eight modern subduction zones is performed to assess the validity of the theoretical relationship between trench curvature slab dip function and lateral strain rate the strain pattern within the eight present day slabs which is reconstructed through an analysis of harvard cmt solutions shows that tectonic plates cannot be considered as flexible inextensible spherical caps whereas the lateral intraslab deformation which is accommodated through seismic slip can be explained in terms of deviations from the mechanical equilibrium

predicting plate velocities with mantle circulation models 1 we predict plate motions from a comprehensive inversion of theoretical estimates of tectonic forces in order to evaluate the relative importance of these and the uncertainties of such models plate driving forces from the mantle are calculated using global flow models that are driven by tomography and subduction derived density fields observed and predicted plate velocities agree well for a variety of models leading to varied conclusions about the relative importance of forces the dominance of the subduction related density pattern in the mantle is confirmed it appears that p wave models do not satisfactorily image all of the slab associated anomalies in the upper mantle furthermore lower mantle structure always improves the plate motion fit with respect to models that are based on upper mantle anomalies and lithospheric thickening only we show that the average torques from the lower mantle scale with the radial flow through the 660 km phase transition the amplitude of the lower mantle torques will be significant for a range of models if there is mass flux through 660 km we also evaluate parameterized edge forces and find that the additional inclusion of such torques does not significantly improve the model fit the main reason for the nonuniqueness of the inversions is plate boundary geometry since all plate motions are dominated by the trench ridge system and plates move from ridges to trenches

sea ice emissivity modeling at l band and application to 2007 pol ice campaign field data sea ice emissivity models for the l band frequency range are described and then tested on pol ice campaign field measurements pol ice was conducted in march 2007 in the northern baltic in preparation for the launch of the soil moisture and ocean salinity smos instrument a satellite microwave radiometer operating at 1 4 ghz the campaign comprised airborne measurements from the emirad l band radiometer and the e m bird ice thickness meter because of the translucency of sea ice at l band it is hoped that smos will render information on ice thickness three variations on radiative transfer are used to model emirad brightness temperatures from collocated e m bird measurements a single plane parallel model an ensemble of such models and a ridged monte carlo model based on geometric optics that includes both the top and bottom surface topography all three models accurately account for the instrument antenna pattern relevant to satellite mounted radiometers that sample a large and heterogeneous area because of ice growth processes salinity and by extension permittivity are partial functions of ice thickness thus the models are further refined so that permittivity varies with ice thickness which was necessary to correctly model the polarization difference other issues related to effective permittivities an intermediate quantity in the models are discussed analysis of partial correlations shows that ice ridging makes a significant contribution to the measured signal commending further study using scattering models that are more appropriate to the scale of the ridging relative to the wavelength

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 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

salinity profiles of antarctic sea ice field data and model results in order to describe and compare sea ice salinity distributions which are of interest in the study of physical and biological ice characteristics as well as ice ocean interaction we have computed composite profiles and fitted third degree polynomials to salinity data of 129 cores from the weddell sea four characteristic profile shapes have been recognized and described through the polynomial coefficients c s i and type profiles the field data have been compared with ideal salinity profiles generated by a simulation scheme based on thermodynamic growth under climatological conditions representative of the weddell sea composite salinity profiles agree well with simulations irrespective of the growth mechanism i e frazil or congelation suggesting that ice properties which depend on salinity or porosity may evolve independent of ice growth conditions analysis of salinity and 18o data in conjunction with the simulations demonstrates that apart from meteorological conditions controlling growth velocity and temperature distribution within the ice flooding and upward brine expulsion are important in raising top salinities as frequently observed low top salinities are typical of ice that has undergone retexturing and differential desalination salinity decreases towards the bottom of a floe are a result of high oceanic heat fluxes and snow cover effects as a consequence of these processes the bulk salinity of weddell sea ice cannot be described by a simple linear age thickness relationship as characteristic of arctic first year ice

effective elastic properties of solid clays clay minerals are perhaps the most abundant materials in the earth s upper crust as such their elastic properties are extremely important in seismic exploration seismic reservoir characterization and sonic log interpretation because little exists in the literature on elastic properties of clays we have designed a method of measuring effective elastic properties of solid clays clays without pores in this method clay minerals are mixed with a material with known elastic properties to make composite samples elastic properties of these clay minerals are then inverted from the measured elastic properties of the composite samples using the weighted hashin shtrikman average using this method we have measured 66 samples of 16 types of clays in this paper we present a comprehensive data set of elastic properties of solid clays that commonly occur in or are related to petroleum reservoirs although uncertainties up to 10 exist the data set reported here is by far the most comprehensive set of e

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

rheology of the upper mantle a synthesis rheological properties of the upper mantle of the earth play an important role in the dynamics of the lithosphere and asthenosphere however such fundamental issues as the dominant mechanisms of flow have not been well resolved a synthesis of laboratory studies and geophysical and geological observations shows that transitions between diffusion and dislocation creep likely occur in the earth s upper mantle the hot and shallow upper mantle flows by dislocation creep whereas cold and shallow or deep upper mantle may flow by diffusion creep when the stress increases grain size is reduced and the upper mantle near the transition between these two regimes is weakened consequently deformation is localized and the upper mantle is decoupled mechanically near these depths

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

dynamic models of downgoing plate buoyancy driven subduction subduction motions and energy dissipation abstract it is much debated whether the forces associated with the downgoing plate the overriding plate passive or active mantle flow are dominant in controlling the paths of plates into the mantle we investigate the dynamics and energetics for a free subduction system driven solely by downgoing plate buoyancy using a finite element model of a viscoelastic plate with a free surface sinking into a passive unbounded mantle represented by drag forces parameters are varied to study effects of an asthenosphere ridge push and a passive overriding plate for a range of subducting plate viscosities and densities such a single free plate achieves subduction mainly through trench retreat most of the energy dissipation occurs in driving the passive mantle response as a result the slab s sinking velocity is its stokes velocity determined by lithospheric buoyancy and mantle viscosity the total subduction velocity and dip adjust to minimize bending dissipation in the lithosphere and are affected by slab rheology as well as buoyancy a low viscosity asthenosphere and ridge push facilitate plate advance increasing plate dips and lowering subduction velocity while suction and buoyancy of a work free passive overriding plate decreases plate dips thus increasing subduction and rollback velocities however the geometrical relation between the different parameters is the same in all model cases because the slabs sink according to their stokes velocity the free subduction models thus provide a reference that can be used to distinguish the signature of downgoing plate buoyancy from that of other driving forces in global compilations of subduction parameters

