anisotropy and the splitting of ps waves the ps wave is radially polarized in an isotropic spherically symmetric earth owing to the p to sv conversion at the free surface if we choose stations with weak sks splitting to minimize the effect of the receiver we can measure the anisotropy beneath the bounce point of the ps wave we find that with a deep source and epicentral range of 90 125 the ps phase can be distinguished from other phases owing to the limitation of recent large deep events with epicentral range between 90 and 125 we analyze data from stations in north america and events beneath the bonin islands and the fiji islands for events in these two regions the bounce points of the ps wave are roughly located northwest of the kuril islands and near the nova canton trough in the central pacific respectively because the first fresnel zone for the ps wave at this distance range is roughly 700 km across each ps splitting observation must be interpreted as a local average of anisotropic properties the average direction of the fast axis of anisotropy below the nova canton trough region is n104 2 e with a standard deviation 12 7 and a typical delay time of 1 8 s landward of the kuril islands the average direction of the fast axis is n127 6 e clockwise from north and the standard deviation is 11 3 with a typical delay time of 1 2 s we have compared the fast axis with the direction of fossil seafloor spreading and with the present day absolute plate motion the fast axis of anisotropy at the nova canton trough agrees well with the direction of absolute plate motion and poorly with the complex fossil spreading pattern this suggests that significant upper mantle shear anisotropy exists in this part of the central pacific and is consistent with mineral alignment owing to strain associated with present day plate motion similarly the fast axis beneath the kuril islands parallels the convergent motion of the slab coupled mode synthetics constructed with the strong born approximation can be used to model the interaction of the ps waves with anisotropic structure that has a horizontal axis of symmetry we use all free oscillations up to 35 mhz in the calculation the coupled mode synthetics show shear wave splitting with delay time and fast axis consistent with the ray theory prediction

observations of first order mantle reverberations we have observed first order mantle reverberations specifically sh polarized scsn and sscsn phases reflected at near normal incidence from upper mantle discontinuities as discrete phases on long period digital seismograms of the hglp and sro networks such arrivals correspond to an n or n 1 member dynamic ray family denoted by scsn sd s where n is the multiple number of the parent phase d signifies a reflection from the top of an internal discontinuity at depth d and d signifies a reflection from the bottom the travel times and attenuation of these phases place important constraints on the nature of the transition zone we have employed the phase equalization and stacking algorithm of jordan and sipkin 1977 to obtain the differential attenuation operators of sscsn s650 s sscsn and scsn s650 s scsn phase pairs from deep focus tonga events recorded by the hglp station kip on the island of oahu the apparent q s of the zeroth order and first order reverberations over the frequency band of 10 to 30 mhz have been inverted for the average quality factors of the upper mantle qum and lower mantle qlm and the reflection coefficient of the 650 km discontinuity r 650 at 20 mhz the results are qum 82 18 qlm 231 60 and r 650 0 080 0 004 at normal incidence the qlm estimate is significantly less than recent normal mode solutions suggesting that lower mantle attenuation structure is frequency dependent at very low frequencies we have measured the differential travel times between the first order reverberations sscsn s400 s and sscsn s650 s which yields a direct estimate of the vertical shear wave travel time between the discontinuities along the tonga to kip path the observed two way time 92 2 1 5 sec is less than predicted by some recent oceanic upper mantle models indicating either a smaller separation of the discontinuities and or greater shear velocity in the transition zone measurements of differential travel times between first order reverberations and multiple scs phases suggest that the former is more likely and are consistent with depths of 400 and 650 km for the transition zone discontinuities observations of first order mantle reverberations can potentially provide unique constraints on lateral heterogeneity of the earth s mantle especially within the transition zone

kinematics of a growth fault raft system on the west african margin using 3 d restoration abstract the ability to quantify the movement history associated with growth structures is crucial in the understanding of fundamental processes such as the growth of folds or faults in 3 d in this paper we present an application of an original approach to restore in 3 d a listric growth fault system resulting from gravity induced extension located on the west african margin our goal is to establish the 3 d structural framework and kinematics of the study area we construct a 3 d geometrical model of the fault system from 3 d seismic data then restore six stratigraphic surfaces and reconstruct the 3 d geometry of the system at six incremental steps of its history the evolution of the growth fault raft system corresponds to the progressive separation of two rafts by regional extension resulting in the development of an intervening basin located between them that evolved in three main stages 1 the rise of an evaporite wall 2 the development of a symmetric basin as the elevation of the diapir is reduced and buried and 3 the development of asymmetric basins related to two systems of listric faults the main fault f1 and the graben located between the rollovers and the lower raft important features of the growth fault raft system could only be observed in 3 d and with increments of deformation restored the rollover anticline associated with the listric fault f1 is composed of two sub units separated by an e w oriented transverse graben indicating that the displacement field was divergent in map view the rollover units are located within the overlap area of two fault systems and displays a mock turtle anticline structure the seaward translation of the lower raft is associated with two successive vertical axis rotations in the opposite sense clockwise then counter clockwise by about 10 this results from the fact that the two main fault systems developed successively fault system f1 formed during the upper albian and the graben during the cenomanian using a new approach of 3 d restoration this study suggests a consistent solution for 1 the processes of deformation of a fault system 2 the faulting kinematics and 3 the incremental steps of deformation

