relationship between non cylindrical fold geometry and the shear direction in monoclinic and triclinic shear zones we investigate the relationship between non cylindrical fold geometry and the shear direction of the hosting high strain zone by numerical modeling and show that apical axes of non cylindrical folds may develop into directions highly oblique to the shear direction if the zone has a pure shear component the common practice of using well developed sheath folds as indicators for the shear direction is not reliable and the use of immature non cylindrical or sheath folds appears more reliable hinge lines of mature sheath folds approach parallelism with the fabric attractor to which all material lines rotate which can have variable angles with respect to the shear direction in thinning zones the fabric attractor is the direction of the maximum principal strain rate of the pure shear component and is parallel to the shear zone boundary in thickening zones it lies somewhere in the quadrant between the direction of the maximum principal strain rate of the pure shear component perpendicular to the shear zone boundary and the simple shear direction and is generally oblique to the shear zone boundary the exact location depends on the flow geometry of the shear zone 2007 elsevier ltd all rights reserved

structural reactivation in plate tectonics controlled by olivine crystal anisotropy structures formed during ancient tectonic events are commonly reactivated during subsequent tectonism numerical models point to mechanical anisotropy arising from the inherited orientation of crystals of the mineral olivine in the lithospheric mantle as the cause of this behaviour

an evaluation of criteria to deduce the sense of movement in sheared rocks some of the most useful criteria for the deduction of the sense of shear are summarized for use in areas where unequivocal field evidence is lacking apparently conflicting evidence from rotated pressure shadow regions around porphyroclasts and porphyroblasts is clarified the use of quartz crystallographic fabric asymmetry to deduce the shear sense in the bulk rock should be treated with caution and used only together with detailed microstructural observations

deformation in the lowermost mantle from polycrystal plasticity to seismic anisotropy in the deep earth deformation occurs at many scales large scale convection produces subduction of slabs and upwelling of plumes in the mantle at the high temperature high pressure conditions strain is accommodated through crystal plasticity either by diffusion or the movement of dislocations slip causes crystal rotations and thus produces a characteristic pattern of crystal preferred orientation and corresponding anisotropy of physical properties at the macroscopic scale in this study we use polycrystal plasticity with experimentally derived deformation mechanisms for perovskite post perovskite and magnesiowuestite to predict texture development along streamlines in a 2d geodynamic convection model of the lowermost mantle strong preferred orientation develops during subduction and upwelling while during spreading along the core mantle boundary the orientation pattern is relatively stable from preferred crystal orientation and single crystal elastic properties bulk elastic properties can be calculated and compared with seismic observations post perovskite with predominant 001 slip and magnesiowuestite with 110 and 111 slip produce anisotropy patterns which are consistent with observed anisotropy i e fast s waves polarized parallel to the core mantle boundary and anti correlation between p and s wave anisotropies in contrast perovskite with dominant 001 slip and two post perovskite models with dominant slip on 010 and 100 produce anisotropy patterns which are inconsistent with seismic observations

the gem lake shear zone cretaceous dextral transpression in the northern ritter range pendant eastern sierra nevada california the gem lake shear zone is a northwest striking steeply dipping dextral transpressional shear zone that provides the first direct evidence for dextral deformation in wall rock pendants in the central part of the sierra nevada batholith the gem lake shear zone is a minimum of 30 km in length and extends at least from the north end of the northern ritter range pendant to the southeast edge of the ritter range pendant the amount of displacement on the zone is uncertain but matching fault slivers of pennsylvanian marble in the northern ritter range pendant to similar exposures north of the mount morrison pendant suggests a minimum dextral offset of 20 km the gem lake shear zone was active in early late cretaceous time from before 91 ma the age of the syntectonic granodiorite of kuna crest to at least 80 ma 40ar 39ar age of syndeformational mica from the shear zone in the ritter range pendant deformation in the gem lake shear zone is characterized by combined dextral simple shear and subvertical stretching which are variably partitioned in anastomosing high strain zones in the shear zone at gem lake predominantly dextral deformation is indicated by porphyroclast asymmetries s c fabric and asymmetric crenulations a component of subvertical stretching is indicated by a moderately to steeply plunging stretching lineation in a segment of the shear zone at kuna crest a strongly developed stretching lineation indicates predominantly subvertical stretching with a lesser component of dextral strike slip the gem lake shear zone is considered to be part of a proposed regional system of shear zones in the eastern sierra nevada the sierra crest shear zone system this dextral transpressional system was active prior to and synchronous with intrusion of the late cretaceous sierra nevada batholiths deformation ceased shortly after pluton emplacement the sierra crest shear zone system includes possibly related shear zones as far north as saddlebag lake pendant and at least as far south as oak creek pendant and the owens valley indicating a possible strike length greater than 150 km