dynamics of outer rise faulting in oceanic continental subduction systems 1 during subduction bending of downgoing oceanic lithosphere gives rise to normal faulting due to the extensional stress state generated in the upper plate as deformation patterns inherently reflect a material s state of stress and rheology extensive global observations of outer rise faulting patterns and subduction dynamics provide a unique opportunity to examine the factors controlling outer rise deformation despite a wide range of observed oceanic plate ages convergence rates and slab pull magnitudes across modern subduction systems however measured outer rise faulting patterns show effectively no correlation to variations in these parameters this lack of correlation may reflect that outer rise faulting patterns are strongly sensitive to all of these parameters are dependent on additional parameters such as downgoing overriding plate coupling or that existing faulting measurements require additional analysis in order to provide a basis for future analysis of outer rise faulting patterns we build on previous thermo mechanical numerical models of outer rise deformation and explore the relationship between outer rise faulting patterns subduction dynamics and brittle rheology in an oceanic continental subduction system analysis of time averaged outer rise faulting patterns indicates that downgoing plate age and velocity downgoing overriding plate coupling and slab pull all significantly affect faulting patterns while variations in brittle rheology have a significantly smaller impact these relationships reflect that the sensitivity of outer rise faulting patterns to the frictional properties of the oceanic crust and mantle is small compared to variations in the overall stress state and deformation rate of subduction systems in order to gain additional insight into the origin outer rise faulting patterns future numerical studies should focus on specific regions in order to place constraints on the structure of the downgoing plate and dynamics of the subduction system

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

the tectonic expression slab pull at continental convergent boundaries examination of five thrust belt systems developed at continental subduction boundaries suggests that they comprise two distinct groups that display pronounced and systematic differences in structural style topographic elevation denudation metamorphism postcollisional convergence and foredeep basin geometry and facies the distinctive geological features developed within each thrust belt group appear to be causally linked to the relative rates of subduction and convergence via the magnitude of horizontal compressional stress transmitted across the subduction boundary at subduction boundaries where the rate of overall plate convergence is less than the rate of subduction termed here retreating subduction boundaries the transmission of horizontal compressive stress across the plate boundary is small and regional deformation of the overriding plate is by horizontal extension the tectonic expression of these retreating subduction boundaries includes topographically low mountains little erosion or denudation low grade to no metamorphism little to no involvement of crystalline basement in shortening little to no postcollisional convergence anomalously deep foredeep basins and a protracted history of flysch deposition within the adjacent foredeep basin analysis of deflection and gravity data across three retreating subduction boundaries apennine carpathian and hellenic systems shows that subduction is driven by gravitational forces acting on dense subducted slabs at depths between about 40 and 80 km carpathians 50 and 150 km apennines and 50 and 250 km hellenides the total mass anomalies represented by the slabs are approximately 3 1012 6 1012 and 12 1012 n m respectively the slabs are partially supported by flexural stresses transmitted through the subducted lithosphere to the foreland and partially supported by dynamic viscous stresses in the asthenosphere at subduction boundaries where the rate of overall plate convergence is greater than the rate of subduction termed here advancing subduction boundaries the transmission of horizontal compressive stress across the plate boundary is large and regional deformation of the overriding plate is by horizontal shortening the tectonic expression of these advancing subduction boundaries includes topographically high mountains antithetic thrust belts large amounts of erosion and denudation exposure of high grade metamorphic rocks at the surface extensive deformation of crystalline basement to midcrustal depths protracted postcollisional convergence tens of millions of years and a protracted history of molasse deposition within the adjacent foredeep basins analysis of gravity and deflection data across two advancing subduction boundaries developed within the continental lithosphere western to eastern and southern alps and himalayas shows that the thrust sheets have been translated for great distances over the foreland lithosphere relative to the point at which the subduction forces are applied thus obscuring any flexural and gravity signals from the subducted slab however it appears that far field stresses presumably related to global plate motions drive most of the convergent motion across these subduction boundaries the concept that orogenic belts formed above retreating subduction boundaries have recognizable tectonic signatures that differ from those of orogenic belts formed above advancing subduction boundaries suggests that it may be possible to interpret the plate boundary settings in which ancient orogenic belts evolved appendix b is available with entire article on microfiche order from the american geophysical union 2000 floridaavenue n w washington d c 20009 document t92 004 2 50 payment must accompany order

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 dynamics of the eastern mediterranean and eastern turkey summary in this study we investigate the dynamics of the region that includes greece the aegean sea and asia minor in a least squares inversion we solve for a continuous strain rate field and corresponding velocity field that satisfies 872 gps data the estimate of the geodetic strain rate field provides constraints for our dynamic analysis next we separately solve the depth integrated 3 d force balance equations for depth integrated deviatoric stresses within the lithosphere in which body force input comes from differences in vertically integrated vertical stress or differences in gravitational potential energy per unit area gpe these gpe estimates calibrate the absolute magnitudes of deviatoric stresses that are acting within the lithosphere further we investigate the sensitivity of our stress field solutions by using two different crustal structure models one from compiled crustal structure estimates obtained primarily from relatively recent seismic observations and the other from the crust 2 0 model in an iterative least squares inversion we then solve for stress field boundary conditions that when added to the contribution of deviatoric stresses associated with gpe differences provides a best fit to the directions of principal axes and relative magnitudes of the principal axes of the rates of strain obtained in the kinematic analysis robust features that arise from the boundary condition solution are nne forcing along the southern boundary east of about 33 e 0 5 1 2 1012 n m 1 with a rapid anticlockwise rotation of forces to the west of this along with an outward pulling force 0 4 1012 n m 1 directed ssw along the entire hellenic arc segment this force system along the hellenic arc can be interpreted as a result of slab rollback the total depth integrated 3 d deviatoric stresses in the final dynamic solution provides an excellent match to the deformation indicators throughout the region with vertically integrated stress magnitudes of order 0 5 2 5 1012 n m 1 we use constraints from derived stress magnitudes together with gps defined scalar values of strain rate magnitude to define bulk effective viscosities of the lithosphere depth averaged effective viscosities for the entire lithosphere are high within the black sea of order 0 7 3 1023 pa s relative to surrounding continental lithosphere north anatolian shear zone northern aegean sea and gulf of corinth are characterized by low depth averaged viscosities of order 1 5 1021 pa s deviatoric stresses from gpe differences and boundary condition effects combine in surprising ways in some regions resulting in near total stress cancellation in areas such as the southern aegean sea and portions of the central anatolian block gpe differences combine with boundary condition effects along the eastern segment of the north anatolian fault naf in a way that is compatible with the hypothesis that motion on the naf was facilitated by slab detachment beneath east anatolia and dynamic uplift of east anatolian plateau in general gpe differences play a nearly equal role as boundary condition influences in their contribution to the total deviatoric stress field the low depth integrated deviatoric stress magnitudes throughout the region suggest that zones of active deformation are facilitated by dramatic weakening mechanisms throughout the lithosphere

