a fractal model for crustal deformation abstract we hypothesize that crustal deformation occurs on a scale invariant matrix of faults for simplicity we consider a two dimensional pattern of hexagons on which strike slip faulting occurs the behavior of the system is controlled by a single parameter the fractal dimension deformation occurs on all scales of faults the fractal dimension determines the fraction of the total displacement that occurs on the first order or primary faults the value of the fractal dimension can be obtained from the frequency magnitude relation for earthquakes our results are applied to the san andreas fault system in central california earthquake studies give d 1 90 we associate the main strand of the san andreas fault with the primary faults of our fractal system we predict that the relative velocity across the main strand is 2 93 cm yr the remainder of the relative velocity of 5 5 cm yr between the pacific and north american plates occurs on higher order faults the predicted value is in reasonably good agreement with the value 3 39 0 29 cm yr obtained from geological studies

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

internal deformation in clay models of extension by block faulting clay and sand have provided useful analogues for the failure by block faulting of continental crust under extension we performed experiments on clay models of such faulting and found that the total horizontal displacement on the major faults provided only 40 50 of the known extension similar experiments on sand showed that the displacement provided 70 80 of the known extension examination of the differential tilt in both models also underestimated the extension the hidden extension is due to internal deformation within the blocks assuming that the sand and clay deform exclusively by slip and rotation on four families of faults and that these faults have many scales we propose that the hidden extension occurs on faults below the visible scale we observed much of the deformation in sand because the grain size the lower limit for faulting was close to the minimum observable scale for the model on the other hand in clay two or three orders of faults lay below this scale giving rise to a hidden extension of 50 or more we cannot apply our results directly to the block faulting behavior of continental crust however our method of analysis suggests an approach that may have value deformation within the continental crust occurs at many scales some of these scales remain hidden when determining the amount of extension in such cases our postulated behavior for clay may present a useful analogue as it suggests that deformation within the blocks may play an important role for example estimates of extension found by summing the horizontal displacement on normal faults observed on multichannel seismic lines are lower than those given from analyses of the subsidence of many sedimentary basins and continental margins hidden deformation at a scale below that observable on the seismic line could account for this difference

early stage rifting of the northern tyrrhenian sea basin results from a combined wide angle and multichannel seismic study extension of the continental lithosphere leads to the formation of rift basins and ultimately may create passive continental margins the mechanisms that operate during the early stage of crustal extension are still intensely debated we present the results from coincident multichannel seismic and wide angle seismic profiles that transect across the northern tyrrhenian sea basin the profiles cross the corsica basin france to the latium margin italy where the early rift stage of the basin is well preserved we found two domains each with a distinct tectonic style heat flow and crustal thickness one domain is the corsica basin in the west that formed before the main rift phase of the northern tyrrhenian sea opening 8 4 ma the second domain is rifted continental crust characterized by tilted blocks and half graben structures in the central region and at the latium margin these two domains are separated by a deep 10 km sedimentary complex of the eastern portion of the corsica basin travel time tomography of wide angle seismic data reveals the crustal architecture and a subhorizontal 15 17 1 km deep moho discontinuity under the basin to estimate the amount of horizontal extension we have identified the pre syn and post tectonic sedimentary units and calculated the relative displacement of faults we found that major faults initiated at angles of 45 50 and that the rifted domain is horizontally stretched by a factor of 1 3 8 10 mm a the crust has been thinned from 24 to 17 km indicating a similar amount of extension 30 the transect represents one of the best imaged early rifts and implies that the formation of crustal scale detachments or long lived low angle normal faults is not a general feature that controls the rift initiation of continental crust other young rift basins like the gulf of corinth the suez rift or lake baikal display features resembling the northern tyrrhenian basin suggesting that half graben formations and distributed homogeneous crustal thinning are a common feature during rift initiation