sedimentary flattening and multi extensional deformation along the west african margin abstract the structural world is usually divided into compressional and extensional zones and this tectonic style is representative of the regional deformation which leads to shortening or extension along the west african margin there is no evidence of crustal extension since 100 my ago but the post salt series are intensely deformed by gravity and sedimentary loading normal faults as well as reverse faults are present the modes of deformation of such an area are described using large 3d seismic data sets analogue models and cross section and map restorations results show that 1 surface rotations are large at a regional scale 2 plane deformation is not a valid hypothesis across the margin the amount of extension parallel to the coast being on the same order of magnitude as the extension perpendicular to the margin 3 the surface area of the beds are not preserved the data indicate that the deformation of the shale in such a context is a ductile flow due to body forces and sedimentary loading here called sedimentary flattening competent layers sand prone such as sheet sand lobes or channels constitute passive markers which follow the ductile flow in a brittle mode resulting in boudinage

compressional and shear wave anisotropy in the oceanic lithosphere the ngendei seismic refraction experiment summary synthetic seismogram modelling of seismic refraction data from the 1983 ngendei expedition to the south pacific indicate seismic anisotropy both within the top kilometre of oceanic crust and in the uppermost mantle we calculate average p and s wave velocity versus depth functions for two orthogonal azimuths n3ooe approximately aligned with the fast mantle direction and n120 e close to the fast crustal direction probable lateral heterogeneities at the ngendei site prevent perfect matching of data and synthetic waveforms crustal anisotropy is indicated by a 28 pattern of both p and s wave travel times as a function of azimuth and is consistent with an approximate 0 2 km s difference in p wave velocities and 0 1 km s difference in s wave velocities upper mantle anisotropy is characterized by pn velocity differences of 7 95 8 4 km s l and a nearly uniform s velocity of 4 65 km s we use these velocity profiles and traveltime data to calculate bounds on the properties of the elastic constants of the crust and upper mantle the crustal anisotropy can be explained by a model involving aligned cracks parallel to the original spreading ridge resulting in a fast direction perpendicular to the fossil spreading direction the upper mantle anisotropy is consistent with aligned olivine crystal models in which the fast direction is parallel to the fossil spreading direction for both of these models we use bounds from the ngendei data to place constraints on the physical properties of the lithosphere

internal structure kinematics and growth of a salt wall insights from 3 d seismic data the detailed kinematics of natural salt walls remain elusive because such structures are typically poorly exposed at outcrop only partly exposed in mine workings and diapiric salt is typically poorly reflective in seismic data we use three dimensional seismic and borehole data from offshore brazil to investigate how structural styles vary along strike within a spectacularly well imaged salt wall deformed layering in the salt allows us to map complex seismic scale structures in the wall within the wall s relatively simple external shape is a range of previously undocumented structural styles produced by 1 initial upwelling and formation of a wall parallel anticline due to regional extension and differential overburden load 2 breaching of the anticline rayleigh taylor overturn and emplacement of an intrasalt allochthonous sheet driven by a density inversion and 3 internal thrusting of the mature diapir caused by regional compression this study is arguably the first detailed documentation of the internal structure and kinematics of a natural salt wall highlighting the presence of abruptly varying intrasalt structural styles the structures identified and the inferred kinematics suggest that given specific mechanical stratigraphy density driven overturn within salt diapirs can play a key role in their growth

depth and age in the north pacific the concept of the oceanic lithosphere as a cooling thermal boundary layer on top of a viscous upper mantle accounts for the increase in depth with age of the ocean floor analyses of the exact nature of this relation provide constraints on the rheology and structure of this layer in past studies problems with uncertainties of age and in sediment thickness have limited the value of this relation on older ocean floor in this study we evaluate different tectonic histories for the quiet zones and construct a revised isochron chart for the north pacific we check and modify the current sediment thickness charts using new deep sea drilling data and revised ideas concerning reflectors in the southwestern north pacific averaging the synbaps digital data base into half by half degree elements and correcting for sediment load we plot basement depth versus age for the entire north pacific because of the skewness in the data associated with seamounts we present the data as contours about the mode and find that two thirds of the observations lie within 300 m of this value on crust between 0 and 80 ma the ocean floor subsides with the square root of age on ocean floor older than 100 ma the depths in general flatten with age with areally correlateable swells and valleys the hawaiian and line island swells correlate positively and the mariana basin valley negatively with geoid height the flattening in the depths indicates that the thermal boundary layer has reached equilibrium conditions under older ocean floor further the correlation of the swells and valleys with geoid height presents evidence for organized convection in the upper mantle beneath older lithosphere in the north pacific

application of a three dimensional finite element method to strain field analyses abstract i have programmed a three dimensional finite element model to spatially integrate distributed strains the mathematics is based on cobbold and percevault 1983 the method finds the pre strain configuration of a region by unstraining rectangular prisms into parallelepipeds then rotating and translating them iteratively to minimize the interelement deviations a numerical singular value decomposition calculates the necessary rotations and the final cycle of further strains to make a best fit of the elements the deviation of elements from holes formed by their nearest neighbors indicates the degree of compatibility of strain measurements the program reproduces the rotations required in examples with analytic solutions even though only a single horizontal layer of elements is used the fitting procedure correctly calculates rotations in all three dimensions from the constraints of strain compatibility three dimensional strains measured in an archean greenstone belt of northeastern minnesota were integrated using a layer of nearly equant finite elements rotations calculated from the pre tectonic configuration accord with field observations of fabrics indicating variable amounts of shear rotations about horizontal axes are minimal precluding large vertical shears an estimate of 40 true horizontal north south shortening across the belt can be made from the undeformed configuration

