on the shape and velocity of fluid filled fractures in the earth summary in this paper i present a model to estimate the shape and velocity of slowly ascending buoyancy driven fluid filled fractures the model considers elastic deformation linear fracture mechanics and fluid flow an attempt is made to incorporate the effect ofthe 2 d fluid pattern on the viscous pressure drop most other models assume that the viscous pressure drop can be approximated by flow through a channel with constant width although the form of the fracture is known to deviate from such a simple shape the 2 d flow in my model has an important consequence for the mechanism of buoyancy driven fracture propagation it predicts a large pressure gradient at the tail of the propagating fracture indicating that the tail of the fracture is most important in hindering the fracture propagation a singularity at the tail of the fracture can be avoided when a small amount of fluid trails in the channel left behind the propagating fracture the trailing and decoupling of fluids at the tail seems to be accompanied by small flow and shape instabilities which is indicated by the jerky movement of the tail observed in propagating air filled fractures in solidified gelatine and by numerical boundary element solutions of the coupled flow deformation fracturing problem by comparing the predictions for propagation velocities with laboratory observations of buoyancy driven fracture propagation in gelatine i derive a non dimensional effective thickness at the tail of the fracture for which trailing of fluids may occur the model is applied to earth relevant problems such as oil and water filled fractures in pressurized sediments or magma filled dykes in the lithosphere which are discussed in the paper

the mechanics of intersecting echelon veins and pressure solution seams in limestone abstract many studies that describe the formation of echelon vein arrays relate the causative stresses implicitly to the deformation reliant on simple shear kinematics such that the vein to array angle and the array width are the primary physical quantities in contrast we identify twelve physical quantities to describe echelon veins in two dimensions including coeval vein intersecting pressure solution seams a finite element method is used to reproduce vein shapes in linear elastic and elastic perfectly plastic model limestone model vein geometries are designed using values within the range of geometries measured from echelon veins at raplee anticline and comb monocline utah four physical quantities are significant for describing echelon vein shapes vein spacing vein array angle limestone elastic stiffness and closing of orthogonal pressure solution seams pressure solution seam closing influences the mechanical interaction between adjacent veins and for a range of conditions causes a nearly linear vein opening distribution triangular shapes and encourages straight vein propagation both of which approximate field measurements model results show that small spacing of veins with seams and large vein array angles promote straight vein traces in limestone with stiffness typical of laboratory measurements given the physical geologic conditions inferred from the burial history of the limestone strata

the geometry of echelon fractures in rock implications from laboratory and numerical experiments abstract the traces of echelon joints veins and dikes in rock range from curving to straight theoretical analyses using boundary element numerical methods have concluded that straight open fractures imply a significant remote differential stress whereas curving traces imply a more nearly isotropic stress we present a series of laboratory experiments which investigate the two dimensional propagation paths of echelon fractures in pmma plates as a function of the applied biaxial loading and the initial geometry of a simple fracture array the experimental results support the theoretical conclusions and verify the accuracy of the numerical method at the grain scale rock does not rigorously conform to the assumptions of isotropy homogeneity and linear elasticity demanded by the numerical method nevertheless results from crack path stability theory suggest that small scale deviations of a fracture from the ideal path generally do not affect its large scale behavior fracture paths which become kinked or curved by local heterogeneities are found to self correct to a path governed by competition between the fracture tip and remote stress fields provided the remote differential stress is non zero this enhances our confidence that the numerical method can be used to produce and explain realistic fracture geometries in rock an unexpected experimental result is the non perpendicular intersection of fractures grown in the laboratory free surface boundary conditions require that the walls of an open fracture be free of shear stress the principal stresses are therefore aligned with the crack wall and we might consequently expect an approaching opening mode fracture either to intersect the free surface at a right angle or to turn away and follow an asymptotic nonintersecting path experimental and numerical modeling however shows how the near tip stresses generated by an approaching fracture dominate the local stress field and allow it to propagate along an oblique path very close to intersection with the adjacent free surface

buoyancy driven fracture ascent experiments in layered gelatine laboratory experiments on air filled fracture propagation in solidified homogeneous and layered gelatine have been carried out providing an analogue model for magma filled dikes ascending in the crust the effects of layering on fracture velocity and shape have been analyzed in detail the free surface is found to accelerate approaching fractures layering accelerates or decelerates fractures approaching discontinuities of the elastic parameters depending on the value of the rigidity contrast the shape of fractures are strongly influenced as they pass from one layer to another the observed cross sectional shape when crossing a layer interface and the acceleration with decreasing rigidity can be explained with theoretical models our experiments also reproduce the arrest of fractures in proximity of joints and the formation of sills in the layer below the interface these findings could help in the interpretation of accelerated seismicity and deformation rates observed in volcanic areas

the pattern of circumferential and radial eruptive fissures on the volcanoes of fernandina and isabela islands galapagos maps of the eruptive vents on the active shield volcanoes of fernandina and isabela islands galapagos made from aerial photographs display a distinctive pattern that consists of circumferential eruptive fissures around the summit calderas and radial fissures lower on the flanks on some volcano flanks either circumferential or radial eruptions have been dominant in recent time the location of circumferential vents outside the calderas is independent of caldera related normal faults the eruptive fissures are the surface expression of dike emplacement and the dike orientations are interpreted to be controlled by the state of stress in the volcano very few subaerial volcanoes display a pattern of fissures similar to that of the galapagos volcanoes some seamounts and shield volcanoes on mars morphologically resemble the galapagos volcanoes but more specific evidence is needed to determine if they also share common structure and eruptive style

