an experimental study of the relationship between joint spacing and layer thickness abstract two methods for measuring joint spacing are described and compared the area method is a constant for a given outcrop area and is not affected by joint distribution within that area in contrast the line method depends on the location of the linear traverse two kinds of joint sets are distinguished on bedding surfaces 1 a poorly developed set represents the early stages of development when typical joint lengths are less than typical spacing 2 a well developed set represents later stages when lengths are much greater than spacing the area method is applicable to both poorly and well developed sets whereas the line method produces inconsistent results for poorly developed joint sets surface textures on many joints indicate point fracture origins and propagation parallel to bedding whereas most numerical model studies of spacing assume linear origins and propagation perpendicular to bedding the laboratory experiments described in this paper do not suffer from these restrictions an important concept confirmed during these experiments is fracture saturation when the applied strain reaches a certain value fracture spacing stops evolving and remains nearly constant these fracture sets are well developed spacing at saturation is a function of layer thickness but is independent of strain whereas spacing before saturation varies strongly with applied strain thus plotting spacing vs thickness and comparing the slopes of lines fit to such data for poorly developed joint sets in different layers is unlikely to be a diagnostic test for differences in material properties on the other hand spacing may be a sensitive indicator of strain for layers with poorly developed joint sets assessing fracture saturation is a lirst order consideration when gathering spacing data

probabilistic modeling of faults below the limit of seismic resolution in pelican field north sea offshore united kingdom faults which can compartmentalize a reservoir and which are too small to be seen on seismic can be predicted using a self similar or fractal model of faulting at various scales a computerized method has been developed for statistical analysis of a fault pattern interpreted from three dimensional 3 d seismic in order to fractally derive the distributions of fault size frequency and spatial variations and to verify their invariance within the seismic resolution range this analysis can be used for quality control of seismic interpretation and as input for extrapolation toward smaller scales using probabilistic techniques the application of this program to pelican field united kingdom north sea validated the interpretation of the complex fault pattern of that field but suggested that only limited extrapolations could be confidently made probabilistic maps showing distribution of faults down to 3 m 10 ft of throw and not resolved by 3 d seismic were made these maps subsequently were used as a qualitative aid in full field reservoir simulations to model differently zones of potential dense faulting from zones of reduced faulting this was done because nearby field behavior had shown that faulting is a significant factor in reservoir behavior and ultimately field deliverability field development planning therefore could be optimized

variability in fault size scaling due to rock strength heterogeneity a finite element investigation abstract practical application of fault size scaling relationships usually involves extrapolation of a limited data set over a scale range beyond that observed or into adjacent unstudied areas here we investigate the validity of such extrapolations by considering the variability in the size frequency distributions of fault populations that develop under identical tectonic conditions using a numerical model to generate conjugate normal fault populations in cross section the deforming material is modelled using a strain softening von mises rheology with gaussian heterogeneity in yield strength distributed randomly throughout the mesh we present eight deformation experiments that differ only in the random spatial pattern of yield strengths we observe power law size frequency scaling i e n ax c where n is the cumulative number of faults and x is a measure of fault size but with a range of values of c the ensemble average value of c decreases with increasing percentage extension however for individual model runs the dependence of c on total strain shows significant variability that we can relate to small but important differences in fault growth and strain localisation at any particular strain the range of values of c is 10 times greater than the error estimate derived from least squares regression of the cumulative frequency data our results suggest therefore that large uncertainties should be associated with extrapolating fault population data from one scale or region to another even if the lithology and tectonic history are similar

fault growth model and the universal fault length distribution we propose and solve a simple fault growth model describing the powerlaw dependence of the fault length distribution observed both in nature and in laboratory models of the lithosphere starting from an arbitrary initial fault length distribution and assuming that the rate of growth of a fault is proportional to a power of its size we show that the fault length distribution evolves towards a universal powerlaw curve comparison between this theory and experimental results is encouraging

experimental evidence for different strain regimes of crack populations in a clay model we report results from clay extension experiments used as a model for the evolution of fault populations due to stress interactions at yielding cracks begin to appear and the brittle strain due to them quickly reaches a rate matching the applied stretching rate the crack density number of cracks per unit area initially increases apace then reaches a maximum at a critical strain decreasing thereafter at low strains where the crack population is dilute a power law length distribution is observed which at high strain gradually transitions to an exponential this agrees with fault populations data observed in low and high strain settings these results indicate that fault populations ranging from power law to exponential size frequency distributions reflect the population evolution with increased strain