interplay of thrust back thrust strike slip and salt tectonics in a fold and thrust belt system an example from zakynthos island greece the southwestern flank of the hellenic fold and thrust belt situated along the southern edge of the dinarides albanides hellenides continental convergent zone was examined for reconstructing the tectonic deformation this investigation presents an integrated study of onshore sedimentological and structural analyses as well as offshore seismic lines across the pliocene pleistocene sedimentary succession in zakynthos island back thrust faults using the triassic evaporites as decollement surface during the pliocene and coeval diapiric intrusions formed three sub basins on the hangingwall of the kalamaki back thrust fault this interaction is responsible for the growth of the skopos mountain and the soft sediment deformation that formed synclines and slumps respectively back thrust and strike slip faults were active during the early pleistocene and diapiric intrusions modified the bathymetry on the sea floor giving rise to slumps and recumbent folds at least five events of synsedimentary diapiric intrusions have been recognized and are marked by five slump horizons during the holocene the diapiric intrusions between the kalamaki back thrust and the vrachionas anticline could be either related to normal faults or gravitationally driven

mathematical removal of regional ductile strains in central brittany evidence for wrench tectonics abstract hercynian deformation in central brittany is responsible for folding of paleozoic and earlier sediments with concurrent development of cleavage essentially e w and vertical and stretching lineation essentially horizontal in the past the regional motion was inferred to be a n s shortening more recent studies emphasize e w transcurrent motions associated with major crustal faults values and orientations of ductile strain at 29 localities in central brittany show that the regional deformation is basically a horizontal plane strain with local three dimensional perturbations we first remove the perturbations rendering the problem two dimensional then a selected domain is divided into an array of finite elements parallel to strain trajectories using strain values extant at element centroids each element is unstrained independently of its neighbours resulting gaps and overlaps are minimized using a least squares technique which allows elements to translate and rotate rigidly thus we obtain the configuration of the domain in the undeformed state to within an unknown but constant rigid rotation the domain has undergone a heterogeneous dextral simple shear with vertical shearing plane striking n125 and horizontal shear direction a band of low strain running through guer is flanked by two zones of more intense strain the banding is approximately parallel to a major transcurrent fault in the area the south armorican shear zone

3d structural modelling of the southern zagros fold and thrust belt diapiric province 3d modelling of geological structures is a key method to improve the understanding of the geological history of an area and to serve as a drive for exploration geomodelling has been performed on a large 60000 km 2 area of the zagros fold and thrust belt of iran to reconcile a vast but heterogeneous dataset topography geological surface data and dips outcrop surveys and well and seismic data were integrated into the model the method was to construct a key surface maximizing the hard data constraints the oligo miocene top asmari layer was chosen as this formation was regionally deposited before the main zagros collision phase and because the numerous outcrops allow proper control of the bed geometry in the fold cores interpreted seismic data have been integrated to interpolate the surfaces at depth within the synclines several conceptual models of fold geometry have been applied to estimate the best way to convert seismic time signal to depth several deeper horizons down to palaeozoic strata were deduced from this key horizon by applying palaeo thickness maps during the construction the 3d interpolated surfaces could be reconverted to time using a velocity model and compared with previous seismic interpretations this exercise obliged us to revise some early interpretations of seismic lines that were badly tied to wells the 3d modelling therefore clearly improves regional interpretation in addition the 3d model is the only tool that allows drawing consistent cross sections in areas where there are no seismic lines emerging hormuz salt diapirs were added to the model dimensions and shapes of the individual diapirs were modelled using a statistical survey on the cropping out hormuz structures modelling reliably demonstrated that the diapirs when piercing show a constant mushroom shape whose diameter depends on the stratigraphic depth of observation this observation allowed us to exemplify relations between the pre existing diapirs and the anticlines of the area and to highlight the morphological changes from the inner onshore areas to the coastal and offshore areas in addition one of the surprising results of this study was the observation of the increasing diameter of the diapirs at the time of the zagros collision and folding event with growth strata and overhangs on the flanks of the diapirs

palinspastic reconstruction of structure maps an automated finite element approach with heterogeneous strain existing methods for the palinspastic reconstruction of structure maps do not adequately account for heterogeneous rock strain and hence cannot accurately treat features such as fault terminations and non cylindrical folds we propose a new finite element formulation of the map reconstruction problem that treats such features explicitly in this approach a model of the map surface with internal openings that honor the topology of the fault gap network is constructed of triangular finite elements both model building and reconstruction algorithms are guided by rules relating fault gap topology to the kinematics of fault motion and are fully automated we represent the total strain as the sum of a prescribed component of locally homogeneous simple shear and a minimum amount of heterogeneous residual strain the region within which a particular orientation of simple shear is treated as homogenous can be as small as an individual element or as large as the entire map for residual strain calculations we treat the map surface as a hyperelastic membrane a globally optimum reconstruction is found that unfolds the map while faithfully honoring assigned strain mechanisms closes fault gaps without overlap or gap and imparts the least possible residual strain in the restored surface the amount and distribution of the residual strain serves as a diagnostic tool for identifying mapping errors the method can be used to reconstruct maps offset by any number of faults that terminate branch and offset each other in arbitrarily complex ways