effects of overpressure variations on fracture apertures and fluid transport abstract for an isolated rock fracture in a homogeneous isotropic rock subject to constant internal fluid overpressure or constant external driving stress the ideal opening displacement aperture profile or variation is that of a flat ellipse for many mineral veins dykes tension fractures normal faults and other rock fractures however the opening displacements show irregular aperture thickness variations very different from that of a flat ellipse here we present field data on typical fracture aperture variations as well as new numerical and analytical models to explain these data we present the overpressure variation by fourier cosine series a very flexible method that can be used to model abrupt overpressure and driving stress variations in vertical and lateral sections for fractures of various sizes and types we calculate the opening displacements of typical hydrofractures and discuss the results with reference to mineral veins and dykes we also present numerical models showing that when a fracture dissects layer or parts of a single layer such as a lava flow with different stiffnesses young s moduli the opening displacement may show irregular variation even when the overpressure is constant from the cubic law the volumetric flow rates in the large aperture segments of the mineral veins and dykes discussed in the paper may have been as much as 3 5 times the flow rates in the small aperture segments we propose that differences in volumetric flow rates are related to irregular opening displacement variations in feeder dykes is one principal reason for the development of crater cones a universal feature of volcanic fissures

formation and interpretation of dilatant echelon cracks the relative displacements of the walls of many veins joints and dikes demonstrate that these structures are dilatant cracks we infer that dilatant cracks propagate in a principal stress plane normal to the maximum tensile or least compressive stress arrays of echelon crack segments appear to emerge from the peripheries of some dilatant cracks breakdown of a parent crack into an echelon array may be initiated by a spatial or temporal rotation of the remote principal stresses about an axis parallel to the crack propagation direction near the parent crack tip a rotation of the local principal stresses is induced in the same sense but not necessarily through the same angle incipient echelon cracks form at the parent crack tip normal to the local maximum tensile stress further longitudinal growth along surfaces that twist about axes parallel to the propagation direction realigns each echelon crack into a remote principal stress plane the walls of these twisted cracks may be idealized as helicoidal surfaces an array of helicoidal cracks sweeps out less surface area than one parent crack twisting through the same angle thus many echelon cracks grow from a single parent because the work done in creating the array as measured by its surface area decreases as the number of cracks increases in cross sections perpendicular to the propagation direction echelon cracks grow laterally each crack overlapping its neighbors until the mechanical interaction of adjacent cracks limits this growth dilation of each crack pinches the tips of adjacent cracks into an asymmetrical form and introduces local stresses that can cause lateral growth along a curving sigmoidal path sigmoidal echelon cracks may link at tip to plane intersections leaving a step in the through going crack wall the geometry of dilatant echelon cracks may be used to infer spatial or temporal changes in the orientation of principal stresses in the earth

hybrid veins from the southern margin of the bristol channel basin uk sinistral and dextral en echelon hybrid calcite veins are exposed on the southern margin of the bristol channel basin north somerset on a liassic carbonate platform these hybrid veins are transitional between pure extensional mode i and shear fractures mode ii mode iii and experienced both extensional and shear displacements during their formation in the study area they occur in conjugate sets with the conjugate angle ranging between 10 and 50 based on the kinematic analysis of these veins a new model for the opening of the bristol channel is proposed

form and dimensions of dykes in eastern iceland abstract a study was made of about 700 dykes in eastern iceland the majority of these belong to three swarms about 73 dip within 10 of the vertical most strike between 10 and 40 ne the strike of the dykes within the southernmost swarm alftafjordur changes along its trace from almost n at the north end to nne ssw southward along the swarm the average thickness of the dykes is about 4 1 m and the thickness does not change notably along the alftafjordur swarm the thinner dykes tend to have smaller grains than the thicker dykes of five dykes followed laterally the longest is over 22 km the thickness of individual dykes changes irregularly along their length and the dyke is often offset where its thickness changes many dykes appear to be completely discontinuous but some parts are connected by veins where the dykes end in a vertical section most of them simply taper away only about 10 5 of the dykes occupy faults the mechanical and thermal effects of the dykes on the country rock are small many of the dykes appear to be non feeders i e dykes that never reached the surface to feed lava flows using the length width ratio the depth of origin of three dykes has been estimated the maximum depth of origin of these three dykes is 7 5 km 9 km and 10 km below the original surface

a numerical model of dyke propagation in layered elastic media summary we develop a mathematical model describing dyke propagation in proximity of an elastic discontinuity of the embedding medium the dyke is modelled as a fluid filled crack in plane strain configuration employing the boundary element method the pressure gradient along the crack is assumed proportional to the difference between the densities of the host rock and the fluid mass conservation is imposed during propagation and fluid compressibility is taken into account the path followed by the crack is found by maximizing the total energy release given by the sum of the elastic and gravitational contributions the mathematical simulations provide a sort of refraction phenomenon that is a sudden change in the direction of propagation when the crack crosses the boundary separating different rigidities if the dyke enters a softer medium its path deviates towards the vertical if the dyke enters a harder medium its path deviates away from the vertical and may even become arrested as a horizontal sill along the interface if the rigidity contrast is large gravitational energy plays a major role during propagation in particular in proximity of layer boundaries this role is enhanced by the shift of the centre of mass due to changes of dyke shape mathematical results were validated by laboratory experiments performed injecting tilted air filled cracks through gelatin layers with different rigidities

mechanical models for dikes a third school of thought abstract geological and geophysical data from continental volcanic centers and giant radial swarms and from oceanic shield volcanoes and rift zones indicate that dikes propagate laterally for distances that can be 10 to over 100 times their height what traps dikes within the shallow lithosphere and promotes these highly eccentric shapes gravity induced stress gradients in the surrounding rock and pressure gradients in the magma are the primary loading mechanisms pressure gradients due to magma flow are secondary to insignificant because the flow direction is dominantly horizontal this configuration of vertical blade shaped dikes with horizontal dike propagation and magma flow is fundamentally different from the two dike model configurations described in a recent review paper as two schools of thought for mechanical models of dikes in school i a dike is disconnected from its source and ascends under the influence of buoyancy in school ii a dike is connected to a magma reservoir and is driven upward by magma flux from the source we review the geological and geophysical data supporting the vertical dike horizontal flow propagation configuration and suggest the abundance and veracity of these data in many different geological settings and the modeling results that address this physical process warrant adding this as a third school of thought a new analytical solution for the boundary value problem of a homogeneous isotropic and linear elastic solid with a vertical fluid filled crack is used to investigate the effects of gravitationally induced stress and pressure gradients on the aperture distribution dike tip stress intensity and stable height model results indicate that in a homogeneous crust dikes can achieve stable heights greater than a kilometer only if the host rock fracture toughness k ic 100 mpa m 1 2 however density stratification of the crust is an effective mechanism for trapping kilometer scale dikes even if the host rock is very weak k ic 0 this analysis may explain why vertical dikes propagate laterally for great distances but reside within a narrow range of depths in the crust

