effective medium theories for fluid saturated materials with aligned cracks there is general agreement between different theories giving expressions for the overall properties of materials with dry aligned cracks if the number density of cracks is small there is also very fair agreement for fluid filled isolated cracks however there are considerable differences between two separate theories for fluid filled cracks with equant porosity comparison with recently published experimental data on synthetic sandstones gives a good fit with theory for dry samples however although the crack number density in the laboratory sample is such that first order theory is unlikely to apply expressions correct to second order in the number density provide a worse fit it also appears that the ratio of wavelength to crack size is not sufficiently great for any detailed comparison with effective medium theories which are valid only when this ratio is large the data show dispersion effects for dry cracks and scattering neither of which will occur at sufficiently long wavelengths data from the water saturated samples indicate that the effect of equant porosity is significant although the two theories differ strongly as to just how significant once again and in spite of the reservations mentioned above a reasonable fit between theory and observation can be shown

hatton bank northwest u k continental margin structure summary the continent ocean transition near hatton bank was studied using a dense grid of single ship and two ship multichannel seismic mcs profiles extensive oceanward dipping reflectors in a sequence of igneous rocks are developed in the upper crust across the entire margin at the landward shallowest end the dipping reflectors overlie continental crust while at the seaward end they are formed above oceanic crust beneath the central and lower part of the margin is a mid crustal layer approximately 5 km thick that could be either stretched and thinned continental crust or maybe newly formed igneous crust generated at the same time as the dipping reflector sequence beneath this mid crustal layer and above a well defined seismic moho which rises from 27 km continental end to 15 km oceanic end across the margin the present lower crust comprises a 10 15 km thick lens of material with a seismic velocity of 7 3 to 7 4 kds we interpret the present lower crustal lens as underplated igneous rocks left after extraction of the extruded basaltic lavas a considerable quantity of new material has been added to the crust under the rifted margin the present moho is a new boundary formed during creation of the margin and cannot therefore be used to determine the amount of thinning

effective velocities in fractured media a numerical study using the rotated staggered finite difference grid the modelling of elastic waves in fractured media with an explicit finite difference scheme causes instability problems on a staggered grid when the medium possesses high contrast discontinuities strong heterogeneities for the present study we apply the rotated staggered grid using this modified grid it is possible to simulate the propagation of elastic waves in a 2d or 3d medium containing cracks pores or free surfaces without hard coded boundary conditions therefore it allows an efficient and precise numerical study of effective velocities in fractured structures we model the propagation of plane waves through a set of different randomly cracked media in these numerical experiments we vary the wavelength of the plane waves the crack porosity and the crack density the synthetic results are compared with several static theories that predict the effective p and s wave velocities in fractured materials in the long wavelength limit for randomly distributed and randomly orientated rectilinear non intersecting thin dry cracks the numerical simulations of velocities of p sv and sh waves are in excellent agreement with the results of the modified or differential self consistent theory on the other hand for intersecting cracks the critical crack density porosity concept must be taken into account to describe the wave velocities in media with intersecting cracks we propose introducing the critical crack density concept into the modified self consistent theory numerical simulations show that this new formulation predicts effective elastic properties accurately for such a case

x ray micro computed tomography and ultrasonic velocity analysis of fractured shale as a function of effective stress abstract ultrasonic velocity is a key shale gas reservoir property especially in the context of gas production or co 2 injection for geo sequestration this ultrasonic velocity reflects the dynamic elastic properties of the rock and it thus depends on the fracture morphology which varies significantly with effective stress however the precise relationship between ultrasonic velocity and fractured shale morphology is only poorly understood we thus measured p and s wave velocities of fractured shale in two orthogonal directions and imaged the shale with x ray micro computed tomography as a function of applied effective stress and investigated how fracture morphology p and s wave velocity young s modulus shear velocity and poisson s ratio are interconnected with effective stress clearly most of the small fractures the width is around 0 1 mm closed with increasing effective stress resulting in a different fracture size distribution which again had a dramatic effect on the elastic rock properties furthermore with increasing effective stress p and s wave velocities increased significantly such that the orthogonal waves gave a similar response at 2000 psi effective stress despite significant sample heterogeneity we conclude that the fracture aperture direction and network characteristics severely influence wave propagation and thus elastic properties these results can be used to assess natural fracture networks monitor fracture development during hydraulic fracturing and predict fracture closure scenarios during production

the relative timing of serpentinisation and mantle exhumation at the ocean continent transition iberia constraints from oxygen isotopes legs 173 and 149 of the ocean drilling program profiled a zone of exhumed mantle peridotite at the ocean continent transition oct beneath the iberia abyssal plain the zone of exhumed peridotite appears to be tens of kilometers wide and is situated betw

the ocean continent boundary off the western continental margin of iberia i crustal structure at 40 30 n summary the western continental margin of the iberian peninsula has the characteristics of a rifted non volcanic margin with half graben and tilted fault blocks seen in several places the ocean continent boundary ocb is therefore expected to be where thinned continental crust and oceanic crust are juxtaposed as at many similar margins worldwide it is particularly useful to locate the ocb off western iberia in order to constrain the pre rift fit of north america to iberia and by implication the shape of the proto bay of biscay the fit is only marginally constrained by sea floor spreading magnetic anomalies because anomaly 34 is believed to be far to the west of the ocb and it is even possible that all older oceanic crust was created during the cretaceous constant polarity interval the best way to distinguish oceanic crust from thinned continental crust appears to be the crustal seismic velocity structure therefore in 1986 a series of seismic refraction lines was shot parallel to and normal to the continental margin these lines enabled us to bracket the location of the ocb a further constraint on the location was obtained by modelling an east west magnetic profile which included the enigmatic j anomaly this anomaly can be explained as either just pre anomaly mo or as part of the cretaceous constant polarity interval depending on whether spreading began about 127 or after 118 myr ago respectively the evidence favours the former explanation lastly the depth to acoustic basement was contoured from a compilation of seismic reflection profiles this indicated a new fracture zone at 41 15 n which offsets the ocb a few key reflection profiles also suggest that the ocb can be identified by an abrupt landward step down in acoustic basement we conclude that the ocb in the eastern iberia abyssal plain lies between 12 10 and 12 30 w and has a trend just east of north this westerly location is consistent with recent estimates of the location of the ocb off the grand banks but brings into question the proposed location at about 11 w of the ocb in the tagus abyssal plain

quantifying damage saturation and anisotropy in cracked rocks by inverting elastic wave velocities crack damage results in a decrease of elastic wave velocities and in the development of anisotropy using non interactive crack effective medium theory as a fundamental tool we calculate dry and wet elastic properties of cracked rocks in terms of a crack density tensor average crack aspect ratio and mean crack fabric orientation from the solid grains and fluid elastic properties using this same tool we show that both the anisotropy and shear wave splitting of elastic waves can be derived two simple crack distributions are considered for which the predicted anisotropy depends strongly on the saturation reaching up to 60 in the dry case comparison with experimental data on two granites a basalt and a marble shows that the range of validity of the non interactive effective medium theory model extends to a total crack density of approximately 0 5 considering symmetries up to orthorhombic in the isotropic case kachanov s 1994 non interactive effective medium model was used in order to invert elastic wave velocities and infer both crack density and aspect ratio evolutions inversions are stable and give coherent results in terms of crack density and aperture evolution crack density variations can be interpreted in terms of crack growth and or changes of the crack surface contact areas as cracks are being closed or opened respectively more importantly the recovered evolution of aspect ratio shows an exponentially decreasing aspect ratio and therefore aperture with pressure which has broader geophysical implications in particular on fluid flow the recovered evolution of aspect ratio is also consistent with current mechanical theories of crack closure in the anisotropic cases both transverse isotropic and orthorhombic symmetries were considered anisotropy and saturation patterns were well reproduced by the modelling and mean crack fabric orientations we recovered are consistent with in situ geophysical imaging

seismic response of fractures by numerical simulation summary fractures occur on a wide range of scales and are important in the study of hydrocarbon reservoirs seismic simulation by finite difference modelling using an equivalent medium method can devise the elastic parameters of a cell intersected by a fracture as those of a medium with an equivalent seismic response numerical experiments confirm that diffractions from the fracture tips are a strong component of the total wavefield however a comparison of boxcar linear angular and elliptic tapering suggests that there is little dependence on shape because the energy involved in a single diffraction is much lower than the incident energy an open fluid filled fracture has stronger effect on the wavefield than the wet and dry multiple crack models because an open fracture would have a stronger dissimilarity to the background rock the density of microcracks within a fracture also has strong effect on the seismic response however the properties of those cracks are not significant to the overall seismic response considering a distribution of a large number of fractures even when the overall density of fractures is held constant longer fractures attenuate seismic energy more than smaller ones for the orientation effect fractures oriented in the direction of propagation seem to affect the wavefield more than those perpendicular because of the incident wave striking the fracture at an angle greater than the critical angle experiments on clustering of the fractures indicate that although clusters which are large compared to the wavelength may attenuate and shield more than for a uniform distribution smaller ones in fact attenuate less because of the healing effect these are important results when trying to characterize the fracture properties including density clustering size and orientation of a fractured reservoir from field seismic data