a comparison of seismic and structural measurements of scaling exponents during tensile subcritical crack growth abstract the observed fractal nature of both fault length distributions and earthquake magnitude frequency distributions suggests that there may be a relationship between the structure of active fault systems and the resulting seismicity in previous theoretical work a positive correlation between the exponent d from the fracture length distribution and the seismic or acoustic emission ae b value has been inferred from a simple dislocation model of the seismic source here we present the first experimental evidence for a correlation between d and b from a series of tensile fracture mechanics tests on crystalline rock carried out in different environmental conditions both air dry and water saturated and at ambient temperature and pressure the microseismic acoustic emissions were monitored during subcritical crack growth under controlled conditions of constant stress intensity k i and quantitative analyses of the resulting fracture patterns were carried out on the same specimens it is found that ae b values ranging from 1 0 to 2 3 correlate negatively with the normalized stress intensity k i k ic where k ic is the fracture toughness of the specimen the microcrack length distribution exponent d ranges from 1 0 to 1 7 fluid presence has a first order influence on both the ae and structure produced in these experiments for experiments at low stress intensity or high fluid content the activation of the stress corrosion mechanism for k i k ic leads to a greater relative proportion both of small cracks and of low amplitude acoustic emissions reflected in higher values of d and b the exponent d is found to correlate positively with the ae b value

scaling properties of normal fault populations in the western corinth graben greece implications for fault growth in large strain settings abstract a variety of one dimensional and two dimensional map techniques of fractal analysis have been employed to investigate the scaling properties of the dominant wnw trending normal fault population of the western corinth graben in central greece to assess possible constraints on fault geometry during fault growth the data have been compiled separately from the northern and southern domains of the graben which have experienced differing amounts of finite strain based on power law distributions of the fault throw the applied extension is estimated at 30 and 22 for the northern and southern domains respectively however the fault spacing and fault length populations in both domains obey similar power law relationships these conclusions are also supported by maximum throw vs trace length data which demonstrate that the faults in the northern domain have systematically higher values for the slip to length ratios than those in the southern domain it is proposed that the corinth graben has reached fracture saturation that is the fault spacing stops evolving and displacement increases rather than faults lengthening to accommodate the increasing extension this growth process consistent with throw distributions along individual faults may be explained either in terms of a stress feedback mechanism or by the mechanical interaction between the wnw trending normal faults with a set of nne trending transverse faults

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

fault spacing in the el teniente mine central chile evidence for nonfractal fault geometry we utilize the excellent rock exposure provided by the network of mining tunnels in el teniente mine central chile to test the applicability of fractal fault spacing laws to a 2 km 3 km 1 3 km body of crystalline rock in an andean shear zone fractal spacing laws can be particularly useful because they allow prediction of fault spacing at unsampled scales because of the restrictions of tunnel geometry in the mine we use only scanline one dimensional analyses the large number of parallel tunnels allows us to assess the consistency of one dimensional scanline samples over a two dimensional area we use two methods 1 an interval counting technique and 2 standard cumulative statistics to test the hypothesis of fractal fault geometry in the shear zone the interval counting method produces deceptively good fits to a fractal distribution in fact by analyzing the residuals and differential slopes of interval counting and cumulative statistical plots and by comparison with synthetic fractal negative exponential and log normal distribution data we conclude that a negative exponential distribution best describes fault spatial distribution at the mine we present three possible explanations for the negative exponential spacing distribution 1 the rock body is at the earliest stage in a deformational path that will produce varying spacing distributions as deformation proceeds 2 the spacing distribution is inherited through joint reactivation and 3 the present spacing distribution is the result of a superposition of two spacing distributions each of which is not necessarily negative exponential additionally we attempt to use the deviation of mean spacings in parallel scanlines after wu and pollard 1995 to further classify deformational maturity we show that this method cannot be used to compare population development in faults which follow a negative exponential spacing distribution because of the negative exponential s equivalence of mean and standard deviation instead we use a relative measure of parallel scanline deviation to compare regions the distinctly smaller standard deviation of mean spacings in one region the t3 isla region may be a signature of increased local finite strain accumulation