neutral buoyancy and the structure of mid ocean ridge magma reservoirs the mechanical structure of the regions for shallow storage and lateral intrusion of mid ocean ridge basalt morb is explored in part by examining the density range appropriate for picritic to tholeiitic liquids and liquid crystal mixtures and its relationship to the nonlinear density depth structure of the ridge magma density spans the range 2 6 to at least 2 82 mg m 3 and incorporates the effects of fractional crystallization on the density evolution the incorporation of olivine phenocrysts and the contributions of water in melt phase density reductions the melt and melt crystal density band crosses the in situ rock density curve over the 1 to 3 km depth interval beneath the volcanic surface within that averaged interval picritic to tholeiitic melt and melt crystal mixtures are in approximate mechanical equilibrium with their surroundings and the interval is referred to as the morb horizon of neutral buoyancy hnb the detailed locations of the transition regions between the negative and neutral buoyancy and between the neutral and positive buoyancy regimes are dependent on melt phase composition as well as the presence of suspended mineral phases and their identity in the east pacific rise the hnb has a 1 1 correspondence with the inferred location of the sheeted dike complex and the seismically detected minimum compressional wave velocity region in ophiolite complexes the region corresponds to the sheeted dike complex and the uppermost isotropic gabbros above the hnb is the region of negative buoyancy seafloor to an averaged 1 km depth within which negative buoyancy forces may induce the descent of nonvesiculated melt this region corresponds to the pillow basalt sediment sequence the region of positive buoyancy extends from 3 km to the depth of melt generation and picritic melt ascends in dikes and veins of finite height 500 m to 11 km and relatively narrow width 20 mm to 100 cm the finite strengths of high temperature fluid weakened rocks mandate finite height melt parcels along the ascent pathway the magmatic source region is therefore never hydraulically connected with the surface nor with the near surface reservoir thus relatively locally integrated buoyancy has a natural role in the ascent of melt from the source region to the region of neutral buoyancy during the final stages of magma ascent hydrothermal fluid circulation enshrouds the hnb in a three dimensional envelope as suggested by the depth extent of alteration mineralogy in ophiolite complexes while hydrothermal cooling may play an important role in arresting the ascent of magma in very low spreading rate environments gravitational equilibrium represents the effectively dominant theme in intermediate and high spreading rate regions such as the east pacific rise elastic crack penetration of rheological transition zones near the hnb identify modes of crack tip morphologic changes as a function of young s modulus ratios e2 e1 above and beneath the transition and affect the style of intrusion while melt buoyancy determines the ultimate equilibrium resting place elastic crack stability considerations relate the vertical magma pressure gradients for tholeiitic pt and picritic pp magmas to the vertically varying gradient in the horizontal stress component h and suggest further subdivision into two horizons of neutral buoyancy one for tholeiitic magma hnbt and one for the picritic liquid olivine mixtures hnbp these intervals are very approximate but are estimated as 600 m to 1400 m and 1400 to 3000 m depth respectively beneath the east pacific rise axis as oceanic lithosphere is created at the rise axis and spreads laterally the horizons of negative buoyancy and neutral buoyancy ride with it and may continue to modulate the subsurface magma dynamics that influence off axis volcanism

thermal and mechanical aspects of magma emplacement in giant dike swarms we consider the thermal history and dynamics of magma emplacement in giant feeder dikes associated with continental flood basalts for driving pressure gradients inferred for giant dike swarms thicknesses of 10 m would enable dikes to transport magma laterally over the distances observed in the field up to thousands of kilometers without suffering thermal lock up using time dependent numerical solutions for the thermal evolution of a dike channel under laminar and turbulent flow conditions in the presence of phase transitions we investigate the possibility that the observed dike thicknesses of the order of 100 m result from thermal erosion of the country rocks during dike emplacement this implies that the observed range of dike widths in giant dike swarms may reflect variations in the source volume and not the excess magma pressure it is found that the total volume of intruded magma required to produce an order of magnitude increase in dike width via wall rock melting broadly agrees with the estimated volumes of individual flows in continental flood basalts the presence of chilled margins and apparently low crustal contamination characteristics of some giant dikes may be consistent with turbulent magma flow and extensive melt back during dike emplacement in this case measurements of the anisotropy of magnetic susceptibility most likely indicate magma flow directions during the final stages of dike intrusion shear stresses generated at the dike wall when the dike starts to freeze strongly decrease with increasing dike width which implies that thicker dikes may have less tendency to produce consistent fabric alignment our results suggest that if the dike was propagating downslope off a plume related topographic swell the mechanism responsible for flow termination could possibly have been related to underpressurization and collapse implosion of the shallow magma plumbing system feeding the intrusion radial dikes that erupted at the periphery of the topographic uplift might have increased rather than decreased extensional stresses in the crust within the topographic uplift upon their solidification

inverse modeling for estimating fluid overpressure distributions and stress intensity factors from an arbitrary open fracture geometry abstract we present a new solution for estimating the fluid overpressure driving pressure or net pressure acting on the walls of a fracture with an arbitrary opening displacement in the paper we first present a forward modeling solution using fourier cosine series for the opening displacement of a fracture subject to an overpressure that varies irregularly along the length of a fracture by changing the form of the solution we provide a matrix equation for estimating the fourier coefficients and thereby obtain the overpressure variation from the fracture geometry as numerical tests of this inverse analysis we estimated the overpressure variation from fracture opening displacements given by well known analytical solutions and found that this method can be used for overpressure estimates for a variety of fluid driven fractures we apply our solutions to a mineral vein hosted by gneiss west norway and conclude from the aperture variation that at the time of vein formation the overpressure increased toward the vein tip we also discuss the physical meaning of the fourier coefficients by applying our results to man made hydraulic wing fractures the results indicate that the coefficients of n 0 and n 1 relate to the fluid overpressure and the critical stress intensity factor

