3d fold growth in transpression abstract geological folds in transpression are inherently 3d structures hence their growth and rotation behavior is studied using 3d numerical finite element simulations upright single layer buckle folds in newtonian materials are considered which grow from an initial point like perturbation due to a combination of in plane shortening and shearing i e transpression the resulting fold growth exhibits three components 1 fold amplification vertical 2 fold elongation parallel to fold axis and 3 sequential fold growth perpendicular to axial plane of new anti and synforms adjacent to the initial fold generally the fold growth rates are smaller for shearing dominated than for shortening dominated transpression in spite of the growth rate the folding behavior is very similar for the different convergence angles the two lateral directions always exhibit similar growth rates implying that the bulk fold structure occupies an increasing roughly circular area fold axes are always parallel to the major horizontal principal strain axis max i e long axis of the horizontal finite strain ellipse which is initially also parallel to the major horizontal instantaneous stretching axis isa max after initiation the fold axes rotate together with max sequential folds appearing later do not initiate parallel to isa max but parallel to max i e parallel to the already existing folds and also rotate with max therefore fold axes do not correspond to passive material lines and hinge migration takes place as a consequence the fold axis orientation parallel to max is independent of convergence angle and viscosity ratio therefore a triangular relationship between convergence angle amount of shortening and fold axis orientation exists if two of these values are known the third can be determined this relationship is applied to the zagros fold and thrust belt to estimate the degree of strain partitioning between the simply folded belt and the bordering strike slip fault system

compression of oceanic lithosphere an analysis of intraplate deformation in the central indian basin intraplate compressional deformation in the central indian basin is expressed as linear e w trending topographic undulations and geoid anomlies with characteristic spacings of approximately 200 km to elucidate the nature of this deformation we develop models of an oceanic lithosphere in a state of horizontal compression the lithosphere is treated as a viscous or plastic layer of uniform strength which overlies a viscous half space in which strength decreases exponentially with depth we compare models in which deformation with a dominant wavelength develops in response to flexural buckling and the hydrodynamic growth of instabilities for the viscous flexural buckling model deformation is constrained to occur in the antisymmetric mode by flexural folding which is characterized by uniform bending of the layer in the hydrodynamic flow model a range of deformational styles are possible in a strong viscous lithosphere deformation of the layer occurs by flexural folding at a wavelength which agrees with that predicted from flexural buckling theory in a lithosphere of intermediate strength the layer deforms by folding characterized by thickening which localizes beneath topographic highs in a relatively weak lithosphere the layer incurs an even greater amount of localized thickening and deforms in the symmetric or pinch and swell mode by inverse boudinage if the layer has a plastic rheology deformation occurs by inverse boudinage independent of the yield stress results from models in which the layer folds either flexurally or with periodic thickening are consistent with the observed depth distribution of seismicity in the central indian basin and with experimental rock rheological data because of the trade off between buoyancy forces and layer strength in determining the dominant wavelength a lithosphere which was overlain by weak sediments when intraplate deformation initiated can be characterized by a compressive layer strength almost a factor of 3 less than a lithosphere which was initially sediment free for a range of plausible models which consider both a sediment covered and sediment free lithosphere the observed wavelength requires deviatoric stresses in the indian plate of several hundreds of mpa

new extended thin sheet approximation for geodynamic applications i model formulation thin sheet approximations are widely used in geodynamics because of their potential for fast computation of 3 d lithospheric deformations using simple numerical techniques however this simplicity

dynamics of the india eurasia collision zone we present simple new dynamic calculations of a vertically averaged deviatoric stress field over a depth average of 100 km for asia from geodetic geologic topographic and seismic data a first estimate of the minimum absolute magnitudes and directions of vertically averaged deviatoric stress is obtained by solving force balance equations for deviatoric stresses associated with gravitational potential energy differences within the lithosphere plus a first order contribution of deviatoric stresses associated with stress boundary conditions this initial estimate of the vertically averaged deviatoric stress field is obtained independent of assumptions about the rheology of the lithosphere absolute magnitudes of vertically averaged deviatoric stresses vary between 5 and 40 mpa assuming bulk viscous behavior for the lithosphere the magnitudes of deviatoric stresses together with the magnitudes of strain rates inferred from quaternary fault slip rate and gps data yield vertically averaged effective viscosities for tibet of 0 5 5 1022 pa s compared with 1 2 5 1023 pa s in more rigid areas elsewhere in the region a forward modeling method that solves force balance equations using velocity boundary conditions allows us to refine our estimates of the vertically averaged effective viscosity distribution and deviatoric stress field the total vertically averaged deviatoric stress and effective viscosity field are consistent with a weak lower crust in tibet they are consistent with some eastward motion of tibet and south china lithosphere relative to eurasia and they confirm that gravitational potential energy differences have a profound effect on the spatially varying style and magnitude of strain rate around the tibetan plateau our results for the vertically averaged deviatoric stress argue for a large portion of the strength of the lithosphere to reside within the seismogenic upper crust to get deviatoric stress magnitudes there to be as high as 100 300 mpa in accord with laboratory and theoretical friction experiments indicating that stress drops in earthquakes are small fractions of the total deviatoric stress