geodynamics of rifting and implications for hydrocarbon habitat abstract rifting activity is probably mainly governed by frictional forces exerted on the base of the lithosphere by the convecting sub lithospheric upper mantle combined with deviatoric tensional stresses developing over upwelling branches of the asthenospheric convection system and by far filed stresses controlling the interaction of lithospheric plates moving relative to each other mantle plumes rising from the deep mantle do not appear to be a major driving force of rifting therefore it is questioned whether a distinction between active and passive rifts is still justified lithospheric extension triggers by decompression partial melting of the lower lithosphere and upper asthenosphere magmatic processes contribute materially to thinning of the subcrustal lithosphere and probably also of the lower crust this could explain the frequently observed discrepancy between upper crustal extension by faulting and lower crustal attenuation as defined by refraction and deep reflection seismic data the duration of the rifting stage of palaeorifts and passive margins is highly variable depending on plate interaction crustal separation can be achieved after as little as 7 ma and as much as 280 ma of rifting activity the availability of crustal discontinuities does not appear to play a significant role in the time required for crustal separation to be achieved the structural style of rifts is controlled by the physical state of the lithosphere the mode and amount of its extension and the lithological composition of pre and syn rift sediments subsidence of rift basins is controlled by the balance between isostatic adjustment of the crust to lithospheric stretching and uplift induced by mechanical and thermal attenuation of the subcrustal lithosphere post rift basin subsidence is mainly governed by the decay of rift induced thermal anomalies densification of the lower crust and intra plate stresses provide overprinting effects in view of this it is unlikely that quantitative analyses of post rift basin subsidence give a direct measure of lithospheric extension tectonically active rifts palaeorifts and passive margin basins contain major hydrocarbon provinces their hydrocarbon charge can rely exclusively on pre rift syn rift or post rift sedimentary sequences or a combination thereof maturation of source rocks can be achieved during the syn and or post rift stage of basin evolution during rifting conductive and convective heat transfer accounts for elevated geothermal gradients these play an important role in the maturation of pre and syn rift source rocks thermal gradients decrease asymptotically during the post rift stage

ageostrophic fluctuations in cozumel channel 1 the cayman current flows to the west and most of it turns north as it approaches the yucatan coast producing a persistent northwesterly flow on both sides of cozumel island the transport between the yucatan peninsula and cozumel island i e through the cozumel channel is close to 5 sverdrups in the mean with velocities at midchannel ranging from 20 to 180 cm s a recent study of the subinertial flow and pressure difference across cozumel channel by chavez et al 2003 showed the existence of periods lasting over 1 month with large 3 day to 1 week ageostrophic fluctuations the flow was measured again for a year now at four locations around cozumel island including two instruments along the axis of the channel 8 6 km apart thus allowing estimations of the along channel velocity gradients the new measurements reveal that as suggested in the previous study the centripetal or curvature acceleration of the current is the most significant contribution in the departure from geostrophy indeed the curvature is at times so large that the pressure difference implies a geostrophic flow in the direction opposite to that of the actual flow that is the curvature is anticyclonic with amplitude in rossby number larger than unity measures of the intensity of suprainertial variations in pressure differences and velocity show that periods of ageostrophic fluctuations are consistently much richer in high frequency fluctuations than periods of nearly geostrophic behavior nonetheless the large scale reynolds stresses play an insignificant role throughout

analysis of the fractal clustering of ore deposits in the spanish iberian pyrite belt the iberian pyrite belt ipb contains one of the greatest known concentrations of volcanic hosted massive sulfides vhms on earth investigation of the spatial attributes of the mineralization using fractal methods over a range of scales and integrated within a gis provides new information of potential import to the exploration of vhms deposits at the mine scale stockworks which act as feeders for hydrothermal fluids show vein thickness distributions that are power law dt 0 65 in one dimension at length scales from about 10 2 to 102 m box counting of veins indicates a capacity dimension dc in the range of 1 60 1 65 in two dimensions which is consistent with the vein thickness data at larger scales in the range 103 to 105 m the distribution of mines and mineral prospects can be modelled as a fractal dust when all the known mineral deposits and prospects are analyzed they have a capacity dimension dc 1 3 the vhms deposits alone have a capacity dimension dc 0 9 indicating that they are clustered with some indication that the world class deposits may be even more clustered the different fractal analyses are integrated with information from geological and geophysical maps using a gis the distribution of prospects has been simulated using a simple multifractal model of the ore concentration and is constrained by known geological controls such a model has been implemented through the gis

evidence for anomalous earthquake size distributions in regions of minimal strain some regions have no earthquakes above magnitude 5 5 and thus apparently contain only small active faults with length less than the thickness of the brittle upper crust britain and ssw turkey are examples with strain rates 3 10 20 and 3 10 17 s 1 their seismicity has gutenberg richter parameter b 1 5 larger than 1 typical elsewhere sufficient for equal strain to be associated with each order of magnitude of fault length present these regions deform by increasing lengths and number densities of small faults when strain reaches 0 01 these faults will be so closely spaced that they may interact forming large faults that cut the brittle layer and take up most later deformation deformation involving only small faults will last 1 myr in regions with strain rate 10 15 s 1 and is unlikely to be observed