physical processes of shallow mafic dike emplacement near the san rafael swell utah some 200 shonkinite dikes sills and breccia bodies on the western colorado plateau of south central utah were intruded from approximately 3 7 to 4 6 ma contemporaneous with mafic volcanism along the nearby plateau margin thicknesses of dikes range to about 6 m the log normal mean thickness is 85 cm despite the excellent exposures of essentially all dikes in strata of the jurassic san rafael group their number is indeterminate from their outcrop and spacing because they are everywhere greatly segmented by our grouping of almost 2000 dike segments most dikes are less than 2 km in outcrop length the longest is 9 km because the san rafael magmas were primitive and probably ascended directly from the mantle dike lengths in outcrop are much less than their heights the present exposures probably lie along the irregular upper peripheries of dikes that lengthen and merge with depth orientations of steps on dike contacts record local directions of dike fracture propagation about half of the measurements plunge less than 30 showing that lateral propagation at dike peripheries is as important as the vertical propagation ultimately responsible for ascent the san rafael dikes now exposed after erosion of about 0 5 1 5 km appear to thicken and shorten upward probably because near surface vesiculation enhanced magmatic driving pressures propagation likely ceased soon after the first dike segments began to feed nearby sills or vented to initiate small volume eruptions most of the dikes are exposed in clastic strata of the jurassic san rafael group they probably acquired their strikes however while ascending along well developed joints in massive sandstones of the underlying glen canyon group rotation of far field stresses during the emplacement interval cannot account for disparate strikes of the dikes which vary through 110 most lying between north and n25 w rather the two regional horizontal principal stresses were probably nearly equal and so the dominant n75 e direction of dike opening was not strongly favored across the center of the swarm about 10 to 15 dikes overlap and produce 15 20 m of dilation many are in sufficient proximity that later dikes should be thinner than earlier ones if neither the magma pressures nor regional stresses were changing during the emplacement interval however dike thicknesses vary systematically neither along the length of the swarm nor in proportion to the number of neighboring dikes it appears that crustal extension during the magmatic interval relieved compressive stresses localized by intrusion

magma reservoirs and neutral buoyancy zones on venus implications for the formation and evolution of volcanic landforms we examine the production of magma reservoirs and neutral buoyancy zones nbzs on venus and the implications of their development for the formation and evolution of volcanic landforms the high atmospheric pressure on venus reduces volatile exsolution and generally serves to inhibit the formation of nbzs and shallow magma reservoirs for a range of common terrestrial magma volatile contents magma ascending and erupting near or below mean planetary radius mpr should not stall at shallow magma reservoirs such eruptions would be characterized by relatively high total volumes and effusion rates for the same range of volatile contents at 2 km above mpr about half of the cases result in direct ascent of magma to the surface and half in the production of neutral buoyancy zones in general neutral buoyancy zones and shallow magma reservoirs begin to appear as gas content increases and are nominally shallower on venus than on earth for a fixed volatile content nbzs become deeper with increasing elevation over the range of elevations treated here 1 km to 4 4 km depths differ by a factor of 2 4 these analyses reveal several factors that may help to account for the low height of volcanoes on venus larger primary reservoirs cause the wide dispersal of conduits building edifices models of the position of the shallow nbz reservoir during edifice growth show that for earth the magma chamber center remains at a constant depth below the growing edifice summit thus keeping pace with the increasing elevation while on venus the chamber center becomes deeper relative to the summit of the growing edifice because of the major change in atmospheric pressure as a function of altitude therefore neutral buoyancy zones and magma reservoirs on venus will remain in the prevolcano substrate longer and in many cases may not emerge into the edifice at all the lower rate of vertical migration implies that magma reservoirs would tend to stabilize undergo greater lateral growth and become larger on venus than earth the proportion of the available magma going into production of the edifice relative to that intruded into the substrate is smaller on venus than earth large reservoirs would encourage multiple and more widely dispersed source vents and large volumes for individual eruptions in large reservoirs positively buoyant materials are likely to be produced from differentiation substrate remelting and volatile exsolution nonbuoyant materials exsolving volatiles in a shallow reservoir will need higher gas bubble concentrations to produce eruptions than on earth and when this gas enriched melt emerges at the surface it is more likely to retain its bubbles than to undergo explosive disruption due to the high surface atmospheric pressure therefore there is the potential for the production of a range of erupted lavas that have very high gas bubble concentrations leading to anomalous more viscous rheological properties inhibition of disruption of volatile rich magma for both basaltic and more evolved compositions can lead to the production of 1 more bubble rich vesicular flows characterized by higher viscosity and greater thicknesses the venus equivalent of effusions that would have lost much of their volatiles in the fire fountaining process on earth 2 high volume high discharge rate extremely gas rich basaltic effusions that increase viscosity considerably upon surface extrusion and produce domes whose volumes are considerably higher than their dense rock equivalent and 3 more evolved compositions that are gas rich but do not undergo disruption upon effusion and produce domes and flows of high viscosity the venus equivalent of terrestrial ignimbrites on the basis of these analyses we predict that intrusions and dike emplacement should be common particularly around both shallow and deep magma reservoirs and the tops of dikes should be manifested as radial fractures there should be a range of diameters of circular features associated with the presence of both shallow nbz related and deep plumerelated magma reservoirs large volume lava outpourings should be favored at lower elevations and shallow reservoirs and edifices should be more common at intermediate elevations at the highest elevations magma reservoirs are predicted to be large and relatively deep with low associated edifices direct ascent of magma where neutral buoyancy zones are unlikely low elevations and the propensity for relatively larger magma reservoirs on venus when they do form are both factors which will tend to favor high volume eruptions independent of variations in magma temperature or chemistry individual volcanic features should be interpreted in terms of regional geologic setting and the dynamics of elevation changes commonly associated with various scales of mantle processes and magma emplacement in order to assess global crustal growth processes on venus