radial gravitational gliding on passive margins abstract gravitational gliding of uppermost sediments down a passive margin is possible if there is a basal layer of evaporite or other soft material to allow detachment in examples from the gulf of mexico and the brazilian margin gliding has produced three main structural domains an uppermost domain of downdip extension an intermediate domain of rigid gliding and a lowermost domain of downdip contraction domain boundaries are established by changes in slope in this paper we examine three kinds of gravitational gliding depending on the paths followed by material particles in ideal parallel gliding particle paths are parallel straight lines trending downslope this should occur where the margin is perfectly straight in ideal radial gliding particle paths are radii of a circle and the margin is shaped like a circular cone natural margins will not have ideal shapes but divergent gliding will tend to occur off coastal salients convergent gliding off coastal re entrants a simple kinematic model based on ductile behaviour illustrates some essential features of radial gliding changes in radius during divergent gliding produce strike parallel extension during convergent gliding they produce strike parallel contraction vertical strains also differ divergent gliding produces an uppermost domain of strong vertical thinning balanced by extensions in all horizontal directions similarly convergent gliding produces a lowermost domain of strong vertical thickening balanced by contractions in all horizontal directions these deformed states cannot be restored by simple techniques based on section balancing we have done three experiments using analogue materials sand to model the brittle behaviour of sediments silicone putty to model the ductile behaviour of basal layers of evaporite the experiments were properly scaled to account for gravitational forces experiment i reproduced convergent gliding above a basement with a conical upper surface strike parallel contraction was responsible for radial folds on the lower slopes the lowermost domain had a complex fold pattern indicating contraction in all horizontal directions experiment 2 reproduced divergent gliding above a basement with a pyramidal upper surface strike parallel extension produced radial rifts on the upper slopes the uppermost domain had a complex polygonal pattern of normal faults indicating extension in all horizontal directions experiment 3 also reproduced divergent gliding but due to non uniform sediment thickness we have examined the many seismic profiles both downdip and alongstrike available for the brazilian margin alongstrike profiles show structures which we attribute to strike parallel strains around the santos re entrant syn sedimentary growthfolds indicate strike parallel contraction increasing downslope this argues for a mechanism of convergent gliding in contrast around the campos salient normal growth faults and associated salt rollers indicate strike parallel extension decreasing downslope this argues for a mechanism of divergent gliding the pattern of oil fields in the campos area including the giant marlim field seems to be closely controlled by divergent gravitational gliding and associated processes radial gliding should occur on other passive margins as well especially where the coastline is sinuous structures around the western gulf of of mexico seem to indicate convergent gliding at the scale of the entire gulf structures at a smaller scale around the mississippi delta seem to indicate divergent gliding

compatibility constraints on folded and faulted strata and calculation of total displacement using computational restoration unfold program abstract a balanced surface method is proposed that allows one to test the reliability of the interpretation of the structural geometry of folded and faulted strata it also estimates both the finite total displacement field linked to the folding and faulting processes and the finite displacement field linked to the folding the method describes a thin competent folded and faulted sedimentary layer using rigid triangular elements their sizes depending on the curvature of the surface the elements are laid flat and are automatically fit to form a horizontal surface which represents the initial state of the layer the degree of compatibility given by different indicators tests the reliability of the geometric fitting of the layer if folding and faulting occur without bed stretching or if this change is known and introduced as a parameter in the code a plausible interpretation can be perfectly retrodeformed just as a folded and torn sheet of paper may be smoothed with an iron the method has been applied to two natural examples in oil field regions using three or two dimensional depth migrated seismic data the main results reveal in general that the petroleum company s interpretations of the data were nonoptimal a careful reinterpretation of the seismic data was necessary to obtain balanced folded and faulted surfaces the estimation of the finite displacement fields revealed the compatibility between fold and fault deformation and also the strike slip movement or rotation associated with the deformation

vertical axis rotation in the bolivian orocline south america 2 kinematic and dynamical implications an analysis is presented of the kinematic consequences and dynamical causes of paleomagnetically determined rotations about a vertical axis documented in the central andes south america between 15 s and 25 s at these latitudes there is a pronounced bend in the topographic and structural trends defining the bolivian orocline the observed vertical axis rotations during the last 10 myr are used in conjunction with observations of horizontal dilatation to calculate the finite strain and displacement field in a network of triangles spanning the bolivian orocline assuming that the rotations represent the rotational component of finite strain this shows that rotation during the last 10 myr has accommodated bending of the bolivian andes increasing the curvature of the eastern margin of the bolivian orocline by 10 to 27 with a systematic variation in strains around the oroclinal hinge which is consistent with the observed pattern of upper miocene to recent deformation vertical axis rotations greater than that inferred for regional oroclinal bending can be explained in terms of simple kinematic models of vertical axis rotation and reverse faulting in margin parallel zones of sinistral and dextral shear the dynamical controls of vertical axis rotation are analyzed using a simple thin sheet model of viscous flow in a narrow channel this model suggests that in general regional bending is controlled by a combination of along strike gradients of 1 boundary normal stresses at the subduction zone 2 bulk lithospheric viscosity 3 gravitational potential energy buoyancy stress contrasts and 4 width of the fluid like channel if along strike gradients of boundary normal stresses and viscosity are small then the pattern of vertical axis rotation can be explained as a consequence of along strike gradients in buoyancy stress for a bulk lithospheric viscosity in the bolivian andes 7 1021 pa s in detail the organization of vertical axis rotation and horizontal shortening suggests that there are both horizontal and vertical gradients of velocity and rheology in the lithosphere