measurement and characterisation of spatial distributions of fractures abstract a variety of line sample 1 d and map 2 d datasets of faults and joints has been used to investigate the spatial distributions of fractures and to test techniques of fractal analysis the natural fracture datasets have been supplemented by synthetic datasets with known characteristics the fault datasets investigated range in scale from regional to outcrop and the joint datasets are derived from outcrop 1 d datasets were analysed by the spacing population interval counting and fracture number interval counting techniques 2 d datasets were analysed by box counting and fracture number box counting techniques results indicate that fracture spacing can be characterised in line samples using either the 1 d interval counting technique or more simply by measuring the spacing population as the cumulative frequency distribution of spaces between adjacent fractures tectonic faults frequently show a power law spacing population indicating fractal dimensions of between 0 4 and 1 0 but except for outcrop data truncation effects degrade the analysis unrefined joint datasets commonly show negative exponential or lognormal spacing cumulative frequency distributions however single orientation joint sets are characterised by a regular spacing and are therefore non fractal for both fault and joint map data box counting techniques do not yield the power law relationship between box size and the number of boxes that is expected of fractal geometries it is concluded that 2 d box counting techniques are too insensitive to characterise the many different parameters of a fracture array the fracture density technique appears not to discriminate between very different fracture patterns and therefore does not provide useful results a fracture pattern incorporates several attributes e g size distribution orientation linkage density roughness each of which may scale independently and each of which may be fractal with its own fractal dimension full characterisation of fracture patterns will therefore require independent analysis of each of these attributes

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

the sampling of fault populations in dolerite sills of central sweden and implications for resolution of seismic data abstract geological mapping of faults affecting dolerite sills was carried out along the baltic coast in central sweden and scaling relationships for the faults analysed in order to assess the seismic imaging of the sills the sills are 250 400 m thick and dip at low angle

relationship between deeper lithospheric processes and near surface tectonics of sedimentary basins interactions between upper lithosphere deformation as manifested in the structure and evolution of sedimentary basins and lower lithospheric deformation presumably reflect large scale regional or global tectonic events we review the current state of knowledge regarding these interactions and suggest areas of research which may lead to an improvement in this knowledge understanding the development of sedimentary basins requires insight into the processes responsible both for basin subsidence and also for distribution and preservation of sediments within the basins while some classes of basins are better understood than others there remain significant gaps both in our ability to account for available data and also in the data available to test current models and develop new ones subsidence in some classes of basins can be related to lithospheric scale processes occurring as part of the overall plate tectonic paradigm for example it is widely accepted that passive margin basins subside as a result of lithospheric extension mckenzie 1978 and that foreland basins are flexural consequences of collision between a continent and outboard terranes beaumont 1981 on the other hand models for the origin of intracratonic forearc and trans tensional basins are essentially still at cartoon level involving processes that are difficult to quantify and evaluate in the following we review a number of fundamental questions of vital interest for understanding of the relationship between deeper lithospheric processes and near surface tectonics

crustal extension in the oslo graben se norway a method incorporating magmatism and erosion abstract three methods for determining crustal extension were examined for use in the late paleozoic oslo graben of southeast norway 1 1 analysis of faults and dikes 2 2 volume budget isostasy 3 3 analysis of crustal thickness distribution assuming constant crustal volume during extension these methods were found not to be suitable mainly due to rift age and magmatism instead a new integrated model which combines the effect of moho contours volumes of mantle injecta and erosion was used volumes of intracrustal mantle injecta are found from a model combining data on upper crustal felsic magmatic rocks with petrological and gravity inversion models for the vestfold graben segment in the south this implies twice the stretching estimate as compared to stretching derived from moho contours alone and two to three times the estimate from an inadequate set of fault and dike information the batholiths mark zones of high crustal thinning and magmatism was most likely caused by a combination of a thermal anomaly and lithospheric stretching

faulting and graben formation in western and central europe rifts and rift related basins play a pre eminent role among the sedimentary basins of western and central europe through time grabens developed in a number of different megatectonic settings whereby the principal mechanisms governing their subsidence was crustal stretching and subcrustal erosion the level of volcanic activity associated with rifting is highly variable and can change significantly during the development history of a rift some rifts are totally non volcanic the development of rift domes is generally associated with volcanic activity uplifting of a rift dome can induce a reversal in the subsidence pattern of a rift intracontinental rifts with their thinned crust are prone to inversion when the respective craton is subjected to tangential stresses in the process of inversion the crust of rifts is mechanically thickened again

