distributed deformation and block rotation in three dimensions the focus of this paper is to understand distributed deformation in particular the relationship between fault slip and rotation of faults and blocks in a three dimensional stress field regions of distributed deformation such as southern california are organized in complex arrays of contemporaneously active block faulted domains we believe that the present day orientation of faults in many domains is due to the contemporaneous slip and rotation of the faults and of the blocks they bound traditional friction models cannot explain active unfavorably oriented faults and do not consider how faults become unfavorably oriented to solve this problem we propose a three dimensional block rotation model that tracks the orientation of blocks and their bounding faults during rotation mechanically we consider coulomb criteria for rock fracture as an upper bound and slippage on a frictional surface as a lower bound the key parameter in our model is the value of 2 3 1 3 principal stress directions are assumed irrotational through time this model predicts up to 75 of vertical axis rotation along a single set of faults during rotation fault slip may change sometimes dramatically giving rise to mixed vertical as well as horizontal axis of rotation of blocks and faults for very unfavorably oriented faults the model predicts rotations about a vertical axis in both the normal and reverse stress regimes and about a horizontal axis in the strike slip stress regime therefore paleomagnetically inferred rotations may not always be directly related back to a specific stress regime combining frictional constraints of the block rotation model with paleomagnetic structural and geological data we show how only one set of faults preexisting and rotating in an irrotational strike slip stress field can account for the three major phases of deformation observed in the western transverse range domain southern california preexisting north northeast faults were reactivated as normal faults rotated and became strike slip and subsequent rotations of faults resulted in their present east west high angle reverse orientation this example demonstrates that it is not necessary to invoke complex regional and local changes in the stress regime or erratic changes in plate motion to account for alternate periods of compression and extension

a simple kinematic model for crustal deformation along two and three dimensional listric normal faults derived from scaled laboratory experiments abstract we have derived a simple kinematic model of the deformation that results from extension accommodated by movement of a crustal block along two and three dimensional listric fault surfaces the model accurately reproduces deformation observed in a series of scaled analogue models the kinematic model is based on the simple assumption that lines within the hangingwall that are normal to the fault surface before deformation remain so following deformation an additional constraint built into the model is that of incompressibility deformation in the hangingwall block as observed in the laboratory experiments and predicted by the kinematic model is characterized by 1 a key stone structure or crestal collapse graben at some finite distance from the fault tip and 2 pure solid body rotation of the hangingwall head area near the tip of the fault in three dimensions the central region of the model undergoes extension in a direction normal to the direction of imposed displacement in such a way that the direction of dip of the upper surface of the hangingwall is aligned with the direction of extension this result provides quantitative support for the use of dip analysis to infer tectonic transport direction we also show how the distribution of extension within the hangingwall is affected when the constraint of constant displacement along the fault is relaxed

the importance of small scale faulting in regional extension a recurring observation in many studies of extensional basins has been that the amount of extension visible on normal faults for example on seismic reflection profiles is significantly less than the amount of extension indicated by crustal thickness and thermal subsidence1 5 one mechanism suggested to account for this discrepancy is small scale faulting with offsets too small to be resolved seismically6 7 but earthquake studies8 10 indicate that small faults are responsible for only a small fraction of the total seismic moment in an active area scholz and cowie11 have recently attempted to extend this approach to the total strain at the end of a finite deformation interval by combining scaling laws describing the distributions of fault lengths and displacements here we present fault displacement data that directly conflict with scholz and cowie s conclusions and imply that up to 40 of the extension may be missed by summing fault offsets on basin profiles the fault population at the end of a long deformation interval may differ substantially from that responsible for the earthquake population at any one time