flow variation in layered rocks subjected to bulk flow of various kinematic vorticities theory and geological implications abstract flow variation is studied analytically in rocks with layers of varied competence and varied orientation with respect to constant bulk flow fields of given kinematic vorticity 0 w k 1 the results explicitly demonstrate that flow varies significantly from layer to layer and with time in any individual layer even though the bulk flow is constant any flow regime can occur and the instantaneous stretching axes isa spin all the time reverse sense of non coaxiality can occur in the same layer at different times and in different layers at the same time this study further reveals the significance of heterogeneity and non steadiness in natural flows the assumption of a time independent flow history for natural deformation is highly unrealistic the spinning of the instantaneous stretching axes isa and the variation of flow regimes have bearings on the progressive development of fabrics and structures such as folded boudins refolded folds in shear zones and double rotation of porphyroclasts that are often interpreted as being due to multi deformational events

modelling the bulk viscosity of two phase mixtures in terms of clast shape abstract the rheological behaviour of many rock types will depend on how mixtures of different minerals and rock clasts behave together this paper develops two dimensional modelling of the bulk viscosity of two phase viscous mixtures with different shape fabrics in pure shearing based on self consistent mechanics and behaviour of inclusion matrix systems an equation is presented for the bulk viscosity in terms of the phase viscosity contrast phase fractions and clast shape results are given for idealised two dimensional mixtures of circles squares or ellipses with a variety of phase viscosity contrasts in pure shearing parallel perpendicular to the shape fabric the normalised bulk viscosities of all these mixtures fall between the theoretical upper and lower viscous bounds given by homogeneous strain rate and homogeneous stress respectively but nearer to the upper bound with increasing shape fabric mixtures with a particular geometry are shown to have a constant relative horizontal distance between these two bounds as proposed by p d bons using graphs for the normalised bulk viscosities of mixtures with variably elliptical aligned shape fabrics the results for fabrics orthogonal to pure shearing can be extrapolated to a diagonal fabrics in pure shearing and b orthogonal or diagonal fabrics in simple shearing these reveal the bulk viscous anisotropy of mixtures with shape fabric in two dimensions it is speculated that during a progressive finite deformation two phase mixtures might undergo changes in bulk viscosity over time with steady stiffening during pure shear and perhaps cyclic stiffening and softening during simple shear the two dimensional models provide an approximation to the three dimensional properties of mixtures with shape fabrics with potential applications to rocks including conglomerates

reading history of folding from porphyroblasts abstract the observation that inclusion trails in porphyroblasts commonly exhibit a more or less constant orientation over a large area even though the enclosing rocks have been folded has been considered puzzling by geologists and has generated considerable debate an analysis of vorticity during multilayer folding in response to layer parallel shortening shows that the observation is in fact theoretically expected folding of multilayers in response to layer parallel shortening bulk folding can be considered kinematically as a time variable combination of flexural flow and pure shear components the rotation of a spherical porphyroblast during folding is related to the vorticity history in the vicinity of the porphyroblast by a set of differential equations for likely folding histories in nature the solutions to these equations are in agreement with naturally observed patterns therefore it is unnecessary to invoke other mechanisms such as assuming porphyroblasts to be in islands irrotational with respect to the fold axial plane more importantly the theory allows constraints to be placed from current data sets of porphyroblast inclusion trail geometry on the history of folding and the competence properties of rocks at the time of folding

