the limitations of three dimensional kinematic vorticity analysis abstract the kinematic vorticity number wk can be calculated for three dimensional as well as two dimensional geologic deformations for steady state deformations wk can be correlated to and analyzed in terms of finite strains the analysis shows that assumptions commonly made for two dimensional deformations are not applicable to three dimensional deformations a single wk describes an infinite number of three dimensional deformations further even knowledge of flow apophyses orientation instantaneous stretching axes orientation and or wk are not sufficient to describe deformation three dimensional deformations also require knowledge of the deformation type or boundary conditions of deformation e g transpression hence in addition to being difficult to estimate the value of knowing wk for three dimensional deformations is greatly reduced compared with plane strain the most useful methods of determining wk from naturally deformed rocks are presented

progressive localization of deformation during exhumation of a major strike slip shear zone norumbega fault zone south central maine usa detailed structural studies along with 40ar 39ar thermochronology provide important constraints on the temporal spatial and structural evolution of a major orogen parallel strike slip shear zone the norumbega fault zone in maine detailed structural analysis in south central maine reveals two very different styles of dextral noncoaxial deformation a wide zone 25 km of heterogeneously distributed ductile shear structures and a relatively narrow zone 1 km of lower greenschist facies high strain mylonitization 40ar 39ar thermochronology indicates that these two zones of deformation developed during a prolonged period of regional exhumation following middle devonian amphibolite facies metamorphism the wide zone of dextral shear is interpreted to reflect a major episode of moderate temperature post amphibolite facies metamorphism but pre regional cooling below 320 c late devonian to early carboniferous transcurrent tectonism the narrow zone of dextral shear represents both a younger latest carboniferous and significantly cooler 320 c deformational event occurring at much higher structural levels a general model of increasingly narrow but more highly focused noncoaxial deformation during progressive regional exhumation is supported by the observations

three dimensional reference deformations and strain facies abstract in an attempt to categorize three dimensional deformations the concepts of kinematic axes three dimensional reference deformations and strain facies are utilized we have chosen 12 reference deformations each being an idealized end member of deformation involving a simultaneous combination of a three dimensional coaxial component constriction flattening or pure shear and an orthogonal simple shear component velocity and displacement fields infinitesimal deformation parameters and finite deformation parameters can be calculated for each reference deformation assuming steady state deformation there are three possibilities for the orientation of foliation and three possibilities for the orientation of lineation depending on the relative contributions of the coaxial and non coaxial components the six emerging combinations of foliation and lineation orientations each give rise to a characteristic strain facies each of the strain facies is correlated to the reference deformations and thus deformation parameters which caused its formation however since the coaxial deformation component accumulates more effectively than the non coaxial component a change from one strain facies to another i e a change in the orientation of lineation or foliation is possible during steady state deformation the strain facies emphasize the boundary conditions of deformation and together with the reference deformations provide a framework for three dimensional deformations

flow in natural shear zones the consequences of spinning flow regimes abstract the ancient flow regime in natural shear zones is often considered to have followed a deformation path comparable to that in theoretical shear zones i e progressive simple shear between rigid wall rocks with a persistent flow plane orientation parallel to the edges of the zone this is often based on the presence of monoclinic fabric elements in the zones which indicate a dominantly non coaxial flow regime though not necessarily persistent simple shear the deformation fabric of a shear zone from the pyrenees illustrates that even at a kinematic vorticity number of w 1 simple shear along the entire deformation path obliqueness of the flow planes with the edges of the zone is possible for some time if incremental stretching axes were rotating with respect to zone edges this implies that ductile deformation must have taken place in the wall rock of the zone such a flow regime may be difficult to recognize with the fabric criteria used at present but leads to an unusual kinematic significance of the shear zone involved in extreme cases the zone may have acted as a passive marker in a ductilely deforming medium it also means that not only w must be known to reconstruct the ancient flow regime in natural shear zones but at least also the time dependence of the orientation of the incremental stretching axes