lithospheric scale folding numerical modelling and application to the himalayan syntaxes we describe the eastern and western himalayan syntaxes which are large scale antiforms situated at geodynamically similar locations and the metamorphic evolution of which is coeval in the india asia collisional history to understand the mechanical plausibility of the structural interpretation we present two dimensional finite element modelling of lithospheric folding the models reveal the coeval development of adjacent synformal basins analogous to the peshawar and kashmir basins on both sides of the western syntaxis similarities between geological data and calculated models indicate that lithospheric buckling is a basic response to large scale continental shortening and an efficient mountain building process

folding of oceanic lithosphere folding of the lithosphere just south of the bay of bengal appears as 1 undulations in acoustic basement topography and 2 as linear geoid undulations in the seasat altimeter data from the seasat data we find that the east west trending folds have wavelengths ranging from 130 to 250 km and clustering about 190 km the horizontal gravity disturbances due to the folds range in amplitude from 15 to 50 mgal elastic models of oceanic lithosphere have in the past been used to demonstrate the implausibility of lithosphere buckling or folding in response to compression these elastic models typically predict that compressive stresses of about 5 gpa are required to buckle oceanic lithosphere with an age comparable to that of the northeastern indian ocean 40 70 ma these stresses exceed the strength of lithospheric rock we use an elastic plastic model to show that oceanic lithosphere of this age should have a net compressive strength equal to about 12 of the elastic buckling stress we further demonstrate that loads approaching the net compressive strength cause the lithosphere to fold with a wavelength about 200 km i e the wavelength observed from seasat our results reinforce earlier speculation that this folding may be related to the himalayan orogeny

do faults trigger folding in the lithosphere a number of observations reveal large periodic undulations within the oceanic and continental lithospheres the question if these observations are the result of large scale compressive instabilities i e buckling remains open in this study we support the buckling hypothesis by direct numerical modeling we compare our results with the data on three most proeminent cases of the oceanic and continental folding like deformation indian ocean western gobi central asia and central australia we demonstrate that under reasonable tectonic stresses folds can develop from brittle faults cutting through the brittle parts of a lithosphere the predicted wavelengths and finite growth rates are in agreement with observations we also show that within a continental lithosphere with thermal age greater than 400 my either a bi harmonic mode two superimposed wavelengths crustal and mantle one or a coupled mode mono layer deformation of inelastic folding can develop depending on the strength and thickness of the lower crust

decollement tectonics in the jura forelandfold and thrust belt abstract interpretation of more than 1500 km of industry seismic reflection lines from theswiss and french jura mountains and the western swiss molasse basin demonstrates that themesozoic and cenozoic cover of the jura fold and thrust belt has been deformed over a veryweak basal decollement and displaced for many kilometers toward the nw and that thebasement is not involved a depth to the basement map derived from depth conversion of theseismic lines shows a rather smooth flat basement dipping 1 3 to the s se the low amplitudebroad folds of the molasse basin and the external plateau jura are controlled by evaporitepillows or anticlines of middle triassic age the high amplitude folds of the haute chaine jura however are related to nw or se vergent thrusts with at least kilometric dipslip displacementthat has doubled the entire jurassic sequence the plateau jura evaporite related folds located in the foreland are interpreted as early stage buckle folds with further deformation afault ramp nucleates and develops into thrust related folds as observed in the haute chaine thus within the fold and thrust belt deformation increases toward the hinterland in the molassebasin however low amplitude folds represent an early deformation stage which could notdevelop further owing to the load of the overlying thick tertiary clastic wedge

continental lithosphere folding in central asia part ii constraints from gravity and topography abstract periodical sub parallel fold like structures observed in the western gobi have two characteristic dominant wavelengths of approximately 50 and 300 360 km we explain these observations in terms of independent quasi viscous folding of the crustal and upper mantle parts of the lithosphere due to horizontal transpressional stresses in central asia induced by the collision with the indian plate we derive a model for the mechanical response of the continental lithosphere to horizontal stresses for a rheologically layered plate with non newtonian power law rheology overlying a low viscosity asthenosphere the differentiation in the effective viscosity and thickness of the strong upper crust and upper mantle lithosphere along with the presence of a low viscosity lower crust between them leads to their partial decoupling during compressional deformation these features result in the appearance of different wavelengths of the folds in the western gobi region we derive simple semi analytical estimates for the dominant wavelengths and rates of growth of surface undulations constrained by data from experimental rock mechanics topography and gravity