deformation path partitioning within a transpressive shear zone marble cove newfoundland detailed study of the structures in marble cove newfoundland indicates that they formed during a single transpressional event during which deformation was partitioned between dominantly strike slip and dominantly dip slip domains marble cove exhibits steeply dipping foliations steeply to shallowly plunging stretching lineations greenschist facies mineral assemblages and abundant quartz veins within the broad domain where stretching lineations plunge steeply sense of shear indicators and asymmetry of quartz c axis distributions in mylonitized quartz veins indicate dominantly reverse motion with a component of dextral shear adjacent greenschists exhibit orthorhombic symmetry and apparently accommodated pure shear the abrupt transition to a narrow high strain domain of shallowly plunging stretching lineations is accommodated by a rheologically distinct serpentinite body shear bands in this domain indicate dextral strike slip movement with a reverse component smaller conjugate shear bands are evident in thin section indicating a component of pure shear sense of shear indicators and asymmetry of c axis distributions in mylonitized quartz veins also record dextral strike slip and reverse shear with a component of pure shear crenulations and asymmetric folds in foliation overprint all other fabrics in marble cove and record a final phase of reverse shear with a dextral component with partitioning of this kind structures recording strike slip movement may be limited in areal extent and therefore less likely to be exposed than structures recording dip slip motion such partitioning within transpressional shear zones may therefore impede recognition of strike parallel motions within orogenic belts

flow perturbations a tool to study and characterize heterogeneous deformation the classification of the myriad of small scale structures that are used in tectonic analysis is presently based on their geometry which makes it difficult to discover transitions and groups amongst them an alternative would be to classify structures according to the flow type by which they form but this is difficult although most structures form by heterogeneous flow modelling studies are often focussed on bulk homogeneous flow since the mathematical treatment of heterogeneous flow is cumbersome also heterogeneous deformation patterns seem to occur in as many types as there are small scale structures this paper introduces the use of the geometry of flow perturbations to improve our understanding of heterogeneous flow and to allow classification of structures based on kinematics a flow perturbation is the deviation of a heterogeneous flow pattern from the background homogeneous flow perturbation patterns can be visualised as open or closed loops of vectors which occur in pairs rows or groups of four they usually cross cut rheological interfaces and can be subdivided into those that cross interfaces twice or four times most geological structures belong to the first group while initiating buckle folds belong to the second group q 2005 elsevier ltd all rights reserved

vorticity determination distribution partitioning and the heterogeneity and non steadiness of natural deformations abstract an investigation on vorticity in general heterogeneous and non steady flows is presented the bulk vorticity of a flow is solely determined by the imposed boundary conditions and it exerts no constraints on local flow the distribution of bulk vorticity in different rheological domains and the partitioning of the distributed vorticity into shear induced vorticity and spin are both time dependent this indicates that heterogeneous flows are inevitably non steady in a quantitative example it is demonstrated that even though the imposed boundary movement is a constant simple shear local flow can be non steady spinning and non coaxial super simple shear flow with internal kinematic vorticity number greater than i occurs but the finite strain does not necessarily pulsate the geological implications of this investigation are discussed the significance of heterogeneity and non steadiness in natural deformations are emphasized it is concluded that vorticity distribution and partitioning is the link between different scale structures the internal kinematic vorticity number is not a criterion of finite strain oscillation

flow and finite deformation of surface elements in three dimensional homogeneous progressive deformations rocks are heterogeneous materials deformation structures and fabrics in the ductile lithosphere can result from the history of the three dimensional flow field or the progressive deformation of some rheologically distinct elements embedded in the 3d flow field or a combination of both the flow and progressive deformation of a rheologically distinct element is generally non steady even if the hosting 3d flow field is steady vorticity decomposition is the key to following the progressive history of the deformation of specific elements a general theoretical background to the problem is presented flow and progressive deformation of surface and layer like elements in 3d homogeneous flows are investigated specifically analytical procedures to calculate the sectional vorticity number and the sectional dilatancy number on a general section in a 3d flow field are introduced the theoretical analysis is applied to various examples of sectional flow embedded in different types of 3d homogeneous and steady flow fields implications of this investigation for kinematic analysis of natural rock deformation are discussed all types of material line histories are expected in sectional flows of layer like elements shortened boudins can be formed in a single progressive deformation in sequences of rocks with a well developed transposition foliation common in large scale high strain zones each layer unit may have undergone a unique deformation history during its rotation to the final shear zone boundary parallel orientation in kinematic analysis of such areas it is important to ascribe the correct kinematic significance to structural associations and fabrics