oblique slip deformation in extensional terrains a case study of the lakes tanganyika and malawi rift zones the east african rift system ear is the archetypal continental rift and a widely proposed analogue for the early stages of evolution of passive continental margins the three dimensional structure of parts of the ear has been recently elucidated by a multifold seismic mfs survey of lakes tanganyika and malawi project probe analysis of fault geometries displayed on the probe mfs data coupled with the more extensive 28 khz echosounder data has improved understanding of the geometry and kinematics of the linked fault systems that underlie the lakes in particular it has been recognized that profiles across i e at high angles to the rift elongation commonly display fault geometries that are not readily retrodeformable there must therefore be significant displacement out of the plane of what would conventionally be regarded as dip lines that is perpendicular to rift elongation and parallel to the tectonic transport or extension direction careful determination of fault plane dip and the dip of synrift reflectors in the hanging wall demonstrates that the dip directions of the shallowest faults and the steepest hanging wall sediment dips are oriented either nw or se this defines the direction of maximum fault block rotation and therefore the direction of extension or tectonic transport as nw se oblique to the trend of the regional rift axis and to the apparent strike of many of the major border faults in the survey area the border faults and many other faults imaged on the probe mfs data must therefore have significant components of strike slip motion and the tanganyika and malawi rift zones have undergone extension oblique to and not perpendicular to their axes near dip slip normal faults steeply dipping oblique slip faults and subvertical strike slip or transfer faults have all been recognized in a complex linked fault system that accomplishes the extension the overall orientation of the rift lakes and their internal segmentation are influenced by major preexisting subvertical fault zones within the basement complex accommodation zones act principally as transfer zones that allow switches in gross polarity of the border fault system the detailed geometries of the accommodation zones result from the specific relations between juxtaposed half graben and the strike and internal geometry of the influencing basement structure the variations in fault geometry subsidence water depth and basin or rift morphology can be better explained by an oblique slip extensional model influenced by basement structures than by a simple orthogonal extensional model

the relationship between the geometry of normal faults and that of the sedimentary layers in their hanging walls abstract we derive an analytical expression that relates the shape of a fault in cross section to the shape of the bedding horizons in its hanging wall block the expression assumes that the hanging wall deforms by simple shear and that the footwall remains undeformed throughout although this paper concentrates on normal faults the expression is equally valid and applicable to thrust faults the direction of simple shear in the hanging wall block is arbitrary and has a dramatic effect on the predicted fault or bedding geometry there is no reason to believe that the simple shear occurs on vertical planes as is commonly assumed in graphical approaches to this problem and ignoring the presence of inclined simple shear is likely to lead to considerable underestimates of the amount of extension across normal faults and in the amount of shortening across thrusts similar though more complicated expressions can be obtained when compaction within the hanging wall block is taken into account for a planar normal fault such compaction may result in the development of a hanging wall syncline

development of pull apart basins a comparative study of well mapped active and ancient pull apart basins suggests a qualitative model for their continuous development pull aparts evolve from incipient to extremely developed basins through a sequence of closely related states new and compiled map data from several areas including the northern caribbean and turkey suggests the following stages in pull apart development 1 in rigid intracontinental strike slip plate boundary zones larger pull aparts nucleate at releasing fault bends along segments of the principal displacement strike slip fault zone which are oblique to the theoretical interplate slip lines 2 initial opening across releasing fault bends produces spindle shaped basins defined and often bisected by oblique slip faults connecting the discontinuous ends of the strike slip faults 3 increased strike slip offset produces basin shapes which we colloquially call lazy s shape for basins between sinistral faults and lazy z shape for basins between dextral faults 4

analysis of scale exaggeration on seismic profiles 1 seismic profiles have become an important medium for illustrating interpreted structural geometry and style in areas of steep dip and complex geologic structure however these profiles often yield distorted structural views due to vertical or horizontal exaggeration geological misinterpretation may result if the effects of this exaggeration are not recognized seismic profiles from the central rocky mountain basins illustrate the geometrical distortion produced by significant scale exaggeration to assist in analysis of these profiles three nomograms have been constructed the nomograms show graphically the relationships between exaggeration factors exaggerated dips unexaggerated dips and correction factors which are derived from the ratio of exaggerated orthogonal thicknesses to true orthogonal thicknesses with knowledge of the horizontal scale the nomograms also can be used to estimate average velocities on exaggerated profiles in areas of steep dip and uniform stratigraphic thicknesses

