surface stresses associated with arrested dykes in rift zones many theoretical models predict that arrested dykes may generate major grabens at rift zone surfaces arrested dyke tips in eroded rift zones however are normally not associated with major grabens or normal faults that could be generated by dyke induced stresses ahead of the tips and normal faults and grabens tend to be less common in those parts of eroded rift zones where dykes are comparatively abundant similarly there are feeder dykes as well as dykes arrested a few metres below the surface that do not generate faults or grabens at the surface here i propose that this discrepancy between theoretical models and field observations may be explained by the mechanical layering of the crust numerical models presented here show that abrupt changes in young s moduli layers with high dyke normal compressive stresses stress barriers and weak horizontal contacts have large effects on the dyke induced stress fields for the models considered the surface tensile stresses induced by arrested dykes are normally too small to lead to significant fault or graben formation at the rift zone surface the only significant dyke induced surface tensile stresses 2 mpa in these models are for a dyke tip arrested at 1 km depth below the surface of a rift zone with a weak contact at 400 m depth and subject to extension that tensile stress however peaks above the ends of the weak horizontal contact which in the model considered occur at distances of 4 km to either side of the dyke and shows no simple relation to the depth to the dyke tip thus for a layered crust with weak contacts straightforward inversion of surface geodetic data to infer dyke geometries may result in unreliable results

strain localisation and weakening of the lithosphere during extension we explore the sensitivity of extensional systems to the thermal structure of the lithosphere using numerical simulations that fully couple the energy momentum and continuity equations the rheology of the lithosphere is controlled by weakening processes such as shear heating that localises strain into shear zones and faults numerical models show that during extension of an initially unpatterned lithosphere structures develop spontaneously out of basic thermodynamic energy fluxes and without the imposition of ad hoc rules on strain localisation this contrasts with the classical mohr coulomb theory for brittle localisation which prescribes the angles of faults by a mathematical rule our results show that the mode of extension is sensitive to subtle changes in rheology heat flux and geometry of the system this sensitivity lies at the core of the variety and complexity observed in extensional systems localisation processes make the lithosphere weaker than previously estimated from the brace goetze quasi static approach consequently typical estimates for plate tectonic forces are capable of splitting the lithosphere under extension even without the role of active magmatism

magma influence on propagation of normal faults evidence from cumulative slip profiles along dabbahu manda hararo rift segment afar ethiopia abstract measuring displacement length profiles along normal faults provides crucial information on fault growth processes here based on satellite imagery and topography we analyze 357 normal faults distributed along the active rift of dabbahu manda hararo dmh afar which offers a unique opportunity to investigate the influence of magmatism on fault growth processes our measurements reveal a large variety of slip profiles that are not consistent with elastic deformation their analysis contributes towards a better understanding of the lateral propagation of faults especially when nucleation points and existence of barriers are included using the fault growth model of manighetti et al 2001 we determine the preferred direction of lateral propagation for each fault our results suggest that lateral propagation of faults is easier away from areas where magma has been stored for long time at crustal depth and has thus modified the thermo mechanical properties of the host rock however these areas correspond also to areas where the initiation of fault growth appears as easiest along the rift in combining these results with the analysis of rift width and the position of magma reservoirs along dmh rift we show that fault growth keeps track of the magma presence and or movement in the crust

earthquakes in the ductile regime pseudotachylytes from a crustal scale shear zone in central australia have developed in a cyclical manner once developed an individual pseudotachylyte is deformed in a ductile manner only to be overprinted at a later stage by a new generation of pseudotachylytes such cyclic generation and deformation of pseudotachylyte has been interpreted in the past as representing conditions at the brittleductile transition a different interpretation however is presented here it is proposed that psuedotachylytes and associated ultramylonites can develop entirely within the ductile regime as ductile instabilities such instabilities are different in nature to those previously discussed at length in the geophysical literature but are identical in principle with the instabilities that develop for velocity weakening frictional behavior in spring slider systems at a given strain rate a critical temperature tc is defined at which the transient work hardening equals the product of stress relaxation due to a thermal fluctuation and the heat generated by shearing a necessary condition for ductile instability at a given strain rate is that the temperature is belowtc then the rate of change of stress with respect to strain is negative an additional requirement is that this rate of change exceeds in magnitude the effective elastic stiffness of the loading system ductile instabilities are marginally possible at geological strain rates in quartzites but are possible at mid crustal temperatures in other rock types on the basis of these observations a new interpretation is presented for the base of the seismogenic zone in crustal regions