stretching lineations in transpressional shear zones an example from the sierra nevada batholith california abstract ductile shear zones and associated stretching lineations are generally considered to be the result of two dimensional simple shear deformations with stretching lineations interpreted to rotate into parallelism with the direction of tectonic transport with increasing deformation however stretching lineations perpendicular to the inferred tectonic transport direction are displayed by some shear zones field studies in the sierra nevada batholith have revealed a single shear zone the rosy finch gem lake shear zone that contains both steeply plunging stretching lineations in older metamorphosed sedimentary and granitic rocks and shallowly plunging stretching lineations in syntectonic granitoids dextral sense of shear indicators are found in all these units and deformation occurred simultaneously along the length of the shear zone theoretical strain modeling indicates that stretching lineations can be either horizontal or vertical within transpressional shear zones to investigate the kinematics of three dimensional deformation we examine the role of stretching lineations which form as a result of finite strain including the possibility of partitioning a component of the strike slip movement onto shear bands comparing the field data with the strain modeling we interpret the along strike variation in lineation behavior within the rosy finch gem lake shear zone to be a result of the differences in finite strain recorded by different units the older units showing steeply plunging lineation have recorded more finite strain across a narrower shear zone than the syntectonic granites which record shallowly plunging lineations we conclude that the orientation of the lineation within transpressional shear zones does not necessarily correlate with the transport direction but may reflect along strike variations in finite strain and or strain partitioning

characteristics and dynamic origin of the large scale jiaoluotage ductile compressional zone in the eastern tianshan mountains china abstract the jiaoluotage ductile compressional zone jdcz in the eastern tianshan mountains china developed in volcanic and sedimentary rocks that were deposited in a carboniferous back arc basin situated between the jungar plate and middle tianshan terrane the ductile compressional zone 500 km long and 20 50 km wide consists of a number of east trending vertical foliation zones that display an augen geometry in plan view and a fan like geometry in transverse profiles ductile compressional deformation has produced pervasive foliation radial stretching lineations contemporaneous folds and various macroscopic to microscopic symmetric structures within the jdcz rotations of most clasts and porphyroclasts are bidirectional the preferred orientation patterns of the optical axes of calcite and quartz display axial or orthorhombic symmetry three kinds of strain patterns have been determined in the jdcz apparent flattening plane strain and apparent constriction the overall strain character of the jdcz is cream cake style the volcanic and sedimentary rocks within the jdcz were metamorphosed into greenschist facies with temperature of 400 600 c and pressure of 300 400 mpa development of the jdcz is interpreted as due to n s coaxial compression caused by the collision between the tarim plate and the middle tianshan arc jiaoluotage basin jungar plate system during the permian between 270 and 290 ma

trophodynamic studies on the condor seamount azores portugal north atlantic abstract compared to the surrounding ocean waters seamounts are commonly considered habitats where biological productivity is higher and consumers proliferate despite their high productivity studies of seamount trophic webs are still scarce and fragmentary and little is known about the connections between the different compartments what are the trophic interactions of seamount fauna how do the pelagic and benthic environment couple in order to answer these questions stable isotopes 15n and 13c were measured in the organisms collected during the course of numerous campaigns at the condor seamount in the north atlantic the condor seamount food chain is composed of five trophic levels mesopelagic organisms are the link between the epipelagic environment and the benthic and benthopelagic organisms bridging the gap between primary consumers and the 4th and 5th trophic chain levels our results demonstrate through stable isotope analysis the important role of mesopelagic organisms in the transfer of energy within the seamount food web as modeling theoretical studies have previously suggested

using along strike variation in strain and kinematics to define the movement direction of curved transpressional shear zones an example from northwestern superior province manitoba a review of current understanding of structures in shear zones reveals that correlating the orientation of stretching lineations with movement direction once a common practice based on the simple shear model is not generally applicable to transpressional zones it is difficult to determine the movement direction of a transpressional zone based on internal structures we show that the movement direction can be better defined by considering the variation in strain geometry and kinematics of differently oriented and kinematically related shear zones or different segments of a curved shear zone application of this method to a shear zone in the northwestern superior province of manitoba shows that the movement direction there is approximately north south in contrast to a commonly held view for similarly oriented shear zones in the superior province that the movement direction is approximately east west