dike propagation through layered rocks 1 dike penetration through a succession of upper crustal layers with different densities is studied with a new numerical code for an individual layer to significantly affect dike ascent its thickness must be of order 1 when scaled to the characteristic length scale for the inflated nose region that develops below the dike tip this characteristic length is l q 1 6 g 1 1 2 g 2 3 where and are the viscosity and buoyancy of magma g and are elastic moduli for the encasing rocks q is the magma flow rate and g gravity for basaltic dikes l is 1 km which is of the same order of magnitude as the typical thickness of sedimentary strata and volcanic deposits in such conditions dike ascent proceeds irregularly with large changes of velocity and width at an interface scaling laws for the ascent rate and dike width are derived penetration through low density layers is determined by a local buoyancy balance in the inflated nose region of the dike independently of the total buoyancy of the magma column between source and tip in such conditions a dike develops an internal overpressure that may be large enough to generate a horizontally propagating sill for this to occur the thickness of the low density layers must exceed a threshold value which depends only on the rock strength and on the average negative buoyancy of magma for basaltic melt we estimate that this threshold thickness cannot be less than about 700 m and is 2 km on average

fluid filled fractures in earth s lithosphere gravitational loading interpenetration and stable height of dikes and veins abstract we present two analytical solutions for the boundary value problem of a homogeneous isotropic and linear elastic solid with a vertical fluid filled crack and use these to investigate the effects of gravitationally induced stress and pressure gradients on the opening distribution fracture tip stress intensity and stable heights of veins and dikes stable fractures are not propagating or closing anywhere along their tipline so the vein or dike is in its final arrested configuration as preserved in the rock record the solutions do not preclude interpenetration of crack surfaces so we propose special constraints to avoid such ill posed problems veins and dikes both grow as fluid filled opening fractures in earth s brittle lithosphere but attain markedly different heights we show how gravity induced pressure gradients in water and magma and stress gradients in the host rock lead to different stable heights dikes but not veins can attain stable heights near the level of neutral buoyancy in a density stratified rock mass even if the host rock fracture toughness is zero depth to center and opening distributions for dikes are different if host rock density is stratified or continuously variable these solutions offer a new set of analytical tools for interpreting field data from veins and dikes

soil erosion by surface water flow on a stony semiarid hillslope soil erosion on hillslopes occurs by processes of soil splash from raindrop impacts and sediment entrainment by surface water flows this study investigates the process of soil erosion by surface water flow on a stony soil in a semiarid environment a field experimental method was developed whereby erosion by concentrated flow could be measured in predefined flow areas without disturbing the soil surface the method allowed for measurements in this study of flow erosion at a much wider range of slopes 2 6 to 30 1 per cent and unit discharge rates 0 0007 to 0 007 m2 s 1 than have been previously feasible flow velocities were correlated to discharge and hydraulic radius but not to slope the lack of correlation between velocity and slope might have been due to the greater rock cover on the steeper slopes which caused the surface to be hydraulically rougher and thus counteract the expected effect of slope on flow velocity the detachment data illustrated limitations in applying a linear hydraulic shear stress model over the entire range of the data collected flow detachment rates were better correlated to a power function of either shear stress r2 0 51 or stream power r2 0 59 published in 1999 by john wiley sons ltd

conditions for the arrest of a vertical propagating dyke magma ascent towards the earth s surface occurs through dyke propagation in the vast majority of cases we investigate two purely mechanical effects unrelated to cooling or solidification that lead to the arrest of propagation so that no eruption occurs the first is that the input of magma from the source is not maintained continuously such that a fixed volume of magma is released laboratory experiments show that in this case the dyke stops at a finite distance from the source this behaviour is specific to the fracturing process in 3 d we derive a relationship for the minimum magma volume required for an eruption as a function of magma buoyancy and source depth when large magma volumes are available eruption may also be prevented by a thick low density layer in the upper crust numerical studies of dyke propagation show that the dyke continues to rise even though it is negatively buoyant magma accumulates in a swollen nose region at the interface between the low density layer and the dense basement magma overpressure is largest at this interface and increases with increasing penetration into the upper layer it may become large enough to induce horizontal fractures in the dyke walls and lateral intrusion of a sill which prevents eruption this requires that the thickness of the low density layer exceeds a threshold value that depends on the density contrast between magma and host rock if the magma volume is smaller than a threshold value neither sill intrusion nor eruption are possible and magma gets stored in a horizontal blade shaped dyke straddling the interface scaling laws for variations of ascent rate and for the minimum magma volume allow diagnosis of a failed eruption

the roles of elastic properties magmatic pressure and tectonic stress in saucer shaped sill growth near surface igneous sills commonly exhibit saucer like shapes formed due to interaction with the earth s surface once some critical sill length is reached relative to its depth sill geometry has been strongly linked to the host material conditions particularly in terms of the elastic properties and shear cohesion of the host rock operating as primary controls on sill geometry here we conduct dynamic numerical simulations for sill growth in the near surface in which we vary the host rock properties magma pressure profile internal to the sill p and the externally applied tectonic stress r to consider their contributions to sill geometry we find that elastic properties alone have little impact on sill geometry saucer shapes reflect the additive stress components of the magma overpressure within the sill and the tectonic stress controlled by the locus of the maximum energy release rate gmax initially gmax is in plane with the sill but deflects to 25 at a critical base length rc relative to depth due to interaction between the sill and the free surface increasing r decreases this angle and increases rc of the sill p controls sill growth rate but has little effect on overall geometry host rock cohesion and elastic properties control the absolute magnitudes of r required to effect a change in sill geometry plain language summary horizontal magma pathways sills are a crucial part of volcanic plumbing systems acting as potential feeder conduits to volcanic eruptions and as magma storage systems saucer shaped sills which exhibit a flat inner region and inclined outer region are a common type of magma pathway in the shallow crust models for saucer shaped sills both as physical analogue models or numerical simulations typically under predict the length of the inner flat region and over predict the outer inclined region models are typically too short and too steep here we use numerical simulation to investigate parameters that may control sill shape we find that the dominant controls on sill shape are the competing effects of 1 bending of the rocks above the sill which promotes a transition to inclined growth typically at 25 and 2 plate tectonic shortening which serves to decrease the angle of incline towards 0 when the horizontal force is high increasing the applied horizontal tectonic force can produce sills that are up to five times longer in the inner region before growing as inclined sills at 5 this matches very closely with observations of natural sills indicating that tectonic forces are an important consideration in the growth of sills