extent of oceanic crust in the labrador sea1 this paper examines the mode of formation of the northern margins of the labrador sea observations of faulted and rotated crustal blocks across the northwest margin of greenland had led to the suggestion that this region is underlain by extended continental crust a detailed analysis of all geophysical data from this region presented here suggests on the contrary the possibility that it could have been formed by an excessively slow seafloor spreading process and ridge axis propagation this gave rise to rotated fault blocks at a time when spreading was mainly confined to the greenland side prior to its shift to the west supporting evidence for such a reconfiguration of the spreading axis comes from gravity and magnetic observations of this and neighbouring regions modelling of magnetic anomalies in the area based on the average rate of spreading for the entire labrador sea shows that a gradual shift of the ridge axis to the west started after the formation of anomaly 32 because the earliest seafloor spreading anomalies are highly attenuated in amplitudes other models like extended and intruded continental crust are possible if one only considers the magnetic anomalies however an extended continental crustal model poses problems in accounting for other geophysical observations based on a slow spreading model it is shown that oceanic crust extends fairly close to the foot of the slope with a narrow belt of extended continental crust along the west greenland margin while a much wider zone of perhaps attenuated continental crust extends off labrador breakup of the continental landmass occurred much closer to the west greenland coast than to labrador the applicability of a slow spreading model to other passive margins where similar geophysical observations have been reported is discussed

propagating rifts and continental breakup a simple quantitative model is proposed whereby continental breakup starts with a phase of continental rifting and continues with the propagation of rifts toward locked zones these zones are deformed in the rifting process while oceanic crust is generated in the wake of the rift tip the deformed zones will cause overlaps when a continental reassembly is attempted the model accounts for the shape and distribution of magnetic quiet zones at ocean continent boundaries and for the detailed geometry of some v shaped zones of oceanic magnetic anomalies the former provide an estimate of the scale at which the hypothesis of rigid plates fails and the latter are used to measure the velocity of rift propagation illustrations are provided for present rifting in the red sea and gulf of aden and for early rifting of the south atlantic and breakup of pangea

finite difference modeling of wave propagation on microscale a snapshot of the work in progress digital rock methodology combines modern microscopic imagingwithadvancednumericalsimulationsofthephysicalproperties of rocks modeling of elastic wave propagation directly from rock microstructure is integral to this technology we survey recent development of the rotated staggered grid rsg finite difference fd method for pore scale simulation of elastic wavepropagationindigitalrocksamples includingthedynamic elastic properties of rocks saturated with a viscous fluid examination of the accuracy of this algorithm on models with known analytical solutions provide an additional accuracy condition for numerical modeling on the microscale we use both the elastic and viscoelastic versions of the rsg algorithm to study gas hydratesandtosimulatepropagationofbiot sslowwave weapply rsg method ology to examine the effect of gas hydrate distributions in the pore space of a rock we compare resulting p wave velocities with experimentally measured data as a basis for buildinganeffective mediummodelforrockscontaininggashydrates we then perform numerical simulations of biot s slow wave in a realistic 3d digital rock model fully saturated with a nonviscous fluid corresponding to the high frequency limit of poroelasticity and placed inside a bulk fluid the model clearly demonstrates biot s slow curve when the interface is open between the slab and bulk fluid we demonstrate slow wave propagation in a porous medium saturated with a viscous fluid by analyzing an idealized 2d porous medium represented alternating solid and viscous fluid layers comparison of simulation results withtheexactsolutionforthislayeredsystemshowsgoodagreementoverabroadfrequencyrange

ocean continent boundary in the iberia abyssal plain from multichannel seismic data abstract the ocean continent boundary of the west iberia margin is marked by a basement ridge trending n s four segments of this ridge are recognized each of them being progressively offset westward from 40 n to 43 n because the setting and seismic character of the ridge in the iberia abyssal plain are similar to those of the galicia margin ridge which is made of serpentinized peridotite we think that the southern segments of the ridge are also made of the same mantle material the segmentation of the ridge suggests that the northward propagation of the continental break up during the north atlantic opening in early cretaceous times was discontinuous each segment possibly corresponding to a propagation step east of the ridge the basement of the whole iberia abyssal plain consists of highly thinned continental crust locally resting on a seismic reflector that resembles the s reflector previously recognized off galicia by analogy with the galicia margin we propose that the tilted crustal blocks lay on serpentinized peridotite derived from the upper mantle the s reflector corresponding to the contact between crustal rocks and serpentinite

triple junctions of bay of biscay and north atlantic new constraints on the kinematic evolution recently surveyed triple junction trajectories in the bay of biscay and newly available magnetic maps constrain the early oceanic evolution of the north atlantic and bay of biscay from chrons m0 to a33o 118 to 80 ma the opening of the bay of biscay is of the scissors opening type with a pole of rotation located near bordeaux lat 44 6 n long 0 3 w and predicted simultaneous compression in the central and eastern pyrenees structural directions west of iberia do not fit the north america iberia motion therefore a second triple junction of the ridge ridge fault type is postulated just south of the first one which propagated north ward from a more southerly position

the ocean continent boundary off the western continental margin of iberia crustal structure west of galicia bank a seismic refraction transect across the galicia bank continental margin shows that the original continental crust thins westward from 17 to 2 km immediately east of a margin parallel peridotite ridge pr immediately west of the pr oceanic crust is only 2 5 3 5 km thick but farther west oceanward it thickens to 7 km the pr caps a similar to 60 km wide lens shaped serpentinized peridotite body underlying both thinned continental and thin oceanic crust when superimposed on a reflection time version of the velocity model the s reflector is clearly intracrustal at its east end westward s cuts down to lower crustal levels eventually coinciding with the top of the serpentinized peridotite lens original crust mantle boundary these observations render almost impossible the seafloor exposure of the pr by s acting as a top to the west detachment fault numerical models of melting and borehole subsidence information constrain our rifting model the easternmost continental crust experienced a total stretching factor of 4 3 most likely in two stages it probably occurred over similar to 25 m y with the highest fate of stretching at the beginning of the main earlier rift phase valanginian 141 135 ma the 3 4 7 km thick continental crust depending on whether serpentinized peridotite is assigned to crust or mantle which may include melt products requires stretching factors 6 more than 11 7 and a rift duration of more than 25 13 m y the thin oceanic crust immediately west of the pr is explained by conductive cooling of the mantle during the long prebreakup stretching phase which temporarily caused reduced melting immediately after breakup

magnetic mineralogy of the lower continental crust rocks that were once present in the deep continental crust can be found in surface exposure as xenoliths as parts of high grade metamorphic and plutonic terrains and as obducted lower crustal cross sections a review of magnetic and mineralogic studies of samples representing all such occurrences shows that magnetite is the only magnetic phase present in significant amounts in these rocks thermodynamic considerations indicate that tipoor magnetite is the expected magnetic oxide under equilibrium conditions that exist in the lower crust regardless of the primary magmatic composition of the spinel phase furthermore it seems unlikely that serpentinites with metal alloys contribute significantly to the magnetization of the lower crust or mantle thus magnetite in the deep crust is the most likely candidate for the source of the long wavelength magnetic anomalies observed in regional aeromagnetic and satellite magnetometer surveys if so the entire crust should be magnetic in most continental areas including shields in areas of high heat flow the bottom of the magnetic crust may lie considerably above the moho

magnetic properties and opaque mineralogy of drilled submarine intrusive rocks summary measurements of natural remanent magnetization nrm curie temperature ferrimagnetic and paramagnetic susceptibility saturation induced and remanent magnetizations coercive forces alternating field properties and viscous magnetization are reported for 50 submarine intrusive rocks drilled during legs 30 37 and 45 of dsdp the collection includes doleritic sill rocks fresh and serpentinized cumulate gabbros and serpentinized cumulate peridotites and serpentinized lherzolites believed to have originated in layers 2b 3b and 4 respectively magnetite with a curie temperature between 520 and 580 c is the principal magnetic mineral in all samples there is no indication of maghemitization or of metamorphism to greenschist facies or above the magnetite in the doleritic and cumulate gabbros is a product of deuteric alteration of titanomagnetite and pyroxene the stable nrm is a primary trm the magnetite in the serpentinized rocks is a secondary product of serpentinization the stable nrm is a crm in most rock types the magnetite is of single domain or pseudo single domain size and soft components of nrm are small the magnetite grain size in some of the doleritic gabbros is much coarser these rocks acquire large viscous magnetizations which however are readily removed by alternating field cleaning the cleaned nrms of legs 30 and 45 rocks have approximately dipole inclinations but the nrms of most of the mutually intruded leg 37 units have been dispersed by tectonic rotations the doleritic gabbros and the serpentinized peridotites have stable directionally coherent nrms 10 3emu cm 3 in intensity their counterparts in layers 2b and 3b 4 are likely contributors to oceanic magnetic anomalies layer 3b cumulate gabbros and tectonic serpentinites in the middle and upper crust are less likely anomaly sources

incremental linear elastic response of rocks containing multiple rough fractures similarities and differences with traction free cracks fractures in the subsurface serve as conduits for fluids and gas connecting remote hydrocarbon reservoir sections to production wells seismic and sonic data are popular sources for information on fracture properties the most commonly used model to extract fracture information from such data is based on the paradigm of the displacement discontinuity interface without a direct link to relevant characteristics such as the surface roughness properties of a fracture indeed fractures can be modeled as displacement discontinuity surfaces and in this sense they resemble traction free cracks in literature cracks and fractures are not always properly distinguished perhaps because the terms are often perceived as synonyms however microstructural parameters that control magnitudes of the discontinuities and thus the effective stiffnesses are entirely different statistics of contacts for fractures versus crack density for traction free cracks we explore the effective elasticity of rocks containing multiple fractures using a model of a fracture as two rough surfaces with isolated contacts this is done in the context of the incremental linear elastic response to small stress changes typical in wave propagation problems fractures are dry or may have diverse orientations and contacts may or may not be hertzian a link exists between contact characteristics and effective stiffness of single and multiple fractures our work examines and accounts for the strong effect of interactions between individual contacts by means of a double sum over mutual positions as well as outlines the differences and similarities between theories for cracks and fractures