basement structure of hokkaido komagatake volcano japan as revealed by artificial seismic survey abstract we investigate the basement structure of the hokkaido komagatake volcano japan by an artificial seismic survey by inverting first arrival time data a three dimensional p wave velocity model down to 3 km b s l is obtained the resultant velocity model reasonably reflects regional geological features and is consistent with bouguer anomalies around the komagatake volcano the velocity basement deepens to nnw on the whole reflecting the deepening of the geological basement toward that direction higher velocities are observed in oshima and kameda mountains where neogene volcanic and sedimentary rocks are present on the contrary lower velocities are observed in lowlands surrounding the volcano where komagatake deposits and quaternary sediments crop out at the volcano a prominent high velocity zone was detected from the surface down to a depth of 1 5 km b s l above the base probably a contrast between the core part with higher proportion of massive lavas and intrusions and flank areas dominated by loose pyroclastic deposits caused the prominent high velocity below the base it is thought that solidified intrusive bodies largely contribute to making the high velocity further a high velocity elongates from kameda mountains to beneath the summit this is due to a shallower of the volcano substratum

properties of fault populations in the gullfaks field northern north sea abstract there are many published examples of the size frequency distributions of natural fault populations that have been interpreted as showing scale invariant power law scaling in this paper we present the statistics of the fault throw population in the gullfaks field and show that the distribution can not be described by a single power law instead the throw population when plotted in log log space displays two distinct slopes with different exponents at scales well above the limit of seismic resolution at scales ranging from 10 to 90 m we obtained a slope of approximately 0 3 while at scales ranging from 90 to 165 m the slope is approximately 1 0 a systematic variation in fault orientation with fault size does not appear to be the cause of this break in slope and a simple explanation has yet to be found however the documentation of such a change in scaling above seismic resolution implies that similar breaks may occur equally well below the resolution limit this suggests that extrapolation of the straight line segments of population curves to sub seismic scales may give incorrect estimates of small scale faults and fractures separation of the gullfaks fault data set into subareas and sub populations based on geometric criteria revealed several sub populations of faults that do exhibit simpler power law relationships however the wide range of values found for the scaling exponent varying from 0 73 to 2 05 suggests that the choice of such subdivisions is an important step in the analysis procedure we argue here that a more thorough understanding of fault populations can be achieved by documenting this sub population variability as well as by characterizing the combined data set

finite element modelling of the competition between shear bands in the early stages of thrusting strain localization analysis and constitutive law influence finite element simulation of a sandbox model of thrusting is performed using large strain analysis and two different non associated elastoplastic constitutive laws namely druckerprager and van eekelen criteria the analysis of strain localization using the rice bifurcation criterion coupled with a kinematic indicator shows that in the early stages of imbricated thrusting the development of major shear bands can be influenced by some competition with second order bands the influence of the vertical horizontal stress ratio is checked as well as the influence of lode angle in the constitutive law significant differences are found between a classical plasticity criterion drucker prager and a more realistic one van eekelen regarding the resistance of the model and the stress paths these differences may result in erroneous fault type prediction sandbox experiments have been used extensively for many years to assist structural interpretation and validation of tectonic models main interests of this method corne from the very large range of initial geometries which can be investigated and from the large amount of strain which can be applied physical parameters obtained are mainly displacement fields at different stages especially since non destructive methods are used e g x ray tomography colletta et al 1991 the finite element method is also an attractive method for geological modelling as it enables computation in several parameters examples of which are displacement strain and stress fields and also more recently strain localization analysis moreover it allows the explicit choice of mechanical characteristics constitutive laws and boundary conditions abilities of the finite element method for the investigation of strain localisation along shear bands and particularly thrusting mechanism have already been shown see for example miikel walters 1993 the present paper aims to show the relative influence of the constitutive law in the results and also to analyse information obtained from localization analysis in the first part some theoretical considerations are presented basics of the large strain formulation used and principle of the finite element method are given the choice of a representative constitutive law for sand between mohr coulomb druckerprager and van eekelen models is discussed a short literature overview of the strain localization analysis performed in finite element method is presented eventually the localisation analysis used in the present paper is detailed the second part is mainly concerned with the simulation of a sandbox model of thrusting carried out with the lagamine finite element code early stages of thrust development are analysed in a first simulation in the light of the rice bifurcation criterion and of a kinematic indicator of localization a non associated drucker prager yield criterion is used a remeshing procedure is also performed in this first simulation to increase the applied loading value the influence of the vertical horizontal stress ratio is checked in a second simulation the last simulation investigates the influence of the third stress invariant in the plasticity surface definition using a more sophisticated yield criterion namely the van eekelen in the last part finite element simulation results obtained are compared with some experiments performed on sandbox models