predicting reservoir scale faults with area balance application to growth stratigraphy a reservoir that appears to lack faults at one scale of resolution or at one sampling density may nevertheless contain faults that are below the resolution of the observations the area depth relationship from a balanced cross section is shown to contain the necessary information for predicting the sub resolution fault heave existing area depth theory is extended to include growth units allowing structural length and thickness changes to be separated from the depositional changes the technique is validated with a numerical model of a growth full graben and a sand box model of a half graben then field tested in the gilbertown graben a growth structure within the regional peripheral fault trend along the northern margin of the gulf of mexico a cross section developed from wells alone is used to infer the abundance of sub resolution faults by the area balance technique a small but significant amount of sub resolution extension is predicted and then confirmed with a highresolution seismic line q 2003 elsevier science ltd all rights reserved

the relationship between sticky spots and radar reflectivity beneath an active west antarctic ice stream isolated areas of high basal drag or sticky spots are important and poorly understood features in the force balance and dynamics of west antarctic ice streams characterizing sticky spots formed by thin or drying subglacial till using ice penetrating radar is theoretically possible as high radar bed returned power brp is commonly related to an abundance of free water at the ice bed interface provided losses from englacial attenuation can be estimated in this study we use airborne radar data collected over evans ice stream to extract brp profiles and test the sensitivity of brp to the adopted englacial attenuation correction we analyse 11 20 km profiles in four fast flow areas where sticky spots have been inferred to exist on the basis of model and surface data inversions in the majority of profiles we note that the increase in basal drag is accompanied by a decrease in brp and suggest that this is evidence both for the presence of a sticky spot in those locations and that local variations in subglacial hydrology are responsible for their existence a comparison is made between empirical and numerical modelling approaches for deriving englacial attenuation and our findings generally support previous studies that advocate a modelling approach

crustal thinning and subsidence in the north sea we present here the results of a detailed study of subsidence and crystal thinning across the central graben of the north sea basin two independent lines of evidence have been used to test how well the uniform extensional model1 2 can account for the evolution of the north sea basin a long range seismic profile was shot perpendicular to the central graben from edinburgh to southern norway and data were analysed from 11 exploration wells situated close to the seismic line fig 1 the estimates of the increase in surface area due to extension from the crustal structure determined using the seismic data and from the well subsidence patterns are both compatible with a simple uniform extensional mechanism for the post palaeozoic evolution of the north sea

the structural evolution of the northern viking graben and its bearing upon extensional modes of basin formation recent advances in the understanding of rift basin formation coupled with the increasing public availability of seismic and well data across the northern viking graben 60 61 n have enabled a detailed analysis of its development two rifting episodes can be recognized late permian early triassic and bathonian ryazanian major regional unconformities thought to be primarily tectonic rather than eustatic in origin separate and subdivide the rifting episodes the earlier episode involved extension about a n s axis ensuing triassic mid jurassic thermal subsidence was accommodated on steep faults during the later episode a new ne sw fault trend was superimposed on pre existing patterns major block rotation marking active rifting ceased at the end of the ryazanian during the second post rift episode there was a progressive migration of active faulting towards the basin margins and as a result a widening with time of the area undergoing subsidence asymmetric subsidence of the central part of the basin was hinged at the western margin of the horda platform and accommodated to the nw on major faults within the tampen spur factors for the second rifting episode were calculated both by relating subsidence to extension and by measuring observed extension values calculated by both methods increase consistently towards the basin axis for both rifting and thermal subsidence phases but are greater for the latter phase subsidence patterns are similar for both rifting and thermal subsidence episodes so that there is vertical stacking of relatively thick sequences in the axis of the northern viking graben these factors preclude the application of models involving uniform and non uniform stretching and also preclude oblique extension depth dependent stretching is preferred

fault size distributions are they really power law abstract power law fault size throw distributions spanning ca seven orders of magnitude are analysed using sample lines from seismic coal mine plan and outcrop data sets outcrop data sets generally have lower power law exponent values than seismic data sets consistent with a general decrease in exponent value with decrease in fault size if such a relationship does exist then probably it cannot be accounted for by sampling bias alone we suggest that either i fault size populations are not power law over a large scale range or ii they are power law but at smaller scales show a greater range of exponent values due to spatial clustering