dike induced faulting in rift zones of iceland and afar geodetic data and field observations demonstrate that the emplacement of dikes in volcanic rift zones frequently generates normal faulting and graben subsidence at the earth9s surface elastic modeling of the vertical ground surface displacements above dikes and faults indicates that the extent of graben subsidence can be achieved only if fault slip extends virtually to or beyond the dike plane at depth a mechanical model that includes dikes and frictional faults shows that dike opening tends to compress and lock faults located to either side of the dike therefore slip extending into or beyond the dike cavity must occur either 1 on faults that intersect the dike near its top above the zone of dike induced compression or 2 on faults that slip ahead of the dike as it propagates laterally data from iceland indicate that slip occurred on deep faults that presumably slipped in advance of the laterally propagating dike

relation between continental strike slip earthquake segmentation and thickness of the crust 1 high resolution maps of large continental strike slip earthquake surface ruptures show that they are formed of fault segments these segments are bounded by fault bends step overs or combinations of the two the lowest limit in size for such segments may not be relevant in the understanding of earthquake mechanics as it pertains to the granular properties of fault zones the maximum limit in segment length however is important as it is directly relates to the maximum extent of seismic rupture to measure the length of the segments a new quantitative method based on piecewise linear fitting is developed and is used to automatically retrieve segments from earthquake rupture maps next this approach is tested against a set of ten continental strike slip earthquake ruptures derived from similar high quality maps the test suggests that segments have a maximum length of 18 km independent of regional tectonic setting slip inversions for earthquakes based on seismological and or geodetic data most often are not unique and can show some variability even for one particular event some basic characteristics however such as total moment release or general source geometry seem to persist that are relevant to earthquake mechanics measurements of the maximum horizontal extent of individual slip patches derived from seismic source inversion for strike slip ruptures show that their strike dimension does not increase infinitely with magnitude but instead reaches a maximum value of 25 km these two independent lines of observations complemented by earlier data and analog experiments suggest that it is the thickness of the seismogenic crust that controls the structural scaling of the length of seismic segments and that it is independent of the ultimate size of individual earthquakes

fluid controlled faulting process in the asal rift djibouti from 8 yr of radar interferometry observations the deformation in the asal rift djibouti is characterized by magmatic inflation diking distributed extension fissure opening and normal faulting an 8 yr time line of surface displacement maps covering the rift constructed using radar interferometry data acquired by the canadian satellite radarsat between 1997 and 2005 reveals the aseismic behavior of faults and its relation with bursts of microseismicity the observed ground movements show the asymmetric subsidence of the inner floor of the rift with respect to the bordering shoulders accommodated by slip on three of the main active faults fault slip occurs both as steady creep and during sudden slip events accompanied by an increase in the seismicity rate around the slipping fault and the fieale volcanic center slip distribution along fault strike shows triangular sections a pattern not explained by simple elastic dislocation theory these observations suggest that the asal rift faults are in a critical failure state and respond instantly to small pressure changes in fluid filled fractures connected to the faults reducing the effective normal stress on their locked section at depth

the afar depression transition between continental rifting and sea floor spreading abstract detailed geophysical and geological studies were undertaken in the 1970 s in the afar depression ethiopia in order to study the processes of continental break up occurring in this unique setting the afar is located between the ethiopian and somali plateaus and the red sea we have re evaluated the available seismic refraction and gravity data using modern interpretation techniques and incorporated new information derived from magnetic gravity seismicity and seismic refraction data the results of the re evaluation indicate that the afar depression is a transition zone between the continental rifts of kenya and the present ongoing sea floor spreading of the red sea and the gulf of aden in the depression itself the crust is greatly attenuated and is underlain by a low velocity 7 4 7 5 km s high temperature upper mantle material however it is still a continental crust which thins to the northeast and east towards the red sea and the gulf of aden it is not a newly formed oceanic crust as has been suggested in the past the trends of the areas of crustal thinning are indicated by the gravity anomalies the trend of the ethiopian rift reaches south afar where the trend of crustal thinning changes and becomes parallel to the red sea trend it is offset en echelon from the spreading area of the red sea which is marked by an alignment of gravity maxima the gulf of aden trend continues west towards the ethiopian rift the gravity trends coincide with areas of maximum crustal thinning and may thus suggest a possible triple junction in development