prediction of faulting from the theories of elasticity and plasticity what are the limits elasticity rigid plasticity and elasto plasticity are the simplest constitutive models used to describe the initiation and evolution of faulting however in practice the limits of their application are not always clear in this paper we test the behaviour of these different models using as examples tectonic problems of indentation of a die compression with basal shear bending of a plate and normal faulting around a dike by comparing the results of these tests we formulate some guidelines that may be useful for the selection of an appropriate constitutive model of faulting the theory of elasticity reasonably predicts the initiation of the fault pattern but gives erroneous results for large strains the theory of rigid plasticity is more appropriate for large deformations where the geometry of faults can be found by the method of characteristics this method works well for zones of failure that are not severely constrained by elastic material outside e g when faults are connected to the free surface a viscous substratum or a zone of weakness non associated elasto plasticity is the most complete theory among those considered in this paper it describes the evolution of faults from the initiation of localized deformations to the formation of a complicated fault network

normal faulting in the upper continental crust observations from regions of active extension abstract observations of present day normal faulting in regions of active continental extension may be helpful when interpreting the geological record in older extensional basins the most obvious manifestation of active extension is normal faulting in earthquakes earthquake foci are mostly confined to the upper seismogenic continental crust whose thickness imposes a scale on the observed deformation large earthquakes move faults with lengths similar or large compared with the thickness of the seismogenic layer large seismogenic normal faults on the continents appear to be restricted to a dip range of around 30 60 dips significantly gentler than 20 have not been observed in fault plane solutions of large earthquakes large seismographic normal faults are approximately planar in cross section and cut through the base of the upper seismogenic layer rotating about a horizontal axis as they move a reasonable estimate of the regional extension can often be made from the dip of the large normal faults and the tilt of the blocks they bound the domino model such faults are rarely continuous for more than 15 20 km but commonly change strike or step in an en echelon fashion this segmentation may occur on a scale controlled by the thickness of the seismogenic layer and is an important influence on sedimentation and drainage these observations are common to large seismogenic normal faults from a variety of tectonic settings and suggest that the kinematics of normal faulting may not be strongly influenced by the forces responsible for the extension which can vary widely in nature and magnitude small earthquakes which move faults that are small compared with the seismogenic layer thickness show no simple pattern and often can be interpreted as internal deformation of blocks bounded by large faults in some places the seismogenic basement faults do not reach the surface but are decoupled from the sedimentary cover by layers of weak lithology faults in the sedimentary cover may be strongly curved in cross section requiring their hangingwalls to deform internally estimating extension from such faults is not straightforward and requires a knowledge of the hangingwall deformation estimates made in this way are often very non unique and prone to large errors we postulate that the thickness of the seismogenic upper crust controls both the maximum length of large normal fault segments along strike and the maximum size of blocks that can rotate coherently about a horizontal axis

faulting patterns near 19 30 s on the east pacific rise fault formation and growth at a superfast spreading center 1 structural mapping from high resolution sonar and bathymetric data collected near 19 30 s on the southern east pacific rise epr reveals multiple packets of small closely spaced outward dipping faults that form antithetic to larger inward dipping faults the mean spacing and height of inward dipping scarps are 1 6 and 1 9 times greater than those of outward dipping faults and the median spacing and height of inward dipping scarps are 2 0 and 1 7 times greater respectively accordingly inward dipping faults are less abundant 35 45 but accommodate more 50 55 of the roughly 4 0 strain although previous studies have shown that epr fault populations exhibit exponential size frequency distributions one dimensional throw and spacing data from the 19 30 s region are not described well by this model the first major 40 m scarp height fault is observed within 1 4 km of the ridge crest and invariably dips inward further off axis a transition from greater inward dipping to greater outward dipping fault abundance constrains the minimum half width of the active plate boundary zone to be 5 15 km inspection of additional data sets from 16 and 18 30 s indicates a pattern of large inward dipping faults with associated hanging wall deformation similar to that observed in the 19 30 s region this pattern is distinct from the horst and graben morphology observed along the fast spreading northern epr the pervasive hanging wall deformation observed on the flanks of the southern epr suggests master fault geometries that are more sharply curved or kinked at depth relative to their abyssal hill equivalents on the northern epr boundary element modeling indicates the pattern and geometry of faulting observed along the southern epr is consistent with fault nucleation above a shallow sill like magma chamber with internal overpressure since the influence of the sill on fault growth is strongly dependent on the depth of the sill the different patterns of faulting observed along the northern and southern epr may reflect the small difference in axial magma chamber depth between these two regions with a slightly shallower chamber beneath the southern epr