forearc basin formation in the tectonic wake of a collision driven coastwise migrating crustal block the example of the north andean block and the extensional gulf of guayaquil tumbes basin ecuador peru border area trench parallel extensional strain resulting from the northward drift of the north andean block has controlled the tectonic evolution of the gulf of guayaquil tumbes basin at least for the past 1 8 1 6 ma industrial multichannel seismic and well data document that e w to ene low angle detachment normal faults the posorja and jambeli detachment systems to the north and the tumbes detachment system to the south accommodated the main subsidence step along the shelf area during late pliocene quaternary times 1 8 1 6 ma to present two tectonic regimes showing different styles and ages controlled the evolution of the southern ecuador and northern peru continental margin and shelf the n s extensional regime along the shelf area is related to north andean block drift whereas the e w extensional regime along the continental margin results from tectonic erosion at depth strain rotation takes place along a major n s trending transfer system formed by the inner domito fault and the inner banco peru fault which bound the detachment systems to the west the strike slip component along this transfer system roughly located at the continental margin shelf break evolved as a response to slip along the detachment systems bounding the basin to the north and to the south the tumbes detachment system is the master fault controlling basin evolution through time and it may represent the shallower expression of a reactivated obduction megathrust it connects landward with the continental structures assumed to be part of the eastern frontier of the north andean block for the past 2 ma the total lengthening calculated along a complete n s transect of the gulf of guayaquil tumbes basin ranges between 13 5 and 20 km this lengthening is compatible with the documented drift of the north andean block for the same period of time the gulf of guayaquil tumbes basin is not a classical pull apart basin it exemplifies a particular type of pull apart basin basically controlled by 1 detachments extending downward across the brittle crust and 2 plate coupling along the subduction decollement which controls the inward segmentation of deformation

comparison of earthquake strains over 102 and 104 year timescales insights into variability in the seismic cycle in the central apennines italy in order to study the existence of possible deficits or surpluses of geodetic and earthquake strain in the lazio abruzzo region of the central apennines compared to 15 3 kyrs multi seismic cycle strain rates horizontal strain rates are calculated in 5 km x 5 km and 20 km x 20 km grid squares using slip vectors from striated faults and offsets of late pleistocene holocene landforms and sediments strain rates calculated over 15 3 kyrs within 5 km x 5 km grid squares vary from zero up to 2 34 0 54 x 10 7 yr 1 and resolve variations in strain orientations and magnitudes along the strike of individual faults surface strain rates over a time period of 15 3 kyrs from 5 km x 5 km grid squares integrated over an area of 80 km x 160 km shows the horizontal strain rate of the central apennines is 1 18 0 04 0 12 x10 8 yr 1 and 1 83 4 43 3 80 x 10 10 yr 1 parallel and perpendicular to the regional principal strain direction 043 degrees 223 degrees 1 degrees associated with extension rates of ms 6 0 magnitude historical earthquakes have been reported to be as low as zero this demonstrates the importance of comparing the exact same areas and that strain rates vary spatially on the length scale of individual faults and on a timescale between 10 2 yr and 10 4 yr in the central apennines we use these results to produce a fault specific earthquake recurrence interval map and discuss the regional deformation related to plate boundary and sub crustal forces temporal earthquake clustering and the natural variability of the seismic cycle

characterization of natural fracture systems analysis of uncertainty effects in linear scanline results the exploitation of hydrocarbon reserves in naturally fractured reservoirs composed of different types of rocks has drawn considerable attention from the fracture characterization research community because of the importance of fractures to the prediction of fluid flow one of the most common methods for rapidly analyzing fracture features is the scanline technique which provides an estimate of fracture density and frequency despite the confidence provided by the systematic use of this method errors and uncertainties caused by sampling biases exist the problems caused by these uncertainties can detrimentally affect the construction of a computational model due to misleading trends this study evaluated the uncertainty caused by sampling biases in the scanline data of opening mode fractures in outcrops of naturally fractured aptian laminated limestone from the crato formation araripe basin northeastern brazil the monte carlo method was chosen to introduce random values into the sampled values which enabled us to verify the importance of errors in the accuracy of the method of representing the fracture network in this study errors and uncertainties were grouped into one parameter termed the coefficient of uncertainty which was defined as the ratio between the uncertainties created by the errors and artifacts introduced artificially and the original scanline data the propagation of errors and uncertainties in the scanline data to the coefficients of the corresponding power law were determined this evaluation can be applied in the construction of more reliable geomechanical models using analog geological models for naturally fractured reservoirs