simultaneous pure and simple shear the unifying deformation matrix abstract any simultaneous combination of finite simple shear and finite pure shear is a linear transformation which can be expressed as a single transformation matrix for two dimensions the matrix is upper triangular with an off diagonal term called the effective shear strain is a simple function of the pure and simple shear components for three dimensions a simultaneous combination of thrusting in the x direction thrusting in the y direction and a wrench in the x direction in addition to 3 orthogonal components of coaxial strain can also be represented by a 3 3 upper triangular matrix here three off diagonal terms xy x y and y z occur xy is a simple function of the horizontal coaxial strain values and thrusting in the x direction yz depends on the coaxial strain components in the y and z directions and the thrusting in the y direction while xz is related to all six strain components the matrix also allows for volume change either homogeneously or preferentially in a single direction a method of decomposing the deformation matrix into a series of incremental deformation matrices where each incremental deformation records the same kinematic vorticity number as the finite deformation is shown the orientation and magnitude of the finite strain ellipsoid ellipse is easily and accurately found at any increment during the deformation

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

the eigenvalues of steady flow in mohr space abstract the eigenvalues of the velocity gradients tensor and of the position gradients tensor describing instantaneous flow or incremental deformations are easily determined in mohr space as the points of intersection between a mohr circle and the horizontal mohr axis intersections occur only if the tensor has real eigenvalues eigenvectors associated with the eigenvalues are directions of no rotation a line of material particles under an eigenvector does not rotate during steady flow although the line is instantaneously stretching at a rate equal to its corresponding eigenvalue for non spinning steady sub simple shearing there will always be two eigenvectors the angle between the eigenvectors is dependent on the ratio of pure to simple shearing rates this angle decreases as the pure shearing component decreases relative to the simple shearing component superimposed increments of pure shear and simple shear produce an equivalent set of non rotated material lines but the deformation histories of these lines are rotational the influence of eigendirections on geological structures is constrained by the rheology of a rock during deformation in homogenous steady flow no influence may be obvious spatially periodic material softening along eigenvectors during bulk hardening may result in a complex fabric of intersecting shear zones the geometry of the fabric elements provides important information on the bulk deformation of the rock particularly on the bulk shear sense

progressive deformation in anisotropic rocks abstract field observations show that the majority of crustal rocks possess a penetrative foliation defined by either compositional layering preferred orientations of crystals or both ductile deformation involving planar anisotropy of viscosity can be characterized by an anisotropy factor q n r s the ratio of the bulk viscosities in pure and simple shear respectively this ratio of the normal and shear viscosities may be determined analytically if the anisotropy is resolvable in a multilayer sequence with individual laminae of isotropic viscosity in that case the resistance to normal compression will be largely controlled by the competent layers whereas the resistance to shear is controlled by the soft layers more specifically the viscosities of the individual laminae add up like resistances in series and in parallel in the expressions for the normal and shear viscosities respectively the reorientation of the bulk stress within an anisotropic multilayer is systematically investigated for a range of anisotropy factors the mode of progressive deformation is controlled only by the anisotropy factor and the orientation of the principal deviatoric stress the rate of deformation can be scaled if the bulk normal viscosity and the magnitude of the principal deviatoric stress are also known the results are illustrated in a series of nomograms showing the spectrum of strain and rotation histories possible in rock volumes deforming with planar anisotropy it appears that with increasing anisotropy factor the deformation spectrum will narrow on simple shear irrespective of the orientation of the background or bulk deviatoric stress axes plane strain and isochoric conditions are assumed throughout the analysis