initiation of salt diapirs with frictional overburdens numerical experiments we have studied the initiation of salt diapirs with frictional overburdens under lateral compression and extension the overburden is assumed to be elasto plastic with mohr coulomb yield criterion and non associated flow rule plastic flow localizes into narrow shear bands which may represent faults the geometry and the evolution of these shear zones are simulated for various rheological parameters the dilational and frictional properties of frictional overburdens are found to be important controls on the types of shear zones formed in lateral compression and extension the friction and dilation angles influence the angle of shear and the width dip spacing and development history of conjugate zones of shear plus dilation fault zones that define wedges and grabens

fault growth in brittle ductile experiments and the mechanics of continental collisions using laboratory models of continental collisions we study the mechanisms responsible for large scale deformation and the nature of the penetrative deformation localized or homogeneous and its characteristic scales and structure in order to focus the study one of the most spectacular cases of continental collisions namely the india asia collision is considered different models with varying rheologies are analyzed which attempt to respect the brittle ductile stratification corresponding to the crust and mantle structure in the earth each experiment is quantified by studying the strain field and the fault pattern as a function of the position p of the indenter within the system the strain field is characterized by 1 the second invariant of the two dimensional strain tensor and its variation with position for a fixed p the evolution of its average as a function of p 2 the evolution with p of the participation ratio s2 which quantifies the fraction of the system surface area which participates in the deformation 3 the evolution of the escape ratio calculated as the surface increase gained by the system during its eastward lateral escape divided by the surface covered by the indenter penetration qualitatively we find that the deformation first spreads out but later on undergoes localization once the fault pattern is mature the cumulative fault length does not increase anymore we observe that the strain field is essentially controlled by the kinematics of the larger faults each fault pattern is quantified by studying 1 the histograms of fault orientations 2 the capacity and barycenter fractal dimensions 3 the multifractal generalized dimensions and 4 the distribution of fault lengths the fractal dimension d is found to almost constant within experimental uncertainty d 1 7 0 1 and thus appears rather insensitive to the particular chosen rheology we find a correlation between the generalized multifractal dimensions and two exponents the barycenter fractal dimension b and the exponent a of the fault length distribution this shows that the scaling properties of fault patterns can be characterized by the knowledge of only two exponents b and a of the spatial and length distributions of faults our main results are 1 observation of the growth of self similar fault patterns 2 complete characterization of the fault patterns with two scaling exponents a and b 3 wide distribution of undeteriorated domains and large heterogeneity of the deformation field 4 maturation of the fault structure corresponding to a localization of the deformation on a few large faults in the late stage of the deformation

quantitative fault studies on the east pacific rise a comparison of sonar imaging techniques a synthesis is presented of published statistics on the lengths scarp heights and spacing of normal faults on the flanks of the east pacific rise epr between 19 s and 21 n nine data sets are included which were collected at different times employing one of four different sonar mapping systems the scripps deep tow instrument seamarc i seamarc ii and gloria with widely ranging data collection capabilities the epr in this region is morphologically quite similar and in some cases the data sets were obtained from the same area of the seafloor it is assumed therefore that data collection procedure and system resolution have had a greater influence on the fault statistics observed than varying tectonic processes we try to account for these sampling effects such that quantitative comparisons of fault development at midocean ridges may then be made we discuss the problem of identifying faults in sonar images and the errors associated with measurements of the relevant parameters we also investigate the statistical properties of the fault populations and derive expressions for correcting observed values of the population means at finite resolution to obtain the corresponding values at infinite resolution the theoretical predictions compare well with the results of a decimation procedure applied to real data sets to simulate diminishing resolution we also discuss the effects that surveying geometry can have on the interpretation of fault lengths the data synthesis is augmented by an analysis of the correlation between scarp height and fault length for areas near 3 5 s and 12 n on the epr the correlation which we find to be linear is used to estimate 1 the minimum operational fault target size for each of the four mapping systems and 2 the topography due to faulting in an area where only fault lengths are known

