site effects investigation in the city of chlef formerly el asnam algeria using earthquake and ambient vibration data weak motion recordings of local earthquakes and ambient vibration data in the 0 2 15 hz frequency range were used to quantify site effects in downtown chlef city algeria nine short period stations were installed in the city a total of 15 local events with 3 1 m l 4 9 were selected three experimental techniques were applied standard spectral ratios receiver functions and horizontal to vertical spectral ratios using ambient vibrations hvsrn theoretical hvsrn curves were also calculated from suggested soil models for each site fundamental frequencies obtained from all techniques showed good agreement two groups of fundamental frequencies were distinguished in the city in the northern part of the study area the frequency peaks varied from 0 3 to 0 4 hz in the southern part they varied from 0 6 to 1 6 hz the amplification factors of these frequency peaks were 4 8 earthquake and ambient vibration data were able to identify fundamental frequency peaks successfully however the amplitudes of the peaks were slightly lower for ambient vibrations moreover the fundamental frequency peak progressively increased from northwest to southeast which is consistent with the direction of decreasing thickness of a miocene layer overlying the basement we infer as expected that the large impedance contrast between miocene deposits and mesozoic basement which can be interpreted as seismic bedrock is the cause of the fundamental frequency furthermore earthquake data were more appropriate for identifying peaks at frequencies higher than the fundamental one indeed a clear peak was observed at all northwestern sites in the 3 4 hz range with an amplification factor of 3 5 at the other sites particularly in the center of the city the peak was less evident

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

evidence for mechanically coupled lithosphere in central asia and resulting implications the recent dramatic increase in seismic anisotropy and surface global positioning system gps data for central asia permits a comprehensive examination of the mantle s role in mountain building a joint analysis of 178 shear wave splitting and 2000 gps observations using a new technique reveals that the crust and lithospheric mantle deform coherently arguing for crust mantle mechanical coupling during deformation the observed spatial variations in anisotropy refl ect the large scale pattern of lithospheric deformation as well as a change in deformational style from simple shear on the tibetan plateau transitioning to pure shear in surrounding regions

elastic wave velocities in sandstones with non load bearing clay the elastic moduli and acoustic velocities of shaley sandstones strongly depend on the amount of clay as well as on its position among sand grains in many cases clay may fill pores without noticeably affecting the stiffness of the rock such clays are non load bearing here the stiffness of the rock is determined primarily by the load bearing quartz frame we examine several data sets and show that in this case a simple unique relation exists between the acoustic velocity and the porosity of the load bearing frame of the rock this porosity can be calculated as the sum of the effective porosity total porosity minus microporosity inside clay and the volumetric fraction of clay in the rock also it is the sum of the total porosity and the volumetric fraction of solid clay particles in the rock

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

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

active deformation and shallow structure of the wagner consag and delfin basins northern gulf of california mexico oblique rifting began synchronously along the length of the gulf of california at 6 ma yet there is no evidence for the existence of oceanic crust or a spreading transform fault system in the northern gulf instead multichannel seismic data show a broad shallow depression 70 200 km marked by active distributed deformation and six 10 km wide segmented basins lacking well defined transform faults we present detailed images of faulting and magmatism based on the high resolution and quality of these data the northern gulf crust contains a dense up to 18 faults in 5 km complex network of mainly oblique normal faults with small offsets dips of 60 80 and strikes of n n30 e faults with seafloor offsets of tens of meters bound the lower and two upper delfin basins these subparallel basins developed along splays from a transtensional zone at the nw end of the ballenas transform fault twelve volcanic knolls were identified and are associated with the strands or horsetails from this zone a structural connection between the two upper delfin basins is evident in the switching of the center of extension along axis sonobuoy refraction data suggest that the basement consists of mixed igneous sedimentary material atypical of mid ocean ridges on the basis of the near surface manifestations of active faulting and magmatism seafloor spreading will likely first occur in the lower delfin basin we suggest the transition to seafloor spreading is delayed by the lack of strain partitioned and focused deformation as a consequence of shear in a broad zone beneath a thick sediment cover

oblique dilation melt transfer and gneiss dome emplacement the upward transfer of partially molten crust and the formation of gneiss domes and metamorphic core complexes commonly take place by localization of normal or oblique extension in the middle and upper crust in marie byrd land antarctica a transition from wrench to oblique extension occurred during oblique plate divergence along the east gondwana margin and intracontinental crustal extension associated with the west antarctic rift system in mid cretaceous time migmatites in the fosdick dome record steep fabrics formed during wrenching and associated granite networks display crystallization ages of 117 115 ma these steep fabrics are overprinted by subhorizontal foliation and leucogranite sheets with crystallization ages in the 109 102 ma range syntectonic emplacement of granite sheets in the south fosdick detachment zone indicates that detachment tectonics led to rapid exhumation of the terrain by 100 ma this study has implications for understanding melt transport magma accumulation and the formation of detachments in an oblique tectonic setting