timing and rate of granulite facies metamorphism and cooling from multi mineral chronology on migmatitic gneisses sierras de la huerta and valle fertil nw argentina abstract migmatitic paragneisses of the valle fertil la huerta ranges at the western margin of the sierras pampeanas are composed of garnet cordierite plagioclase biotite quartz bearing units that experienced peak metamorphic conditions of ca 800 c at 6 7 kbar based on petrological studies pseudosection modeling and petrographic observations an anticlockwise p t path with a small pressure increment is proposed rare earth element la icp ms patterns acquired from rutile bearing garnets suggest a single stage of garnet growth at high t at pressures above the ilmenite rutile transition u pb dating of zircon rims from the migmatites indicates two distinct metamorphic u pb ages of 525 9 ma and 478 9 ma the older age is suggested to record an amphibolite facies event of the pampean orogeny the younger metamorphic age is contemporary with igneous zircons from metatonalites and pegmatites that yield 478 4 ma we suggest that the prograde high t metamorphic famatinian event is associated with the emplacement of large magmatic bodies in which large scale magmatic activity gave rise to an increased geothermal gradient of about 35 c km sm nd garnet ages of 447 3 ma indicate a time span of around 30 ma for which temperatures above the garnet closure temperature prevailed using u pb sm nd and rb sr isotope systems a cooling rate of 3 to 6 c myr is inferred

interaction of folding and thrusting during fold and thrust belt evolution insights from numerical simulations and application to the swiss jura and the canadian foothills abstract we use two dimensional numerical simulations to investigate the interaction of folding buckling and thrusting localized shearing during the structural evolution of fold and thrust belts ftb we model layer parallel shortening of mechanically strong layers resting above a weaker layer referred to as detachment we consider a viscoplastic rheology with linear viscosity and frictional plastic drucker prager yield criterion the detachment thickness is larger in one model half and only this geometrical thickness perturbation triggers folding and thrusting in the simulations we conduct a systematic analysis to quantify the impact of model parameters such as magnitude of the thickness perturbation or detachment rheology frictional or viscous on the ftb evolution the magnitude of the perturbation determines whether or not folding is favoured over thrusting and hence controls the progressive interaction of folding and thrusting during ftb evolution the asymmetry of modelled anticlines is proportional to the relative height of the initial perturbation we also adapt the model configuration to specific mechanical stratigraphies of two regions in natural ftb namely the haute chaine of the jura mountains switzerland and the foothills of alberta canada the modelled fold and thrust geometries agree with different types of observed anticlinal structures such as symmetric detachments folds and asymmetric thrust folds our results suggest that an initial stage of low amplitude buckling likely occurred prior to the main folding and thrusting phase we argue that folding and thrusting are equally important and interacting processes during the structural evolution of many natural ftb

a thin viscous sheet model for continental deformation summary for the purposes of describing its large scale and long term deformation the continental lithosphere is regarded as a continuum obeying a newtonian or a power law rheology the flow of a thin sheet of power law material overlying an inviscid substrate is studied under the assumption that vertical gradients of the horizontal velocity are negligible a numerical model is used to investigate the deformation of such a sheet under conditions approximating those of continent continent collision the material flows in response to forces applied to its boundaries for example the indenting of one continent by another and to forces in its interior arising from gradients in crustal thickness the horizontal divergence of the flow produces changes in the crustal thickness and hence a time dependent form to the flow itself for a given set of boundary conditions the flow depends on the stress exponent in the power law rheology n and on the argand number which is a measure of the ratio between the stress arising from crustal thickness contrasts and the stress required to deform the material at the ambient strain rates when the effective viscosity of the medium is very high ar o crustal thickness variations do not influence the flow if the material is newtonian n l the deformation associated with an influx of material approximating an indenter is of much greater lateral dimension than the width of the indenter whereas when material has a power law rheology n 3 5 are used the deformation is confined to a region of lateral extent comparable to that of the indenter as ar increases the forces arising from crustal thickness contrasts exert more influence on the flow and the maximum crustal thickness that can be sustained by a given influx of material is related by a simple expression to the effective viscosity of the medium at the ambient strain rates in the limit of a very weak medium ar 10 the lithosphere is unable to sustain appreciable crustal elevation contrasts the results of these numerical experiments show that systems in which the effective viscosities are such that the maximum deviatoric stresses are between 1 kbar

stretching instabilities and lithospheric boudinage a competent layer with a nonlinear rheology can under extension exhibit pinch and swell instabilities such instabilities can explain small scale regular deformations of rock recently they have also been invoked in relation to the distribution of basins and ranges fletcher and hallet 1983 and the undulation of the bouguer map froidevaux 1986 in the western part of north america for the case of a simple stratified structure different authors have expressed mathematical solutions describing these instabilities in this paper we elucidate the general physical meaning of these nonhomogeneous deformations in the simplest case where the competent layer is fully embedded in a softer material a fundamental mode develops with a preferred wavelength equal to 4 times the thickness of a competent layer the novelty is the occurrence of overtones with alternate symmetrical and antisymmetrical deflections of the interfaces between layers these modes have a large amplitude when the rheology tends to perfect plasticity the presence of a free surface like the earth s surface for the upper crust is shown to double the preferred wavelength of the fundamental mode and to forbid one overtone out of two this new effect is caused by gravity which inhibits the growth of surface topography another shift is of opposite sign to that caused by a free surface numerical solutions for multilayer structures can elucidate the nature of couplings between various layers the case of a three layer lithosphere having a soft lower crust and overlying a mantle asthenosphere has been analyzed in some detail it shows that in the range of wavelengths larger than 30 km up to five preferred modes may be superimposed this should encourage further analysis of the western u s topography and gravity pattern which is known to contain at least two wavelengths about 40 km for the individual basins and ranges and about 200 km for the bouguer troughs in nevada and their associated broad topographies