seismic structure of the upper mantle in a central pacific corridor the seismic structure of the tonga hawaii corridor has been investigated by combining two data sets revenaugh and jordan s reflectivity profile from scs reverberations which provides travel times to and impedance contrasts across the major mantle discontinuities and 1500 new observations of frequency dependent phase delays for the three component s ss and sss body waves and the r1 and g1 surface waves which constrain the velocity structure within this layered framework the shear waves turning in the upper mantle showed significant splitting of the sh and sv components indicative of shallow polarization anisotropy the data set was inverted in conjunction with attenuation and mineralogical constraints to obtain a complete spherically symmetric radially anisotropic structure the final model pa5 is characterized by a high velocity anisotropic lid bounded at 68 km depth by a large negative g discontinuity a low velocity anisotropic layer below g extending to a small l discontinuity at 166 km an isotropic steep gradient region between 166 km and 415 km and transition zone discontinuities at 415 507 and 651 km the depth of the radial anisotropy in pa5 is shallower than in most previous studies based on surface waves and higher modes the average value of radial shear anisotropy in the lid 3 7 is consistent with the magnitude expected from the spreading controlled models of olivine orientation while anisotropy in the low velocity zone which is required by our data set could be induced either by paleostrains that took place near the ridge crest or by shearing in the asthenosphere as a result of present day plate motions on the basis of recent work by hirth and kohlstedt we suggest that the g discontinuity is caused by a rapid increase in the water content of mantle minerals with depth marking the fossilized lower boundary of the melt separation zone active during crust formation the high gradient zone between 200 and 400 km is a characteristic feature of convecting oceanic upper mantle and is probably controlled by a steady decrease in the homologous temperature over this depth interval the average shear velocity gradient in the transition zone is lower than in most previous seismic models in better agreement with the predictions for a pyrolitic composition

restoration of transpression transtension by generating the three dimensional segmented helical loci of deformed lines across structure contour maps abstract in transpression transtension zones the strain is three dimensional and rotational this causes material to move through the plane of cross section often invalidating balancing and restoration within this plane methods are presented which allow the three dimensional segmented irregular helical locus of an originally straight line to be constructed in any direction on a structure contour map of a folded and faulted surface this construction depends on a knowledge of the kinematics of folding and faulting and can be modified to suit local conditions the ratio of the length of the cylindrical envelope bounding this helical locus to the sum of the lengths of the helical fragments between faults gives the true stretch in the direction of the envelope when the traces of the segmented helices are constructed in different directions on a deformed surface the sectional finite strain ellipse can be found for that surface knowledge of the dimensions of this ellipse and its orientation with respect to the kinematic axes of the transpression zone allows the tensor components to be constrained this permits the three dimensional boundary conditions to be determined and thus restored the methods are applied to the ardross fault zone in central scotland the solutions suggest this fault zone underwent a phase of dextral transpression along a nw zone boundary during hercynian e w compression in the scottish midland valley contemporaneous e w dyke swarms and n s regional flexures support these kinematics

restoration of cross sections to constrain deformation processes of extensional terranes abstract restoring balanced cross sections constrains the possible deformation processes affecting extensional terranes with a ductile substratum such as salt and syndeformational sedimentation cross sections are divided into fault blocks and shear domains each of which can be undeformed with a different set of parameters the success of restorations is judged by compatibility between the blocks and the reasonableness of the restored structures fault blocks in physical models restore with simple shear at about 60 dipping in the direction which removes extension corresponding to an antithetic orientation in the hangingwalls of normal growth faults and subparallel to the fault in the footwall other components of the deformation are rigid rotation translation and decompaction shear angles inferred from natural examples are more varied ranging from vertical to moderately inclined nearly always dipping in a direction that removes extension

restoration in plan view of faulted upper cretaceous and oligocene horizons and its bearing on the history of salt tectonics in the campos basin brazil abstract in the campos basin atlantic margin of brazil cretaceous and tertiary sediments show abundant evidence for thin skinned deformation above a layer of aptian salt near the coast there is a domain of downslope extension further offshore a domain of donwslope contraction thus we attribute the domainal pattern to gravitational gliding on the salt layer gravitational gliding appears to be driven primarily by surface slopes each material particle tends to move in the direction of steepest slope if topography is irregular particle paths diverge or converge deformation then differs from a plane strain and vertical cross sections cannot be individually balanced or restored we have therefore developed a method for restoring non plane deformation in extensional domains assuming that blocks between faults are rigid we restore stratigraphic horizons in plan view by least squares minimization of distances across fault separations cut off lenses obtaining fields of finite horizontal displacements for selected areas in the extensional domain of the campos basin where divergent gravitational gliding has led to extension in various horizontal directions we have restored two stratigraphie markers an upper cretaceous and an oligocene horizon for each horizon displacement vectors diverge seawards forming a fanlike pattern with a degree of mirror symmetry nevertheless there are major differences between the upper cretaceous and oligocene patterns both for faults and for displacements we infer that this resulted from the development during the tertiary of a propagating deltaic front whose sediment load drove the divergent gravitational gliding and induced a new fault pattern

polygonal fault systems and channel boudinage 3d analysis of multidirectional extension in analogue sandbox experiments abstract a systematic set of analogue models has been carried out to study the structural evolution of a sedimentary pile consisting of superposed brittle and ductile lithologies in a regional context of passive margins the models are composed of silicone representing a ductile basal layer of evaporites or overpressured shales and sand progressively sedimented on top to simulate brittle overburden sediments channels with various shapes are embedded in the silicone deformation is triggered by gravitational instability of the growing sedimentary pile and basal slope angles ranging from 0 to 5 the main results follow a polygonal fault pattern developed due to the 3d boudinage of the overburden sand above the silicone layer during multidirectional extension if a sandy channel was embedded in the ductile base it was immediately cut by faults which were perpendicular to the channel boundaries no matter what the angle between channel and slope direction the boundaries of the channel preferentially localised faults which propagated through the sedimentary pile above ongoing deformation along these faults therefore strongly influenced further accumulation of sediments