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

the development of slabs in the upper mantle insights from numerical and laboratory experiments we have performed numerical and laboratory experiments to model subduction of oceanic lithosphere in the upper mantle from its beginnings as a gravitational instability to the fully developed slab a two dimensional finite element code is applied to model newtonian creep in the numerical experiments scaled analog media are used in the laboratory a sand mixture models the brittle crust silicone putty simulates creep in the lower crust and mantle lithosphere and glucose syrup is the asthenosphere analog both model approaches show similar results and reproduce first order observations of the subduction process in nature based on density and viscosity heterogeneities in a stokes flow model subduction nucleates slowly and a pronounced slab forms only when the viscosity contrast between oceanic plate and mantle is below a threshold we find that the subduction velocity and angle are time dependent and increase roughly exponentially over tens of millions of years before the slab reaches the 670 km discontinuity the style of subduction is controlled by the prescribed velocity of convergence the density contrast between the plates and the viscosity contrast between the oceanic plate and the mantle these factors can be combined in the buoyancy number f which expresses the ratio between driving slab pull and resisting viscous dissipation in the oceanic plate variations in f control the stress in the plates the speed and the dip of subduction and the rate of trench retreat reproducing the contrasting styles of subduction observed in nature the subduction rate is strongly influenced by the work of bending the lithosphere as it subducts

mantle convection with strong subduction zones because mantle viscosity is temperature dependent cold subducting lithosphere should be strong which implies that the rapid localized deformation associated with subduction should strongly resist plate motions due to computational constraints the deformation of a subducting plate cannot be accurately resolved in mantle scale convection models so its effect on convection is difficult to investigate we have developed a new method for implementing subduction that parametrizes the deformation of the oceanic lithosphere within a small region of a finite element grid by imposing velocity boundary conditions in the vicinity of the subduction zone we enforce a geometry for subduction producing a slab with a realistic thermal structure to make the model dynamically consistent we specify a rate for subduction that balances the energy budget for convection which includes an expression for the energy needed to deform the oceanic lithosphere as it subducts this expression is determined here from a local model of bending for a strong viscous lithosphere by implementing subduction in this way we have demonstrated convection with plates and slabs that resemble those observed on earth but in which up to 40 per cent of the mantle s total convective resistance is associated with deformation occurring within the subduction zone this additional resistance slows plate velocities by nearly a factor of two compared to models with a weak slab for sufficiently strong lithosphere the bending deformation slows surface plates sufficiently that they no longer actively participate in global scale convection which occurs instead beneath a sluggish lid by introducing a low viscosity asthenosphere beneath the oceanic plate we demonstrate that small scale convection at the base of oceanic lithosphere may limit plate thickness and thus the resistance to bending and cause plate velocities to depend on the strength of the bending lithosphere rather than on the viscosity of the underlying mantle for a cooling earth the effective lithosphere viscosity should be nearly constant but the mantle viscosity should increase with time thus subduction resisted convection should produce nearly constant plate velocities and heat flow over time which has implications for the earth s thermal evolution we estimate that this style of convection should apply if the effective viscosity of the bending lithosphere is greater than about 10 23 pa s but only if some mechanism such as small scale convection prevents the bending resistance from stopping plates altogether such a mechanism could be fundamental to plate tectonics and earth s thermal history

mantle rheology and the scaling of bending dissipation in plate tectonics 1 plate tectonics on earth involves the bending deformation of plates at subduction zones and because plates are generally considered to be stiff owning to the rheology of mantle minerals the role of energy dissipation by plate bending in the global energy balance has been frequently debated in the recent literature here we consider how bending dissipation should scale with slab parameters such as dip angle plate age the radius of curvature and plate velocity by systematically exploring the parameter space with instantaneous stokes flow calculations we derive the scaling of bending dissipation for a range of mantle viscosity functions including pseudoplastic rheology with olivine flow laws our results indicate that as we move away from the isoviscous case the scaling gradually deviates from what has commonly been assumed in previous studies most notably for the radius exponent which exhibits more than threefold reduction and even a sign reversal in some cases these modifications in scaling exponents originate in the complication of the deformation field caused by viscosity variations within the bending plate approximating the lithospheric rheology by a single effective viscosity in the dynamical models of subduction has been a common practice but we suggest that such approximation may limit the geological relevance of modeling studies in particular when estimating the significance of bending dissipation

lithospheric 3 d flexure modelling of the oceanic plate seaward of the trench using variable elastic thickness summary whendescribingthemechanicalbehaviourofthelithospheremodelledasathinplate themost important parameter corresponds to itsflexural rigidity which is commonly expressed through the effective elastic thickness te this parameter is a measure of the stiffness of the plate and defines the maximum magnitude and wavelength of those surface loads that can be supported without suffering unelastic deformation realistic 3 d models of the flexural response of the lithosphere near the trench are scarce because of the mathematical and computational complexity we present a method for determining the flexure of the lithosphere caused by the combined effect of 3 d seamount loading and bending of the lithosphere near the trench our method consists on solving numerically the flexure equations of the reissner mindlin thin plate theory including variable thickness using the finite element method with mesh adaptation the method was applied to study the flexure of the oceanic nazca lithosphere beneath the o higgins seamount group which lies 70km seaward of the chile trench the results show that an elastic thickness te of 5km under the seamounts a te of 15km far from the trench and a te of 13km near the trench can explain both the down deflection of the oceanic moho and bending of the oceanic lithosphere observed in seismic and gravity profiles in order to study the impact of high trench curvature on the morphology of the outer rise we apply the same methodology to study and model the flexure of the lithosphere in the arica bend region 14 s 23 s results indicate that the te values are overestimated if the 3 d trench curvature is not included in the modelling