the motion of deformable ellipsoids in power law viscous materials formulation and numerical implementation of a micromechanical approach applicable to flow partitioning and heterogeneous deformation in earth s lithosphere abstract earth s lithosphere is heterogeneous in rheology on a wide range of observation scales when subjected to a tectonic deformation the incurred flow field can vary significantly from one rheologically distinct element to another and the flow field in an individual element is generally different from the bulk averaged flow field kinematic and mechanical models for high strain zones provide the relations between prescribed tectonic boundary conditions and the resulting bulk flow field they do not determine how structures and fabrics observed on local and small scales form to bridge the scale gap between the bulk flow field and minor structures eshelby s formalism extended for general power law viscous materials is shown to be a powerful means this paper first gives a complete presentation of eshelby s formalism from the classic elastic inclusion problem to newtonian viscous materials and to the most general case of a power law viscous inhomogeneity embedded in a general power law viscous medium the formulation is then implemented numerically the implications and potential applications of the approach are discussed it is concluded that the general eshelby formalism together with the self consistent method is a powerful and physically sound means to tackle large plastic deformation of earth s lithosphere

deformation path in high strain zones with reference to slip partitioning in transpressional plate boundary regions abstract the current status of the kinematics and strain geometry of high strain zone studies is briefly summarized a general high strain zone has a triclinic deformation path and monoclinic shear zones are special end member cases fabrics observed in natural shear zones and theoretical considerations based on continuum mechanics are compatible with this conclusion non steady deformation paths remain difficult to deal with and may ultimately rely on a realistic mechanical treatment of high strain zones which may be possible when our knowledge of the mechanical behavior of rocks under natural deformation conditions is improved an examination of the phenomenon of slip partitioning in transpressional plate boundary regions shows that the bulk deformation path in the forearc area trench parallel high strain zone is generally triclinic the alpine fault in the south island of new zealand provides an example of a currently active triclinic shear zone the southern knee lake shear zone of manitoba canada provides an archean example of a triclinic shear zone

kinematics of rock flow and the interpretation of geological structures with particular reference to shear zones abstract current interpretations of structures are generally based on homogeneous and steady deformation models despite the fact that both the heterogeneity of rocks materially rheologically and geometrically and the time dependence of imposed geological conditions give rise to significant heterogeneous and non steady flow in concert with field observations we emphasize that the expectation of heterogeneity and non steadiness is the key to understanding natural deformation and that in order to carry out successful structural analysis and tectonic interpretation it is necessary to recognize the first order distinction between imposed boundary conditions typically used to define the tectonic regime e g transcurrent transpression and the response recorded by rocks within the zone structures and fabrics using s c fabric as an example it is demonstrated how flow with a non zero spinning component resulting from the rheological contrasts and or geologically realistic time dependent boundary displacement can drastically change the ideal geometric and kinematic relations between the fabric and the host zone in agreement with both theoretical analysis and field observation it is shown that natural flow regimes range from pure shear to pure rotation including super simple shear in consideration of the heterogeneity and non steadiness of natural deformation kinematic analysis is justifiable only within a homogeneous domain and steady period flow kinematics and mechanisms are interrelated in that firstly mechanisms provide internal constraints on kinematics ensuring that only certain flows are possible and secondly flow kinematics will favour development of certain mechanisms

sustainable transpression an examination of strain and kinematics in deforming zones with migrating boundaries most orogenic belts owe their development to oblique convergence and commonly have many orogen parallel transpressional high strain zones to constrain the tectonic history of orogenic belts by structural and fabric analysis of rocks it is desirable to understand quantitatively the relationship between the boundary conditions and the resulting strain distribution and kinematics in these zones most current models for transpression assume homogeneous deformation confined by boundaries that are fixed to material planes this creates a strain compatibility problem at the margins of the active deforming zone and also requires that the strain rate normal to the zone boundaries increase to implausibly high values soon after the onset of oblique convergence transpressional motion the latter contradicts with the observation that transpressional motion can be sustained throughout an orogeny the assumption that zone boundaries are fixed to material planes is unrealistic the outstanding problems of current transpressional models are resolved in this paper by allowing the zone boundaries to migrate through the rock material the consequence of zone boundary migration for the strain field and kinematics within a transpressional high strain zone is investigated mathematically the implications of the modeling for fabric interpretation are discussed the modeling makes general predictions consistent with observed planar and linear fabric patterns in natural transpressional high strain zones it predicts that foliations in transpressional high strain zones are subparallel to the zone boundaries regardless of variation in the imposed boundary conditions lineations cluster along the great circle girdle subparallel to the average foliation the spread of the lineations may vary from point maxima to complete girdles