seismic characterization of multiple fracture sets does orthotropy suffice as geophysicists rely increasingly on effective media theories to characterize naturally fractured reservoirs they become more and more interested in evaluating the accuracy of different theories estimating their limits of applicability and assessing their usefulness for practice with this in mind we compare two popular seismological theories of hudson and schoenberg with the theory of kachanov developed in the context of mechanics of materials by performing finite element simulations of effective media for models that contain several sets of nonintersecting circular vertical fractures embedded in otherwise isotropic host rock we examine the accuracy of these theories our numeric study reveals that predictions of both the first and second order hudson s theories are typically inferior to those of others especially when the fractures are dry while on average the theories of schoenberg and kachanov fit finite element computations with comparable accuracy the latter appears to be more useful

deep structure of the ocean continent transition in the southern iberia abyssal plain from seismic refraction profiles ocean drilling program legs 149 and 173 transect we present a wide angle seismic refraction study of an 80 40 km region of the southern iberia abyssal plain south of galicia bank an intersecting grid of two e w and four n s wide angle reflection refraction profiles is used to define variations of the basement velocity structure within this unusually wide ocean continent transition oct these structures can be systematically linked to variations in acoustic basement morphology and to results from ocean drilling program odp boreholes lateral changes in the velocity structure of the basement occur abruptly over distances of 20 km where complex variations may be found thinned upper continental crust 2 5 km thick with velocities of 5 0 6 6 km s is limited to a series of n s fault blocks immediately south of galicia bank this crust is underlain by a high velocity layer 7 3 7 9 km s of weakly serpentinized i e 0 25 peridotite which exists throughout the eastern part of the survey area basement within the oct appears to consist dominantly of a broad region of exposed upper mantle that has been serpentinized heterogeneously both vertically and horizontally in the southeast sector of our survey where basement topography deepens and becomes subdued continental fault blocks are absent instead basement contains an upper layer of more pervasively serpentinized i e 25 45 peridotite that is 2 km thick this layer is characterized by low velocity at the top of basement 4 2 km s that increases rapidly with depth and it probably corresponds to a seismically unreflective layer previously identified in reflection profiles to the south of our survey in the western section of our survey beneath a series of elevated basement ridges velocities are reduced within both the upper basement layer 3 5 6 0 km s and lower layer 6 4 7 5 km s these changes suggest that both upper and lower layers have become more highly serpentinized with values of 60 100 in the upper layer and 25 45 in the lower layer probably during the last stages of rifting and immediately before formation of oceanic crust a normal or slow spreading oceanic crustal structure is not found within the survey region thus it appears that the onset of seafloor spreading occurs in the region west of the peridotite ridge sampled at odp site 897 and east of the j magnetic anomaly

deep structure in the vicinity of the ocean continent transition zone under the southern iberia abyssal plain we present results from a seismic and magnetic study of acoustic basement beneath the southern iberia abyssal plain an ocean continent transition zone oct characterized by subdued basement relief and weak magnetization lies seaward of thinned continental crust its western edge is a region with isochron parallel ridges and generally higher basement magnetizations the width of the oct decreases to the north the seaward change in basement morphology coincides with changes in seismic velocity structure but in both regions anomalously high velocities at shallow depths within acoustic basement suggest that the oct consists largely of serpentinized peridotite our magnetic and seismic data support the hypothesis of exhumed upper mantle more than that of ultraslow sea floor spreading for the origin of the oct

rift tectonics on the passive continental margin off galicia spain abstract new migrated multichannel seismic profiles on the starved passive continental margin off galicia spain illustrate the tectonic style of the early cretaceous rifting event which preceded the separation of iberia and north america the main episode of rifting was preceded by other tensional episodes probably of earliest cretaceous and late jurassic age listric faulting associated with rifting was accompanied by large scale mass movements from the crests of the tilted blocks two subaerial erosional surfaces are visible one of late jurassic or earliest cretaceous age was affected by the final faulting episode the other was synchronous with the main phase of rifting and is present only on the upper part of the margin because the central trough was under deep water the significance of a ridge near the ocean continent boundary where altered lherzolite has been dredged and cored is discussed below the tilted blocks which include the basement rocks the seismic horizon s is visible as on the armorican margin its significance is also discussed

comprehensive analysis of marine magnetic vector anomalies we present a comprehensive description of the analysis of marine magnetic vector anomalies the marine magnetic vector field can be measured with a shipboard three component magnetometer stcm the stcm has the advantage of measuring three components but it suffers from several types of noise sources because the principles of its measurement are more complex than that of a proton precession magnetometer we have estimated the quality of stcm data constructed an optimal filter and evaluated the reliability of the filtered data then we have organized an analytical procedure composed of four steps 1 the discrimination between two and three dimensional magnetic sources 2 the determination of magnetic boundaries 3 the calculation of the boundary strikes and 4 the estimation of the boundary magnetization contrasts we show examples of these procedures using the data near the east pacific rise 28 s 31 s collected during leg 5 of the gloria expedition all the results of the above processing are merged in order to illustrate the distinct pattern of the seafloor magnetization in the surveyed area

compressional deformation at the ocean continent transition in the ne atlantic local zones of compressional deformation spatially coincident with the ocean continent transition occur in the ne atlantic off western iberia on the northern margin of the bay of biscay and in the southern rockall trough the deformation zones are typically broad oceanward facing monoclines several tens of kilometres in width the amount of shortening is small although the structures may also accommodate some strike slip motion deformation peaked during the mid late eocene in biscay off galicia bank and in rockall trough and in the mid miocene off western iberia these deformation pulses were contemporary with the pyrenean and betic orogenies in western europe and may have resulted from structural reorganizations within the evolving orogens driven by changes in plate motion possible mechanisms which might concentrate deformation at the ocean continent transition include slip within serpentinized peridotite underlying the transitional region and reactivation of a pre existing detachment fault within the thinned continental crust our observations may imply that rifted continental margins when reactivated can develop into new sites of plate subduction

marine magnetic anomalies the origin of the stripes the results of recent observational and theoretical investigations of lineated magnetic anomalies on the ocean floor are summarized in tables graphs and diagrams and analyzed topics addressed include early lineation models inversions of magnetic anomalies to obtain source functions deep tow studies of magnetic anomalies evidence from the long wavelength component of the magnetic field including magsat observations and direct measurements of the magnetic properties of oceanic rocks it is concluded that the source of the lineated anomalies must reside in most of the oceanic crust not just in the pillow lavas of layer 2a

self consistent rolling hinge model for the evolution of large offset low angle normal faults the nature of the physical processes responsible for the formation of continental and oceanic metamorphic core complexes is widely debated the controversy focuses primarily on whether the low angle normal faults observed in these environments formed and slipped at low angles or were rotated from an original high angle orientation after large offsets we describe a self consistent numerical model for the extension of a brittle layer that can spontaneously produce normal fault structures in our formulation a fault or faults form because strength is locally reduced with increasing strain if the reduction in fault strength is 10 of the total strength of the layer then faults lock after an offset smaller than the layer thickness and new faults form larger strength reduction leads to single faults that continue to slip no matter how large the fault offset if the strength reduction occurs by the loss of cohesion then we see the unlimited offset faults for layers 11 22 km thick for reasonable values of cohesion the key result of this study is that structures very similar to those observed in both oceanic and continental core complexes are produced by rotation of the inactive part of the model fault after very large offset

frequency dependence of anisotropy in fluid saturated rocks part i aligned cracks case a major cause of attenuation in fluid saturated media is the local fluid flow or squirt flow induced by a passing wave between pores of different shapes and sizes several squirt flow models have been derived for isotropic media for anisotropic media however most of the existing squirt flow models only provide the low and high frequency limits of the saturated elastic properties we develop a new squirt flow model to account for the frequency dependence of elastic properties and thus gain some insight into velocity dispersion and attenuation in anisotropic media in this paper we focus on media containing aligned compliant pores embedded in an isotropic background matrix the low and high frequency limits of the predicted fluid saturated elastic properties are respectively consistent with gassmann theory andmukerji mavko squirt flow model results are also expressed in terms of thomsen anisotropy parameters it turns out that the p wave anisotropy parameter tends to zero in the high frequency limit whereas the parameter remains the only indicator of p s anisotropy the s wave anisotropy parameter is not affected by the presence of fluid and remains the same for all frequency ranges a new definition for attenuation anisotropy parameters is also proposed to quantify the attenuation anisotropy in the most important case of liquid saturation analytical expressions are derived for elastic properties velocity anisotropy parameters quality factors and attenuation anisotropy parameters a companion paper considers the case of cracks with an ellipsoidal distribution of orientations resulting from the application of anisotropic stress

feasibility of seismic characterization of multiple fracture sets estimation of parameters of multiple fracture sets is often required for successful exploration and development of naturally fractured reservoirs the goal of this paper is to determine the maximum number of fracture sets of a certain rheological type which in principle can be resolved from seismic data the main underlying assumption is that an estimate of the complete effective stiffness tensor has been obtained for example from multiazimuth multicomponent surface seismic and vertical seismic profiling vsp data although typically only a subset of the stiffness elements or some of their combinations may be available this study helps to establish the limits of seismic fracture detection algorithms the number of uniquely resolvable fracture systems depends on the anisotropy of the host rock and the rheology and orientation of the fractures somewhat surprisingly it is possible to characterize fewer vertical fracture sets than dipping ones even though in the latter case the fracture dip has to be found from the data for the simplest rotationally invariant fractures embedded in either isotropic or transversely isotropic with a vertical symmetry axis vti host rock the stiffness tensor can be inverted for up to two vertical or four dipping fracture sets in contrast only one fracture set of the most general microcorrugated type regardless of its orientation is constrained by the effective stiffnesses these results can be used to guide the development of seismic fracture characterization algorithms that should address important practical issues of data acquisition processing and inversion for particular fracture models