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

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

self consistent generation of tectonic plates in three dimensional mantle convection abstract despite the fundamental importance of plates in the earth s mantle convection plates have not generally been included in numerical convection models or analog laboratory experiments mainly because the physical properties which lead to plate tectonic behavior are not well understood strongly temperature dependent viscosity results in an immobile rigid lid so that plates where included at all in 3 d models have always been imposed by hand an important challenge is thus to develop a physically reasonable material description which allows plates to develop self consistently this paper focuses on the role of ductile shear localization in two dimensional geometry it is well established that strain rate softening non newtonian rheologies e g power law visco plastic cause weak zones and strain rate localization above up and down wellings resulting in a rudimentary approximation of plates three dimensional geometry however is fundamentally different due to the presence of transform plate boundaries with associated toroidal motion since power law and visco plastic rheologies do not have the property of producing shear localization it is not surprising that they do not produce good plate like behavior in three dimensional calculations here it is argued that a strain rate weakening rheology previously shown to produce plate like behavior in a two dimensional sheet representing the lithosphere is a reasonable generic description of various weakening processes observed in nature one and two dimensional models are used to show how this leads to shear localization and the formation of faults this rheology is then applied to the high viscosity lithosphere of 3 d mantle convection calculations and the velocity pressure viscosity solution for the entire 3 d domain lid and underlying mantle is solved self consistently it is found that the lithosphere divides into a number of very high viscosity plates separated by narrow sharply defined weak zones with a viscosity many orders of magnitude less than the plate interiors broad weak zones with dominant convergent divergent motion above up and down wellings are interconnected by a network of narrow weak zones with dominant strike slip motion passive spreading centers are formed in internally heated cases while the resulting plates are not fully realistic these results show that self consistent plate generation is a realizable goal in three dimensional mantle convection and provide a promising avenue for future research

spontaneous development of arcuate single sided subduction in global 3 d mantle convection models with a free surface we present temporally evolving 3 d global mantle convection models with single sided subduction and a free surface in both 3 d cartesian and fully spherical geometry special focus is given to the spontaneous development of three dimensional structures at the surface and in the upper mantle we find that an arcuate shape is the natural form for trenches and slabs cartesian models are used first to study the dynamic evolution of subduction zones spreading ridges and interconnected transform features these experiments highlight the strong variation of spontaneously developing arcuate slab curvature and subduction polarity along the trench strike the spontaneous development of spreading ridges leads to lateral offsets between separated segments that are characterized by normal transform motion spherical models then allow insights into the evolution of plate tectonics on a sphere investigated are the spontaneous evolution of slab geometry trench motion and subduction induced mantle flow two new dynamical features are discovered back slab spiral flow and slab tunneling

bounds on the complex permittivity of sea ice an analytic method for obtaining bounds on effective properties of composites is applied to the complex permittivity of sea ice the sea ice is assumed to be a two component random medium consisting of pure ice of permittivity 1 and brine of permittivity 2 the method exploits the properties of as an analytic function of the ratio 1 2 two types of bounds on are obtained the first bound r1 is a region in the complex plane which assumes only that the relative volume fractions p1 and p2 1 p1 of the ice and brine are known the region r1 is bounded by circular arcs and for any microgeometry with the given volume fractions must lie inside it in addition to the volume fractions the second bound r2 assumes that the sea ice is statistically isotropic within the horizontal plane the region r2 is again bounded by circular arcs and lies inside r1 built into the method is a systematic way of obtaining tighter bounds on by incorporating information about the correlation functions of the brine inclusions the bounding method developed here which does not assume any specific geometry for the brine inclusions offers an alternative to the classical mixing formula approach adopted previously in the study of sea ice in these mixing formulas specific assumptions are made about the inclusion geometry which are simply not satisfied by the sea ice under many conditions the bounds r1 and r2 are compared with experimental data obtained from artificially grown sea ice at the frequencies 4 8 and 9 5 ghz excellent agreement with the data is achieved

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

fine scale modeling of global plate tectonics the tectonic motions on the surface of earth and much of its geological activity can be explained as a part of mantle convection relatively rigid lithospheric plates form the top cold boundary layer of the convecting mantle and the potential energy released during the cooling of the planet is balanced by viscous dissipation during deformation of mantle rocks 1 2 a theory of plate tectonics has to account for compositional and rock strength variations both of which are affected by the dynamics of convective flow such behavior can lead to nonlinear feedback and result in heterogeneity possibly down to sub meter scale on page 1033 of this issue stadler et al 3 present a groundbreaking numerical model for plate tectonics that should help to resolve questions relating to how the strongly deforming and narrow plate boundaries form and evolve