oblique extensional tectonics in the malawi rift africa the malawi rift is the southern segment of the western branch of the east african rift system there has been little agreement as to whether this rift is opening perpendicularly or obliquely to its north south axis and little agreement on a mechanism for the formation of the asymmetric basins that make up the rift our analysis combines landsat image interpretation and field measurement of the latest slip direction on faults to produce a kinematic model of rift evolution the fault slip data are consistently compatible with a late cenozoic northwest southeast directed divergence between the nubian and somalian blocks plates across the rift the northwest striking livingstone fault at the northern limit of the malawi rift and the northwest striking zambezi fault zone to the south serve as dextral intracontinental transform zones between left stepping segments of the western branch of the east african rift system within the rift second order northwest striking transfer faults separate adjacent asymmetric basins the transform and transfer faults form a pattern that is similar to overlapping right stepping strike slip faults with a releasing geometry fault surfaces with two sets of striations indicate a progression from predominantly strike slip toward oblique normal faulting we hypothesize that during initial rift formation most northwest striking faults were dextral and that fault interaction between these structures resulted in curved stress trajectories and a pull apart component arcuate north to northeast striking border faults and subsiding basins then formed between these northwest striking faults in response to the right stepping dextral shear the maximum distance over which fault interaction is significant may control basin dimensions as opening of the rift proceeds slip partitioning and gravity failure result in increasing normal slip perpendicular to major escarpments and decreasing strike slip parallel to them

geometric models of listric normal faults and rollover folds existing geometric models allow master fault shapes to be constructed given the shape and heave or displacement of a deformed marker horizon in the hanging wall these models assist in projecting normal faults to depth where the fault geometry is poorly constrained by available seismic data currently it is unclear which model best predicts the actual relation between rollover and fault geometries to address this deficiency the relative accuracies of the constant heave constant displacement constant bed length slip line and inclined shear constructions are evaluated using clay model analogs and seismic examples each of the geometric models predicts a different fault shape and depth to detachment for the same rollover shape because different hanging wall deformat on mechanisms are assumed a construction is developed for determining the hanging wall geometry from a known fault geometry this construction is based on the inclined shear model and geometric constraints imposed by material displacement paths viewed from different reference frames fixed to the hanging wall and footwall blocks in clay models the inclined shear antithetic shear greek alpha 20 degrees and slip line constructions produce the best agreement between actual and modeled fault and marker bed shapes in rollovers for subsurface examples the inclined shear model antithetic shear greek alpha 20 40 degrees and the constant displacement model predict fault trajectories that are the most similar to the positions and shapes of the master fault segments interpreted fr m offshore norway and gulf of mexico seismic lines the shear angle required in the inclined shear model can often be estimated from the orientation of minor faults in the hanging wall the shear angle may also be determined through iterative modeling in which the shear angle is systematically varied and the resultant model fault shape is compared to the shape of the shallow segment of the master fault interpreted from the seismic record

use of seasat synthetic aperture radar and landsat multispectral scanner subsystem data for alaskan glaciology studies seasat synthetic aperture radar sar and landsat multispectral scanner subsystem mss data of three areas in alaska were studied in order to determine what hydrological information could be extracted using digital data from both sensors the first area is located in northern alaska and contains numerous thaw lakes the other areas contain valley glaciers in the alaska range and a piedmont glacier malaspina in south central and southern alaska respectively sar and mss subscenes of the thaw lakes and subscenes of the malaspina glacier were digitally registered registration of the data in the alaska range study area was not feasible due to a lack of sufficient tie points resulting from shadowing and layover effects in the sar data results of the data obtained from the thaw lake study area showed that the location and identification of some older remnant lake basins were more easily determined in the registered data using an mss sar overlay than in either sar or mss data alone separately both the sar and the mss data were useful for determination of surging glaciers based on their distinctive medial moraines and landsat data were useful for locating the glacier firn zone in the analysis of the malaspina glacier scenes the sar data were useful for locating heavily crevassed ice beneath glacial debris and landsat provided information concerning the extent of the debris overlying the glacier together the data set gave a good representation of the extent of the glacier and crevasse patterns

dip analysis as a tool for estimating regional kinematics in extensional terranes abstract in basin analyses that rely almost solely on seismic reflection data to configure the underlying structure it has become common practice to use extensional fault geometries to infer kinematic histories this procedure relies on the existence of fault geometries predicted by ideal orthogonal extension and assumes the structure is well constrained in areas where data are sparse or of equivocal quality this often leads to circular analysis that is ideal orthogonal extension is assumed to have been operative then under constrained fault geometries are mapped according to model predictions fault geometries so derived are subsequently used as evidence that orthogonal extension was operative and that the direction of extension is determinable we develop an alternative tool for inferring kinematics which is independent of fault geometries the method relies on the empirical evidence that the dip of the hangingwall s is systematic and predictable in extensional systems even when fault geometries are non ideal although not without significant limitations dip analysis can provide additional constraints for structural and kinematic interpretations especially where seismic reflection data are the main source of information and dip domains define discrete crustal blocks