evidence of widespread cretaceous remagnetisation in the iberian range and its relation with the rotation of iberia a palaeomagnetic investigation has been carried out at 13 sites of jurassic age in the iberian range northern spain two components of remanent magnetisation have been found at each site a primary high temperature component shows an average counterclockwise rotation with respect to the north of 33 2o clockwise about a vertical axis corresponding to the absolute rotation of the iberian plate since the jurassic a secondary low temperature component shows a systematic declination difference of 16 4o with respect to the primary component this indicates that a rotation of iberia must have occurred between the two acquisition times comparison of the magnetisation directions with previous palaeomagnetic data and with sea floor spreading data constrains the age of the remagnetisation between 95 and 125 ma the remagnetisation may be associated with the extensional phases in the iberian basin in the early cretaceous barremian early albian or late cretaceous cenomanian a principal characteristic of the remagnetisation is its widespread character in the iberian range 1998 elsevier science b v all rights reserved

a mesozoic time scale we present an integrated geomagnetic polarity and stratigraphic time scale for the triassic jurassic and cretaceous periods of the mesozoic era with age estimates and uncertainty limits for stage boundaries the time scale uses a suite of 324 radiomenc dates including high resolution 40 ar 39 ar age estimates this framework involves the observed ties between 1 radiometric dates biozones and stage boundaries and 2 between biozones and magnetic reversals on the seafloor and in sediments interpolation techniques include maximum likelihood estimation smoothing cubic spline fitting and magnetochronology

relative importance of strain rate and rheology for the mode of continental extension summary both extension rate and rheology have been shown to influence the style of continental rifting so far their effect on the dynamics of extension has been discussed separately in the literature leading to diverging conclusions the rate of extension mostly affects the dynamics of rifting through the occurrence of syn rift cooling at low extension rates this cooling results in an increase of strength if the lithosphere has a temperature dependent rheology england 1983 first suggested that this effect will limit the amount of extension that an area may undergo kusznir park 1987 argued more generally that it will induce a widening of the rift and concluded that extension rate is the major control on wide versus narrow rifting later studies bassi 1991 bassi keen potter 1993 however have demonstrated the importance of rheological layering within the lithosphere for the mode of continental extension by showing that a plasticity dominated rheology will lead to rapid and narrow necking while a creep dominated rheology results in wider rifts and margins gravitational stresses arising from density anomalies due to lithosphere thinning also affect the style of rifting buck 1991 in this paper we examine the combined effect of these different parameters in order to reconcile earlier studies and assess the importance of syn rift cooling for the process of lithospheric necking the approach introduced in a previous study bassi 1991 uses a finite element technique to simulate extension of a vertical cross section of the lithosphere the effect of cooling on the necking pattern depends strongly on the rheology of the thinned lithosphere when it starts to cool if heat diffusion always induces strengthening and delays rupture in time it only modifies significantly the geometry of the rift when the upper mantle is weak and viscous in this case the locus of maximum strain rate migrates laterally once the central area starts to cool and harden as hypothesized by kusznir park 1987 eventually strain concentrates at the transition between deformed and undeformed lithosphere we predict that this pattern will induce asymmetric breakup and produce a very narrow margin and a wide uniformly thinned conjugate margin in all other cases i e when the upper mantle is initially in the low plasticity regime or if it reaches the yield stress during extension the rate of extension appears to have little effect on the rifting pattern

high vp vs ratio saturated cracks or anisotropy effects 1 we measured vp vs ratios of thermally cracked westerly granite thermally cracked carrara marble and 4 porosity fontainebleau sandstone for an effective mean pressure ranging from 2 to 95 mpa samples were fluidsaturated alternatively with argon gas and water 5 mpa constant pore pressure the experimental results show that at ultrasonic frequencies vp vs ratio of water saturated specimen never exceeded 2 15 even at effective mean pressure as low as 2 mpa or for a lithology for which the poisson s ratio of minerals is as high as 0 3 calcite in order to check these results against theoretical models we examine first a randomly oriented cracked medium with dispersion but without anisotropy and second a medium with horizontally aligned cracks with anisotropy but without dispersion the numerical results show that experimental data agree well with the first model at high frequency vp vs ratios range from 1 6 to 1 8 in the dry case and from 1 6 to 2 2 in the saturated case the second model predicts both vp sv and vp sh to vary from 1 2 to 3 5 depending on the raypath angle relative to the crack fabric in addition perpendicular to the crack fabric a high vp vs ratio is predicted in the absence of shear wave splitting from these results we argue the possibility that high vp vs ratio 2 2 as recently imaged by seismic tomography in subduction zones may come from zones presenting important crack anisotropy the cumulative effects of crack anisotropy and high pore fluid pressure are required to get vp vs ratios above 2 2 citation wang x q a schubnel j fortin e c david y gueguen and h k ge 2012 high vp vs ratio saturated cracks or anisotropy effects geophys res lett 39 l11307 doi 10 1029 2012gl051742

elastic wave propagation in fractured media using the discontinuous galerkin method abstractwe have formulated and implemented a discontinuous galerkin method dgm for elastic wave propagation that allows for discontinuities in the displacement field to simulate fractures or faults the approach is based on the interior penalty formulation of dgm and the fractures are simulated using the linear slip model which is incorporated into the weak formulation by including an additional term that is similar to the penalty term but uses the fracture compliance instead of an arbitrary penalty parameter we have calibrated our results against an analytic solution of fracture induced anisotropy for a set of elongated horizontal fractures and we have evaluated numerical examples that simulate the reflection and transmission of waves at a fracture and at fracture interface waves this method can further be used with models containing intersecting fractures and multiple fracture sets in 2d or 3d domains

insight into the nature of the ocean continent transition off west iberia from a deep multichannel seismic reflection profile a high quality multichannel seismic reflection profile across the west iberia margin confirms the existence of a 130 km wide transition zone between tilted continental fault blocks and unequivocal oceanic crust the zone is characterized by a 1 0 2 5 km thick seismically unreflective upper basement layer lying over reflective basement that contains major landward dipping reflectors that mostly truncate against the base of the upper layer and penetrate to depths of 10 19 km below the basement surface and minor seaward dipping reflectors moho reflections are absent in this zone we suggest that the unreflective layer represents tectonically exposed upper mantle that has undergone extensive serpentinization enhanced by vigorous seawater circulation about 40 km farther north the transition zone narrows to 35 km and the unreflective layer is less continuous and widespread

extensional tectonics in the jeanne d arc basin offshore newfoundland implications for the timing of break up between grand banks and iberia

attenuation mechanisms in fractured fluid saturated porous rocks a numerical modelling study seismic attenuation mechanisms receive increasing attention for the characterization of fractured formations because of their inherent sensitivity to the hydraulic and elastic properties of the probed media attenuation has been successfully inferred from seismic data in the past but linking these estimates to intrinsic rock physical properties remains challenging a reason for these difficulties in fluid saturated fractured porous media is that several mechanisms can cause attenuation and may interfere with each other these mechanisms notably comprise pressure diffusion phenomena and dynamic effects such as scattering as well as biot s so called intrinsic attenuation mechanism understanding the interplay between these mechanisms is therefore an essential step for estimating fracture properties from seismic measurements in order to do this we perform a comparative study involving wave propagation modelling in a transmission set up based on biot s low frequency dynamic equations and numerical upscaling based on biot s consolidation equations the former captures all aforementioned attenuation mechanisms and their interference whereas the latter only accounts for pressure diffusion phenomena a comparison of the results from both methods therefore allows to distinguish between dynamic and pressure diffusion phenomena and to shed light on their interference to this end we consider a range of canonical models with randomly distributed vertical and or horizontal fractures we observe that scattering attenuation strongly interferes with pressure diffusion phenomena since the latter affect the elastic contrasts between fractures and their embedding background our results also demonstrate that it is essential to account for amplitude reductions due to transmission losses to allow for an adequate estimation of the intrinsic attenuation of fractured media the effects of biot s intrinsic mechanism are rather small for the models considered in this study

magnetization of the pacific ocean lithosphere deduced from magsat data magsat anomalies over the pacific ocean are related to volcanic plateaus and the edge effect of the pacific cretaceous quiet zone pcqz four prominent plateaus shatsky rise the mid pacific mountains hess rise and manihiki plateau are considered in this study the major lateral magnetization contrasts associated with these plateaus are considered to arise from the topographic swells and the crustal roots with root thicknesses estimated from topography using an airy isostatic model shatsky rise and the mid pacific mountains are older than the cretaceous quiet period and their natural remanent magnetization nrm is not a significant component of the magnetization contrasts that cause the magsat anomalies associated with these plateaus their magnetic properties are characterized by effective magnetic susceptibility contrasts of 0 07 0 01 s i per unit volume averaged over their topographic swells and crustal roots equivalent to 0 04 if averaged over the entire crustal thicknesses swell plus root plus intervening layer this value agrees well with the estimates of previous investigators for these plateaus and for similar plateaus in other oceans two plateaus of cretaceous quiet period age within the pcqz hess rise and manihiki plateau have origins similar to those of shatsky rise and the mid pacific mountains and they probably have similar effective susceptibility contrasts but they may also carry cretaceous quiet period nrm magnetic anomalies due to hess rise and manihiki plateau calculated from the effective susceptibility contrast deduced for shatsky rise and the mid pacific mountains are substantially larger than the observed magsat anomalies of these plateaus there are also magsat anomalies over parts of the pacific where no plateaus exist some of these anomalies are demonstrated as probably due to a contrast in nrm between the pcqz and its surroundings the total remanent magnetization contrast magnetization contrast in amperes per meter times thickness in meters equivalent to the dipole moment per unit area of the pcqz is 14 000 20 000 amperes 30 which cannot be simply explained by the absolute values of remanent magnetization predicted by conventional models of oceanic crustal magnetic properties modelling of the cretaceous quiet zones in the northern atlantic indicates a similar total remanent magnetization contrast these results may be explained by including uppermost mantle remanent magnetization with an intensity of about 1 2 a m 1 if magnetization persists to a depth of 7 below the seismic moho i e down to the depth of the crustal roots of the plateaus including nrm in the uppermost mantle of the pcqz also serves to reduce the calculated amplitude of the hess rise and manihiki plateau magsat anomalies if the nrm of the crustal roots is less than the nrm of the surrounding uppermost mantle on this basis the estimated intensity of nrm in the uppermost 7 km of the pcqz mantle is 1 3 a m 1 in very good agreement with the intensity estimated from the pcqz edge effect anomalies these estimates of uppermost mantle nrm are probably a maximum limit recognizing that other sources may also contribute to the total remanent magnetization contrasts of the cretaceous quiet zones