fracture initiation growth and effect on stress field a numerical investigation a numerical investigation was made of the relationships between fracture initiation growth stress field and boundary conditions two dimensional plane strain continuum models were used in which fractures appeared as zones of strain localization developed through application of a strain softening mohr coulomb constitutive model r and r fractures developed first followed by y fractures at larger strains the models showed that equal development of conjugate r and r fractures is easily changed to favor one or the other set by minor variations in model initial conditions strength loss in fractures caused stress field rotations in regions bounded by fractures altering the orientation of subsequent fractures the amount and sense of stress field rotation is dependent on the strength loss during displacement on the fractures the orientation of fractures and on the boundary conditions y oriented fractures could be explained on the basis of a mohr coulomb failure criterion provided that stress field rotation is accounted for monitoring of fracture slip activity showed that under conditions of constant boundary velocity slip was discontinuous in time alternating on fractures throughout the model

controls on strain localization in a two dimensional elastoplastic layer insights into size frequency scaling of extensional fault populations 1 we use a two dimensional 2 d finite element code to investigate how mechanical properties and boundary conditions influence progressive strain localization during extension of a 2 d elastoplastic layer the deforming medium is modeled using a strain softening von mises rheology with a gaussian heterogeneity in yield strength distributed randomly in space specifically we examine the effects of changing 1 the thickness of the deforming layer 2 the basal boundary condition 3 the range of strengths in the deforming layer 4 the strength loss on failure and 5 the total accommodated strain discrete zones of plastic shear strain are observed to nucleate and grow progressively during each experiment in order to quantify and thus discriminate between the deformation patterns produced under differing conditions we calculate the size frequency distributions of the shear band populations size is defined as the total plastic strain represented by each discrete structure a wide range of size frequency distributions is observed including both power law and exponential as well as distributions that show breaks in scaling with a transition from power law at small sizes to exponential at large sizes we show that these variations in population statistics are directly reflecting a change in strain localization in space and time caused by changing model parameters furthermore by making an analogy between the model shear bands and tectonic faults we provide insights into key features of fault size frequency distributions that have been measured in continental and oceanic extensional settings and also observed in analogue experiments

influence of uniform basement extension on faulting in cover sediments abstract numerical predictions are compared with the results obtained from sandbox experiments intended to reproduce the effects of uniform basement extension for mechanically homogeneous or uniformly layered sediments that are not strain softened faults are not expected to develop during uniform basement extension even in heterogeneous or strain softening sediments subject to uniform basement extension the only faults to develop reveal an irregular and uncharacteristic distribution of displacements along the fault plane it is inferred that minor and inevitable gradients in strain rate are the most important reason why faulting was observed in the sandbox models irregularities such as topographic variation can also lead to faulting numerical experiments show that with increasing thickness of a basal elastic layer rubber membranes in sandbox models faulting of the cover sediments can cause the strain in the underlying elastic basement layer to become non uniform faulting during uniform basement extension is controlled by irregularities particular to each example and thus does not give rise to a characteristic structural style in the overlying sediments thus sandbox experiments of this type cannot be used as templates for structural interpretation except for the rare case when the initial distribution of sediment and basement material properties are known and their influence is explored from extensive numerical experimentation