analysis of tilting near normal faults using calculus of variations implications for upper crustal stress and rheology abstract an initially horizontal surface in the surroundings to a normal fault will after extension tilt towards the fault if in the hanging wall or away from it if in the footwall coseismic deformation of these surroundings can be validly modelled as flexure cumulative deformation on geological time scales has been regarded as flexure also but this has led to the apparent paradox that many observed structures require the effective elastic thickness of the brittle upper crust to be much smaller than its seismogenic thickness this article presents a possible alternative that cumulative deformation of the upper crust near some active normal faults may be regarded instead as partitioned into separation of the blocks that comprise their surroundings through the horizontal component of dip slip on the fault and distributed vertical simple shear in their surroundings which causes them to tilt and takes up the vertical slip on the fault a generalized profile of tilting near a normal fault which approximates a parabola can be derived following two assumptions first the brittle layer retains an elastic term in its rheology on geological time scales such that it resists arbitrary length changes second the brittle layer minimizes its overall vertical deflection thus minimizing the buoyancy force acting on it maximum stress and total strain energy associated with observed profiles of tilting are typically smaller for distributed vertical simple shear favouring this mechanism over flexure

half graben structures balanced models of extensional fault bend folds one common structural style in extensional regimes is a half graben bounded on one side by a master normal fault and on the other side by a domain of beds dipping toward the master fault this geometry is modeled as being caused by a bend in the master fault the hanging wall beds dipping toward the master fault are bounded by axial surfaces formed as the hanging wall moves past the bend resulting in an extensional fault bend fold the footwall beds remain undeformed and unrotated the major assumptions used in the derivation are that the geometry is area balanced and that the axial surfaces in the hanging wall have dips equal and opposite to the dip of the master fault above the bend important consequences of the model include a relationship between master fault dip above and below a bend and the amount of hanging wall dip the horizontal width of the dipping beds in the hanging wall is twice the heave on the master fault above the bend the asymmetry of the axial surfaces in the hanging wall requires that the rotated beds be strained hanging wall beds dipping toward the master fault are predicted for a fault bend wherein the dip decreases downward hanging wall beds dipping away from the master fault are predicted for a bend wherein the dip increases downward the model fits measurements taken from a published ramp and flat clay model by e cloos and is used to develop a balanced and restorable cross section of the schell creek fault a basin and range structure in nevada

miocene tectonic evolution of the basins and fault systems se korea dextral simple shear during the east sea sea of japan opening crustal deformation of se korea caused by back arc opening of the east sea sea of japan commenced locally in the late oligocene intense deformation occurred during the early miocene accompanying extension of parallelogram shaped pull apart basins between nnw striking principal displacement zones clockwise rotation and northwestward tilting of blocks and southwestward propagating rifting at about 17 ma the crustal deformation suddenly expanded westward and northward owing to activation of the yeonil tectonic line resulting in a dramatic change of depositional environment and the subsidence of wedge shaped pull apart basins the yeonil tectonic line and western border faults of the pohang basin are the westernmost limit of the miocene crustal deformation all the features of crustal deformation in se korea support the pull apart model for the east sea opening however they indicate that the nnw striking faults such as the yeonil tectonic line acted as the principal displacement zones rather than the nne striking yangsan fault under a consistent dextral simple shear at about 16 ma the collision of the philippine sea plate with the japanese islands caused a tectonic inversion this inversion resulted in a compositional change of basaltic magma at about 15 ma and crustal uplift in se korea which caused the cessation of sedimentation at about 10 ma

detachment faulting and the evolution of passive continental margins major detachment faults play a key role in the lithospheric extension process in the basin and range province and may also be important in other continental extension terranes such detachment faulting leads to an inherent asymmetry of extensional structure and of uplift subsidence patterns detachment models developed for the formation of metamorphic core complexes can also be applied to the formation of passive continental margins we therefore suggest the existence of upper plate and lower plate passive margins these give rise to a complementary asymmetry of opposing margins after continental breakup transfer faults offset marginal features and allow margins to switch from upper plate to lower plate characteristics along strike