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

the nanogranular acoustic signature of shale a multiscale micromechanics model has been developed for the prediction of anisotropic acoustic properties of shale the model is based on the recently identified nanogranular mechanical response of shale through indentation experiments it recognizes the dominant role of the anisotropic elastic properties of compacted clay in the anisotropic elasticity of shale at different length scales compared to contributions of shape and orientation of particles following a thorough validation at multiple length scales using mineral elasticity data nanoindentation experiment results and ultrasonic pulse velocity tests the model predictions compare adequately with measurements on kerogen free and kerogen rich shales and shaley sandstones the acoustic signature of shale thus is found to be controlled by two volumetric parameters that synthesize the porosity and mineralogy information the clay packing density and the silt inclusion volume fraction through a series of dimensionless isoparametric plots the micromechanics model predicts trends of increasing elastic anisotropy with increasing clay packing density or decreasing porosity which correspond to the intrinsic mechanical response of unfractured shale and quantifies the stiffness reduction induced by the presence of kerogen

geomechanics field characterization of woodford shale and barnett shale with advanced logging tools and nano indentation on drill cuttings the woodford shale and barnett shale have emerged as prolific gas plays in the us midcontinent however the intrinsically low permeability of these gas shales hinders profitable pro duction unless horizontal well drilling and multistage hydraulic fracturing are employed the success of these operations depends on accurate de terminations of the anisotropic elastic and poroelastic properties of these shale formations

thermal mechanical effects of low temperature plasticity the peierls mechanism on the deformation of a viscoelastic shear zone we studied for the first time the effects of low temperature plasticity on the formation of shear zones a thermal mechanical model has been developed for describing the shear deformation of maxwell viscoelastic material with a rheology close to dry olivine we employed a one dimensional model with a half width of l deforming under a constant velocity u at the boundary and the spatially averaged strain rate u l was set to o 10 14 s 1 in addition to diffusion and power law creep we included deformation by low temperature plasticity called the peierls mechanism which is significant at low temperatures and has a strong exponential dependence on the stress when a sufficient magnitude of heat is generated by the rapid conversion from elastically stored energy into viscous dissipation thermal instability takes place and the deformation localizes in a narrow region by comparing the condition for thermal instability we found that the low temperature plasticity inhibits the development of thermal instability in shear zones in case of constant strain rate the peierls mechanism enhances deformation at a significantly lower stress compared to the rheology with solely diffusion creep and power law creep the enhanced deformation by low temperature plasticity produces lower amount of dissipative heating and thus stabilizes the shear zone comparing the stability between constant strain rate and constant stress boundary conditions we found that the peierls mechanism exerts an opposite destabilizing effect in the case of constant stress for dry olivine rheology and realistic magnitude of the strain rate the effect of low temperature plasticity is significant for temperatures between around 800 k and 1000 k this finding suggests that the low temperature plasticity may be crucial in determining the thermal mechanical stability in the shallow portion of slabs

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

abrupt upper plate tilting during slab transition zone collision abstract the sinking remnant of a surface plate crosses and interacts with multiple boundaries in earth s interior here we specifically investigate the prominent dynamic interaction of the sinking plate portion with the upper mantle transition zone and its corresponding surface elevation signal we unravel for the first time that the collision of the sinking slab with the transition zone induces a sudden dramatic downward tilt of the upper plate towards the subduction trench unraveling this crucial interaction was only possible thanks to state of the art numerical modelling and post processing the new model that is introduced here to study the dynamically self consistent temporal evolution of subduction features accurate subduction zone topography robust single sided plate sinking stronger plates close to laboratory values an upper mantle phase transition and simple continents at a free surface to distinguish the impact of the new physical model features three different setups are used the simplest model setup includes a basic high viscosity lower mantle the second adds a 660 km phase transition and the third includes additionally a continental upper plate common to all models is the clear topographic signal upon slab transition zone interaction the upper plate tilts abruptly towards the subduction trench by about 0 05 and over around 10 ma this dramatic increase in upper plate tilt can be related to the slab induced excitation of the high viscosity lower mantle which introduces a wider flow pattern a large change in horizontal extent of inundation of up to 900 km is observed as a direct consequence of the upper plate tilting such an abrupt variation in surface topography and inundation extent should be clearly visible in temporal records of large scale surface elevation and might explain continental tilting as observed in australia since the eocene and north america during the phanerozoic

great earthquakes and slab pull interaction between seismic coupling and plate slab coupling great earthquakes the few largest earthquakes that account for most of the earth s seismic energy release have occurred at only a few subduction zones around the world strong locking or seismic coupling of the interface between plates at certain subduction zones is often invoked to explain these great earthquakes although past studies have correlated strong seismic coupling with a compressional stress environment that is characterized by back arc compression and caused by trenchward motion of the overriding plate the consequences of this compressional environment for the tectonic forces that drive global plate motions are not yet clear to examine these consequences we compared subduction zone earthquake magnitudes to tectonically constrained estimates of the degree to which each slab transmits its excess weight as a direct pull force on a subducting plate at seismically uncoupled subduction zones that generate only moderate sized earthquakes we find that slabs must transmit nearly their entire upper mantle weight as a pull force on the subducting plate at seismically coupled subduction zones that produce great earthquakes however we find that slabs must be nearly completely detached from their subducting plates this suggests that slabs subducting in a compressional environment experience stress induced weakening that prevents the effective transmission of the slab pull force convergent mantle flow above a descending slab that becomes decoupled from its surface plate may induce additional surface compression that further locks the subduction zone and leads to additional slab decoupling and detachment the resulting redistribution of plate driving forces may be responsible for rapid changes in plate motion c 2003 elsevier b v all rights reserved

parameters controlling dynamically self consistent plate tectonics and single sided subduction in global models of mantle convection recent advances in numerical modeling allow global models of mantle convection to more realistically reproduce the behavior at convergent plate boundaries in particular the inclusion of a free surface at the outer boundary has been shown to facilitate self consistent development of single sided subduction this allows for a more extensive study of subduction in the context of global mantle convection as opposed to commonly used regional models our first study already indicated important differences between mantle convection with single sided subduction and mantle convection with double sided subduction here we further investigate the effect of various physical parameters and complexities on inducing earth like plate tectonics and its evolution in time results reinforce the previous finding that using a free surface instead of a free slip outer boundary dramatically changes subduction style with free surface cases displaying many episodes of single sided subduction which leads to more realistic slab dip stress state trench retreat rate and slab induced mantle flow longevity of single sided subduction is promoted by a layer of hydrated crust with a low yield strength to lubricate the subduction channel a low viscosity asthenosphere and a high strength of the slab determined by a combination of high diffusion creep viscosity and intermediate friction coefficient although its effective viscosity is in the observationally constrained range in the bending region the time evolution displays interesting events including subduction polarity reversals subduction shut off and slab break off

low frequency passive microwave observations of sea ice in the weddell sea the microwave emission properties of first year sea ice were investigated from the r v polarstern during the antarctic winter weddell gyre project in 1989 radiometer measurements were made at 611 mhz and 10 ghz and were accompanied by video and visual observations using the theory of radiometric emission from a layered medium a method for deriving sea ice thickness from radiometer data is developed and tested the model is based on an incoherent reflection process and predicts that the emissivity of saline ice increases monotonically with increasing ice thickness until saturation occurs