finite strain calculations of continental deformation 2 comparison with the india asia collision zone numerical experiments on a thin viscous sheet model for deformation of continental lithosphere subjected to an indenting boundary condition yield distributions of crustal thickness of stress and strain rate and of latitudinal displacements that may be compared with observations in the india asia collision zone a simple indenting boundary condition applied to initially laterally homogeneous sheets obeying a power law rheology produces results that are in broad agreement with the observations provided that the power law exponent is three or greater and the sheet can support vertically integrated stress differences of 2 1013 5 1012 n m 1 in regions in front of the indenter under these conditions the calculated deformation shows accommodation of convergence primarily by crustal thickening to produce a plateau in front of the indenter palaeomagnetic data from india and tibet and the observed distribution of topography suggest that much of the post eocene convergence of india with asia has been taken up by deformation within asia that involved crustal thickening the principal difference between calculation and observation is the absence from the calculated strain rate fields of east west extension of the plateau in front of the indenting boundary the calculations show that once such a plateau is formed the buoyancy force associated with the crustal thickness contrast inhibits further thickening and the plateau strains at less than half the rate of its immediate surroundings seismically determined regional strain rates exhibit a similar distribution with the tibetan plateau straining at about one quarter the rate of the tien shan and ningxia gansu regions calculated principal compressive stress orientations and regional strain rates agree with the seismically determined quantities in the mongolia baikal tien shan tibet and ningxia gansu regions of asia to within the uncertainty of the latter the vertically integrated stresses that are calculated for the viscous sheet are comparable with those that can be supported by a theologically stratified continental lithosphere obeying laboratory determined flow laws we suggest that the thin viscous sheet model described in this paper and its companion gives a simple and physically plausible description of the observed deformation in central asia in this description the predominant mechanism of accommodation of continental convergence is diffuse crustal thickening with shear on vertical planes playing a subsidiary role once large crustal thickness contrasts have been established

stress evolution during 3d single layer visco elastic buckle folding implications for the initiation of fractures abstract buckle folds of sedimentary strata commonly feature a variety of different fracture sets some fracture sets including outer arc tensile fractures and inner arc shear fractures at the fold hinge zones are well understood by the extensional and compressional strain stress pattern however other commonly observed fracture sets including tensile fractures parallel to the fold axis tensile fractures cutting through the limb extensional faults at the fold hinge and other shear fractures of various orientations in the fold limb fail to be intuitively explained by the strain stress regimes during the buckling process to obtain a better understanding of the conditions for the initiation of the various fractures sets associated with single layer cylindrical buckle folds a 3d finite element modeling approach using a maxwell visco elastic rheology is utilized the influences of three model parameters with significant influence on fracture initiation are considered burial depth viscosity and permeability it is concluded that these parameters are critical for the initiation of major fracture sets at the hinge zone with varying degrees the numerical simulation results further show that the buckling process fails to explain most of the fracture sets occurring in the limb unless the process of erosional unloading as a post fold phenomenon is considered for fracture sets that only develop under unrealistic boundary conditions the results demonstrate that their development is realistic for a perclinal fold geometry in summary a more thorough understanding of fractures sets associated with buckle folds is obtained based on the simulation of in situ stress conditions during the structural development of buckle folds

control of folding by gravity and matrix thickness implications for large scale folding 1 we show that folding of a non newtonian layer resting on a homogeneous newtonian matrix with finite thickness under influence of gravity can occur by three modes 1 matrix controlled folding dependent on the effective viscosity contrast between layer and matrix 2 gravity controlled folding dependent on the argand number the ratio of the stress caused by gravity to the stress caused by shortening and 3 detachment folding dependent on the ratio of matrix thickness to layer thickness we construct a phase diagram that defines the transitions between each of the three folding modes our priority is transparency of the analytical derivations e g thin plate versus thick plate approximations which permits complete classification of the folding modes involving a minimum number of dimensionless parameters accuracy and sensitivity of the analytical results to model assumptions are investigated in particular depth dependence of matrix rheology is only important for folding over a narrow range of material parameters in contrast strong depth dependence of the viscosity of the folding layer limits applicability of ductile rheology and leads to a viscoelastic transition our theory is applied to estimate the effective thickness of the folded central asian upper crust using the ratio of topographic wavelength to moho depth phase diagrams based on geometrical parameters show that gravity does not significantly control folding in the jura and the zagros mountains but does control folding in central asia applicability conditions of viscous and thin sheet models for large scale lithospheric deformation derived in terms of the argand number have implications for the plate like style of planetary tectonics