the geometry of listric normal faults and deformation in their hangingwalls abstract in cross sections containing listric extensional faults area balancing techniques for depth to decollement are usually based on either bed length conservation or displacement conservation listric fault geometry may be constructed from a hangingwall roll over profile using the chevron construction this construction based on conservation of heave necessitates a reduction in fault displacement with decreasing fault dip a modification of this construction utilizing conservation of fault displacement predicts a listric fault that detaches at a shallower depth a new construction based on slip lines uses fault perpendicular displacement segments to generate listric fault shape fault propagation strain may be responsible for anomalous hangingwall geometries and these can be predicted by forward modelling using either a modified chevron construction or a slip line construction

dip domain method applied to the mesozoic connecticut valley rift basins this paper presents a new approach to structural analysis of u s east coast mesozoic basins a contoured compilation of numerical values of dip data for the connecticut valley rift basins reveals distinct domains related to their broader tectonic development additional more standard geologic constraints are then used to interpret the dip domain patterns most of the tilt deformation involved and hence postdated early jurassic basaltic flow units and overlying jurassic thick alluvial deposits normal drag characterizes the attitude of mesozoic strata along the western border fault of the main hartford basin whereas reverse drag is common along its larger listric eastern border fault strata within the basin mostly along its eastern margin include several subgrabens and or strongly tilted zones associated with early subbasins marked by local changes in strike of the early border fault the meriden cross graben may be a similar structure that extended much farther southwestward across the basin within the hartford basin linear domains of steeper dips are interpreted as surface expressions of the edges of a 5 to 15 km wide late stage central graben that trends n15 e diagonally across the basin possibly a reflection of very late strike slip stress systems

application of grey theory based model to prediction of land subsidence due to engineering environment in shanghai land subsidence is a common geological hazard the long term accumulation of land subsidence in shanghai has caused economic loss to the city since the 1990s the engineering structures have become a new cause of land subsidence many factors affect the process of land subsidence although such a process cannot be explicitly expressed by a mathematical formula it is not a black box whose internal structure parameters and characteristics are unknown therefore the grey theory can be applied to the prediction of land subsidence and provides useful information for the control of land subsidence in this paper a grey model gm gm 1 1 with unequal time intervals was used to predict the subsidence of a high rise building in the lujiazui area of shanghai and the results were compared with the monitored data the prediction of subsidence was also corroborated by laboratory tests and the results were compared with measured data and the predicted data by the adaptive neuro fuzzy inference system anfis it is found that the gm 1 1 with unequal time intervals is accurate and feasible for the prediction of land subsidence

finite extension and low angle normal faulting andersonian theory for infinitesimal strains predicts that normal faults will form at high angles to the surface in extensional terranes in contrast low angle normal faults are sometimes observed on which tens of kilometers of slip has occurred and moderate angle faults with slip of 5 to 15 km are common a simple extension of the theory to account for the stresses required to drive finite deformation shows that low angles are preferred for large extension on individual faults the formation of low angle faults may require inhomogeneities in stress or material properties but once slip begins on a low angle fault it is likely to continue whereas slip on high angle faults is likely to end after modest slip to be replaced by the formation of new high angle faults

nature of the s reflector beneath the galicia banks rifted margin preliminary results from prestack depth migration beneath the tilted fault blocks of the galicia rifted margin a bright reflection termed s has been interpreted as the master detachment fault controlling the extension of the margin however on time migrated sections s appears to be locally offset by the steep faults of the upper section we investigate the true geometry of s and its relation to the overlying faults through iterative prestack depth migration we conclude that it is not significantly offset by the faults which instead appear to stop abruptly at s thus we interpret s as the master detachment and consider its role during extension