seismic anisotropy of fractured rock a simple method for including the effects of geologically realistic fractures on the seismic propagation through fractured rocks can be obtained by writing the effective compliance tensor of the fractured rock as the sum of the compliance tensor of the unfractured background rock and the compliance tensors for each set of parallel fractures or aligned fractures the compliance tensor of each fracture set is derivable from a second rank fracture compliance tensor for a rotationally symmetric set of fractures the fracture compliance tensor depends on only two fracture compliances one controlling fracture compliance normal the other tangential to the plane of the fractures the stiffness tensor which is more useful in the consideration of elastic wave propagation through rocks can then be obtained by inversion the components of the excess fracture compliance tensor represent the maximum amount of information that can be obtained from seismic data if the background rock is isotropic and the normal a

the ocean continent boundary off the western continental margin of iberia ii crustal structure in the tagus abyssal plain summary an 80 km long reversed seismic refraction line line 5 was shot over the tagus abyssal plain off portugal the main p wave reflected and refracted phases were modelled both for traveltime and amplitude the resulting p wave velocity depth model has the following features a an extremely thin crust of about 2 km b the absence of oceanic layer 3 and c very low upper mantle velocities between 7 6 and 7 9 km s this very unusual seismic velocity crustal structure is quite unlike thinned continental crust but is remarkably similar to the seismic crustal structures found at atlantic fracture zones and in particular to the structures found in profiles shot along the transform valley and near ridge transform intersections a magnetic anomaly chart seems to allow the possibility of several fracture zones one of which could intersect the centre of line 5 as an alternative to the fracture zone hypothesis we show that if the oceancontinent transition in the tagus abyssal plain is located at about 11 30 w in a symmetric position with respect to the ocean continent transition in the conjugate south newfoundland basin then magnetic anomalies can be modelled simply by assuming sea floor spreading west of 11 45 w at 10 mm yr beginning at m11 time 133 myr bp and blocks of rifted continental crust to the east the location of the proposed ocean continent transition in the tagus abyssal plain is marked by a well defined n s linear magnetic anomaly which is adjacent to the oldest sea floor spreading block east of the proposed ocean continent transition there is an increase in the depth to basement similar to that found east of the ocean continent transition in the iberia abyssal plain and elsewhere this model also allows us to explain why purdy s 1975 seismic refraction line a ar in the tagus abyssal plain cannot be interpreted as a conventional reversed pair because most of line a was shot over the ocean continent transition zone and most of line ar over thinned continental crust remarkably similar velocity depth structures to that under line 5 are found close to the ocean continent transition zone off the whole of western iberia in areas which show no clear evidence of fracture zones therefore it appears more likely that the seismic structure of line 5 is due to its proximity to the ocean continent transition than to a local association with a fracture zone and further that its structure is typical of this transition off the western margin of iberia we also suspect that the low upper mantle velocities associated with the ocean continent transition indicate the widespread occurrence of serpentinized peridotite

nature of the scattered seismic response from zones of random clusters of cavities and fractures in a massive rock the scattering of elastic energy by random clusters of fractures and or cavities in a massive rock is studied the interpretation of the scattered seismic response reveals crucial information about the clusters of inhomogeneities fractures cavities which may correspond to reservoirs the study is based on a new two dimensional numerical modelling method that relaxes the constraints on the location and orientation of the inhomogeneities accounts for inhomogeneities that have almost no volume but a finite surface area fractures and improves the accuracy of the calculation when the size of the inhomogeneities is comparable to the mesh size it is shown that the nature of the seismic response of zones of diffuse fracturing and or cavities is associated with the non uniformity of micro inhomogeneities in such zones accumulations of these micro inhomogeneities are known as clusters the relationship between the non uniformity of micro inhomogeneities and the strength of the seismic response has been established and measured considerable differences in the structure of the seismic response of zones of diffuse fracturing and diffuse cavities have been identified converted ps waves dominate in the scattered wavefield associated with fractures this is explained as the modelling results show by a greater transparency of fluid filled fractures which reduces the reflected energy of compressional waves the wavefield associated with cavities is characterized by the predominance in terms of strength of compressional pp waves the strength of converted ps waves in the scattered wavefields for both media is approximately the same on the whole according to the results of the modelling the energy of the scattered response of fractured reservoirs is considerably less about two times than that of cavernous reservoirs

kinematic evolution of the southern north atlantic implications for the formation of hyperextended rift systems we focus on the southern north atlantic rifted margins to investigate the partitioning and propagation of deformation in hyperextended rift systems using plate kinematic modeling the kinematic evolution of this area is well determined by oceanic magnetic anomalies after the cretaceous normal polarity superchron however the rift and early seafloor spreading evolution 200 83 ma remains highly disputed due to contentious interpretations of the j magnetic anomaly on the iberia newfoundland conjugate margins recent studies highlight that the j anomaly is probably polygenic related to polyphased magmatic events and therefore does not correspond to an isochron we present a new palinspastic restoration without using the j magnetic anomaly as the chron m0 we combine 3 d gravity inversion results with local structural stratigraphic and geochronological constraints on the rift deformation history the restoration of the southern north atlantic itself is not the primary aim of the study but rather is used as a method to investigate the spatiotemporal evolution of hyperextended rift systems we include continental microblocks that enable the partitioning of the deformation between different rift segments which is of particular importance for the evolution of the iberia eurasia plate boundary our modeling highlights the following 1 the segmentation of the iberia newfoundland rift system during continental crust thinning 2 the northward v shape propagation of mantle exhumation and seafloor spreading 3 the complex partitioning of deformation along the iberia eurasia plate boundary and 4 a three plate propagation model which implies transtension

undercrusting by serpentinite beneath rifted margins the west galicia passive margin spain is bounded by a continuous belt of serpentinized peridotite here we present the results of petrological studies of the peridotite 39ar 40ar dating of high temperature ductile shearing of a dioritic dyke crossing the peridotite and regional seismic stratigraphy which demonstrate that the uplift ductile shearing and pervasive serpentinization of mantle rocks occurred at early cretaceous time during the rifting stage of the margin the serpentinite layer resting on fresh peridotite is probably several kilometres thick at present seismic data and gravity data cannot distinguish serpentinite from crustal material but our results from the galicia margin indicate that the seismic crust beneath rifted margin may include mantle material transformed into serpentinite by syn rift hydrothermal activity in some cases this undercrusting process might explain the young age and mobility of the moho beneath stretched continental basement

effective elastic properties of randomly fractured soils 3d numerical experiments this paper is concerned with numerical tests of several rock physical relationships the focus is on effective velocities and scattering attenuation in 3d fractured media we apply the so called rotated staggered finite difference grid rsg technique for numerical experiments using this modified grid it is possible to simulate the propagation of elastic waves in a 3d medium containing cracks pores or free surfaces without applying explicit boundary conditions and without averaging the elastic moduli we simulate the propagation of plane waves through a set of randomly cracked 3d media in these numerical experiments we vary the number and the distribution of cracks the synthetic results are compared with several most popular theories predicting the effective elastic properties of fractured materials we find that for randomly distributed and randomly orientated non intersecting thin penny shaped dry cracks the numerical simulations of p and s wave velocities are in good agreement with the predictions of the self consistent approximation we observe similar results for fluid filled cracks the standard gassmann equation cannot be applied to our 3d fractured media although we have very low porosity in our models this is explained by the absence of a connected porosity there is only a slight difference in effective velocities between the cases of intersecting and non intersecting cracks this can be clearly demonstrated up to a crack density that is close to the connectivity percolation threshold for crack densities beyond this threshold we observe that the differential effective medium dem theory gives the best fit with numerical results for intersecting cracks additionally it is shown that the scattering attenuation coefficient of the mean field predicted by the classical hudson approach is in excellent agreement with our numerical results

variations in magnetization intensity and low temperature titanomagnetite oxidation of ocean floor basalts the remanent magnetization of the oceanic crust exhibits a systematic long term variation which correlates with the amplitudes of marine magnetic anomalies after a sharp initial decrease of natural remanent magnetization intensity a minimum is reached at 20myr followed by a gradual increase up to ages of 120 myr the progressive sea floor alteration of the magnetic minerals carrying the crustal magnetism is proposed as a cause for this behaviour