nickeliferous opaque minerals associated with chromite alteration in the sakhakot qila complex pakistan and their compositional variation chemical compositions of the awaruite heazlewoodite pentlandite assemblage from the sakhakot qila ultramafic complex pakistan indicate its genesis in highly reducing conditions with f o 2 and f s 2 much below those yielding nickel sulphide ores the compositions from various parts of the complex exhibit larger variations than those reported so far from a single complex and include unusually high ni contents awaruite compositions extend beyond the previously known limit of ni content and are unique in containing cu and not co as the third constituent after ni and fe with sympathetic relation between cu and ni previous reports indicate genesis of such minerals by serpeatinization only but the present example links them to chloritization and the formation of ferritchromit as well their petrographic distribution is related to that of chromite grains and segregations and not to that of serpentine

least squares palinspastic restoration of regions of normal faulting application to the campos basin brazil we have developed an iterative least squares method for palinspastic restoration of regions of normal faulting the method closes the gaps cut off lenses across normal faults on a structure contour map of a given stratigraphie horizon such data are often available for sedimentary basins covered by seismic surveys before restoration we first produce a fault block map where each block is completely surrounded by faults whether real or artificial we then apply an algorithm to minimize d the sum of the squares of the distances across cut off lenses with respect to unknown rigid block translations and rotations minimization results in non linear equations which we solve by an iterative method we deem the solution to have converged when d falls below a given critical level in general restoration not only closes the original gaps but also results in strike slip displacements between blocks thus the deformation need not be a plane strain and displacement vectors need not be parallel we have applied the method to an area of the campos basin on the atlantic margin of brazil where the stratigraphy and structure are well known from seismic surveys and from wells cretaceous and tertiary sediments have glided downslope on a lubricating layer of aptian evaporites producing an uppermost domain of normal faulting the normal faults occupy a strip lying between undisturbed continental crust to the west and relatively unstructured sediments to the east assuming the western boundary to be stationary we have restored an upper oligocene stratigraphie level the marco azul convergence was achieved rapidly and the degree of fit is good according to our restoration the eastern boundary of the area has bowed out seawards since the oligocene block displacement vectors form a fan like pattern with an element of mirror symmetry about a line trending nw se maximum displacements occur in an apical domain bounded by a horseshoe pattern of faults there is a general pattern of block rotations counterclockwise in the northeast clockwise in the southwest some notable exceptions to this general pattern are due to local domino motions we attribute the overall displacement field to divergent gravitational gliding off a local salient in the sea bottom topography because of the three dimensional nature of the displacement field restoration of vertical cross sections alone would yield gross errors this demonstrates the value of palinspastic methods such as ours

balanced cross section construction from seismic sections in areas of extensional tectonics abstract the application of the technique of balanced section construction initially developed for areas of compressional folding and faulting is reviewed with reference to extensional tectonics a number of examples are discussed where these techniques have been successfully applied in the north sea the interpretation of geoseismic sections is considered to be greatly assisted by careful application of geometrical balance and a consideration of strain even in areas of low crustal extensions the nature of seismic sections however places limitations on the validity of balancing which must be borne in mind with such interpretations and wherever possible the balancing of a geoseismic section should be confirmed by complete depth conversion the rapid testing of the integrity of the geoseismic section by attempting to balance the section at the interpretational phase can eliminate many problems as well as allowing the fullest use to be made of the geophysical information

least squares restoration of tertiary thrust sheets in map view tajik depression central asia the tajik depression located west of the pamirs and south of the tien shan is a compressional intermontane basin bounded by basement overthrusts and filled with mesozoic and cenozoic sediments the internal structure is typical of a thin skinned tbld and thrust belt kinematic data available in the literature suggest that indentation of the pamirs into asia durino the cenozoic collision of india and asia has been accommodated in various ways within the depression including westward extrusion thickening combined with wrenching along n s tblds and thrusts and counterclockwise rotations these various detbrmation processes can be analyzed and quantified by reconstruction of the predeformed state of the depression however the combina tion of thrusting wrenching and block rotations implies a nonplane deformation which cannot be restored properly using balanced cross sections alone we have therefore developed a numerical method for restoration of stratigraphic surfaces designed for regions of nonplane compressional tectonics the deformed region is represented in map view as a mosaic of fault bounded blocks overlapping each other along the faults blocks are separately unfolded and then numerically packed together by least squares minimization of overlaps yielding fields of finite horizontal translations and rotations about vertical axes to analyze the deformation postdating the collision of india and asia we have restored a stratigraphic surface at the base of the cenozoic first in order to test the numerical method we restored a map that had previously been restored by a purely manual method restoration of a second map drawn from newly available subsurface data leads to geometrical inconsistencies overlaps and gaps which cannot be reduced remain in the restored state after correction of these inconsistencies restoration yields a complex mode of deformation for the depression individual thrust slices have undergone counterclockwise rotations about verti cal axes the magnitudes increasing from west to east up to a maximum of 40 o near the pamirs horizontal shortening is 150 km 35 in the center of the depression and 240 km 85 in the northeastern part between the pamirs and the tien shan strike slip motions commonly not revealed by balancing cross sections are associated with thrusting on faults striking n s inde pendent paleomagnetic data and slip directions on small scale faults provide positive checks on the results of our restoration