growth of a normal fault system observations from the lake malawi basin of the east african rift abstract we have studied the growth history of the usisya normal fault system which bounds the west side of the lake malawi basin one of the largest rift basins in the east african rift system the lake malawi rift basin is a complex of intrabasins and intrabasin highs formed by three major fault segments each about 100 km in length the basin has been actively subsiding since the late miocene and has a maximum depth of about 3 km unlike the majority of previous studies of fault systems we are able to define the temporal evolution of this fault system using the patterns of sediment infill this is due almost exclusively to the availability of a high density seismic reflection network in combination with several clearly identifiable temporal marker beds an analysis of the seismic reflection data reveals that growth of the basin bounding faults occurred in the following sequence 1 in the early stages of rifting starting about 8 6 ma the northern fault was the most active 2 then extension shifted to the southernmost fault segment and lasted until about 2 5 ma 3 during the interval between about 2 3 ma and 1 6 ma the central segment was most active prior to the last interval the central segment accrued the least total displacement of the three segments this contradicts the common notion that the location of maximum displacement remains at a fixed location from fault inception or that the largest fault in any population of faults always maintained the highest displacement rate consistent with observations on smaller faults there is a marked increase in the displacement gradient on individual faults in the regions of overlapping segments although there is an observable asymmetry in individual segment displacement profiles there is a clear evolution toward a flattened bell shaped total displacement profile for the fault system that is consistent with the shape and scaling relationships of displacement vs length that are observed on a wide range of individual normal faults this suggests that the irregularities in the shape and scaling relationships observed in complex fault systems will eventually smooth out moreover the observed growth pattern suggests that the profile of the fault system will progress toward that of isolated faults provided the system is allowed sufficient time to evolve this in turn describes a process for maintaining a self similar scaling observed in large populations of faults which span several orders of magnitude in fault length

limitations of transient seepage analyses for calculating pore pressures during external water level changes abstractexternal water level variations such as rapid drawdown or flood loading change the internal pore pressures in an embankment as a result of changes in the boundary conditions three different effects result 1 changes in water pressure on the slope change the seepage boundary conditions 2 changes in the total stress applied by the weight of the water on the slope change the confining pressure on the soil and 3 changes in the stabilizing load from the reservoir cause changes in shear stress uncoupled transient seepage analyses which consider only the first effect are increasingly being advocated as an appropriate means to calculate pore pressures for effective stress stability analyses following water level changes this paper discusses the limitations of uncoupled transient seepage analyses for calculating pore pressures during drawdown explains the requirements for more appropriate analyses and gives examples that show the errors incumbent on the use of uncoupled analyses

localization and fault growth in layered brittle ductile systems implications for deformations of the continental lithosphere we present experiments and numerical simulations dealing with the growth of faults in thin brittle ductile systems to understand deformation modes in the continental lithosphere experiments were uniaxial shortening of layers of dry sand and silicone putties of various viscous resistances for large strength ratios between the brittle and ductile layers r 5 10 the deformation localizes into two shear bands the fault pattern is created before reaching 10 shortening and has fractal dimensions varying between 1 6 and 1 8 for small strength ratios r 5 10 deformation never localizes the fault pattern is homogeneous with a trivial dimension of 2 and grows continuously during deformation the transition between localized and homogeneous deformation occurs when the mechanical resistance of brittle layers is 5 10 times larger than the resistance of ductile layers this transition was also investigated by means of electrical analog simulations a fuse network which represents an elasto brittle layer is coupled with a capacitor layer which models strain rate dependent fluids an ac potential is applied and the fuses progressively burned out until they form a connected network the ac potential frequency is a tuning parameter similar to the applied strain rate in experiments a critical frequency is obtained marking a transition between a localization mode where the density of burned fuses decreases as the system size increases and a delocalization mode where the density of burned fuses remains constant with increasing system size the scaling dependency of the fracture process as well as the critical frequency are consistent with experimental results available information on the rheology of the continental lithosphere shows that this mechanical transition is bracketed by the possible range of brittle to ductile strength ratios

spatio temporal evolution of strain accumulation derived from multi scale observations of late jurassic rifting in the northern north sea a critical test of models for lithospheric extension abstract we integrate observations of lithospheric extension over a wide range of spatial and temporal scales within the northern north sea basin and critically review the extent to which existing theories of lithospheric deformation can account for these observations data obtained through a prolonged period of hydrocarbon exploration and production has yielded a dense and diverse data set over the entire viking graben and its flanking platform areas these data show how syn rift accommodation within the basin varied in space and time with sub kilometer scale spatial resolution and a temporal resolution of 2 3 myr regional interpretations of 2d seismic reflection refraction and gravity data for this area have also been published and provide an image of total basin wide stretching for the entire crust these image data are combined with published strain rate inversion results obtained from tectonic subsidence patterns to constrain the spatio temporal evolution of strain accumulation throughout the lithosphere during the 40 myr 170 130 ma period of late jurassic extension across this basin for the first 25 30 myr strain localisation dominated basin development with strain rates at the eventual rift axis increasing while strain rates over the flanking areas declined as strain rates across the whole basin were consistently very low 16 s l thermally induced strength loss cannot explain this phenomenon the strain localisation is manifest in the near surface by a systematic migration of fault activity the pattern and timing of this migration are inconsistent with flexural bending stresses exerting an underlying control especially when estimates of flexural rigidity for this area are considered the best explanation for what is observed in this time period is a coupling between near surface strain localisation driven by brittle or plastic failure and the evolving thermal structure of the lithosphere we demonstrate this process using a continuum mechanics model for normal fault growth that incorporates the strain rate dependence of frictional strength observed in laboratory studies during the final 10 myr of basin formation strain accumulation was focused within the axis and strain rates declined rapidly replacement of weak crust by stronger mantle material plus crustal buoyancy forces can adequately explain this decline