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

strain partitioning in transpression zones abstract transprcssional strain acting upon structurally anisotropic rocks can be partitioned into separate deformational domains of pure shear and simple shear this contrasts with homogeneous transpression in which both the pure shear and the simple shear strain components are uniformly distributed across the zone of deformation structural weaknesses capable of partially or fully accommodating one component of deformation include lithological contacts rheological heterogeneities and faults or shear zones situated within the deformation zone or lying along its boundaries partitioning of transprcssional strain can occur when stress is applied oblique to pre existing structural weaknesses or can occur during later stages of progressive strain when the early deformation of isotropic rocks imparts sufficient anisotropy to allow subsequent strain to be partitioned partitioning of transpressional strain into domains lying parallel to the deformation zone boundaries can be distinguished from fault stepped transpression in which strain is partitioned along the length of a segmented fault zone mesofracture analysis of rocks affected by mid devonian deformation on both sides of the highland boundary fault zone hbfz in central scotland shows that strain was not homogeneous the mesofracture data suggest that regional north south compression orientated oblique to the pre existing ne sw trending hbfz was partitioned into separate deformational domains the hbfz accommodated most of the simple shear component whilst the rocks flanking the zone were deformed predominantly by pure shear a contemporary example is the san andreas fault in central california where analyses of neo tectonic stresses show that the direction of principal compression is perpendicular to the fault zone many examples of the partitioning of transpressional strain have also been recognised at destructive plate margins where the direction of plate motion is oblique to the edge of the over riding plate

estimation of viscosity contrast and finite strain from deformed elliptical inclusions a method of strain analysis is described which takes into account a possible competence difference between the strain markers and the rest of the rock using data consisting of the sectional shapes and orientations of groups of inclusions from conglomerate like rocks limits are placed on the possible effective viscosity contrast between the inclusions and the rock as a whole as well as on the bulk finite strain suffered by the rock these results are calculated using a computer program based on the theory for the deformation of elliptical cylinders the method can be considered an extension of the rf method but provides more information and involves less restrictive assumptions

flow variations in power law multilayers implications for competence contrasts in rocks abstract an idealized bilaminate multilayer of alternating competent and incompetent layers with different proportional thicknesses is used to model theoretically the manner in which flow in rocks may vary from layer to layer during deformation the layers are assumed to flow according to a power law with stress exponent n of 1 newtonian flow 3 or 5 which is in accordance with current experimental data for flow in rocks the theoretical analysis concentrates first on incompressible plane flow and is then extended to some forms of incompressible three dimensional flow strain rate variations from competent to incompetent layers are illustrated for two dimensional flows on rheology graphs of log stress vs log strain rate three types of bulk multilayer deformation are illustrated layer parallel pure shearing lpps layer parallel simple shearing lpss and layer oblique straining in different orientations the degree of flow partitioning varies with the bulk flow layer thicknesses and layer n values for all systems in plane two dimensional flow the greatest partitioning occurs for 45 bulk shortening lpss and is most extreme for high n values such that the strain rate is virtually zero in competent members however for three dimensional flows preliminary results suggest that the value of n may play a less significant role in flow partitioning particularly for bulk pure flattening or constrictional flows these theoretical flow variations provide some meaning to competent contrast in rocks and reveal possible links between relative competence and deformation history such flow variations in space and time may provide the driving mechanism for folding in ductile multilayered systems

palaeoenvironmental changes in the northwestern tethys during the late campanian radotruncana calcarata zone implications from stable isotopes and geochemistry abstract this paper investigates the palaeoceanographic setting and evolution of two biostratigraphically well constrained upper cretaceous sections in the eastern alps of austria the duration of the investigated time interval is confined by the total range zone of radotruncana calcarata which was a very short lived 806 000 yrs species as calibrated using orbital parameters this results in a precise time frame for paleoenvironmental interpretations within this interval stable isotope stratigraphy links both sections to published records the two studied sections are located at the passive northern margin of the european foreland and at the active southern margin of a northwestern tethys ocean branch respectively we use mineralogy clay mineralogy element geochemistry carbonate associated elements and element ratios sr isotope stratigraphy and stable c and o isotopes to characterize the profiles mn sr ratios as well as stable c and o isotopes indicate that the sediments are largely diagenetically unaltered both sections have a similar history concerning their sea level evolution i e a gradual third order regression with short fourth order transgressive intervals the inferred water temperature increases at both locations and the overall primary production and nutrient availability increased slightly with time predominately suboxic conditions are confined to the southern profile and were interrupted by oxic spells of 50 kyr duration and even shorter periods of increases in primary production we also found evidence of a strong aeolian influence on the cyclic deposition of marl limestone couplets in the southern profile the similar history at both geodynamic settings indicates that the southern block close to the subduction zone was relatively stable for the duration of r calcarata total range zone