when do dragfolds not develop into sheath folds in shear zones abstract using a unified model for high strain zones rotation paths of material lines in different flow types are investigated and presented as stereographic projections a material fabric element such as a mineral lineation or a fold axis can be plotted on such stereograms and the rotation path revealed using this method we examine the rotation of folds and the development of sheath folds in general three dimensional zonal deformation we show that the evolution of dragfold geometry in a high strain zone depends on the flow type and the initial perturbation of the fold axis in simple shear zones and thickening zones monoclinic or triclinic dragfolds will evolve into sheath folds in monoclinic thinning zones with biaxially stretching boundaries if the shear direction is parallel to the maximum stretching direction of the boundary sheath folds will develop if the shear direction is parallel to the minimum stretching direction of the boundary dragfolds become more cylindrical as deformation advances in thinning zones with boundaries equally stretched in all directions the likelihood of sheath fold development depends on the ratio of the shear strain rate to the thinning rate in triclinic thinning zones fold evolution depends on the details of the flow and the value of initial fold axis perturbation

post glacial sea levels on the western canadian continental shelf evidence for rapid change extensive subaerial exposure and early human habitation grounded piedmont type glaciers inundated and isostatically loaded the deep troughs which indent the western canadian continental shelf as far west as the shelf edge glaciers do not appear to have covered the offshore banks east of the queen charlotte islands haida gwaii ice retreated from the shelf at approximately 13 500 14c yr b p rapid emergence of the crust followed the ice retreat and resulted in a relative fall of sea level at 10 400 14c yr b p relative sea level on the continental shelf was more than 100 m below that of today and large areas of the queen charlotte basin were subaerially exposed eustatic sea level rise coupled with subsidence of a glacioisostatic forebulge allowed sea levels to rise very rapidly and reach the present shoreline on the queen charlotte islands haida gwaii by about 9100 14c yr b p dated shoreline deposits shells submerged wood remnants and barnacles on stone tools at elevations between 110 m and 14 m suggest a sea level rise of 6 3 cm per year between 12 200 and 11 000 calender years our reconstructions of the paleogeography and paleoenvironments suggest a hospitable environment for human habitation existed in areas that are now submerged stone tools excavated from intertidal deposits support this interpretation significant local variations in the depth of synchronous shorelines are described and attributed to localized differences in isostatic load the documented rates of crustal adjustment are much greater than those used in conventional geophysical forebulge models regional high resolution seismic reflection data 3400 line km shows little evidence for post glacial faulting and suggest that most crustal adjustments appear to have been isostatically rather than tectonically driven subaerial exposure and subsequent sea level transgression were the dominant post glacial processes that determined the morphology texture and paleoenvironment of the western canadian continental shelf

viscoplastic self consistent and equilibrium based modeling of olivine lattice preferred orientations implications for the upper mantle seismic anisotropy anisotropy of upper mantle physical properties results from lattice preferred orientation lpo of upper mantle minerals in particular olivine we use an anisotropic viscoplastic self consistent vpsc and an equilibrium based model to simulate the development of olivine lpo and hence of seismic anisotropy during deformation comparison of model predictions with olivine lpo of naturally and experimentally deformed peridotites shows that the best fit is obtained for vpsc models with relaxed strain compatibility slight differences between modeled and measured lpo may be ascribed to activation of dynamic recrystallization during experimental and natural deformation in simple shear for instance experimental results suggest that dynamic re crystallization results in further reorientation of the lpo leading to parallelism between the main 010 100 slip system and the macroscopic shear thus modeled simple shear lpos are slightly misoriented relative to lpos measured in natural and experimentally sheared peridotites this misorientation is higher for equilibrium based models yet seismic properties calculated using lpo simulated using either anisotropic vpsc or equilibrium based models are similar to those of naturally deformed peridotites errors in the prediction of the polarization direction of the fast s wave and of the fast propagation direction for p waves are usually 15 moreover overestimation of lpo intensities in equilibrium based and vpsc simulations at high strains does not affect seismic anisotropy estimates because these latter are weakly dependent on the lpo intensity once a distinct lpo pattern has been developed thus both methods yield good predictions of development of upper mantle seismic anisotropy in response to plastic flow two notes of caution have nevertheless to be observed in using these results 1 the dilution effect of other upper mantle mineral phases in particular enstatite has to be taken into account in quantitative predictions of upper mantle seismic anisotropy and 2 lpo patterns from a few naturally deformed peridotites cannot be reproduced in simulations these abnormal lpos represent a small percent of the measured natural lpos but the present sampling may not be representative of their abundance in the earth s upper mantle