finite amplitude folding of a continuously viscosity stratified lithosphere we study the development of finite amplitude folding of the lithosphere through the application of finite element models characterized by both discontinuous layer over half space and continuous strength envelope viscosity distributions both models include strongly strain rate dependent rheologies that approximate slip on pervasive faults folding with layers of form contrasting viscosities is driven solely bye magnitudes of discontinuities in viscosity at layer interfaces however folds may also develop in a medium with a continuously varying viscosity distribution the net driving force for folding in a region of continuous viscosity variation is the same as the driving force across a discontinuity with the same net viscosity contrast continuous and discontinuous viscosity variations give essentially identical fold growth rates if the depth over which the viscosity varies is small compared to the wavelength of folding or the depth of the viscosity variation in the uniform viscosity layer model flexural bending of the layer results in a state of extension on topographic highs and compression in topographic lows in contrast the strength envelope model is characterized by significant penetrative shortening near the surface that results in a state of compression everywhere along the fold this model predicts layer thickening beneath fold troughs as observed in the intmpladeformation zone in the central indian ocean buocy forces retard the rate of fold amplification but are inadequato prevent folding for a range of realistic lithospheric theological structures

rheological modelling and deformation instability of lithosphere under extension summary continental break up which precedes oceanic accretion probably results from an unstable extension of the lithosphere analogous to necking of metals when they are submitted to tension by reason of complexity of the rheology no conclusion about lithospheric extension stability may be reached by an a priori analysis we thus examine directly the evolution when the lithosphere is stretched of lateral inhomogeneities represented in our example by small scale variations of thickness the rheological model is derived from the hypotheses of brace kohlstedt 1980 and is consistent with the results of rock mechanics the lithosphere consists of three or four layers of varying thicknesses and mechanical properties the brittle upper crust and eventually the brittle part of the mantle are assimilated to perfectly plastic media and are described in a state of uniform extension by a constant viscosity in the lower crust and ductile mantle lithosphere the effective viscosity is supposed to be exponential the mechanical model relies on a perturbation method developed by fletcher hallet 1983 among others contrary to previous published results no unstable behaviour of the lithosphere is observed unless the latter is more dense than the asthenosphere in which case a gravitational instability may develop this discrepancy can be explained by differences in assumptions concerning the variation of strength in the lithosphere as yet poorly constrained by the data we observe a great sensitivity of the results to the strength stratification and to the artificial discontinuities of density or viscosity implied by the models

lithospheric scale gravitational flow the impact of body forces on orogenic processes from archaean to phanerozoic in the archaean the combination of warmer continental geotherm with a lighter sub continental lithospheric mantle suggests that gravitational forces played a more signifi cant role in continental lithospheric deformation to test this hypothesis we compare the evolution of the deformation and the regional state of stress in archaean like and phanerozoic like lithospheres submitted to the same boundary conditions in a triaxial stress field with imposed convergence in one direction for plausible physical parameters thickening of normal to cold phanerozoic lithospheres produces relatively weak buoyancy forces either extensional or compressional in contrast for archaean continental litho spheres or for anomalously warm phanerozoic lithospheres lateral gravitationally driven flow prevents significant thickening this conclusion is broadly consistent with 1 the rela tive homogeneity of the erosional level now exposed at the surface of archaean cratons 2 the sub aerial conditions that prevailed during the emplacement of up to 20 km of green stone cover 3 the relatively rare occurrence in the archaean record of voluminous detrital sediments 4 the near absence of significant tectonic metamorphic and magmatic age gra dients across archaean cratons 5 the relative homogeneity of strain across large areas and 6 the ubiquitous presence of crustal scale strike slip faults in many late archaean cratons

geometry and kinematics of single layer detachment folds detachment folds form above below or above and below bed parallel thrusts where thrust displacement is transferred into folding geometric and kinematic models are developed for individual single layer detachment folds formed above the tip line of a thrust we analyze three different detachment fold shapes kink bands chevron and box detachment folds and consider three principal detachment fold models 1 constant limb dip where the detachment fold grows by limb lengthening 2 constant limb length where the detachment fold grows by limb rotation and 3 variable limb length and variable limb dip where the detachment fold grows by both limb rotation and limb lengthening the allowance for variable forelimb thickness and excess layer parallel shear enables us to de elop a wide range of possible detachment fold geometry the geometric validity fields for folds with excess parallel shear are reduced when forelimb thinning takes place folds formed with constant limb length are likely to lock up in the initial amplification stages whereas larger amounts of shortening can be taken up by folds formed with variable limb length the manner in which a fold evolves affects the fracture and porosity features of the folded strata therefore determining which mechanism operated to form a specific detachment fold is of particular importance in hydrocarbon exploration the models we present are aimed at permitting more accurate geometric and kinematic interpretations of individual detachment folds examples of detachment folds are analyzed to illustrate the po ential benefits and limitations of the geometric model presented