role of nappe boundaries in subduction related regional deformation spatial variation of meso and microstructures in the seba eclogite unit the sambagawa belt sw japan abstract the seba eclogite unit of the sambagawa high p t metamorphic belt has a kilometre scale synformal structure and its base is the boundary between an overlying eclogite nappe and an underlying non eclogitic nappe the formation of the nappe boundary is related to a phase of strong penetrative ductile deformation d a spatial variations of meso and microstructures of schistose eclogite in the seba unit reveal that there is i a decreasing intensity of d a and ii a time dependent widening of the d a shear zone away from the nappe boundary these features indicate that the nappe boundary behaved as a core zone during the d a phase and furthermore that development of the regional deformation d a is strongly controlled by the presence of the nappe boundary a new model is proposed where each phase of regional deformation in subduction type metamorphic belts is related to ancient activity of a particular nappe boundary in this model a single phase of deformation may be related to exhumation in one nappe and subduction in an adjacent one

rotational quantities in homogeneous flow and the development of smallscale structure abstract a summary discussion is given of attempts to quantify the degree of non coaxiality of rock flow from observations of rock structure and of some principles governing the sensitivity of structure to non coaxiality this is preceded by an extended review of relevant terminology since some of the current confusion about rotational features in rocks stems from confusion about basic concepts and terminology from continuum mechanics the kinematic vorticity number has been estimated for naturally deformed rocks from three localities these yield vorticity numbers ranging from 0 35 to 0 9 corresponding to flows intermediate in character between pure and simple shearing

deformation of granitic rocks across the brittle ductile transition abstract a microstructural analysis has been carried out on mylonites and mylonitic gneisses of the eastern peninsular ranges mylonite zone which were formed over a range of metamorphic conditions from lower greenschist to amphibolite facies composite planar fabrics in the form of c and s planes are found at all metamorphic grades fractured feldspars kinked biotites and ductile deformation of quartz characterize the lower greenschist facies mylonites at mid upper greenschist grade orthoclase grains show dynamic recrystallization textures whereas plagioclase exhibits low temperature plasticity with only minor recovery biotite ribbons form by progressive rotation and coalescence of kink band segments to produce chevron fold patterns at epidote amphibolite grade and above recovery processes and annealing recrystallization predominate in all minerals residual orthoclase porphyroclasts show strain related myrmekite formation along those sides of the grains that face the instantaneous shortening direction myrmekite formation due to replacement reactions cannot explain this geometry it is proposed that the myrmekites formed due to a combination of exsolution replacement and strain enhanced diffusion

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

strain analysis in rocks with pretectonic fabrics abstract a major problem in strain analysis of ellipsoidal fabrics is how to separate the effects of initial preferred orientation of objects from the effects of strain new algebraic methods are presented here which apply to many of the situations previously analysed by graphical and iterative techniques the algebraic solutions are simple and highlight some assumptions implicit in previous methods and the relations between those methods it is shown that many final ellipsoidal fabrics cannot be produced from initial fabrics which were symmetric with respect to bedding and that a three dimensional analysis is preferable to analysis on two dimensional section planes