crustal thickening by tectonic wedging of the ganderian rocks southern new england usa evidence from cataclastic zircon microstructures and u pb ages abstract zircon grains in granites from avalonian and ganderian rocks in southern new england host brittle internal structures that are interpreted here to show the host rocks to be allochthonous significant among these structures are inherited cores that are commonly fractured and even dismembered this intense fracturing is interpreted as reflecting an important cataclastic event the maximum age of fracturing is constrained to be younger than the age of the youngest broken magmatic core 360 4 ma the minimum age must be older than the oldest zircon rim that heals these fractures that is early permian the occurrence of cataclastic zircon requires that these rocks were relatively cold i e in the upper crust during the carboniferous and therefore were not involved in the pervasive high grade acadian metamorphism the present map pattern of inter tonguing high grade and low grade slices of peri gondwanan rocks shows that they were assembled by crustal scale tectonic wedging the consequent thickening ultimately led to anatexis in the lower slices during the permian thus evidence for cataclasis of zircon grains from the avalon and gander terranes of southern new england suggests that these peri gondwanan terranes remained outboard of laurentia during the well documented early devonian acadian orogeny and were first fully accreted to north america during the alleghanian permian orogeny

earthquake scaling fault segmentation and structural maturity abstract slip and length measurements on earthquakes suggest large stress drop variability we analyze an extended set of slip length measurements for large earthquakes m 6 to seek for the possible origin s of this apparent variability we propose that such variability arises from earthquakes breaking a variable number of major fault segments that number depends on the strength of the inter segment zones which itself depends on the structural maturity of the faults we propose new d max l parameterizations based on that idea of multiple segment ruptures in such parameterizations each broken segment roughly scales as a crack while the total multi segment rupture does not stress drop on individual segments is roughly constant only varying between 3 5 to 9 mpa the slight variation that is still observed depends on fault structural maturity more mature faults have lower stress drops than immature ones the new d max l functions that we propose reduce uncertainties with respect to available relationships they thus provide a more solid basis to estimate seismic hazard by integrating fault properties revealed by geological studies

the effect of volcanic constructs on rift fault patterns volcanoes in rift situations often show distinctive hour glass fault patterns with increased fault throw as the volcano is approached we present analogue models that show that this is caused by an interaction of the regional stress field with that set up by the volcano mass for faults to be reorientated there must be a ductile layer below the volcano this can be hot crust at mid ocean ridges continental rifts or weak sedimentary strata increased volcano size or mass and lower brittle ductile ratios lead to increased fault curvature whereas an increased regional extension rate decreases the effect volcanoes on one side of a rift may capture it forming the axis of a new rift with curved or en echelon zones on either side by concentrating extension magma is more easily erupted so volcanoes may erupt more magma of less evolved composition a positive feedback between increased extension and magma eruption rate will lead to rift narrowing which can favor the formation of oceanic crust

strain accommodation by slow slip and dyking in a youthful continental rift east africa continental rifts begin and develop through repeated episodes of faulting and magmatism but strain partitioning between faulting and magmatism during discrete rifting episodes remains poorly documented in highly evolved rifts tensile stresses from far field plate motions accumulate over decades before being released during relatively short time intervals by faulting and magmatic intrusions1 2 3 these rifting crises are rarely observed in thick lithosphere during the initial stages of rifting here we show that most of the strain during the july august 2007 seismic crisis in the weakly extended natron rift tanzania was released aseismically deformation was achieved by slow slip on a normal fault that promoted subsequent dyke intrusion by stress unclamping this event provides compelling evidence for strain accommodation by magma intrusion in addition to slip along normal faults during the initial stages of continental rifting and before significant crustal thinning