fault growth by linkage observations and implications from analogue models abstract using time sequence analyses of extensional fault models we demonstrate the pivotal role played by fault segmentation in the accumulation of displacement and length during the growth of faults experiments are described in which incremental steps during the development of individual faults have been reconstructed from time lapse photographs taken during model deformation these records confirm the composite segment hierarchy of fault structure a pattern that is frequently recognised in many natural arrays they reveal the progressive enlargement of individual faults to be the product of a repetitive cycle of tip line propagation overlap and linkage between nearest neighbours by contrasting the displacement patterns of successive increments during growth convincing evidence is also presented to suggest that individual segments of faults may remain kinematically independent once they are physically linked this behaviour is shown to be responsible for the characteristic saw tooth patterns often recognised in strike parallel fault displacement profiles such patterns are believed to arise where relict segment boundaries remain preserved as asperities to slip so that displacement is confined to discrete parts of a fault plane surface growth in this way also causes the maximum displacement d and surface length l of faults to continually change by different proportions incremental displacement records presented here corroborate field evidence which shows that linkage between fault segments during growth is responsible for a significant component of the spread of values often recorded in d versus l compilations finally we speculate that linkage between fault segments also accounts for transient irregularities recorded in the frequency distribution of the fault length populations of each model

a seismodynamical model of lithosphere deformation development of continental and oceanic rift networks seismicity and lithosphere extension on the scale of a tectonic plate are investigated in two horizontal dimensions and time using a dynamical model for a thin plate overlying a viscoelastic channel the plate consists of two layers a brittle elastic plastic crust that deforms as a result of earthquakes along faults and a strong viscoelastic layer representing the aseismic creeping lower lithosphere numerical experiments of lithosphere rifting are performed for one and two layer lithosphere models using two different rupture criteria in all the calculations earthquakes and faults of various sizes may form anywhere in the numerical domain as a result of the constitutive formulation the differences between the one and two layer model results suggest a mechanical explanation for the difference between continental and oceanic rifting when the lower lithosphere is absent a small number of faults dominate the deformation and a relatively simple narrow rift zone develops corresponding to oceanic rifting when a highly viscous lower lithosphere is included a complex distributed network of faults develops similar to continental rifting the complexity of the fault system also depends on the yield criterion in the crustal layer in our simulations complexity is greater for a yield criterion with strong shear stress dependence than for one with mainly extensional stress dependence whether a result of lower lithosphere stretching crustal heterogeneity or the yield criterion higher complexity increases the timescale for fault development increases self similarity in fault system geometry and stress and strain time series and results in power law moment frequency earthquake size scaling

experimental modeling of extensional fault systems by use of plaster plane strain extension experiments with plaster as the deforming medium produce faults and related structures that closely resemble natural examples the faults with the largest displacement are normally developed at about 25 overall extension 1 25 major faults develop as composite structures and although the main movement may be accommodated by a relatively simple slip surface the fault zones commonly develop internal lense shaped geometries small synthetic faults dipping more steeply than the main zone are typical components of the fault zones particularly on the hanging wall side fault displacements develop over 2 orders of magnitude and the distribution of fault displacements closely follows a power law relationship similar to data from seismic and field mapping the main through cutting faults accommodate about 60 70 of the total deformation while smaller visible faults typically account for ca 10 20 only 20 30 extension is due to faults and ductile deformation that occur below the resolution of the models which roughly corresponds to seismic resolution when scaled up to natural size the internal fault block formation may include zones of normal faults accommodating significant internal shear deformation associated with collapse of fault blocks collapse has been recorded in the upper part of footwalls resulting in a flattening of the upper part of the main faults although internal block deformation by simple shear or other deformations can be shown to play a significant role in the deformation a component of rigid block rotation is demonstrated for example by the rotation of steep normal faults into orientations where they appear as reverse faults