building the zagros collisional orogen timing strain distribution and the dynamics of arabia eurasia plate convergence he zagros mountains are the result of the arabia eurasia collision initiated at 35 ma as the rifted arabian lithosphere was underthrusted beneath the iranian plate due to its negative buoyancy the onset of crustal thickening started at 25 ma as recorded by the hinterland exhumation and foreland clastic deposition deformation throughout the arabia eurasia collision zone and the uplift of the iranian plateau occurred after 15 12 ma as a result of shortening thickening of the thin iranian crust we emphasize that only 42 of the post 35 ma convergence is partitioned by shortening within central iran tomographic constraints show ongoing slab steepening or breakoff in the nw zagros whereas underthrusting of the arabian plate is observed beneath central zagros the current subduction dynamics can be explained by the original lateral difference in the buoyancy of the distal margin that promoted slab sinking in nw zagros and underthrusting in central zagros critical wedge approach applied to the zagros favors the hypothesis of strong brittle crust detached above a viscous lower crust in contrast the weak sedimentary cover deforms by buckling of a thick multilayered cover thrust faulting associated with folding occurs in the competent layers and is responsible for most of the earthquakes there is evidence that the role of the slab pull force in driving the arabian plate motion was reduced after 12 ma large scale mantle flow induced by mantle upwelling at the afar plume appears to be the main driver of the arabia plate motion we stress that the main kinematic change in the zagros region occurred at 15 12 ma as the zagros uplifted before the arabian slab detached the zagros appears key to investigate coupling between continental rheology plate driving forces and mountain building in which the role of rift inheritance appears to be central

large scale crustal deformation of the tibetan plateau the topography velocity and strain fields calculated from a three dimensional newtonian viscous model for large scale crustal deformation are generally in good agreement with results from geological geodetic and earthquake studies in and around the tibetan plateau provided that the model rheology incorporates a weak zone within the deep crust beneath the plateau equivalent to a viscosity of 1012 pa s within a 250 m thick channel or 1018 pa s within a 15 km thick channel model studies and observations show a plateau at 5 km elevation with steep topographic gradients across the southern and northern plateau margins and more gentle gradients across the southeastern and northeastern margins rapid shortening strain is concentrated along the lower portions of the northern and southern plateau margins at rates 20 mm yr model results show north south shortening 10 mm yr in reasonable agreement with gps data 5 8 mm yr of north south shortening across the northern two thirds of the plateau and east west stretching 10 15 mm yr across the eastern half of the high plateau in reasonable agreement with seismic geologic and gps data upper crustal material moves eastward from the plateau proper into a lobe of elevated topography that extends to the south and east clockwise rotation of material around the east himalayan syntaxis at rates up to 10 mm yr occurs partly as a result of dextral shear between indian and asian mantle at depth and partly as a result of gravitational spreading from the high plateau to the south and east there is little difference in model surface deformation for assumptions of moderately weak or extremely weak lower crust except in southern and northern tibet where margin perpendicular extension occurs only for the case of an extremely weak lower crust our results suggest that the tibetan plateau is likely to have gone through a two stage development the first stage produced a long narrow high orogen whose height may have been comparable to the modern plateau the second stage produced a plateau that grew progressively to the north and east east west stretching eastward plateau growth and dextral rotation around the east himalayan syntaxis probably did not begin until well into the second stage of plateau growth perhaps becoming significant after 20 m y of convergence

kinematic model of detachment folding including limb rotation fixed hinges and layer parallel strain abstract detachment anticlines formed above a stratigraphically fixed detachment horizon and without thinning in the syncline will in general require layer parallel shortening a kinematic model for detachment folds is presented that has planar limbs and is area balanced but requires bed length changes that can be expressed as layer parallel strain the fold grows primarily by limb rotation not by limb lengthening at constant dip the kinematic evolution of the geometry and strain is examined fold geometry is well predicted and the strain estimated in applications of the model to two map scale detachment folds a triangle zone from the front of the wyoming thrust belt and a duplex cored anticline from the appalachian plateau