the nature of the crust beneath the afar triple junction evidence from receiver functions the afar depression is an ideal locale to study the role of extension and magmatism as rifting progresses to seafloor spreading here we present receiver function results from new and legacy experiments crustal thickness ranges from 45 km beneath the highlands to 16 km beneath an incipient oceanic spreading center in northern afar the crust beneath afar has a thickness of 20 26 km outside the currently active rift segments and thins northward it is bounded by thick crust beneath the highlands of the western plateau 40 km and southeastern plateau 35 km the western plateau shows vp vs ranging between 1 7 1 9 suggesting a mafic altered crust likely associated with cenozoic flood basalts or current magmatism the southeastern plateau shows vp vs more typical of silicic continental crust 1 78 for crustal thicknesses 2 0 can only be explained by significant amounts of magmatic intrusions in the lower crust this suggests that melt emplacement plays an important role in late stage rifting and melt in the lower crust likely feeds magmatic activity the crust between the location of the miocene red sea rift axis and the current rift axis is thinner 2 0 than beneath the eastern part of afar 26 km vp vs 1 9 this suggests that the eastern region contains less partial melt has undergone less stretching extension and has preserved a more continental crustal signature than west of the current rift axis the red sea rift axis appears to have migrated eastward through time to accommodate the migration of the afar triple junction

rift topography linked to magmatism at the intermediate spreading juan de fuca ridge new seismic observations of crustal structure along the juan de fuca ridge indicate that the axial rift topography reflects magma induced deformation rather than alternating phases of magmatism and tectonic extension as previously proposed contrary to predictions of the episodic models crustal magma bodies are imaged beneath portions of all ridge segments surveyed at average depths of 2 1 2 6 km the shallow rift valley or axial graben associated with each juan de fuca segment is 50 200 m deep and 1 8 km wide and is well correlated with a magma body in the subsurface analysis of graben dimensions height and width shows that the axial graben narrows and graben height diminishes where the magma body disappears rather than deepening and broadening as expected for rift topography due to tectonic extension we propose an evolutionary model of axial topography that emphasizes the contribution of dike intrusion to subsidence and fault slip at the seafloor in this model an evolving axial topography results from feedbacks between the rheology of the crust above a magma sill and dike intrusion rather than episodic magma delivery from the mantle

fabric development in syn tectonic intrusive sheets as a consequence of melt dominated flow and thermal softening of the crust the temperature dependence of ductile deformational processes suggests that the thermal anomaly associated with a cooling syn tectonic intrusion will produce a crustal low viscosity horizon that will concentrate deformation in the vicinity of the pluton during cooling this effect should be most prominent when magma is present but should also occur after solidification of the magma when flow is by solid state processes this paper evaluates this hypothesis for sheet like intrusions using one dimensional time dependent thermal models and accompanying predictions of viscosity vs time history based on experimental flow laws these models predict that for systems with an initial normal geothermal gradient e g extensional systems strike slip systems or thrust systems with low displacement rates the base of a large plutonic sheet cools more slowly than the top and fabric development should be most pronounced on the floor of the pluton in contrast in megathrust systems where displacements are sufficiently rapid to produce temperature inversions cooling is also upside down and fabric development should preferentially occur along the top of plutonic sheets moreover when a pluton is emplaced within a zone of inverted isotherms the heat may be trapped within the inversion a natural system characterized by this history should show a sharp thermal front coincident with the top of a paleo temperature inversion if a pluton is weaker than its country rock it will form a weak horizon in the crust throughout its cooling history and the plutonic sheet should take up the bulk of the deformation throughout its cooling history if a pluton is stronger than its country rock under conditions of solid state flow however models predict a two phase deformational history prior to solidification the deformation should be concentrated in the pluton with the magma representing a weak horizon in the crust but upon crystallization the pluton should become relatively rigid with respect to its country rock and deformation should be concentrated in the wall rocks these two cases predict markedly different structural histories and the history could easily be misinterpreted in the first case static mineral growth might be prominent in the wall rocks and these textures could be misinterpreted as evidence for post tectonic emplacement in the second case the extensive high t deformation of the wall rocks could be readily ascribed to non tectonic emplacement related deformation rather than a consequence of syn tectonic emplacement the model predictions are tested with three examples of well exposed plutonic sheets a neogene extensional system in death valley california and two megathrust systems in southern alaska border ranges fault system and mclaren metamorphic belt structural observations from these systems are broadly consistent with the model predictions and lend support to first order characteristics of the models nonetheless more sophisticated 2 d models of the coupled thermal mechanical system are needed to thoroughly test the hypothesis