strain compatibility and shear zones is there a problem in analyzing deformation in rocks it is important to ensure that the solutions obtained satisfy strain compatibility this creates a challenge to understanding patterns of strain associated with shear zones in which measured strain may appear incompatible with the strain in the shear zone walls flattening strains are common in natural shear zones with locally straight and parallel boundaries to satisfy compatibility conditions such strains require volume loss across the shear zone or deviations from plane strain with or without discontinuities between the shear zone and the wall rock in the case of shear zones for which there is no evidence of volume loss or discontinuities along the shear zone walls problems of strain compatibility may be resolved if individual shear zones are linked together in an appropriate fashion shear zones commonly occur in anastomosing arrays and simple configurations of such arrays and the strains associated with them are examined it is shown that local transpression with strain compatibility can be accounted for in this way quite complex local strain patterns can develop in simple arrays

the deformation matrix for simultaneous simple shearing pure shearing and volume change and its application to transpression transtension tectonics simultaneous simple shearing and pure shearing with or without additional volume change can be combined into a single upper triangular deformation matrix the off diagonal term is named the effective shear strain and is a simple function of the pure shearing and simple shearing components a three dimensional deformation matrix for the simultaneous combination of coaxial deformation with or without additional volume change and up to three simple shearing systems with mutually orthogonal shear planes is also presented by using this matrix one can easily extract the various properties of incremental as well as finite strain and the progressive as well as finite rotation of passive markers during deformation the case of transpression transtension is revised using the unified deformation matrix the orientation of the major axis of the strain ellipsoid 1 is always horizontal if the deformation is transtensional switches from horizontal to vertical during transpressional wrenching 1 wk 0 81 for constant vorticity deformations and is always vertical for highly transpressional deformations wk 0 81 for transpression material lines initially rotate towards the horizontal shearing direction but generally turn to rotate towards the vertical axis after a certain strain for transtension all material lines rotate towards a direction in the horizontal plane which is oblique to the shearing direction

the partitioning of deformation in flowing rock masses abstract most geological structures owe their development to heterogeneous and or non steady flow flow partitioning refers to the division of the instantaneous velocity field into components related to translation strain and rotation flow partitioning during the development of a geological structure usually changes with time and different histories of flow are involved at different points in the developing structure heterogeneity leads to the development of flow domains with different characteristics notably the degree of non coaxiality of deformation and different partitionings of the rotational component of flow into shear induced vorticity and spin during non steady flow there is often continual repartitioning of vorticity between the spin and shear induced components spin is an important aspect of flow leading to the development of structure this paper discusses the partitioning of deformation in a flowing rock mass coaxial flow tends to occur in isotropic materials in regions near weakly constrained boundaries non coaxial flow is favoured by suitably oriented material anisotropy and or the presence of well defined boundary constraints involving parallel relative displacements a developing anisotropy e g a crystallographic fabric in a shear zone can induce a change from coaxial to non coaxial flow other effects are related to the scale of approximation for example bulk shear induced vorticity can be locally converted to spin flow in the crust and mantle of the earth produces geological structures on all scales and involves many different types of rheological response the factors that affect flow partitioning e g spin versus non coaxial deformation are therefore of interest

strain and kinematic analysis in general shear zones we present a unifying theory for the development and distribution of strain markers and kinematic indicators in zones of general shear and thus provide a framework in which data previously considered contradictory may be understood rigid and deformable porphyroclast systems including and complex grains are potential indicators of both strain and flow the shapes and distribution of such porphyroclast systems may be used to distinguish among different tectonic regimes general shear is divided into two fields sub simple shear in which the rotational component of the strain is less than that for simple shear and super simple shear in which the rotational component is greater than for simple shear sub simple shear may involve narrowing or broadening of shear zones super simple shear regimes are possible in local regions such as the vicinities of deformable porphyroclasts but must be enclosed by regimes of sub simple shear the polar mohr constructions for finite deformation and flow are useful to analyze general shear in theory the hyperbolic net is employed for practical plotting of real data and derivation of the kinematic vorticity number wn this number represents the relative contributions of pure and simple shear in steady flow in nature deformation is thought to build up and decay by processes that may invalidate the assumption of constant flow regime we therefore introduce the concept of accelerating deformation and analyze the implications of non steady flow for the shearing histories of deformed objects