kinematic analysis of asymmetric folds in competent layers using mathematical modelling mathematical 2d modelling of asymmetric folds is carried out by applying a combination of different kinematic folding mechanisms tangential longitudinal strain flexural flow and homogeneous deformation the main source of fold asymmetry is discovered to be due to the superimposition of a general homogeneous deformation on buckle folds that typically produces a migration of the hinge point forward modelling is performed mathematically using the software foldmodeler by the superimposition of simple shear or a combination of simple shear and irrotational strain on initial buckle folds the resulting folds are ramsay class 1c folds comparable to those formed by symmetric flattening but with different length of limbs and layer thickness asymmetry inverse modelling is made by fitting the natural fold to a computer simulated fold a problem of this modelling is the search for the most appropriate homogeneous deformation to be superimposed on the initial fold a comparative analysis of the irrotational and rotational deformations is made in order to find the deformation which best simulates the shapes and attitudes of natural folds modelling of recumbent folds suggests that optimal conditions for their development are a buckling in a simple shear regime with a sub horizontal shear direction and layering gently dipping towards this direction b kinematic amplification due to superimposition of a combination of simple shear and irrotational strain with a sub vertical maximum shortening direction for the latter component the modelling shows that the amount of homogeneous strain necessary for the development of recumbent folds is much less when an irrotational strain component is superimposed at this stage that when the superimposed strain is only simple shear in nature the amount of the irrotational strain component probably increases during the development of the fold as a consequence of the increasing influence of the gravity due to the tectonic superimposition of rocks

theoretical strain patterns in ductile zones simultaneously undergoing heterogeneous simple shear and bulk shortening abstract structures observed in ductile shear zones show that deformation is continuous and strain is heterogeneous this leads us to define a simple model for shear strain rate when a shear zone simultaneously undergoes simple shearing and pure shearing contraction or extension the condition of continuity of deformation shows that must be a function of time integration of the deformation rate equations yields the particle paths in the deforming body from these we can determine at any time and at any point in the body the finite strain tensor lengths and orientations of the axes of the finite strain ellipsoid we can therefore define the finite strain trajectories and compare them with orientations of internal structures schistosity tension gashes the particle paths also allow us to study the progressive deformation of passive strain markers

patterns of stretch trajectories and strain rates within spreading gliding nappes abstract stretch trajectories in vertical flow planes through superficial nappes are thought to be specific for some classical mechanical models so that their recognition in the field is of particular interest in order to find a pattern of stretch trajectories related to a gravitational process a strain factorization is attempted from experimental scale models of nappes where spreading and gliding are combined the strain within this type of nappes is schematically considered as the simultaneous combination of two components a simple shearing component and a pure shearing component spatial and time distribution of these two components is computed from both time and spatial evolution of the strain pattern within the scale models a better understanding of stretch trajectories in spreading gliding nappes is consequently provided strain rates are also computed from scale models and the sudden increase of strain rate from top to bottom is explained finally a mechanical model of spreading gliding nappe is briefly discussed

complex strain patterns developed at the frontal and lateral tips to shear zones and thrust zones abstract many of the complex strain patterns seen in shear zones and thrust zones such as variable fabric orientations refolded folds and fabrics together with folds with hinges almost parallel to the main transport direction can be explained in terms of differential movement within the shear zones these strains are developed at the frontal and lateral tips of the zones as they propagate examples are taken from the moine thrust zone of scotland which show variations in strains particularly at the lateral tips the form of differential movement described here may lead to complex strain paths and non plane strain ellipsoids and the spatial variations in finite strain may be used to delineate zones of extensional and compressional flow and differential movement in the shear zones or thrusts

asymmetric quartz c axis fabrics and flow vorticity a study using rotated garnets abstract the development of a type i crossed girdle c axis fabric with an asymmetric density distribution and an internally asymmetrical skeletal outline is examined in a specimen of garnet bearing mylonitic quartzite from the betic movement zone in southern spain the garnets are pre mylonitic skeletal porphyroblasts that rotated during mylonitic deformation but preserved a strain free equilibrium microstructure and a random c axis fabric it follows that the asymmetry of the density distribution must result from the deformation history itself the sense of asymmetry of the c axis population and that of the skeletal outline are consistent with the sense of vorticity inferred from extensional crenulations and asymmetric microboudinage and also with the sense of rotation of the garnets analysis of the rotation angles with aspect ratio of the garnet porphyroblasts demonstrates that a pure shear component was involved in an essentially non coaxial flow this may explain the internal asymmetry of the fabric skeleton and confirms the idea that a spectrum exists of type i fabrics intermediate between the theoretically predicted fabrics for pure and simple shear a tentative reconstruction of the kinematic framework suggests that the central segment of the fabric skeleton is linked to the extensional apophysis of the flow