crustal structure of mauna loa volcano hawaii from seismic refraction and gravity data abstract in october 1978 the u s geological survey established a 100 km long seismic refraction profile normal to the kona coast of hawaii island analysis of these data along with available gravity data suggest that the oceanic crust dips about 3 landward under the submerged flank of the island increasing to 8 5 under the kona coast maximum vertical deflection of the base of crust from beneath the deep ocean to a point beneath the summit of mauna loa is about 9 km high velocity high density rocks vp about 7 1 km sec density about 2 9 gm cm 3 comprise the bulk of the volcanic edifice and reach to within a few kilometers of the surface beneath the north flank of mauna loa the data also suggest that an elongate high velocity high density body lies parallel to the kona coast just below the surface this body probably represents an extinct buried rift zone

variation of rock fragment cover and size along semiarid hillslopes a case study from southeast spain abstract the spatial variation of rock fragment cover rc and rock fragment size rs along semiarid hillslopes and transects in the mediterranean is largely controlled by hillslope gradient total rock fragment cover rc 5 mm often increases in a convex upward curve with hillslope gradient while the d50 of the surface rock fragments 5 mm increases linearly with hillslope gradient on south facing slopes rc 5 mm is slightly higher than on north facing slopes lithology controls the size distribution of the stone pavement rather than its cover percentage spatial variation of rock fragment cover reflects spatial variation in past erosion and deposition rates hillslope sections that are steep south facing or have been abandoned a long time ago have undergone intense interrill and rill erosion and thus have high rock fragment covers tillage erosion leads to high rock fragment covers on convex hillslopes in intensively cultivated areas thus using information on hillslope gradient aspect lithology and landuse we have been able to describe the spatial variation of rock fragment cover and size along semiarid hillslopes in southeast spain such information is crucial for understanding and modelling the spatial variation of the hydrological and erosion response of semiarid hillslopes under environmental change especially in semiarid environments of the mediterranean where vegetation cover is predicted to decrease due to climatic or landuse changes and rock fragments at the surface become the only soil surface stabilisers

mechanical modeling of circumferential and radial dike intrusion on galapagos volcanoes a distinctive and unusual pattern of eruptive fissures is observed on the active volcanoes of the galapagos islands reflecting circumferential dike intrusion near the calderas and radial dike intrusion on the volcano flanks elastic finite element models were used to investigate how a stress field could be produced and maintained to promote both circumferential and radial dike emplacement modeling results show that magma reservoirs of galapagos volcanoes are probably diapiric because this shape promotes both circumferential and radial intrusions but magma pressure alone cannot create the observed pattern of dikes loading by volcano growth and magma reservoir pressure could produce a stress field of suitable orientation but insufficient magnitude the intrusion of circumferential dikes could alter the stress field in a way that promotes future radial diking and vice versa faulting or slumping within the calderas or on the volcano flanks in response to repeated intrusions could also create a stress field conducive to continued intrusion

hydraulics and erosion in eroding rills rills often act as sediment sources and the dominant sediment and water transport mechanism for hillslopes six experiments were conducted on two soils and a uniform sand using three experimental methodologies the results of this study challenge the assumption often used in hydrologic and erosion models that relationships derived for sheet flow or larger channel flow are applicable to actively eroding rills velocity did not vary with slope and reynolds number was not a consistent predictor of hydraulic friction this result was due to interactions of slope gradient flow rate erosion and the formation of rill roughness bed structures and head cuts a relationship for rill flow velocities was proposed stream power was found to be a consistent and appropriate predictor for unit sediment load for the entire data set while other hydraulic variables were not the data for stream power and sediment load fit the form of a logistic curve r2 0 93 which is promising relative to recently proposed erosion models which are based on probabilistic particle threshold theory

kilometer scale upward migration of hydrocarbons in geopressured sediments by buoyancy driven propagation of methane filled fractures several lines of evidence support kilometer scale upward migration of fluids in the gulf of mexico basin discharge of hypersaline brines at the sea floor long term natural hydrocarbon seeps and microseeps gas chimneys lead zinc mineralization in salt dome cap rocks and allochthonous brines in cenozoic sediments we explore the hypothesis that upward fluid transport in geopressured sediments is caused by buoyancy driven propagation of isolated methane filled fractures in other words instead of fluid migrating along a fixed network of interconnected pores or fractures fluid enclosed within an isolated fracture is transported upward by hydrofracturing the mechanically weak geopressured sediments thus the fluid filled fracture propagates upward through the sediments hydrofracture is driven by the pressure difference buoyancy between the enclosed methane and the surrounding sediments our results show that methane filled fractures with half lengths of a few meters should propagate upward through geopressured sediments with velocities of hundreds of meters per year or higher as methane filled fractures increase in volume and decrease in density with decreasing confining pressure they develop the potential to entrain and transport more than 1000 kg m3 of oil or brine methane filled fractures should propagate to the surface unless they are trapped beneath a layer that has high fracture toughness such as salt or are absorbed when they intersect a permeable 10 md sand layer