mantle exhumation at passive margins abstract laboratory models of lithosphere necking have been used to study the modes of passive margin formation and related mantle exhumation at continent ocean boundary four layer models were constructed with sand and silicone putty to represent the brittle and ductile layers respectively of both crust and mantle it is shown that necking of the whole lithosphere model is nearly symmetrical pure shear but that asymmetrical structures simple shear develop internally due to heterogeneous boudinage and or faulting of brittle layers relative movements between brittle layers is accommodated by layer parallel shear in the ductile layers defining a set of conjugate shear zones with increasing stretching lower crust and mantle shear zones become juxtaposed as the lower ductile mantle layer rises up through the separation zone of boudins in the brittle layer the experimental results are used to propose a general model of passive margin formation leading to mantle exhumation they are also compared to the situation observed on the west iberia margin the exhumation of lithosphere mantle is the result of a bulk pure shear at lithospheric scale shearing of exhumed mantle rocks does not correspond to detachment faults cross cutting the whole lithosphere at the onset of rifting but results from heterogeneous stretching and boudinage of the high strength sub moho mantle

magmatism at the west iberia non volcanic rifted continental margin evidence from analyses of magnetic anomalies we discuss the magmatic development of the west iberia non volcanic rifted continental margin in the north atlantic ocean so called non volcanic rifted continental margins are characterized by a lack of syn rift magmatism and are considered to be largely amagmatic however this is clearly an oversimplification since seafloor spreading itself is a magmatic process and it is implausible that seafloor spreading begins instantaneously we concentrate our attention on the recently described zone of exhumed continental mantle zecm to investigate what magmatic processes accompanied the breakup of the continental lithosphere and the subsequent formation of the zecm leading to the onset of seafloor spreading we use magnetic anomalies supplemented by the interpretations of multichannel seismic reflection profiles and wide angle seismic experiments presented elsewhere forward and inverse modelling of a sea surface magnetic anomaly chart and of surface and deep towed magnetometer profiles shows that anomalies within the zecm differ in trend amplitude and source type from those in the adjacent oceanic crust and thinned continental crust the zecm anomalies appear to be caused by elongated source bodies within 8 km of the top of the acoustic basement aligned parallel to the margin we interpret such bodies as syn extensional intrusions that increase in volume oceanward they eventually merge in the vicinity of a margin parallel basement peridotite ridge to give rise to a continuous crust that records reversals in the earth s magnetic field from the time of anomaly m4 n m5 r i e to mark the onset of seafloor spreading we find no evidence for anomalies formed by seafloor spreading at either slow or ultraslow rates before m5 r 128 ma

causes and rate limiting mechanisms of ridge propagation a fracture mechanics model all known propagating rifts pr s are growing away from shallow ridge axis seafloor we examine a model for rift propagation in which the ridge axis conduit like a crack in the lithosphere propagates in response to a stress concentration at its tip the stress concentration near the tip which causes progressive failure of the lithosphere is primarily due to excess gravity spreading stresses associated with anomalously shallow ridge axis along the growing ridge this stress concentration near the tip is characterized by a stress intensity factor k which must exceed a threshold value to cause failure of the plate a remotely applied tensile stress would make a positive contribution to k but would act equally on both ridge segments and not favor the propagation of either the pressure in the crack may depending on its distribution make either a positive or negative contribution to k for a high enough propagation rate viscous flow induced suction due to the growth of the ridge axis as well as the reduced vertical flow near the pr tip would make k 0 this simple model thus includes a mechanism to control the speed of propagation and is consistent with the axial morphology of the spreading segment associated with the well studied 95 5 w pr of the galapagos spreading center analytical solutions for the contribution to the stress intensity factor of viscous forces resisting ridge axis growth and causing the pr axial topography are consistent with the observed propagation rate for asthenosphere viscosities of about 1019 pa s 1020 p we also examine a more general model of a ridge transform ridge system on the basis of energy conservation in terms of energetics this more general model reduces to that of a single propagating ridge axis crack when both the work done by forces driving propagation and the viscous dissipation due to forces resisting propagation are generated along the growing ridge axis however the more general model also includes mechanisms that may stop ridge propagation propagation will stop either when the energy needed for transform migration is larger than that available for ridge axis growth or when the strain energy absorbed at the dying ridge axis is comparable to that released at the growing ridge axis i e if the stress intensity factors for both ridge axes are similar both of these possibilities may occur when the propagating rift completely propagates through a ridge segment as at 85 w in the galapagos finally in this model the slight systematic differences in ridge axis orientation of the growing and dying ridges are a consequence rather than a cause of ridge propagation

sensitivity of three component 3d finite difference elastic seismic modeling to inclusion parameters in hti and tti media with high inclusion density parameters associated with the presence of inclusions cracks or vugs significantly influence seismic responses the t matrix method is used to define approximate anisotropic effective elastic stiffness tensors for media with inclusions this allows 3d three component eighth order staggered grid finite difference modeling to simulate the seismic responses of anisotropic media with high inclusion density various aspect ratios spatial distributions and orientations of inclusions and fluid content the model parameters are chosen to represent aligned inclusions ranging from vertical cracks to vugs in a carbonate reservoir encased in clastics the magnitude of anisotropy increases with increasing inclusion density for p and s waves cracks in a high velocity carbonate reduce the stiffnesses and correspondingvelocities this results in smaller contrasts with the surrounding lower stiffness clastics and hence smaller reflection coefficients s wave splitting and the anisotropy of vp vs are clearly

deep structure of the ocean continent transition in the southern iberia abyssal plain from seismic refraction profiles the iam 9 transect at 40 20 n we present a crust and mantle velocity structure for the west iberia passive continental margin derived from a 320 km long wide angle seismic profile acquired in the southern iberia abyssal plain we observe a 170 km wide ocean continent transition zone which includes a pair of overlapping peridotite ridges and is bounded by oceanic crust and landward by fault bounded blocks of continental crust the profile lies 40 km south of the transect sampled by ocean drilling program odp legs 149 and 173 the transition zone structure can be divided into an upper layer 2 4 km thick with velocities of between 4 5 and 7 0 km s 1 and generally a high velocity gradient 1 s 1 and a lower layer up to 4 km thick with a velocity of 7 6 km s 1 and a low velocity gradient a weak moho reflection in this zone was seen only on wide angle profiles at an offset of 30 km the upper layer has a distinctly lower velocity than thinned continental crust adjacent to the continental slope conversely the lower layer has too high a velocity to be magmatically intruded or underplated lower continental crust on the coincident seismic reflection profile fault bounded crustal blocks identified in unequivocal extended continental crust are not observed in the transition zone the upper layer has velocity bounds and gradient similar to oceanic layer 2 observed west of the peridotite ridges but no oceanic layer 3 velocity structure is present while magnetic anomalies have been identified within the transition zone they have not been modeled successfully as seafloor spreading magnetic anomalies nor do they generally form long linear margin parallel features finally odp boreholes 40 km north of our profile and within the interpreted transition zone have recovered up to 140 m thick sections of serpentinite and serpentinized peridotites with little evidence of mafic igneous material we conclude that the transition zone cannot be dominantly composed of either extended continental crust or oceanic crust although current melting models predict a considerably thicker crust of decompression melt products we interpret this region as exposed upper mantle peridotite with little or no synrift extrusive material and limited amounts of synrift material intruded within the serpentinized peridotite

a new method for precise determination of the position and strike of magnetic boundaries using vector data of the geomagnetic anomaly field summary we present a new method which provides precise determination of the position and strike of magnetic boundaries using vector data of the geomagnetic anomaly field assuming a 2 d magnetic structure the intensity of spatial differential vectors isdv exhibits a peak at the boundary of magnetic structures the strike of the magnetic boundary is obtained using the fact that the magnetic field is zero in the direction parallel to the boundary we have also applied this method to 3 d magnetic structures our method requires only the relative changes of the three components which are more accurately measured than their actual magnitudes we have applied this method to data from the southern juan de fuca ridge obtained on the r v hakuho maru expedition in 1988 kh 88 3 the results are summarized in magnetic boundary strike diagrams mbsd these are maps that show the position strike and character of the magnetic boundaries mbsd provides valuable information for understanding the magnetic structure of oceanic crust such as magnetic lineations pseudo faults fracture zones and the central anomaly magnetic high camh therefore relatively few vector magnetic profiles provide information similar to extensive total intensity geomagnetic surveys

extension of continental crust at the margin of the eastern grand banks newfoundland seismic and gravity observations from the rifted margin of the eastern grand banks newfoundland support a new model for extension of the continental crust from the shelf edge to odp site 1277 where mantle rocks are exhumed we find that the largest decrease in crustal thickness from about 28 km to 6 km occurs beneath the continental slope of the grand banks over a distance of just 20 km this rapid decrease in crustal thickness coincides with anomalously high seismic velocities 7 0 7 2 km s 1 in the lower crust of the shelf edge the thin crust of the continent ocean transition cot in this area has a smooth basement surface void of upper crustal blocks and prerift sediments we compare our geophysical results with a geodynamical model that represents rifting of a relatively hot continental lithosphere and with another numerical model that represents rifting of a cold lithosphere both geodynamic models suggest that crustal thinning beneath the continental slope was achieved by extensional faulting in the upper crust and ductile shear zones in the middle crust the geodynamic models provide an explanation for the formation of distinct continental slopes at rifted margins beneath the continental shelf of the grand banks the moho and the strong lower crust rotated upwards toward to a 50 dip without visible internal deformation the presence of these strong lower crustal rocks at shallow depth in the rift flank subsequently helped to localize the extension farther seaward with ongoing extension some high angle normal faults may have rotated to a sub horizontal orientation which would explain the lack of brittle deformation visible in the seismic reflection data the two geodynamic models produce different amounts of extension of continental crust in the distal margins the hot rifting model localizes strain much more rapidly leaving narrow zones of extended continental crust and it produces a relatively large amount of melt 30 in the final stages of rifting continental breakup may occur rapidly in hot lithosphere 5 myr on the other hand a cold extension model extends the continental crust to a thickness smaller than 10 km over a width of 50 km in the distal margin similar to what we inferred at the eastern grand banks the cold lithospheric model requires about 23 myr of extension before continental breakup and it predicts much less melting in the mantle 13 the long rift duration wide zones of thinned continental crust and small amount of magmatism make the cold rifting model the most applicable to newfoundland iberia rift