stable positions of rigid objects in non coaxial flow a study in vorticity analysis abstract distortions of a homogeneous fabric which occur around rigid objects in rocks deformed by non coaxial ductile flow are useful to determine the sense of shear but also contain information on other aspects of the flow rigid objects in a non coaxial flow fall into two categories those which are permanently rotating and those which can reach stable positions at high finite strain the orientation of such immobilized objects with respect to eigenvectors of instantaneous flow is a function of the vorticity number of the flow the ratio of instantaneous stretches and the axial ratio of the object in naturally deformed rocks immobilized rigid objects may be recognized from the geometry of the surrounding fabric tails of recrystallized material around porphyroclasts in a mylonite rotate towards parallellism with the extensional eigenvector of the flow and the shape of tails reflects the rotational behaviour of the porphyroclast the axial ratio of immobilized porphyroclasts and their orientation with respect to the tails can theoretically be used to determine the vorticity number of the flow and deviations from isochoric plane strain in practice such an analysis is as yet difficult but a tentative example is given of the way in which the vorticity number can be calculated from a population of feldspar porphyroclasts in a quartzite mylonite from the french pyrenees

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

reconstruction of deformation and flow parameters from deformed vein sets abstract in any homogeneously deformed material sets of material lines with a similar stretch history occupy sectors with a scale and orientation that depend on finite strain area change rate and vorticity of the parent flow if the size and shape of these material line sectors are known they can be used to determine the sense of shear and to calculate deformation and flow parameters even if actual stretches along material lines are unknown in rocks which have undergone near homogeneous deformation on a large scale the orientation of sets of boudinaged folded and folded boudinaged or boudinaged folded veins can be used for such calculations a general theoretical background to the problem is presented and a mohr circle construction to carry out the deformation and flow analysis is introduced among other statements the theory predicts that shortened or folded boudins must develop in non coaxial monophase deformation with considerable area change in the plane of observation or in polyphase deformation

vorticity analysis in a metachert from the sanbagawa belt sw japan abstract common tectonic features of deformed metachert include both sets of extended and shortened veins and quartz c axis preferred orientation patterns in such rocks information is also commonly available on the orientation and magnitude of the finite strain these features can be used to derive two independent estimates of the degree of non coaxiality during deformation in an example from the sanbagawa belt sw japan the two methods give consistent results and show that deformation was intermediate between simple and pure shear such types of progressive deformation distributed over a broad region could cause substantial subvertical thinning and be a significant factor in the exhumation of high p t rocks in the region

models of strain variation in nappes and thrust sheets a review abstract strain within nappes and thrust sheets can be modelled using simple boundary conditions an original rectangular prism of material resting on a thrust plane is considered to be subject to various pure and simple shear components operating parallel to the thrust deformation gradient tensors are determined for the models and solutions found for the principal strains a two dimensional model considers heterogeneous simple shear combined with a stretch in the direction of shear simple shear zones arise as a special case where 1 recumbent fold nappes characteristic of gravitational collapse can be modelled with 1 and thrust sheets with layer parallel shortening and folding with differential transport of nappes gives rise to additional wrench type shears solutions for the principal strains in this type of model are found and used to interpret side wall ramps and steep zones parallel to nappe movements by including a stretch in the transport direction these differential transport models produce prolate strains 1 and oblate strains finally a brief consideration of bending strains produced in a sheet passing over a ramp indicates reversals in the shear direction during the strain history these predict possible crenulation of early thrust fabrics at ramps