mantle anisotropy beneath the tibetan plateau evidence from long period surface waves abstract we investigate long period surface waves t 100 s propagating across the tibetan plateau based on the seismic records from a passcal portable array and nearby chinese digital seismic network cdsn stations significant quasi love waveform anomalies associated with fundamental rayleigh love coupling are consistently observed suggesting that strong lateral gradients in azimuthal anisotropy exist beneath the plateau more intense surface wave scattering is observed at intermediate periods t 50 s which suggests that the cause of the long period quasi love waves lies in the upper mantle not the thickened crust of the plateau a detailed analysis of the data indicates that the long period waveform anomalies are generated beneath the central tibetan plateau where the structural trend implies deep deformations induced by continental collision the absence of quasi love anomalies at the westernmost station of the program for array seismic studies of the continental lithosphere passcal array suggests that the east west extent of this mantle deformation is limited some but not all of the quasi love observations are consistent with sks splitting observations both sets of observations predict a strong gradient in anisotropic properties in central tibet however the quasi love waveforms are absent from records collected in the northern plateau for northerly propagation paths which is not consistent with a gradient at the northern edge of the plateau as suggested by sks studies this discrepancy indicates that the simple models used to interpret both body and surface wave data may be inadequate either significant p wave anisotropy exists under the plateau or the s wave anisotropy does not possess a uniformly horizontal symmetry axis or strong east west gradients in anisotropy bias our data synthetic comparison

kinematic analysis of a growth fault system in the niger delta from restoration in map view by restoring six stratigraphic markers in map view we have studied the kinematics of a growth fault system involving a major fault its antithetic and a faulted roll over located within the niger delta offshore nigeria restoration yields for each marker the horizontal displacements due to normal faulting and the associated fields of block rotation about vertical axes as expected for a continuous history of growth faulting the amount of extension computed for each stratigraphic marker increases with depth from the fields of finite displacement and block rotation we find that horizontal extension perpendicular to fault traces is associated with a minor amount of bulk left lateral wrenching accommodated by counterclockwise rotation of blocks because the overall deformation differs from a plane strain balancing of cross sections alone would lead to some errors we also computed incremental displacement fields for time intervals between successive stratigraphic markers according to our results during the first stages of growth faulting displacement occurred only on the major faults whereas during later stages larger horizontal displacements were accommodated by numerous small faults probably responsible for the collapse of the roll over

quasi love phases between tonga and hawaii observations simulations and explanations seismograms of some shallow tonga earthquakes observed at hawaii contain sv polarized phases in the love wave time window most prominently on the vertical component given the geometry of the observations 40 45 such phases may be explained either as body waves or as mode converted surface waves detailed synthetic seismogram modeling of representative events reveals several instances where the body wave explanation is inadequate even when plausible uncertainties in the source mechanism are taken into account the observed sv polarized phase can instead be generated through love rayleigh scattering which requires laterally varying seismic anisotropy along the tonga hawaii path trial and error forward modeling with simple structures based on the transversely isotropic mid pacific velocity model pa5 of gaherty et al 1996 obtains velocity structure that yields synthetic seismograms matching the observations this model while non unique suggests first order constraints on the lateral variation in anisotropic properties and associated mantle flow along the tonga hawaii path by examining trade offs in model parameters we conclude that robust features of the model are 1 a transition from radial to mixed radial and azimuthal anisotropy 3 5 from hawaii 2 the nw se alignment of the axis of azimuthal anisotropy 3 higher degree of p anisotropy relative to s anisotropy and 4 the presence of azimuthal anisotropy within upper 200 250 km of the mantle taken together these features imply a disruption of mantle fabric by the processes forming hawaii emperor volcanic system a model with anisotropic gradients in both the lithospheric lid and shallow asthenosphere is the simplest extension of our starting model however an equivalent data fit can be obtained if the azimuthal anisotropy gradients are restricted to line beneath the high velocity lid of model pa5 so that mantle hot spot flow need not penetrate the lithospheric lid

the sensitivity of seismic free oscillations to upper mantle anisotropy 1 zonal symmetry rayleigh love coupling is a diagnostic tool for detecting anisotropic lateral structure in the upper mantle the inference of mantle anisotropy however is complicated by the 21 independent parameters to be constrained in the fourth order elastic tensor we simplify the elastic tensor to possess hexagonal symmetry about an arbitrary axis a reasonable first order model for deformed peridotite the elastic tensor in this case is determined by the orientation of the symmetry axis and five linear coefficients that can be related to the backus crampin equations for the azimuthal dependence of head wave velocity in marine refraction three anisotropic parameters b c and e govern the p wave cos 2 cos 4 and sv wave cos 2 terms respectively where is the angle from the symmetry axis we estimate coupling interaction between pairs of seismic free oscillations using zonally symmetric lateral structure models with angular wavenumber s zonally symmetric models afford computational simplicity and emphasize forward scattering interaction for mode pairs with angular degrees l l coupling interaction tends to peak near s l 1 and s l l for mode pairs with 20 mhz from distinct dispersion branches particularly fundamental spheroidal and toroidal modes the sensitivity to smooth isotropic lateral structure is very weak relative to anisotropic lateral structure sensitivity to the p wave cos 2 coefficient b tends to peak near the crust mantle interface suggesting poor potential for depth resolution sensitivity to c and e for fundamental and first overtone modes however often peaks at 100 to 250 km depth and is often maximal for symmetry axes oriented between the vertical and horizontal the parameter c 0 01 is small and weakly constrained in most estimates from seismic data and mineralogical studies the parameter e 0 01 0 03 in most estimates and shear wave splitting studies argue for significant shear anisotropy in the uppermost mantle therefore it appears that s wave anisotropy is the likely tool for constraining global scale mantle deformation in the deep lithosphere and asthenosphere with coupled mode surface wave anomalies