new paleomagnetic results from cretaceous sediments near lisboa portugal and implications for the rotation of iberia abstract paleomagnetic study of outer platform sediments of late jurassic early cretaceous age from portugal lisboa area leads to characteristic remanent magnetization directions for the hauterivian barremian d 317 i 58 and the aptian d 344 i 47 the absolute rotation of iberia between 125 and 110 ma is consequently of about 27 in an anticlockwise sense a later rotation of about 14 follows the first one in the same sense from 110 ma the total absolute rotation of iberia from the hauterivian age determined by paleomagnetism is thus about 41 the comparison of declinations measured with paleodeclinations calculated in lisboa from the eurasian and african poles of similar age indicates that the main phase of relative rotation of iberia with respect to eurasia occurs during the first stage of relative motion i e hauterivian to aptian the tectonic history of the bay of biscay is in good agreement with these two stages of rotation the total relative rotation with respect to europe is 34 this value is consistent with results previously established by van der voo 2 3 25 but we have established that the main phase of rotation 30 occurs in the hauterivian aptian interval the movement of iberia is clearly linked to the movement of africa in direction and age but the amount of rotation of iberia during the early cretaceous is much larger and implies that iberia was not a real part of the african plate

models of the development of the west iberia rifted continental margin at 40 30 n deduced from surface and deep tow magnetic anomalies the ocean continent transition oct on nonvolcanic rifted continental margins is important in that it contains evidence concerning the breakup of the continents and the onset of seafloor spreading the nature of the oct off western lberia has recently been attracting attention following seismic and other geophysical studies there and drilling of acoustic basement by leg 149 of the ocean drilling program here we concentrate on the interpretation of a new digital magnetic anomaly chart for the iberia abyssal plain between 39 5 o and 42 2 o n the most striking anomaly is a trough which exists immediately east of and locally parallel to anomaly j and is closely coincident with a basement peridotite ridge we conclude from modeling surface magnetic anomalies and a deep tow magnetometer profile that seafloor spreading began about 129 9 m y ago barremian at a rate of 10 0 mm yr consistent with drilling and seismostratigraphic results from the southern lberia abyssal plain a second feature is the existence of linear low amplitude isochron parallel magnetic anomalies east of the peridotite ridge trough and a clear change in the trend of these anomalies east of about 11 o 15 w it is possible to model these anomalies by a series of 7 to 30 km wide weakly magnetized crustal blocks of about the same thickness as the oceanic crust the west to east anticlockwise change in trend at 11 o 15 w suggests either a major change in stress regime and or in the type of magnetic anomaly source we speculate that the region between the peridotite ridge and 11 o 15 w represents a transitional crust whose formation was dominated by the same stress regime which accompanied eventual seafloor spreading we explain the change in trend at 11 o 15 w by a model featuring a rift which propagated through continental crust from south to north we consider three scenarios for the formation of the transitional zone crust first continental crust is surrounded and impregnated by intrusive and extrusive material formed from passive upwelling of magma created by the limited adiabatic decompression partial melting which occurs as the two continental lithospheric plates first begin to separate second such crust is surrounded by unroofed upper mantle material or third the zone is the product of ultraslow seafloor spreading present evidence tends to support the first scenario in this scenario the top of the asthenosphere eventually becomes shallow enough to enable magma to penetrate the thinnest continental crust fill the space caused by additional extension and form the transitional crust already described over a broad zone at least several tens of kilometers wide at breakup upper mantle rocks become exposed on the seafloor and undergo extensive serpentinization in a final stage we envisage focusing of the igneous activity leading to the onset of seafloor spreading initially producing thin oceanic crust because of a restricted melt supply the width of continuous tectonically extended continental crust in the southern iberia abyssal plain is less than was previously supposed

effective elasticity of fractured rocks a snapshot of the work in progress exploration and development of naturally fractured reservoirs rely on understanding and interpretation of certain signatures associated with seismic waves propagating through cracked rocks this understanding comes primarily from the effective media theories that predict an overall elastic behavior of a solid containing many inhomogeneities cracks in particular whose sizes are too small to be seen individually by the waves to model seismic responses of fractured formations a geophysicist typically has a choice between the effective media schemes of hudson and schoenberg while the two predictions usually deviate slightly for liquid filled cracks the differences are significant when the fractures are dry explaining the origin of these differences and selecting a more accurate scheme is the first goal of this tutorial our second more challenging task is to prove that simply adding the compliance contributions of cracks as if they were isolated and noninteracting remains sufficiently accurate even for fractures that grossly violate the basic theoretical assumption of penny shaped cracks real fractures have notoriously irregular shapes might be partially closed and often form interconnected networks yet these details of fracture microgeometry turn out to be unimportant for the effective elasticity given a typical noise level in seismic data no closed form theory exists for irregular fracture shapes however take into account finite element simulations on so called digital rocks demonstrate which features of the crack geometry have to be taken into account because they influence propagation of long compared to the size of fractures seismic waves and which features can be ignored

propagating rifts crustal extension during continental rifting propagating rifts may not be incompatible with plate tectonic tenets which are considered at the appropriate scale propagation of a rift is a natural consequence of relative motion about a pole of rotation it is not necessarily valid that 1 rifts propagate in one direction or 2 crustal stretching increases with progressive propagation of a rift

azimuthal seismic anisotropy in a zone of exhumed continental mantle west iberia margin summary p wave azimuthal seismic anisotropy of the uppermost mantle has been shown to indicate directions of extension both recent and fossil in oceanic and continental settings we have determined the p wave anisotropy of a zone of exhumed continental mantle beneath the southern iberia abyssal plain as a possible indication of the initial direction of separation of iberia from north america in a region where there are no magnetic lineations or fracture zone lineations adjacent to the margin with which to constrain this direction over 10 000 airgun shots were recorded by 11 ocean bottom seismometers hydrophones from which 24 900 arrivals that had traversed unaltered weakly serpentinized upper mantle were picked complete 360 azimuthal coverage was attained between the shots and receivers for ranges up to 55 km p wave raypaths through the zone of exhumed continental mantle were ray traced through a velocity model that incorporated the 3 d relief of the seabed and acoustic basement time residuals with respect to this model were fitted using an azimuthally dependent function small anisotropy 7 per cent with a fast direction of 143 was determined to exist between 3 1 and 6 7 km below the top of the basement although the fast direction suggests that the post breakup mantle stretching between iberia and north america was northwest southeast this hypothesis is hard to reconcile with other observations instead we conclude that motion along concave downward faults during the exhumation of the upper mantle could have been sufficient to change an initially roughly east west margin normal fast direction to the 143 azimuth observed today the degree of serpentinization was estimated to decrease from 20 to 0 per cent between 3 and 7 km depth into the basement in the zone of exhumed continental mantle the degree of upper mantle anisotropy is similar to that observed in other oceanic and continental settings where similar degrees of serpentinization are inferred from mean p wave velocities

magnetic mineralogy in an archean crustal cross section implications for crustal magnetization a traverse across precambrian rocks from the kapuskasing uplift in ontario provided 31 samples from a crustal cross section that is now exposed at the surface about half the samples are dominantly paramagnetic magnetite accompanied in a few samples by minor amounts of pyrrhotite is the only significant magnetic mineral in the other half magnetic susceptibilities of these samples are constant between room temperature and about 540 c above which temperature they drop rapidly to zero magnetic susceptibility does not depend on rock type apparent original depth in the crust or degree of metamorphism the average induced magnetization of the most magnetic units in this section is less than 1 a m which is much lower than the source requirements for the deep crust deduced from aeromagnetic and satellite magnetometer surveys

late jurassic sedimentation and deformation in the west iberia continental margin insights from fms data odp leg 173 in the iberia abyssal plain ocean drilling program odp site 1065 drilled the top of a continental tilted block penetrating a middle to late jurassic probable pre rift sedimentary unit borehole images of this unit were obtained by the formation microscanner fms logging tool thus allowing the identification and 3d measurement of two block tilting phases the last one is an eastward 15 tilt probably related to the main early cretaceous rifting phase and consistent with the tilted block image on seismic lines the first tilt previously unknown is late jurassic in age the block tilting is 15 to the southeast and is not associated with any noticeable change in the depositional environment both tilting episodes induced sedimentary instabilities leading to listric faults and slumps fms images also showed that the sediments originated from the north galicia bank during late jurassic times