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

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

curvature of subducted lithosphere from earthquake locations in the wadati benioff zone estimates of slab curvature from 133 profiles across 12 major subduction zones are obtained by fitting splines through earthquakes locations several geometric quantities are computed from the spline fits including the minimum radius of curvature we also introduce a quantity called the equivalent radius of curvature to precisely define the bending dissipation in either a viscous or a plastic slab the minimum and equivalent radius of curvature are approximately equal in slabs with simple geometry i e a single bend but deviate substantially when the geometry is more complicated a compilation of estimates shows that the equivalent radius of curvature is insensitive to the age of the plate at the trench mean values are 175 km or 191 km depending on the rheology of the slab when bending occurs by viscous deformation the resulting dissipation can exceed the power available from subduction with reasonable choices for viscosity a more consistent description of the energetics is obtained by assuming a plastic rheology

quantifying the net slab pull force as a driving mechanism for plate tectonics 1 it has remained unclear how much of the negative buoyancy force of the slab fb is used to pull the trailing plate at the surface into the mantle here i present three dimensional laboratory experiments to quantify the net slab pull force fnsp with respect to fb during subduction results show that fnsp increases with increasing slab length and dip up to 8 12 of fb making fnsp up to twice as large as the ridge push force the remainder of fb is primarily used to drive rollback induced mantle flow 70 to bend the subducting plate at the trench 15 30 and to overcome shear resistance between slab and mantle 0 8

global paleo lithospheric models for geodynamical analysis of plate reconstructions we present a general framework to generate time dependent global subduction history models from kinematic plate reconstructions and explore their associated coupled plate mantle dynamic behaviour slabs are constructed by advecting material into the mantle by prescribing its radial velocity and following the absolute tangential motion of the subducting plate a simple geodynamic scenario where plates and slabs define isopycnic and isoviscous regions in an homogeneous or layered mantle was explored using the boundary element method based software bemearth the resulting dynamic behaviour was used to predict the absolute plate motion directions for the present day and a particular mid cretaceous 125 ma kinematic model we show how the methodology can be used to compare and revise kinematic reconstructions based on their effect on the balance of plate driving forces and the resulting euler poles of subducting plates as an example we compare the farallon plate dynamics at 125 ma in a global model with two reconstructions in the context of the evolution of the western north american cordillera our results suggest a method to identify episodes of absolute plate motions that are inconsistent with the expected plate dynamics

constraints on subducting plate strength within the kermadec trench four specially designed surveys parallel to the kermadec trench allow localized estimates of plate strength within the subducting pacific plate to be made the transfer function between topography and gravity is estimated for five trench parallel ship tracks at distances of 25 110 km from the trench axis we find a clear reduction in the magnitude and peak wavelength of the transfer function from the outer rise to the trench axis the change in the transfer function indicates a decrease in plate strength and is consistent with a reduction in flexural rigidity by 3 5 orders of magnitude or a decrease in effective elastic thickness by more than 15 km such a large magnitude decrease in the effective elastic strength suggests that the plate has little or no elastic strength within the trench and that viscous stresses play an important role in transferring slab pull forces to the subducting plate and regulating plate speeds in subduction zones

how mantle slabs drive plate tectonics the gravitational pull of subducted slabs is thought to drive the motions of earth s tectonic plates but the coupling between slabs and plates is not well established if a slab is mechanically attached to a subducting plate it can exert a direct pull on the plate alternatively a detached slab may drive a plate by exciting flow in the mantle that exerts a shear traction on the base of the plate from the geologic history of subduction we estimated the relative importance of pull versus suction for the present day plates observed plate motions are best predicted if slabs in the upper mantle are attached to plates and generate slab pull forces that account for about half of the total driving force on plates slabs in the lower mantle are supported by viscous mantle forces and drive plates through slab suction

fluid flow during slab unbending and dehydration implications for intermediate depth seismicity slab weakening and deep water recycling 1 subducting oceanic plates carry a considerable amount of water from the surface down to mantle depths and contribute significantly to the global water cycle a part of these volatiles stored in the slab is expelled at intermediate depths 70 300 km where dehydration reactions occur however despite the fact that water considerably affects many physical properties of rocks not much is known about the fluid flow path and the interaction with the rocks through which volatiles flow in the slab interior during its dehydration we performed thermomechanical models coupled with a petrological database and with incompressible aqueous fluid flow of a dynamically subducting and dehydrating oceanic plate results show that during slab dehydration unbending stresses drive part of the released fluids into the cold core of the plate toward a level of strong tectonic under pressure and neutral slab normal pressure gradients fluids progressively accumulate and percolate updip along such a layer forming together with the upper hydrated layer near the top of the slab a double hydrated zone dhz where intermediate depth seismicity could be triggered the location and predicted mechanics of the dhz would be consistent with seismological observations regarding double seismic zones dszs found in most subduction zones and suggests that hydrofracturing could be the trigger mechanism for observed intermediate depth seismicity in the light of our results the lower plane of the dsz is more likely to reflect a layer of upward percolating fluid than a level of mantle dehydration in our models a 20 30 km thick dsz forms in relatively old oceanic plates without requiring an extremely deep slab hydration prior to subduction the redistribution of fluids into the slab interior during slab unbending also has important implications for slab weakening and the deep water cycle we estimate that over the whole of earth s history a volume of water equivalent to around one to two oceans can be stored in nominally anhydrous minerals of the oceanic lithosphere and transported to the transition zone by this mechanism suggesting that mantle regassing could have been efficient even without invoking the formation of high pressure hydrous minerals