3 d palinspastic restoration of normal faults in the inner moray firth implications for extensional basin development abstract balanced cross section techniques and the construction of a restored section permit 2 dimensional palinspastic restorations to be made in both compressional and extensional terraines in 3 dimensions an equivalent restoration can be made by assuming conservation of bedding plane area and considering the volume of a stratigraphic interval rather than its cross sectional area extensional basins displaying upper crustal listric normal faulting are particularly amenable to this approach computerised 3 d restorations have been made of the inner moray firth basin offshore scotland this basin is not isostatically compensated and was produced by 7 8 post triassic extension of which 2 5 3 is post jurassic above a detachment surface at 20 25 km depth close to the base of the crust limited lower crustal thinning and lithospheric stretching has affected the eastern part of the basin but this can account for no more than half of the measured upper crustal extension some of this shallow extension is probably coupled by low angle faults or shear zones into major zones of lithospheric stretching such as the north sea grabens where it may help account for discrepancies between estimates of lithospheric thinning and upper crustal extension

flexural unfolding of horizons using paleomagnetic vectors this paper introduces a new restoration method pmag3drest designed for complex folded structures non cylindrical non coaxial it combines paleomagnetic vectors and bedding markers setting up a reference system that allows deformed and undeformed surfaces to be related to one another we assume flexural conditions during the deformation consequently the stratigraphic horizons are considered to be globally developable surfaces with total area preservation except in specific deformation areas using paleomagnetism in the proposed restoration process pmag3drest helps to locate these areas with greater accuracy it is similar to other approaches based on triangulations but it forces the available paleomagnetic data to converge with the paleomagnetic reference vector during the restoration process our experiments use computer and analog models in which the deformed and undeformed surfaces are perfectly known this enables us to apply the restoration method to the deformed surface and compare the parameters of the restored surface with those of the initial undeformed surface to quantify the quality of the method paleomagnetic data anchor the surface leading to more accurate results

mesozoic regional tectonics and south viking graben formation evidence for localized thin skinned detachments during rift development and inversion abstract a regional thin skinned model of south viking graben development is presented in which zechstein marginal evaporites and interpreted salt have acted as a key de collement horizon along which mechanical decoupling of post salt triassic and younger strata from pre salt basement has occurred the western margin of the south viking graben defines an asymmetrical late jurassic half graben controlled by episodic extension along a nne ssw trending eastward dipping fault system an initial minor phase of rifting in the triassic is suggested by the slight westward thickening and associated divergence of interpreted triassic sequences at depth the scarcity absence of upper triassic and lower jurassic sequences is believed to result from a subsequent phase of uplift which affected the region in the mid cimmerian attributed to the development of a thermal dome at the future site of a jurassic rift triple junction to the southwest the onset of large scale extension from the late callovian onwards marked the major phase of half graben formation and created a regional hanging wall tilt which locally caused gravity gliding of post salt section to the wnw with resultant low angle extensional faulting upslope and salt cored buckling downslope the late jurassic half graben was subsequently tightened by a phase of thin skinned inversion in the latest jurassic early cretaceous associated with back steepening of the western margin fault system with resulting reactivation of the extensional detachment system the effects of this inversion have been noted in many parts of the northern north sea within the south viking graben shortening estimates vary between 14 and 18 and are expressed on seismic data by localized hanging wall folds and the back steepening of faults along the western margin fault complex of the graben together with out of graben thrusting up the hanging wall dip slope variation in both the extension and inversion mechanisms appears to be controlled by interpreted nw se transfer systems which compartmentalize the graben into three subgraben within which differential zechstein basin development occurred

seismic determination of elastic anisotropy and mantle flow when deformed many rocks develop anisotropic elastic properties on many seismic records a long period 100 to 250 seconds quasi love wave with elliptical polarization arrives slightly after the love wave but before the rayleigh wave mantle anisotropy is sufficient to explain these observations qualitatively as long as the fast axis of symmetry is approximately horizontal quasi love observations for several propagation paths near pacific ocean subduction zones are consistent with either flow variations in the mantle within or beneath subducting plates or variations in the direction of fossil spreading in older parts of the pacific plate

hunting for azimuthal anisotropy beneath the pacific ocean region lateral variations in azimuthal anisotropy cause significant waveform anomalies in long period surface waves 8 mhz suggesting lateral variations with wavelength twice the spacing of fracture zones in the north central pacific

three dimensional modeling of plume lithosphere interaction in order to understand better the dynamics of hot spots such as hawaii we present a three dimensional numerical model for the interaction of a thermal plume with a moving lithosphere the model domain is a rectangular box filled with fluid whose viscosity depends upon temperature and pressure the lithosphere is represented by a layer of cold highly viscous fluid moving with an imposed horizontal velocity u in the x direction and a thermal plume is generated by a circular temperature anomaly on the bottom of the box the steady flow is determined numerically using a hybrid spectral finite difference technique the flow is characterized by a stagnation streamline of width y x1 5 that represents the edge of the spreading plume material we illustrate the detailed behavior of the model using the example of the hawaiian plume our best fitting hawaiian model is obtained by adjusting the plume buoyancy flux b until the predicted topography anomaly matches the observed hawaiian swell topography we find b 4100 kg s 1 which implies a plume radius of 90 km for an assumed plume mantle temperature contrast of 300 c the predicted topography is supported primarily by density anomalies beneath the lithosphere and cannot be explained by lithospheric erosion we therefore conclude that the classical lithospheric reheating model is unable to account for hotspot swells the horizontal flux of buoyancy associated with the swell exceeds b by up to 80 suggesting that current estimates of b for mantle plumes are too high empirically derived scaling laws for the width of the stagnation streamline and for the topography anomaly exhibit power law dependencies on b and u that agree well with those predicted by the refracted plume model of olson 1990 the principal weakness of the model is that the predicted geoid topography ratio of 0 010 for the hawaiian swell is about twice the observed value of 0 004 0 006