ascent and emplacement of buoyant magma bodies in brittle ductile upper crust 1 the emplacement of silicic magma bodies in the upper crust may be controlled by density such that there is no buoyancy to drive further ascent or temperature such that surrounding rocks are too cold to deform significantly over geological timescales evidence for the latter control is provided by negative gravity anomalies over many granitic plutons conditions of diapir ascent and emplacement in this case are studied with a numerical model for deformation and heat transport allowing for ductile elastic and brittle behavior a large strain formulation is used to solve for temperature stress strain and strain rate fields as a function of time for a range of diapir sizes density contrasts and background geotherms the method allows for large viscosity contrasts of more than 6 orders of magnitude and determines the dominant deformation mechanism depending on the local values of temperature strain and strain rate emplacement depth and final deformation characteristics depend on diapir size and buoyancy small diapirs less than about 5 km in diameter cannot reach shallow crustal levels and do not involve brittle deformation in the ductile regime the diapir flattens significantly upon emplacement due to stiff roof rocks and to the free surface above late stage deformation proceeds by horizontal spreading with little upward displacement of roof rocks and is likely to be interpreted as ballooning large diapirs more than about 5 km in diameter rapidly rise to shallow depths 1 5 km and induce brittle faulting in the overlying rocks in this regime buoyancy forces may lead to faulting in roof rocks in this case late stage ascent proceeds by vertical intrusion of a plug of smaller horizontal dimensions than the main body buoyant diapirs keep on rising after solidification long after the relatively short lived high temperature magmatic stage this may account for some phases of late caldera resurgence in extinct volcanic systems

speculations on the geometry of the initiation and termination processes of earthquake rupture and its relation to morphology and geological structure earthquake initiation and termination processes are commonly described in terms of barriers and asperities barriers fall into two classes geometric barriers are associated with places where the orientation of a failure surface changes and relaxation barriers where stress is low because aseismic creep processes outpace tectonic loading geometric barriers fall into conservative and nonconservative subgroups according to whether finite fault motion can proceed without the creation of new structures or whether it demands the creation of new faulting or void space the multiple faulting or fragmentation associated with some nonconservative barriers can disrupt fault planes and form asperities by means of selected examples it is shown that a description in terms of these barriers can help one to visualise the processes of earthquake rupture and its relation to the geological environment

sequence of rifting in afar manda hararo rift ethiopia 2005 2009 time space evolution and interactions between dikes from interferometric synthetic aperture radar and static stress change modeling thirteen dike intrusions in the manda hararo rift afar ethiopia from september 2005 to june 2009 studied using an extensive interferometric synthetic aperture radar insar data set provide insight into the mechanics of a major active rift kinematic inversions of insar data reveal that dikes opened by 0 8 3 5 m at an average 5 km depth with volumes of 0 04 0 2 km 3 with up to 12 m opening and a volume greater than 1 km 3 for the september 2005 megadike dikes have their source in a midsegment magma reservoir which induces a local shallowing of the brittle ductile boundary presumably due to thermal weakening of the lithosphere the smaller dikes in 2006 2009 were emplaced in regions of minimum opening of the september 2005 megadike above the central magma reservoir in contrast the most voluminous dike intrusions in 2006 2009 occurred near the locus of the peak of maximum opening of the september 2005 megadike 10 km north of the magma source this may suggest that tension on the plate boundary was highest there both prior to 2005 and possibly also after 2005 evolution and distribution of normal stress on the plate boundary throughout the rifting episode may indicate that tension near to the magma reservoir is lower than toward segment ends average relief of normal stresses of tectonic origin coeval to dike intrusions is comparable with shear stress drops for earthquakes presumably because dikes in the manda hararo rift are intruded at low magma pressure and high tectonic stress time space evolution and interactions between dikes from interferometric synthetic aperture radar and static stress change modeling

fast least squares imaging with surface related multiples application to a north sea data set abstract in marine seismic acquisition surface related multiples constitute a significant portion of the acquired data typically multiples are removed during early stage data processing because they can lead to phantom reflectors during migration that might result in erroneous geologic interpretations however if properly dealt with multiples can provide valuable extra information and can complement primaries in illuminating the subsurface reverse time migration has limitations in imaging multiples a computationally efficient inversion procedure is proposed which jointly maps primaries and multiples to the true reflectors and estimates the source function on the fly as a result high quality mostly artifact free broad band images are obtained in which the imprint of the source function is partly removed at a computationally affordable expense compared with the combined costs of wave equation based surface related multiple elimination and reverse time migration all this is achieved by including t