a regime diagram of mobile lid convection with plate like behavior abstract terrestrial planetary bodies that undergo solid state convection can exhibit a variety of tectonic styles from stagnant lid one plate planets to those with a mobilized lithosphere for modeled planetary convection the de facto mode of recycling of lithosphere into the planetary interior is typically achieved through 2 sided and symmetric downwelling flows however lithosphere recycling on earth occurs in a distinctly 1 sided mode known as subduction using numerical models of mantle convection in which the viscosity of planetary mantle material is strongly temperature dependent yet maintains a finite material strength as dictated by its yield stress we investigate the continuum of mobile lid convection with plate like behavior the models span a parameter space of rayleigh number and plate strength and explore convective systems with low yield stresses resulting in weak subduction hinges that bend easily and highly deformable subducted slabs three distinct modes are found to occur in convective systems with weak plates the stagnant lid mode 2 sided downwelling mode and a mode that alternates between 1 sided subduction and 2 sided downwellings we classify the style of convective downwelling for a range of models and show that mode selection strongly depends on the combination of surface mobility and strength of the downgoing plate using these measurements we have developed a regime diagram that can predict whether a particular system will be in one of those three modes

large scale lithospheric stress field and topography induced by global mantle circulation stresses in the lithosphere are one indication of processes in the earth interior here we present a calculation of largescale lithospheric stresses caused by global mantle circulation the mantle flow field is calculated based on density structures inferred from global seismic tomography predicted principal stress directions are compared to interpolations based on observed stresses agreement between predictions and observations is often good in regions where lithospheric stresses and mantle tomography are well constrained predicted magnitudes of scalar stress anomalies vary more strongly than predicted stress directions for various tomographic models hotspots preferentially occur in regions where calculated stress anomalies are tensile or slightly compressive results do not strongly depend on radial mantle viscosity structure lithospheric rheology viscous or elastic or plate motion model the model also predicts the directions of motion well for most plates misfits in the predicted magnitudes can be explained qualitatively stress anomalies due to causes within the lithosphere oceanic cooling with age variations in crustal thickness topography isostatically compensated at subcrustal levels are also computed predicted stress directions in the absence of mantle flow can explain observations almost as well as mantle flow nevertheless current models of mantle flow are largely in accord with interpolations of observed principal stress directions and the observed plate motions fl 2001 elsevier science b v all rights reserved

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

merging sequence stratigraphy and geomechanics for unconventional gas shales the recent revelation of vast global quantities of potentially gas and oil productive shales has paved the way for rapid advancements in understanding their geological properties many of which affect their geomechanical properties and ultimately reservoir operations and performance because of shale s unique and very intricate geological physical and mechanical properties at all scales from nano to macro scale abousleiman et al 2010 compared with sandstones and carbonates the ad jective unconventional has often been applied to their characterization although many shale characteristics are different than those of sandstones and carbonates and require new technologies to measure them other characteristics mentioned below are similar as such customized conventional methodologies and concepts can be applied to exploration and production of shale gas and oil

cenozoic plate driving forces past studies of plate driving forces have concluded that the forces due to subducted slabs in the upper mantle and those due to the thickening of the oceanic lithosphere are the principal driving forces we reexamine the balance of driving forces for the present day and extend our analysis through the cenozoic using an analytical torque balance method which accounts for interactions between plates via viscous coupling to the induced mantle flow we use an evolving mantle density heterogeneity field based on the last 200 myr of subduction to drive plate motions an approach which has proven successful in predicting the present day mantle heterogeneity field we find that for plausible upper mantle viscosities the forces due to subducted slabs in the cenozoic and mesozoic account for in excess of 90 of plate driving forces and those due to lithospheric thickening for less than 10

rheologic controls on slab dynamics several models have been proposed to relate slab geometry to parameters such as plate velocity or plate age however studies on the observed relationships between slab geometry and a wide range of subduction parameters show that there is not a simple global relationship between slab geometry and any one of these other subduction parameters for all subduction zones numerical and laboratory models of subduction provide a method to explore the relative importance of different physical processes in determining subduction dynamics employing 2 d numerical models with a viscosity structure constrained by laboratory experiments for the deformation of olivine we show that the observed range in slab dip and the observed trends between slab dip and convergence velocity subducting plate age and subduction duration can be reproduced without trench motion i e slab roll back for locations away from slab edges successful models include a stiff slab that is 100 1000 times more viscous than previous estimates from models of plate bending the geoid and global plate motions we find that slab dip in the upper mantle depends primarily on slab strength and plate boundary coupling with a small dependence on subducting plate age once the slab sinks into the lower mantle the primary processes controlling slab evolution are 1 the ability of the stiff slab to transmit stresses up dip 2 resistance to slab descent into the higher viscosity lower mantle and 3 subduction induced flow in the mantle wedge corner

on the relationships between slab dip back arc stress upper plate absolute motion and crustal nature in subduction zones 1 statistical analysis of modern oceanic subduction zone parameters such as the age of a downgoing plate or the absolute plate motions is performed in order to investigate which parameter controls the dip of a slab and conversely what the influence of slab geometry is on upper plate behavior for that purpose parameters have been determined from global databases along 159 transects from all subduction zones that are not perturbed by nearby collision or ridge plateau seamount subduction on the basis of tomographic images slabs that penetrate through or lie on the 670 km discontinuity are also identified the results of the statistical analysis are as follows 1 back arc stress correlates with slab dip i e back arc spreading is observed for deep dips deeper than 125 km larger than 50 whereas back arc shortening occurs only for deep dips less than 30 2 slab dip correlates with absolute motion of the overriding plate the correlation is even better when the slab lies on or even more penetrates through the 670 km discontinuity 3 slabs dip more steeply by about 20 on average beneath oceanic overriding plates than beneath continental ones 4 slabs dip more steeply on average by about 10 near edges 5 slab dip does not correlate with the magnitude of slab pull the age of subducting lithosphere at the trench the thermal regime of the subducting lithosphere the convergence rate or the subduction polarity east versus west the present study provides evidence that the upper plate absolute motion plays an important role on slab dip as well as on upper plate strain retreating overriding plates are often oceanic ones and thus may partially explain the steeper slab dips beneath oceanic upper plates one can infer that low slab dips correlate well with compression in continental advancing upper plates whereas steep dips are often associated with extension in oceanic retreating upper plates excess weight of old slabs is often counterbalanced by other forces probably asthenospheric in origin such as lateral mantle flow near slab edges or anchor forces to determine slab dip