three dimensional compressional wavespeed model earthquake relocations and focal mechanisms for the parkfield california region we present a new three dimensional 3d compressional wavespeed v p model for the parkfield region taking advantage of the recent seismicity associated with the 2003 san simeon and 2004 parkfield earthquake sequences to provide increased model resolution compared to the work of eberhart phillips and michael 1993 epm93 taking the epm93 3d model as our starting model we invert the arrival time data from about 2100 earthquakes and 250 shots recorded on both permanent network and temporary stations in a region 130 km northeast southwest by 120 km northwest southeast we include catalog picks and cross correlation and catalog differential times in the inversion using the double difference tomography method of zhang and thurber 2003 the principal v p features reported by epm93 and michelini and mcevilly 1991 are recovered but with locally improved resolution along the san andreas fault saf and near the active source profiles we image the previously identified strong wavespeed contrast faster on the southwest side across most of the length of the saf and we also improve the image of a high v p body on the northeast side of the fault reported by epm93 this narrow body is at about 5 to 12 km depth and extends approximately from the locked section of the saf to the town of parkfield the footwall of the thrust fault responsible for the 1983 coalinga earthquake is imaged as a northeast dipping high wavespeed body in between relatively low wavespeeds 5 km sec extend to as much as 10 km depth we use this model to derive absolute locations for about 16 000 earthquakes from 1966 to 2005 and high precision double difference locations for 9 000 earthquakes from 1984 to 2005 and also to determine focal mechanisms for 446 earthquakes these earthquake locations and mechanisms show that the seismogenic fault is a simple planar structure the aftershock sequence of the 2004 mainshock concentrates into the same structures defined by the pre 2004 seismicity confirming earlier observations waldhauser et al 2004 that the seismicity pattern at parkfield is long lived and persists through multiple cycles of mainshocks online material 3d v p model and earthquake relocations

tectonosedimentary evolution of the deep iberia newfoundland margins evidence for a complex breakup history most of the conceptual ideas concerning sedimentary architecture and tectonic evolution of deep rifted margins are based on either intracontinental rift basins or proximal margins both of which underwent only small amounts of crustal thinning in this paper we investigate the tectonosedimentary and morphotectonic evolution related to continental breakup of the highly extended deep iberia newfoundland margins our results show that continental breakup is a complex process distributed in time and space on the basis of mapping of dated seismic units and borehole data we are able to identify two major phases of extension during a first phase dated as tithonian to barremian 145 128 ma deformation is related to exhumation of mantle rocks basins become younger oceanward and fault geometry changes from upward to downward concave resulting in complex sedimentary structures and basin geometries a second phase dated as latest aptian 112 ma overprints previously exhumed mantle and accreted juvenile oceanic crust over more than 200 km leading to the formation of basement highs the observed complex breakup history challenges classical concepts of rifting and leads to new interpretations for the tectonosedimentary evolution of deep rifted margins

structural comparison of archetypal atlantic rifted margins a review of observations and concepts abstract in this study we compare three pairs of conjugate rifted margins that are often referred to as archetypes of rift systems despite numerous differences a remarkable first order structural similarity appears between the magma poor iberia newfoundland the magma rich mid norway east greenland and the sediment rich angola brazil rifted margins typical is the seaward arrangement of distinct domains proximal necking distal and outer that each present specific comparable structural characteristics our study also suggests that magma rich systems may go through a stage of hyper extension indicating that extreme crustal thinning does not preclude a magmatic breakup in this contribution we clarify the definition of a number of terms introduced recently in rifted margin studies we review the major features constitutive of these key referenced systems discuss their similarities and differences and examine how the related deformation modes develop in the life cycle of a rift that goes to seafloor spreading we conclude that the distinct domains observed in the margin architecture represent distinct stages in the evolution of rifted margin independently of their later evolution into magma poor or magma rich environments

tectonic implications of exposure of lower continental crust beneath the iberia abyssal plain northeast atlantic ocean geophysical evidence we present new seismic data from a basement high beneath the southern iberia abyssal plain that appears from the latest ocean drilling program odp results and indirectly from various seismic observations to consist of lower continental crustal material this is a unique opportunity to use seismic profiles and other geophysical evidence to investigate the tectonic process which led to the exhumation of these rocks we infer that the lower crust was exhumed at the seafloor and then uplifted toward the end of rifting our results lead to the following new observations low angle detachment faults previously reported along the east west lusigal 12 profile across the southern iberia abyssal plain penetrate both the 3 10 km thick continental crust and unusually the uppermost mantle processing of new multichannel seismic reflection profiles across the basement high on which odp sites 900 1067 and 1068 are located reveals that the high is bounded by a previously unsuspected steep landward dipping normal fault on its east flank basement cores from the above odp sites also reveal that the high is not capped by the previously predicted early syn rift sediment but by rocks from the lower continental crust these unexpected observations are incorporated into a new tectonic model of the development of this part of the west iberia margin which is also consistent with other geophysical observations a novel feature of this model is the proposal that the seaward edge of the continental crust is thinned to 3 6 km by a currently poorly understood process the model implies three stages of deformation 1 lithospheric extension principally by symmetric pure shear which leads to a 10 km thick crust in which the lower crust is largely absent over the axial zone and the crust mantle boundary forms a shear zone 2 further thinning and then dissection of the most distal continental crust by seaward dipping low angle normal faults 3 inception of a high angle landward dipping normal fault that offsets the tectonized crust mantle boundary and uplifts the lower crust to the crest of the basement high on which odp sites 900 1067 and 1068 were drilled

mantle thermal structure and active upwelling during continental breakup in the north atlantic seismic reflection and refraction data acquired on four transects spanning the southeast greenland rifted margin and greenland iceland ridge gir provide new constraints on mantle thermal structure and melting processes during continental breakup in the north atlantic maximum igneous crustal thickness varies along the margin from s 30 km in the near hotspot zone 6 500 km from the hotspot track to v18 km in the distal zone 500 1100 km magmatic productivity on summed conjugate margins of the north atlantic decreases through time from 1800 300 to 600 50 km 3 km ma in the near hotspot zone and from 700 200 to 300 50 km 3 km ma in the distal zone comparison of our data with the british faeroe margins shows that both symmetric and asymmetric conjugate volcanic rifted margins exist joint consideration of crustal thickness and mean crustal seismic velocity suggests that along margin changes in magmatism are principally controlled by variations in active upwelling rather than mantle temperature the thermal anomaly vt at breakup was modest v100 125 c varied little along the margin and transient data along the gir indicate that the potential temperature anomaly 125 50 c and upwelling ratio v4 times passive of the iceland hotspot have remained roughly constant since 56 ma our results are consistent with a plume impact model in which 1 a plume of radius v300 km and vt of v125 c impacted the margin around 61 ma and delivered warm material to distal portions of the margin 2 at breakup 56 ma the lower half of the plume head continued to feed actively upwelling mantle into the proximal portion of the margin and 3 by 45 ma both the remaining plume head and the distal warm layer were exhausted with excess magmatism thereafter largely confined to a narrow 6 200 km radius zone immediately above the iceland plume stem alternatively the warm upper mantle layer that fed excess magmatism in the distal portion of the margin may have been a pre existing thermal anomaly unrelated to the plume fl 2001 elsevier science b v all rights reserved

magnetic evidence for slow seafloor spreading during the formation of the newfoundland and iberian margins there is considerable debate concerning the nature and origin of the thin crust within the ocean continent transition oct zones of many passive non volcanic continental margins located between thinned continental and true oceanic crust this crust is usually found to be underlain by upper mantle material of 7 2 7 4 km s velocity at shallow depths 1 2 km it has been proposed that such crustal material could have originated either by exhumation of upper mantle material during rifting of continents or by slow seafloor spreading one of the examples of occurrence of such a crust are the conjugate margins of newfoundland and iberia here we present an interpretation of magnetic data from these regions to show that their oct zones are underlain by crustal material formed by slow seafloor spreading 6 7 mm yr soon after iberia separated from the grand banks of newfoundland in the late jurassic similarities in the magnetic anomalies and velocity distributions from these regions with those from the sohm abyssal plain a region lying immediately south of the newfoundland basin and formed by seafloor spreading at a similar rate of spreading give further support to such an interpretation the idea that these regions were formed by unroofing of upper mantle during rifting of iberia from newfoundland may be likely but the presence of weak magnetic anomalies in these regions which bear all the characteristics of seafloor spreading anomalies makes it difficult to ignore the possibility that these regions could be underlain by oceanic crust formed during slow seafloor spreading the similarities in velocity structure and the presence of small amplitude magnetic anomalies both across this pair of conjugate margins of the north atlantic and that of the labrador sea suggest that this oct velocity structure may be the norm rather than the exception across those passive non volcanic margins where the initial seafloor spreading was slow furthermore the existence of similar velocity distributions along a few active spreading centers raises the possibility of formation of similar crust across slow spreading ridges fl 2000 elsevier science b v all rights reserved

effective elasticity of rocks with closely spaced and intersecting cracks the noninteraction approximation nia is the simplest effective media theory that describes the overall elasticity of fractured rocks if the nia is used for fracture characterization its accuracy and the range of applicability must be estimated we do it by performing a series of 3d finite element simulations of effective elasticity for models that contain several sets of fractures embedded in otherwise isotropic host rock we intentionally place the cracks close to each other to create strong interactions in their local stress fields in addition we allow the cracks to intersect in such a way that they do not break a rock specimen apart perhaps surprisingly we find that fracture interactions and intersections have little influence on the effective elasticity and the nia performs well in all cases while it has a tendency to slightly underestimate the effective stiffnesses the incurred errors are small their typical magnitudes are just a few percent in the entire range of the crack densities expe

the effect of the aspect ratio on crack induced anisotropy1 media containing aligned cracks show anisotropy with respect to elastic wave propagation there are several models describing the wave propagation in cracked media most of them only valid for cracks with small aspect ratios one of these models crampin s model is compared with a model valid for all aspect ratios nishizawa s model the elastic constants and the group velocities are compared for both dry and liquid filled inclusions with aspect ratios ranging from 0 0001 flat cracks up to 1 spheres the difference between both models is small for small aspect ratios but becomes larger for increasing aspect ratios at a crack density of 0 05 both models give within an error of 5 the same results for aspect ratios up to 0 3 therefore crampin s model can be applied to a large range of cracked media even if the aspect ratio of the inclusions is not small the variation of the anisotropy as a function of the aspect ratio can be studied using thomsen s dimensionless parameters e and y they show how inclusions with large aspect ratios result in elliptical anisotropy