lateral extrusion in transpression zones the importance of boundary conditions the homogeneous transpression strain model formulated by sanderson and marchini journal of structural geology 6 449 458 1984 has proved to be a useful tool in the analysis of complex three dimensional deformation patterns however some of the boundary conditions introduced in the mathematical model may be unrealistic and unnecessarily restrictive in this paper a strain matrix for unconfined transpression and transtension is derived in which material is allowed to move not only vertically but also horizontally in and out of the deforming zone parallel to its length lateral extrusion three end member plane strain components are defined wrench simple shear pure shear in xy lateral stretch and pure shear in yz vertical stretch these biaxial strains can be viewed as the apices of a strain triangle for unconfined transpression or transtension the edges of the triangle correspond to triaxial pure shear non coaxial biaxial lateral extrusion and the triaxial confined transpressional or transtensional strain of sanderson and marchini during unconfined transpression the orientation and in particular the geometry k value of the finite strain ellipsoid depends upon not only the amount of shortening across the zone and the amount of strike slip parallel to the zone but also upon the ratio of vertical to lateral stretch this can present serious difficulties when attempting to use finite strains to infer the direction and magnitude of zone boundary displacements examples of transpression zones in which there is evidence of a component of lateral extrusion are described from sw cyprus and central scotland these examples illustrate that antithetic strike slip shearing is a kinematic requirement of laterally unconfined transpression implying that synchronous shear sense indicators may give opposite senses of movement in shear zones specific geometric and mechanical boundary conditions together with internal fault zone rheologies may favour the lateral extrusion of material kinematic partitioning can occur to form fault bounded domains in which end member biaxial and or non coaxial strains are developed analysis of such domains can give a clearer understanding of regional scale triaxial deformations these findings illustrate the importance of establishing displacement boundary conditions when qualitatively or quantitatively analysing crustal deformation zones

partitioning of non coaxiality in deforming layered rock masses abstract partitioning of non coaxiality and other flow parameters in deforming layered rock masses with nearly incompressible newtonian rheology is examined in two dimensions by the finite element method the results show that layers with viscosity contrast in suitable orientation deform by different and even by a reverse sense of non coaxiality this remarkable partitioning of non coaxiality is due to a large rotation rate of instantaneous stretching axes in a heterogeneous body as a result of geometry changing through deformation rather than through rotation of material lines

constraints on deformation path from finite strain gradients we present a methodology for analyzing finite strain gradients in high strain zones in order to place constraints on the zone s possible deformation path to accomplish this the high strain zone is divided into several sub zones within each of which finite strain is described by a single ellipsoid based on knowledge of the spatial and temporal evolution of deformation strain observed in less deformed sub zones is then mathematically removed from more deformed sub zones to calculate incremental finite strains the mean kinematic vorticity number of each of these increments must be constant if deformation was steady state we use the methodology to analyze two natural examples of high strain zones at different scales both natural examples have non steady state likely deformation paths which may be a common characteristic of high strain zones although results of the methodology are not unique identification of likely paths considerably narrows the range of possible deformation paths consequently useful kinematic information can be extracted from finite strain data even in instances where the detailed spatial and temporal evolution of a high strain zone cannot be determined conclusively

shear zones and rock history abstract shear zones that have widened with time can display margin to interior microstructural profiles unlike the real microstructural history of the interior rocks shear zones that have not widened with time can provide more reliable views of microstructural history and therefore of deformation processes even the latter zones can mislead however where there has been an annealing overprint during or following the shearing interval these sources of uncertainty need to be acknowledged more regularly and if possible eliminated by workers interpreting deformation processes from shear zone strain gradients

strain refraction in layered systems abstract strain refraction across competence contrasts is presented as a simple model consisting of two components a homogeneous strain and a heterogeneous simple shear for newtonian materials the ratio of the layer parallel simple shear component in adjacent layers is the inverse of their viscosity ratio strong changes in ellipsoid size shape and orientation are predicted across viscosity contrasts the geological implications of strain refraction theory are considered within the context of the cleavage strain debate the particular relationships of relative competence and strain revealed by the refraction model may contribute to the problem of why cleavages of different morphologies in rocks of different lithologies and kinematic histories should appear to be subparallel to the xy planes of measured strain ellipsoids competent rocks should develop dominantly layer orthogonal strain and incompetent layers shear dominated deformation a variety of structural features ranging from cleavage refraction changing lineation orientations folds transected by cleavage changes from coaxial to non coaxial deformation and ramp flat fault geometry may be the result of stress and strain refraction in rocks