evolution of the slab bending radius and the bending dissipation in three dimensional subduction models with a variable slab to upper mantle viscosity ratio abstract three dimensional laboratory subduction models are presented investigating the influence of the slab upper mantle viscosity ratio sp um on the slab bending radius r b with sp um 66 1375 here r b is non dimensionalized by dividing it by the upper mantle thickness t um the results show that r b t um varies with time reaching a maximum when the subduction velocity is maximum furthermore r b t um increases approximately linearly with increasing sp um for the investigated viscosity range the model results show that the slab bending force f be and the energy dissipation during bending be are small compared to the negative buoyancy force of the slab f bu and the potential energy release during sinking bu maxima in be bu f be f bu are reached in the early stage of subduction when r b t um is minimum and the slab tip is at 220 440 km depth maximum be bu increases with increasing sp um with be bu max 0 06 0 11 0 18 and 0 22 for sp um 66 217 709 and 1375 respectively for subduction depths 220 440 km be bu 0 02 0 11 for all viscosity ratios assuming that in nature sp um r b t um and be bu to natural subduction zones implies that in nature sp um 1 7 10 2 and um 0 8 2 7 10 20 pa s finally the laboratory models which use glucose syrup and silicone oil as modelling materials highlight the importance of accurate control on temperature during an experiment new material investigations show that the viscosity of these two materials decreases exponentially with temperature in the range 3 33 c their density decreases approximately linearly with temperature and their coefficient of thermal volumetric expansion is 3 8 4 2 10 4 c 1 glucose syrup and 9 2 10 4 c 1 silicone oil

evidence of lower mantle slab penetration phases in plate motions it is well accepted that subduction of the cold lithosphere is a crucial component of the earth s plate tectonic style of mantle convection but whether and how subducting plates penetrate into the lower mantle is the subject of continuing debate which has substantial implications for the chemical and thermal evolution of the mantle here we identify lower mantle slab penetration events by comparing cenozoic plate motions at the earth s main subduction zones with motions predicted by fully dynamic models of the upper mantle phase of subduction driven solely by downgoing plate density whereas subduction of older intrinsically denser lithosphere occurs at rates consistent with the model younger lithosphere of ages less than about 60 myr often subducts up to two times faster while trench motions are very low we conclude that the most likely explanation is that older lithosphere subducting under significant trench retreat tends to lie down flat above the transition to the high viscosity lower mantle whereas younger lithosphere which is less able to drive trench retreat and deforms more readily buckles and thickens slab thickening enhances buoyancy volume times density and thereby stokes sinking velocity thus facilitating fast lower mantle penetration such an interpretation is consistent with seismic images of the distribution of subducted material in upper and lower mantle thus we identify a direct expression of time dependent flow between the upper and lower mantle

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

plate bending at subduction zones consequences for the direction of plate motions abstract bending of lithospheric plates at subduction zones is thought to be an important source of dissipation for convection in the earth s mantle however the influence of bending on plate motion is uncertain here we use a variational description of mantle convection to show that bending strongly affects the direction of plate motion subduction of slabs and subsidence of oceanic lithosphere with age provide the primary driving forces dissipation is partitioned between plate bending and various sources of friction at plate boundaries and in the interior of the mantle due to viscous flow we determine the poles of rotation for the pacific and nazca plates by requiring the net work to be stationary with respect to small changes in the direction of motion the best fit to the observed rotation poles is obtained with an effective lithospheric viscosity of 6 1022 pa s bending of the pacific plate dissipates roughly 40 of the energy released by subduction through the upper mantle

effects of plate and slab viscosities on the geoid abstract the effects of plate rheology strong plate interiors and weak plate margins and stiff subducted lithosphere slabs on the geoid and plate motions considered jointly are examined with three dimensional spherical models of mantle flow buoyancy forces are based on the internal distribution of subducted lithosphere estimated from the last 160 ma of subduction history while the ratio of the lower mantle upper mantle viscosity has a strong effect on the long wavelength geoid as has been shown before we find that plate rheology is also significant and that its inclusion yields a better geoid model while simultaneously reproducing basic features of observed plate motion slab viscosity can strongly affect the geoid depending on whether a slab is coupled to the surface in particular deep high viscosity slabs beneath the northern pacific that are disconnected from the surface as a result of subduction history produce significant long wavelength geoid highs that differ from the observation this suggests that slabs in the lower mantle may be not as stiff as predicted from a simple thermally activated rheology if the slab model is accurate

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

an analytic model of convection in a system with layered viscosity and plates summary we present an analytic boundary layer model for thermal convection with a finite strength plate and depth dependent viscosity the model permits solutions in which convective flow rates in the mantle exceed the plate velocity the energy balance equations for the lithosphere and convective cell are distinct and the model yields the plate velocity plate thickness and heat flow as well as the laterally averaged horizontal flow profile for a convective cell we demonstrate by inspection of the lithospheric energy balance that the dominant plate driving force depends not only on the material properties of the mantle and lithosphere but also on the velocity of the plate multiple solutions are possible with three solution branches for the plate velocity representing three distinct modes of thermal convection the branch of solutions with the largest plate velocity corresponds to the classic boundary layer solution with a plate velocity approximately equal to the maximum mantle velocity this branch reproduces the classic convective scaling laws for an isoviscous fluid and its dynamics are controlled by the mantle material properties the branch of solutions with intermediate plate velocity represents a convective cell with a sluggish lid and a plate velocity that is less than the underlying mantle velocity the dynamics for this solution branch depend on the material properties of both the mantle and the lithosphere finally the lower branch of solutions for the plate velocity yields a convective solution in which the plate velocity is determined entirely by the local dynamics of a thick and strong relative to the mantle lithosphere the dynamics of this solution branch are independent of the material properties of the mantle and depend entirely on the properties of the lithosphere the introduction of an asthenosphere or low viscosity layer lvl beneath the plate can significantly alter the dynamics of the system by affecting plate mantle coupling lowering the lvl viscosity relative to the lower mantle can promote plate motion by providing a lubricating layer however a very low viscosity lvl beneath a strong plate can decouple plate and mantle and inhibit plate motion producing a solution with a slow moving plate and a channelized flow in the lvl thus a lvl can sometimes inhibit rather than promote plate tectonics