strain analysis of a northern apennine shear zone using deformed marble breccias abstract the alpi apuane region of the northern apennines appears to have been deformed within a large scale low angle shear zone with an overthrust sense of movement the presence of mineral stretching lineations folds progressively rotated into the x strain direction and schistosities which intersect the nappe boundaries at small angles suggest that a component of shear strain occurred during the deformation the strain ratios and orientations on two dimensional sections have been determined from deformed marble breccias reduction spots and oncalites data from three or more non perpendicular non principal sections have been combined to determine the finite strain ellipsoids at 33 sites within the shear zone the finite strains have been separated into components of simple shear longitudinal strain and volume change algebraic expressions have been derived and graphs constructed which enable components of and and and to be determined directly from a knowledge of strain ratio r within the shear zone and the angle between the principal strain direction and the shear zone boundary the alpi apuane data indicate that neither simple shear alone nor simple shear with volume change can satisfactorily explain the observed strains consideration of simple shear plus longitudinal strain leads to a general relationship in which the value of shear increases and the values of longitudinal strain change along a sw ne profile across the zone integration of the resulting shear strain distance curves gives a minimum displacement of 4 km within the shear zone combination of the finite strains with the total time of deformation known from k ar studies leads to average strain rates from 1 4 to 9 6 10 15 sec 1 a characteristic flat ramp flat geometry initially formed the boundaries of what was later to develop into the overthrust shear zone and deformation of the underlying crystalline basement is believed to have occurred by ductile shearing estimates of 21 crustal shortening for the region suggest that the crustal thickness prior to deformation was approximately 20 km in this part of the northern apennines

kinematics stress deformation and material behavior abstract a compact review is given of some fundamentals of the theory of flow in materials and of the bulk behavior of experimentally deformed rocks kinematics is discussed first because it provides an easy introduction to second order tensor quantities these are explained as quantities linking the components of pairs of vectors to one another for example velocity vectors to position vectors the velocity gradient tensor or stress vectors to plane normal vectors the stress tensor the fundamental theorem of stress theory is derived from the requirement of force balance at a point here and elsewhere the treatment is mostly two dimensional this saves space yet provides an introduction to principles that are important again in three dimensions mohr circles are used extensively to represent two dimensional tensor quantities geometrically including asymmetric velocity gradient and deformation tensors the decomposition of a general deformation into components of translation rotation and strain is explained and this may lead to greater appreciation of such unfamiliar possibilities as coaxial accumulation of a simple shear deformation the section on experimental deformation is concerned mainly with the measured strengths of rocks and how these can be extrapolated to strengths at geological strain rates the text is followed by a glossary

deformation path partitioning within the transpressional white mountain shear zone california and nevada most numerical simulations of transpression zones predict a change in finite stretching direction from subhorizontal to subvertical for simple shear dominated zones we provide a detailed description of a dextral transpression zone the white mountain shear zone wmsz with a range of lineation orientations and compare these natural data to numerical models the wmsz is characterized by steeply dipping foliations with dominant shallowly plunging lineations and coeval subordinate domains of steeply plunging lineations within shallowly lineated domains foliation geometry shear sense indicators and quartz c axis fabrics indicate a large component of simple shear while microstructural and quartz c axis fabric data from steeply lineated domains indicate a large component of pure shear geometric relationships between foliations and lineations and quartz c axis fabrics demonstrate that lineation orientation has remained constant during much of the deformation history comparison of numerical models with the data collected from wmsz shows that the shear zone geometry and the observed strain path partitioning do not match any of these models we propose a conceptual kinematic model for the wmsz involving stable segregated coeval kinematic domains of simple shear dominated fabrics and pure shear dominated fabrics that accommodate the transcurrent and contractional components of deformation respectively

displacement and strain patterns of extensional orogens rock fabrics that result from displacement in extensional orogens provide a means of identifying geometric models responsible for extension of continental crust strain compatibility arguments indicate that a finite extension can be accommodated by displacements across 1 planar nonrotating faults or ductile shear zones 2 shear zones which rotate above a horizontal detachment the domino model or 3 shear zones which rotate as a result of a horizontally oriented pure shear stretching component the plastic model listric normal shear zone geometries may develop as the result of a depth dependent change in the pure shear component in the plastic model or the area loss component in the planar shear zone model within the geometric framework of these various models the effects of superposed simple shear pure shear extension and area change on the rock fabric are investigated these displacement components which may be superposed sequentially or simultaneously determine the state of finite strain associated with a given magnitude of tectonic extension the relationships between displacement and strain are expressed as graphs of foliation dip or strain ratio versus shear strain and as graphs of foliation dip or strain ratio versus tectonic extension the shear strain graphs illustrate the effects of the different displacement components on the rock fabric in a single shear zone whereas the tectonic extension graphs better illustrate these effects on the regional scale the shear strain and tectonic extension graphs can be used by field geologists 1 to determine tectonic extension across a region from measurements of strain ratio or orientation and fluctuation of foliation 2 to distinguish between possible extension models from field data and 3 to evaluate the influence of shear zone attitude and thickness upon the amount of displacement applications of these methods are illustrated for field areas in metamorphic core complexes of arizona and in the basin and range province of the north america cordillera