seismicity during lateral dike propagation insights from new data in the recent manda hararo dabbahu rifting episode afar ethiopia seismicity released during lateral dike intrusions in the manda hararo dabbahu rift afar ethiopia provides indirect insight into the distribution and evolution of tensile stress along this magma assisted divergent plate boundary in this paper 5 dike intrusions among the 14 that form the 2005 present rifting episode are analyzed with local and regional seismic data during dike intrusions seismicity migrates over distances of 10 15 km at velocities of 0 5 3 0 km h away from a single reservoir in the center of the rift segment confirming the analogy with a slow spreading mid ocean ridge segment comparison with geodetic data shows that the reservoir is located 7 km down rift from the topographic summit of the axial depression dikes emplaced toward the north are observed to migrate faster and to be more voluminous than those migrating southward suggesting an asymmetry of tension in the brittle elastic lithosphere seismicity during dike injections is concentrated near the propagating crack front in contrast faults and fissures in the subsurface appear to slip or open aseismically coeval with the intrusions the seismic energy released during dike intrusions in the manda hararo rift appears to be primarily modulated by the local magnitude of differential tensile stress and marginally by the rate of stress change induced by the intrusion the low level of seismic energy accompanying dike intrusions despite their significant volumes is likely an indicator of an overall low level of tension in the lithosphere of this nascent plate boundary

growth of faults by accumulation of seismic slip the accommodation of large strains in the upper crust is largely achieved by the accumulation of displacement on faults observation shows that as a fault accumulates displacement it grows in size i e its surface area and its length increase here we address the question for an increase in the amount of displacement on a fault by how much would the length of the fault change it is argued by cowie and scholz 1992a that the displacement on a fault is linearly related to the length of the fault this simple result is expanded upon in this paper by assuming that a fault accumulates displacement by repeated earthquakes two different approaches are presented the first approach considers the balance that must be achieved between the energy available for deformation and the work involved in creating new fault surface area as the fault grows the available energy is provided by changes in strain energy when the fault slips the second approach is to construct a geometrical model for fault growth using the scaling relationship between the slip during a single earthquake and the length of the rupture the total displacement on a fault is the sum of the slips contributed by many earthquakes the usefulness of these two approaches is that the growth of a fault over geologic time can be described by parameters that can be obtained from earthquake and fault data the models presented here predict that 1 the maximum amount a fault can grow in a single earthquake that ruptures the entire fault is of the order of 1 of its previous length and 2 the work of faulting may account for 10 of the total energy available during an earthquake the energy lost from the system is accounted for by work done against friction and seismic radiation consequences of fault growth for the segmentation and thus seismogenic potential of a fault over geologic time are discussed using predictions of the theory

dyke emplacement in a layered and faulted rift zone abstract in rift zone eruptions magma is normally transported to the surface through dykes most injected dykes however do not make it to the surface but rather become arrested at certain depths in the rift zone surface deformation studies are routinely used to infer the depths to the tips as well as the geometries of arrested dykes most such studies model the rift zone as a homogeneous isotropic elastic half space all rift zones however contain normal faults and are composed of rock layers with different mechanical properties the numerical models presented here indicate that when the upper tip of a vertically propagating dyke reaches the same crustal level as the bottom tips of the boundary faults of an active graben the faults close as the tip continues its propagation up into the graben the overpressured dyke encourages reverse slip on the boundary faults the present numerical models also indicate that mechanical layering has strong effects on dyke emplacement and the surface deformation associated with arrested dykes in rift zones in particular soft low young s modulus layers and weak contacts at shallow depths contribute to offset arrest and aperture thickness variations of the dykes and suppress the dyke induced surface stresses and associated brittle deformation when the magmatic overpressure of a dyke is the only loading the dyke tends to be thicker inside soft layers than inside stiff high young s modulus layers soft layers and weak contacts discontinuities common at shallow depths in rift zones suppress dyke tip tensile stresses thereby encouraging dyke arrest and may result in little if any surface stresses and brittle deformation being induced by an arrested dyke weak contacts also encourage transfer of the dyke induced surface tensile stresses to the regions above the lateral ends of the contacts then the tensile stresses at the rift zone surface in a large area above the dyke itself become small or negligible all the tensile stress occur above the lateral ends of the contact which may be many kilometres from the dyke tip for a dyke arrested in a layered rift zone straightforward inversion of surface deformation data may therefore yield geometric results that have little relation to the actual geometry of the arrested dyke the results of the numerical models presented here are generally supported by field observations of dykes in rift zones