strain localisation and population changes during fault system growth within the inner moray firth northern north sea abstract the evolution of fault populations is established for an area within the late jurassic inner moray firth sub basin of the north sea sedimentation rates outstripped fault displacement rates resulting in the blanketing of fault scarps and the preservation of fault displacement histories displacement backstripping is used to establish the growth history of the fault system fault system evolution is characterised by early generation of the main fault pattern and progressive localisation of strain onto larger faults this localisation is accompanied by the death of smaller faults and an associated change in the active fault population from power law to scale bound fault length populations evolve from a power law frequency distribution containing all faults to a power law distribution with a marked non power law tail containing the largest faults this change in population character is synchronous with the development of a fully connected fault system extending across the mapped area and the accommodation of displacements almost exclusively on the largest faults strain localisation onto fewer and better connected faults represents the most efficient means of accommodating fault related deformation and is considered to be a fundamental characteristic of the spatio temporal evolution of fault systems progressive strain localisation requires complementary changes in the characteristics of associated earthquake populations

the accommodation of large strains in the upper lithosphere of the earth and other solids by self similar fault systems the geometrical origin of b value plate tectonics has provided a method of visualizing the geometry of the deformation of the earth s lithosphere on a large scale the description is so concise that for many purposes it provides an explanation of geological processes that overshadows the need to understand the driving processes the mechanics of the zones between the plates are less well understood particularly in continental regions where large areas are subject to deformation both continuous and discontinuous models have been tried but both have obvious drawbacks

temporal variations in seismicity during quasi static and dynamic rock failure abstract a comprehensive model is presented which can explain temporal fluctuations in seismic b values in the period leading to mechanical failure in terms of the underlying physical processes of time varying applied stress and stress corrosion enhanced crack growth under conditions of constant strain rate the form of the b value anomaly in the period leading to failure depends on the form of the stress time relationship for the case where dynamic failure occurs at peak stress after a period of strain hardening the model predicts a single cusp like b value anomaly reaching a critically low value of 0 5 at failure for the physically most realistic case where dynamic failure is preceded by a period of precursory strain energy release during strain softening the model predicts two minima in the b value separated by a temporary maximum or inflection point these fluctuations in the b value are consistent with reported intermediate term and short term earthquake precursors separated by a period of seismic quiescence for the case of quasi static cataclastic flow the b value mirrors the stress and never falls to the critical value because there is no critical rupture new results from a series of controlled laboratory experiments are presented in which microseismic event rates and b value were monitored contemporaneously with stress time data for all variants of the stress time relationship recent field observations of temporal changes in seismicity rates and b value preceding major earthquakes are also reported both data sets exhibit b value anomalies which are consistent with the model predictions

fault scaling laws and the temporal evolution of fault systems abstract through an analysis of the temporal evolution of duplex fault systems this contribution shows that it is unlikely that all faults in a deformed area will conform to a single frequency size scaling relationship the development of a duplex leads to different size frequency relationships for the faults that compose the duplex and those confined to individual horses the faults that compose the duplex define segments with relatively steep stopes on a log n number of faults i e frequency vs log d displacement magnitude i e size plot faults within individual horses define segments with relatively shallow slopes on a log n vs log d plot the distinction between these two types of faults in a duplex is akin to the distinction between large active faults which cut the entire seismogenic layer and small active faults which do not extend across the seismogenic layer if as is often the case the faults that compose a duplex do not extend across the seismogenic layer the stepped nature of the resulting log n vs log d plot may make it particularly difficult to assess the contribution of these small faults to regional deformation since duplex geometries result in part from anisotropies present in deforming rocks the anisotropy present in nearly all crustal rocks will affect the size frequency relationship observed for systems of faults different parts of a deforming rock mass are likely to have different initial anisotropies combining data on fault systems from markedly different portions of a deforming region may then obscure the unique characteristics of the size frequency relationship in either area and may lead to inaccurate assessments of the relative contributions of small and large faults to regional fault accommodated strains