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

analysis of a strike slip fault network using high resolution multibeam bathymetry offshore nw devon u k abstract imaging of the sea floor offshore from hartland point north devon u k using high resolution multibeam bathymetry reveals a strike slip fault network this consists of ne trending left lateral faults and nw trending right lateral faults that cut folded and steeply dipping strata 60 faults were accurately mapped using the multibeam imagery and lateral separations of marker beds measured along fault traces these data are used to examine the spatial arrangement fault displacement and strain distribution within the network at different displacement cut offs at high displacement cut offs the fault network is dominated by a few long isolated right lateral fault segments that bound fault blocks but at lower displacement cut offs shorter left lateral and right lateral fault segments make up fault tips and infill fault blocks the majority 70 of fault trace length is taken up by small fault segments that have 10 m displacement the topology and relative connectivity of the network is analysed in terms of a system of fault branches between tips i nodes or intersections x or y nodes the relative proportions of which reflect the connectivity of the network although the kinematic behaviour of the fault network is controlled by large fault segments connectivity is very dependent on the small fault segments a comparison with a similar nearby strike slip fault network at westward ho north devon shows many similarities and indicates that fault networks are better connected with increasing strain and that the network becomes better connected when strain is localized within damage zones rather than on individual faults

tension fractures and extensional tectonics a characteristic pattern of normal faults that we have studied in several regions illustrates successive geometries relating to increasing amounts of extension from 10 50 gulf of suez egypt to 50 100 western gulf of california mexico up to 200 southern basin and range usa tension fractures formed at an early stage of extension have an essential role the resulting structure is described as a multiple tilted packs of cards model in which rotational deformation within the major blocks is accommodated by normal faulting on previously formed tension fractures thus defining smaller blocks of second and third generation

the role of small scale extensional faulting in the evolution of basin geometries an example from the late palaeozoic petrel sub basin northwest australia abstract during continental extension the kinematic collapse of the hangingwall of major normal faults and the subsequent isostatic response imposes a strong control on the evolving basin geometry the interaction of the flexural wavelength and the magnitude and location of faults may allow the development of basin geometries which deviate from a classic half graben style particularly if some of this deformation is below the scale of observation commonly seismic reflection data in particular the development of a lateral partitioning between large and small scale faults within a basin may exert a significant control on the resulting basin geometry using the petrel sub basin in northwest australia as an example it is demonstrated that an extensional basin geometry consisting of a classic half graben can be overprinted by a significant sag geometry which can be related to the lateral offset of sub resolution faulting this lateral partitioning and resulting basin geometry may also have an application to other extensional basins particularly if a mechanism is present to allow this partitioning of fault styles to develop in the petrel sub basin this has been related to the presence of older basement features of the halls creek mobile zone beneath the axis of the basin however a comparison with physical models also suggests that this may be applicable to basins formed by oblique rifting a component of which may also be present within the petrel sub basin particularly if this is imposed upon a weak zone or suture within the upper mantle

fault populations and their relationship to the scaling of surface roughness the relationship between the scaling properties of faulted geological surfaces and parameters describing the underlying fault population are investigated using simulations of a dip slip faulted surface analysis of multiple simulations of sections through the surface allowed the construction of a statistical relationship between the parameters defining the fault population and the fractal dimension of the surface the results indicate a direct if complex relationship between the fault population and the scaling of the surface roughness the main determining factor is the displacement distribution with spacing and dip having only a minor contribution this relationship is tested against examples from the moray firth scotland and the central indian ocean

quantitative analysis of populations of small faults abstract tectonic strain includes contributions from small faults with length less than the thickness of the brittle upper crust this study derives algebra to determine the strain associated with small faults that follow a power law i e fractal distribution independent of assumptions concerning how they relate to large faults in the same region and discusses how to apply this algebra for a range of small fault sample types the method is illustrated using as case studies the jurassic extension in the north sea the miocene and younger extension in the gulf of suez and the hercynian strike slip faulting the badajoz cordoba fault zone in southern spain my preferred estimates for the strain accommodated on small normal faults with length

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