propagation and arrest of dikes under topography models applied to the 2014 bardarbunga iceland rifting event dikes along rift zones propagate laterally downslope for tens of kilometers often becoming arrested before topographic reliefs we use analogue and numerical models to test the conditions controlling the lateral propagation and arrest of dikes exploring the presence of a slope in connection with buoyancy and rigidity layering a gentle downslope assists lateral propagation when combined with an effective barrier to magma ascent e g gelatin stiffness contrasts while antibuoyancy alone may be insufficient to prevent upward propagation we also observe that experimental dikes become arrested when reaching a plain before opposite reliefs our numerical models show that below the plain the stress field induced by topography hinders further dike propagation we suggest that lateral dike propagation requires an efficient barrier rigidity to upward propagation assisting antibuoyancy and a lateral pressure gradient perpendicular to the least compressive stress axis while dike arrest may be induced by external reliefs

synrift magmatism in a cenozoic rift basin from 3d seismic data wichianburi sub basin phetchabun basin thailand part 1 distribution and timing of intrusions and forced folds the late oligocene pliocene wichianburi sub basin phetchabun rift thailand has undergone three phases of development late oligocene early miocene c 16 ma east west extension on predominantly nnw sse to north south striking faults 16 ma c 3 ma ne extension on nnw sse north south and ne sw trending faults and 3 ma to present post rift subsidence the basin was also affected by intrusive and extrusive igneous activity from 24 to 2 ma the relationships among the structure rift basin stratigraphy and sheet intrusions are unusually well documented as a result of extensive hydrocarbon exploration drilling and 3d seismic data together with the production of hydrocarbons from igneous sills the oldest igneous activity c 24 13 ma lies sw of the wichianburi sub basin where extrusive rocks exposed at the surface have been dated by k ar and 40ar 39ar methods the overall igneous activity youngs from the south of the basin to the north 11 9 ma numerous domal folds occur across the basin the sill and laccolith dimensions the rate of fold development the variable timing of fold formation and the fold geometry all indicate that the folds are related to magma emplacement not tectonic inversion fold formation occurred at c 16 15 and 12 11 ma in single or multiple stages the timing of folding coupled with the radiometric dating of some sills k ar 39ar 40ar indicates that the greatest amount of intrusive activity occurred between 16 and 11 ma the 16 ma date coincides with the switch from east west to nw se extension which promoted dilatancy within the upper crust along a range of synrift fault orientations and some pre rift trends the burial history of the main depocentre shows that miocene sill emplacement occurred at depths

numerical modelling of dyke interaction and its influence on oceanic crust formation abstract dykes are an essential element in building oceanic crust most prominent in sheeted dyke complexes in the upper crust since dykes alter the magnitude and orientation of the local stress field they cannot be treated as passive infillings of extensional fractures we use a quasi static iterative 2 d boundary element method allowing for a wholesale movement of fluid filled fractures effects of stress and pressure gradients buoyancy and enclosed fluid mass are considered the implications of the dyke induced stress field are analysed combining the simulation of fracture propagation with computation of dyke interaction dyke interaction occurs by the adaptation of ascending dykes to the stress field caused by previous fractures arrested in the crust and leads to focussing and crossing of dykes examples for applications are introduced concerning e g the generation of a magma chamber and the formation of the sheeted dyke complex our main results are that the interaction between dykes can be considerable and that the most important controlling factor is stress the interaction is small when the horizontal tensional stress is large compared to the pressure in the dyke head otherwise dykes tend to attract each other and to form centres of high dyke density or sill layers

the relation between surface rock fragment cover and semiarid hillslope profile morphology abstract rock fragment covers veneer hillslopes in many parts of the world and influence the operation of hydrologic and geomorphic processes on those surfaces the purpose of this investigation was the examine the spatial variability of rock fragment cover on morphological units of hillslopes in southeastern arizona u s a simple statistical models based upon hillslope gradient as well as a soil slope factor ssf were developed and validated for the estimation of percent rock fragment covers rfc on these units although reasonably accurate estimates were made using either hillslope gradient or the ssf it appears more efficient to utilize hillslope gradient alone likewise reasonably accurate estimates of rfc can be made using either a composite model for the entire hillslope or unit specific models however it appears more efficient to utilize the gradient composite model

relationship between discharge velocity and flow area for rills eroding loose non layered materials a relationship between discharge flow velocity and flow area in rills is established using data from four field and laboratory studies the proposed relationship is shown to predict successfully flow velocities measured in six other studies although slopes range from 0 035 to 0 45 and soil materials range from stony sands over silt loams to vertisols mean flow velocity can be well predicted from discharge alone thus there is no important influence of slope and or soil material characteristics on flow velocities in rills the proposed relationship may be used to improve performance of deterministic flow routing models when applied to rilled catchments furthermore it allows the calculation of unit stream power which has been shown to be related to the transporting capacity of overland flow in terms of slope and discharge

rill hydraulics on a semiarid hillslope southern arizona seventy field experiments were conducted in seven rills located on a semiarid rangeland hillslope underlain by gravelly soils at walnut gulch arizona the rills which are characterized by wide shallow cross sections and gravel covered beds have mean at a station hydraulic geometry exponents of b 0 33 f 0 34 and m 0 33 although the differences between these values and typical values of b 0 30 f 0 40 and m 0 30 for cropland rills are not statistically significant they are thought to be real as cropland rills often have more rectangular cross sections and steeper sides than the rangeland rills under study for rills formed in silty loamy soils govers developed an empirical relation between mean flow velocity and discharge emphasizing the generality of this relation he suggested that it may be used as a simple means of routing runoff through rills he also noted that this relation appeared to be unaffected by either slope or soil materials the present data represent rills underlain by coarser and somewhat more varied gravel rich soils these data do not conform to govers relation and a multiple regression analysis reveals that slope and soil materials either directly or indirectly through bed roughness exert almost as much influence on flow velocity as does discharge three alternative methods are developed for predicting flow velocity in the rills under study all three methods give good results with the largest root mean square deviation being 3 115 cm s 1