tectonic systems tract and depositional architecture of the western border of the triassic iberian trough central spain abstract during the permian and triassic a sedimentary wedge developed overlying a listric normal fault on the western border of the iberian trough central spain an area was selected for study that provides optimal conditions for a detailed analysis to be made of relationships between geometric strata arrangements tectonic control and sedimentary responses the excellent quality of the outcrops allows the observed patterns of strata to be related to fault growth and developmental of the basin the recognition and mapping of local discontinuities throughout the study area were possible packages of similar strata with different angularity can be discerned between the two main discontinuities geometrical relationships can be established for depositional unit boundaries the architectural style and sediment dispersal patterns interpreted as the results of interactions between sedimentation and tectonics are integrated into a three dimensional tectono sedimentary facies model to explain the basin s infilling is interpreted to be tectonic the rift related three dimensionally linked depositional systems recognized might be defined as tectonic systems tract prosser s 1993 rift related linked depositional systems and their seismic expression in williams g d dobb a eds tectonics and seismic sequence stratigraphy geol soc london spec publ 71 35 66 five such tracts are recognized and related to specific phases of tectonic development

relations between normal fault geometry tilting and vertical motions in extensional terrains an example from the southern gulf of suez abstract earthquakes and data from subsurface oil exploration suggest that large active normal faults in the southern gulf of suez are approximately planar with dips of 30 40 from the surface to around 10 km depth these faults and the blocks they bound appear to rotate about a horizontal axis as they move causing tilting this tilting is seen both in young vertical movements of the coastline such as raised beaches and marshlands and in the distribution of middle miocene marine rocks which are uplifted to elevations of 400 500 m in footwalls of faults and found at depths of around 3500 m in the adjacent grabens the absolute amplitude of the observed vertical motions can be approximately modelled by planar rotating normal faults that impose a saw tooth topography on a regional subsidence caused by crustal and lithospheric thinning the observations required for this simple model are the present day fault dip the amount of tilting and the width of the rotating blocks the virtues of the model are its simplicity and its compatibility with our knowledge of how large active normal faults move elsewhere on the continents

normal vs strike slip faulting during rift development in east africa the malawi rift kinematic analysis of neogene and quaternary faults demonstrates that the direction of extension in the malawi rift rotated from east northeast to southeast rift development commenced with the formation of half grabens bounded by northwest north and northeast striking normal faults owing to slightly oblique rifting the northwest striking faults in the northernmost rift segment show a small dextral oblique slip component whereas north and northeast oriented faults in the central part of the rift display a sinistral oblique slip component this first event resulted in block faulting and basin subsidence which is largely responsible for the present day basin morphology of lake malawi a major change in fault kinematics occurred because of rotation of the extension direction and permutation of the principal compressive and intermediate axes the structural pattern inherited from the first rifting phase was no longer suitably oriented to accommodate extensional deformation and strike slip faulting assumed a major role the strike slip regime amplified uplift of basement ridges within the rift in regions of local transpression but it also created alluvial basins because of local transtension this new kinematic style is compatible with the recent seismicity older faults that show mainly the first deformational increment are restricted to the outermost parts of the rift toward the center the faults depict an increase in strike slip components of movement suggesting deformation propagation toward the rift center which results in a narrowing of the active rift environments with time

extension in high grade terranes of the southern omineca belt british columbia evidence from paleomagnetism paleomagnetic observations are used to construct a map of structural tilts in metamorphic and plutonic rocks of the southern omineca belt in southeastern british columbia during eocene extension midcrustal rocks were exhumed in footwalls of low to moderate angle normal faults that dip east and west in the eastern and western parts of the study area respectively tilts averaging 30 to 40 are consistent over large areas and generally antithetic to the major faults in the central part of the study area however the eastern half of the coryell pluton is untilted and its western half in the hanging wall of the east dipping kettle river fault is tilted down to the east in the opposite sense to that expected north of the pluton these eastward tilted rocks are juxtaposed against westward tilted rocks to explain the anomalous tilts a major west dipping eocene normal fault arrow lake fault is inferred and a revised kinematic history for the area proposed observations of magnetic polarity 86 normal laboratory unblocking temperatures and isotopic age data suggest that magnetizations in the west were acquired during chron 23n and in the east in chron 23n and or chron 24n unless extension postdated the acquisition of magnetization tilts would not be observed thus it is argued that extension in the west occurred after 50 6 ma and in the east between 51 6 possibly 53 3 and 50 6 ma these time intervals do not correspond to any known global plate reorganization event indicating that the last phase of eocene extension in the southern omineca belt was governed by regional rather than global processes