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

a theory of finite strain variation through contrasting layers and its bearing on cleavage refraction abstract a theory of finite strain variation in contrasting viscous layers is presented the theory is applicable to layers which are oblique to two principal strains but parallel to the third and is not restricted to plane strain results may be obtained algebraically or by use of the mohr diagram for strain solutions are given for various examples of layering attitude and viscosity ratio measured with respect to a reference layer it is shown that the finite strain ellipsoid changes in shape and orientation across contrasting layers and in some cases the principal axes may be exchanged low strain is indicated in relatively more viscous layers and high strain with extension at a smaller angle to the layering in less viscous layers the latter may approximate simple shear parallel to layering if the strain is sufficiently high the geological implications of the theory are strong strain variations in layered rock sequences it is suggested that in general strain will be inhomogeneous from layer to layer both in orientation and amount the relationship of strain and cleavage are reviewed in the introduction to establish the validity of predicting cleavage patterns from strain data qualitative comparisons between the theoretical results of strain variation and natural cleavage refraction in layered rocks would appear to justify the assumption that cleavages of varied morphologies are sub parallel to the xy planes of strain with this assumption some three dimensional features of planar and linear fabric refraction in contrasting rocks are predicted

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

grain size evolution and the rheology of ductile shear zones from laboratory experiments to postseismic creep abstract geologic experimental and geodetic studies indicate that ductile shear zones do not deform in steady state we present a theoretical model for an elastically loaded ductile shear zone deforming by combined dislocation and diffusion creep in which grain size is allowed to evolve toward its equilibrium recrystallized value several grain size evolution laws are considered simulations of laboratory experiments show that grain size evolution can lead to changes in the dominant deformation mechanism that are accompanied by transient strain weakening or strain strengthening episodes reminiscent of laboratory observations ductile shear zones can also produce postseismic creep as observed in geodetic data following large earthquakes non steady state ductile creep is difficult to differentiate from frictional sliding with velocity strengthening friction hence ductile creep may play a role in the transition from velocity weakening to velocity strengthening friction with increasing temperature

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

controls on lineation development in low to medium grade shear zones a study from the cap de creus peninsula ne spain lineations composed of similarly oriented elongate mineral aggregates or grains are a common feature in deformed rocks but it is unclear which factors control the development of such lineations field observations and microstructural analysis of samples which were taken from discrete greenschist to lower amphibolite facies shear zones of the easternmost variscan pyrenees show that strain is only one of several factors that control the strength and type of a lineation dynamic recrystallization metamorphic reactions and rigid body rotation are also important controlling factors for the development of lineations the most important of these is dynamic recrystallization the way in which dynamic recrystallization influences lineation development is largely a function of the initial fabric in a specific rock type different lithologies with different initial fabrics produce distinctly different types and strengths of lineations even if deformed to the same finite strain in the same shear zone an initial fine grain size and a monomineralic composition of the parent rock type commonly hinder the development of lineations in contrast in initially coarse grained polymineralic rocks well developed lineations commonly develop therefore the ratio of initial to dynamically recrystallized grain size determines to a large extend the development of such lineations

composite magnetic fabrics and s c structure in granitic gneiss of cerro de los viejos la pampa province argentina the cerro los viejos gneiss in la pampa province argentina is a mylonitized granite which lies along the late paleozoic deformed boundary zone between the patagonia block and mainland gondwana to the north petrofabric and anisotropy of magnetic susceptibility ams analyses were compared for this body unexpectedly it was found that the kmin poles deviate from the poles of the main foliation s1 by about 25 similarly but not so noticeably the kmax poles trend ne sw with a near horizontal plunge whereas the principal lineation l1 plunges gently sw this unusual situation is attributed to the existence of superimposed fabrics arising from s c structures examination of oriented cores in a modified universal stage and of oriented thin sections revealed that the kmin poles are clearly associated with a younger but less obvious metamorphic c foliation s2 biotite and magnetite the main contributors to the ams response are distributed along both s1 and s2 the dominance of s2 in the ams anisotropy suggests that magnetite is preferentially distributed on s2