analysis of deformation paths in shear zones the geometry of ductile shear zones can be used to solve problems of regional tectonics if the deformation path of material in the zones is sufficiently understood flow in many shear zones may have deviated from simple shear and consequently data on the final deformation state such as finite strain and volume change are insufficient for reconstruction of the deformation path even if flow parameters were constant during progressive deformation additional information on the flow vorticity number is also needed and can be obtained from fabric elements such as sets of folded boudinaged veins rotated porphyroblasts and blocked rigid objects mohr circle constructions are presented as a tool to calculate deformation parameters from fabric data to represent the deformation path graphically and to reconstruct flow parameters from the shape of this path if the vorticity number or the volume change rate changed during progressive deformation the deformation path can be partly reconstructed using sets of fabric elements which register mean and final values of these parameters

high strain zones a unified model abstract where a shear zone is bounded by undeformed wall rocks and there is no volume change the deformation path within the zone on the bulk scale approximates a simple shear where the zone boundaries are stretched and the shear direction between the two boundaries is parallel to one of the principal stretching directions of the boundaries the deformation path within the zone is not a simple shear but still has monoclinic symmetry both simple shear and general monoclinic deformation paths should be regarded as special cases in nature because generally not only are the zone boundaries stretched but also the shear is oblique to the principal stretching directions of the boundaries in this general case the deformation path is triclinic we establish a model which includes this general case also taking into consideration volume change five independent parameters are required to characterize the rate of deformation of the flow four are sufficient to characterize the flow kinematics the model is generally triclinic and orthorhombic and monoclinic deformations are subgroups by varying the values of the characterizing parameters the various types of high strain zones can be represented the kinematics of flow within such zones and the accumulated finite deformation geometry are investigated many field observations such as for example lineations in transcurrent shear zones that vary between vertical and horizontal cleavage transected folds and the absence of sheath folds in some shear zones where folds have been significantly rotated can sometimes be better interpreted in the context of our general model

a micromechanical approach for simulating multiscale fabrics in large scale high strain zones theory and application 1 deformation fabrics in earth s crust and mantle are commonly used to constrain the tectonic history deformation mechanisms and rheological properties of the lithosphere their formation involves heterogeneous and multiscale deformation processes that current single scale models cannot capture here we present a micromechanics based multiorder power law approach mopla for the simulation of multiscale fabrics in crustal scale high strain zones we consider the progressive deformation in a crustal high strain zone on three different scales on the macroscopic scale representing the average assemblage of rock units at a point we regard the rock mass as a continuum made of many first order elements the progressive deformation of first order elements in the macroscopic flow field simulates tectonic transposition on the scale of an individual first order element we regard it as an eshelby inhomogeneity embedded in a poly element continuum we apply eshelby s inhomogeneity formalism for power law materials to relate the flow field inside a first order element to the macroscopic flow field on the scale pertinent to structures observed on the outcrop or smaller scale the partitioned flow fields inside individual first order elements are used to examine the fabric development we implement mopla in mathcad apply the approach to a natural example of the cascade lake shear zone and discuss the implications of multiscale deformation our model predicts lineation patterns observed in natural high strain zones that have remained unexplained by single scale models

a fundamental problem with the kinematic interpretation of geological structures abstract non steady flows are ubiquitous in nature not only do imposed boundary conditions vary with time and rock rheology change during the course of deformation but also deformation is generally heterogeneous and all of these conditions lead to non steady flow histories in modern kinematic analysis flow apophyses the instantaneous stretching axes and the vorticity vector collectively referred to as the eigen directions of deformation are used in place of bruno sander s kinematic axes for deformation with a steady flow history this practice is well justified and has led to great advances in structural geology but for non steady flow histories the geometrical relationships among eigen directions flow pattern vary with time this makes it inappropriate to correlate an association of structures and fabrics with certain time invariant flow patterns and hence raises the question how should we interpret geological structures and fabrics kinematically without the assumption of homogeneous and steady deformation we suggest that the answer lies primarily in forward modeling of deformation based on a knowledge of rock properties