a forward approach to the problem of nonlinear viscoelasticity and the thickness of the mechanical lithosphere the physical significance of the mechanical lithosphere is clarified using a nonlinear maxwell flexure model this model reconciles high temperature creep data for rock with the observed long term strength of the mechanical lithosphere an approximate correspondence is established between the nonisothermal maxwell model and an elastic flexure model to define an effective lithosphere thickness he the model calculations are essentially forward since he does not depend in a significant way upon the nominal or prescribed value of beam thickness depending rather upon such variables as temperature and creep activation energy the effective thickness of the maxwell model though a function of time is stable enough over appropriate time scales to explain the long term integrated strength of the lithosphere the strength index is defined as the ratio of axial stress to the axial stress that would be present in a purely elastic fiber suffering the same strain the base of the effective lithosphere is marked by a critical isopleth of strength c 0 3 this critical level though not its position is independent of time since loading the strength index also maps out zones of predominant rheology the narrowness of the transition zone between the elastic lithosphere and the viscous asthenosphere explains the success of the elastic plate in modeling many examples of lithosphere flexure the elastic plate approximation may apply best where the lithosphere is relatively young and hot isolated weak zones in the continental crust may or may not weaken the lithosphere as a whole depending upon the distribution of these zones and the manner in which they deform in general such weakening is likely to be most effective when the base of the crust occurs at midlithospheric depths

decollement folding as a mechanism for thrust ramp spacing the hypothesis that early formed decollement folds localize thrust ramps explaining the regular spacing of major thrust ramps observed in many mountain belts is examined the model for folding instability consists of a rigid basement a weak decollement zone and a stiff thrust sheet the model incorporates the effects of topographic stresses and syntectonic erosion and redeposition and uses a linearized power law rheology for the thrust sheet this approximation is valid for small angles of fold limb dip 15 and is appropriate for analysis of the wave length selection of folds at the onset of deformation the spacing of major thrust ramps and the stratigraphic thicknesses of the decollement zone and thrust sheet from the wyoming portion of the sevier fold and thrust belt are used to test the model the ratio of the fold dominant wavelength to thrust sheet thickness ld h2 increases with the ratio r of the viscosity of the stiff layer to that of the decollement zone and decreases with the power law stress exponent n2 the fold amplification factor increases with both n2 and r as the topographic decay ratio d increases ld h2 increases at fixed n2 and r acceptable models for the absaroka and darby thrust sheets have n2 3 only when r 1000 and significant erosion and redeposition of sediments accompany the folding of the thrust sheet d 103 does the required r fall below a reasonable limit thus a model in which decollement folding is accompanied by syntectonic erosion and redeposition precedes thrusting is consistent with the available observational constraints

crustal thickening versus lateral expulsion in the indian asian continental collision since the beginning of the continental collision between india and asia there has been about 2500 km of convergence and the northward movement of india has been accommodated by major internal deformation of the asian lithosphere the crustal thickening in and around the tibetan plateau is clearly a direct consequence of this collision but there is considerable debate as to whether a large fraction of the indentation has been accommodated by eastward motion of the lithospheric blocks of southeastern asia and southern china numerical experiments described here test this hypothesis for a range of indentation geometries and rheological models of the lithosphere we employ a thin viscous sheet model of the lithosphere with a depth averaged nonlinear viscous rheology described by a stress strain rate exponent n and including gravitational buoyancy forces scaled by the dimensionless argand number ar the eastern boundary for the collision region is described as a lithostatic boundary the precollision normal stress is determined by static balance and that constant stress is applied throughout the collision the experiments show that during collision the eastern boundary is smoothly displaced to the east at a rate about 1 4 of the indentation rate with only minor variation due to geometry or rheology crustal thickening rates in the region of the plateau are reduced by between 10 and 25 of the corresponding rates determined for similar experiments with a rigid eastern boundary to generalize from the results of these experiments the total north south shortening strain produced by the collision is partitioned between crustal thickening and eastward displacement in the ratio of at least 3 1 and more probably 4 1

new extended thin sheet approximation for geodynamic applications ii two dimensional examples the potential of the new extended thin sheet approximation etsa has been investigated by application to a representative range of 2 d problems the system of governing equations presented by medv

gravity anomalies over the ferghana valley central asia and intracontinental deformation gravity anomalies over the ferghana valley a deep sedimentary basin in the western tien shan differ from those expected for local airy isostatic equilibrium by 120 mgal and imply a deficit of mass beneath the basin equivalent to a moho deeper by 10 km than prevails where isostasy holds although the ferghana valley is underlain by thick mesozoic and cenozoic sediment measurements of density show that this material cannot account for the deficit of mass gravity anomalies over both the surrounding mountain belts and the kazakh platform farther north imply that local airy isostatic equilibrium is approached flexure of a relatively thin effectively elastic plate thickness 10 15 km loaded by the present topography can account for the range of bouguer anomalies of 50 to 450 mgal over these regions we infer that approximately north south shortening of the relatively thin lithosphere has created mountains north and south of the basin has warped the basement of the immediate surroundings of the basin up by folding the mantle lithosphere and has forced the basin floor down beneath the ferghana valley it appears that the preexisting thermal structure and variations in crustal thickness have dictated the styles and distribution of deformation in this region

periodic instabilities during compression or extension of the lithosphere 1 deformation modes from an analytical perturbation method we argue that the plastic rheology of the lithosphere rather than its recoverable elastic properties is responsible for the systematic development of periodic instabilities during compression or extension we use a linear perturbation model with analytical solutions to calculate the instability modes for various rheologies the growth of such periodic instabilities is enhanced by the highly nonlinear stress strain rheologies encountered in the brittle layers of the lithosphere on the contrary ductile layers deforming according to high temperature creep flow laws tend to inhibit these instabilities for oceanic domains we assume that the only brittle layer is the upper part of the lithosphere in compression the only valid instability is a buckling whose wavelength is around 4 times the thickness of the brittle layer calculated wavelengths and growth rates are consistent with observations available for the indian ocean for continental domains a reasonable assumption is the existence of two plastic layers one in the upper crust the other in the upper mantle for moho temperatures between 450 c and 600 c in compression and extension two instabilities develop a long wavelength instability involving the whole lithosphere coupling mode and a short wavelength instability involving the crust and controlled by the upper brittle layer intrinsic crustal mode in compression the coupling mode is a whole lithosphere buckling with a wavelength about 4 times the thickness of the active lithosphere the two plastic layers plus the intermediate ductile layer in extension the coupling mode is a boudinage of opposite phase in the two plastic layers and a folding of the intermediate ductile layer the intrinsic crustal mode is a crustal buckling in compression crustal boudinage in extension neither deflects the moho the intrinsic crustal mode is favored by an increase in thermal gradient and by a decrease in strength of the ductile lower crust

present day and future tectonic underplating in the western swiss alps reconciliation of basement wrench faulting and decollement folding of the jura and molasse basin in the alpine foreland abstract the western alps form a geodynamically active mountain belt showing the typical features of an evolving orogenic wedge with its pro wedge geometry to the nnw and its retro wedge structures to the sse renewed tectonic underplating of european continental crust occurred after the orogenic wedge underwent major dynamic disequilibrium following the break off of the southward subducting slab of the european passive margin the most important of these basement imbricates are the mont blanc aiguilles rouges and gastern aar crystalline massifs also forming the alps highest mountains the upper plate present day orogenic wedge of the western alps includes the molasse basin and the jura fold and thrust belt both decoupled from the basement over a basal decollement surface the overall geometry of this wedge appears to be strongly unstable according to simple wedge models in its attempt to regain stability out of sequence thrusts form in the existing basement nappes but also new basement nappes should develop beneath the southern portion of the molasse basin new out of sequence thrusts in the cover trigger higher than average uplift rates concentrated around the newly forming structures and are accompanied by a concentration of earthquakes tectonic underplating is further corroborated by neotectonics and the tectonic structures observed in the prealpes molasse basin and jura similarly uplift rates and earthquakes along the southern edge of the jura mountains seem to witness the development of a new incipient basement nappe at depth partial inversion of former permo carboniferous grabens in the basement a possible spatial coincidence of areas with strong earthquake activity and zones with uplift rates above surrounding values suggest a common mechanism for their origin in the western swiss alpine foreland combined with information from basement geometry and wedge dynamics it is proposed that the common mechanism is the development of basement imbricates by tectonic underplating the proposed model for ongoing and possible future tectonic underplating beneath an active alpine orogenic wedge also allows to reconcile the models of basement wrench faulting in the molasse basin and jura with the distant push theory where the molasse basin and jura develop over a basal decollement horizon

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

flow mechanism of glaciers on soft beds subhourly measurements of bed deformation bed shear strength subglacial water pressure and surface speed at storglaciaren a glacier in northern sweden showed that the shear strain rates of the bed decrease during periods of high water pressure and surface speed high water pressures appear to be accompanied by a reduction in the coupling of ice with the bed that is sufficient to reduce or eliminate shearing the instability of large ice masses may result from similar decoupling rather than from pervasive bed deformation as has been commonly thought

strain and competence contrast estimation from fold shape a new method to estimate strain and competence contrast from natural fold shapes is developed and verified by analogue and numerical experiments strain is estimated relative to the nucleation amplitude an which is the fold amplitude when the amplification velocities caused by kinematic layer thickening and dynamic folding are identical an is defined as the initial amplitude corresponding to zero strain because folding at amplitudes smaller than an is dominantly by kinematic layer thickening for amplitudes larger than an estimates of strain and competence contrast are contoured in thickness to wavelength h l and amplitude to wavelength a l space these quantities can be measured for any observed fold shape contour maps are constructed using existing linear theories of folding a new nonlinear theory of folding and numerical simulations all for single layer folding the method represents a significant improvement to the arc length method the strain estimation method is applied to folds in viscous newtonian power law non newtonian and viscoelastic layers also strain partitioning in fold trains is investigated strain partitioning refers to the difference in strain accommodated by individual folds in the fold train and by the whole fold train fold trains within layers exhibiting viscous and viscoelastic rheology show different characteristic strain partitioning patterns strain partitioning patterns of natural fold trains can be used to assess the rheological behaviour during fold initiation d 2001 elsevier science b v all rights reserved