dynamics of dikes versus cone sheets in volcanic systems igneous sheet intrusions of various shapes such as dikes and cone sheets coexist as parts of complex volcanic plumbing systems likely fed by common sources how they form is fundamental regarding volcanic hazards yet no dynamic model simulates and predicts satisfactorily their diversity here we present scaled laboratory experiments that reproduced dikes and cone sheets under controlled conditions our models show that their formation is governed by a dimensionless ratio 1 which describes the geometry of the magma source and a dynamic dimensionless ratio 2 which compares the viscous stresses in the flowing magma to the host rock strength plotting our experiments against these two numbers results in a phase diagram evidencing a dike and a cone sheet field separated by a sharp transition that fits a power law this result shows that dikes and cone sheets correspond to distinct physical regimes of magma emplacement in the crust for a given host rock strength cone sheets preferentially form when the source is shallow relative to its lateral extent orwhen the magma influx velocity or viscosity is high conversely dikes form when the source is deep compared to its size or when magma influx rate or viscosity is low both dikes and cone sheets may form fromthe same source the shift fromone regime to the other being then controlled by magma dynamics i e different values of 2 the extrapolated empirical dike to cone sheet transition is in good agreement with the occurrence of dikes and cone sheets in various natural volcanic settings

structural development of dike swarms controlled by the change of magma supply rate the cone sheets and parallel dike swarms of the miocene otoge igneous complex central japan abstract dike and sheet swarms of the post cauldron activity of the miocene otoge igneous complex central japan show systematic structural and petrological evolution a concentric cone sheet swarm otoge cone sheets measuring 10 15 km3 was formed at the beginning of the post cauldron stage and was later succeeded by the formation of a parallel dike swarm shitara central dike swarm measuring 3 5 km3 the otoge cone sheets have a less fractionated character with little compositional variations whereas the shitara central dike swarm has a fractionated character with wide compositional variations this despite that both swarms reflect a single fractionation trend the compositional change from the otoge cone sheets to the shitara central dike swarm can be explained by fractional crystallization due to the decline in the supply of less fractionated hot magma into the reservoir the structural change from the otoge cone sheets to the shitara central dike swarm reflects the change in the stress field from a local compressive field to a regional extensive one with the decline of magma replenishment into the reservoir during the final stage of volcanic activity the concentrated distribution of the cone sheets suggests the sill like or flat top shaped magma reservoir beneath the center of the otoge cone sheets

an experimental investigation of sill formation and propagation in layered elastic media a series of experiments are described where dyed water a magma analogue was intruded into solid gelatine a crustal analogue to investigate the formation of sills we considered a layered gelatine system with contrasting adjacent layers by varying the density and rigidity of the gelatine we found that experimental sills form when the upper layer is more rigid than the lower layer with intrusion occurring in a plane directly below the interface experimental dykes were observed to propagate to the surface when the young s modulus ratio of upper to lower gelatine layers was less than one experimental dyke arrest occurred when the upper layer was more rigid and the interface was strong two varieties of experimental sill formed when the upper layer was more rigid than the lower layer and the interface was sufficiently weak the form of the intrusion depends on the balance of driving pressures and the young s modulus ratio of contrasting adjacent layers when the rigidity ratio is high and there is a large driving pressure the experimental feeder dyke completely converts to propagate as a sill however when the rigidity ratio and driving pressure are both close to one a dyke sill hybrid forms under these conditions the experimental sill formation is accompanied by contemporaneous dyke intrusion into the overlying more rigid layer during sill propagation deformation structures such as faults and en echelon fractures are formed into the lower layer experimental sill propagation dynamics are controlled by viscous dissipation along the length of the sill causing acceleration with increasing length our study suggests that rigidity contrasts may play a major role in the location of sills and development of igneous complexes in ancient cratonic areas the moho is a suitable site for the preferential formation of sills with higher rigidity continental crust overlying weaker mantle mantle plumes impacting ancient continents provide a situation in which large sills can form to fractionate prior to eruption of flood basalts the boundary between the upper and lower crust conrad discontinuity may provide a preferential focus for the emplacement of sheets of silicic magma at continental arcs where the lower crust is weakened by prolonged heating and possible hydration

on the propagation path of magma filled dikes and hydrofractures the competition between external stress internal pressure and crack length mixed mode fl uid fi lled cracks represent a common means of fl uid transport within the earth s crust they often show complex propagation paths which may be due to interaction with crustal heterogeneities or heterogeneous crustal stress previous experimental and numerical studies focus on the interplay between fl uid overpressure and external stress but neglect the effect of other crack parameters in this study we address the role of crack length on the propagation paths in the presence of an external heterogeneous stress fi eld we make use of numerical simulations of magmatic dike and hydrofracture propagation carried out using a two dimensional boundary element model and analogue experiments of air fi lled crack propagation into a transparent gelatin block we use a 3 d fi nite element model to compute the stress fi eld acting within the gelatin block and perform a quantitative comparison between 2 d numerical simulations and experiments we show that given the same ratio between external stress and fl uid pressure longer fl uid fi lled cracks are less sensitive to the background stress and we quantify this effect on fl uid fi lled crack paths combining the magnitude of the external stress the fl uid pressure and the crack length we de fi ne a new parameter which characterizes two end member scenarios for the propagation path of a fl uid fi lled fracture our results have important implications for volcanological studies which aim to address the problem of complex trajectories of magmatic dikes i e to forecast scenarios of new vents opening at volcanoes but also have implications for studies that address the growth and propagation of natural and induced hydrofractures

surface deformation in volcanic rift zones abstract the principal conduits for magma transport within rift zones of basaltic volcanoes are steeply dipping dikes some of which feed fissure eruptions elastic displacements accompanying a single dike emplacement elevate the flanks of the rift relative to a central depression concomitant normal faulting may transform the depression into a graben thus accentuating the topographic features of the rift if eruption occurs the characteristic ridge trough ridge displacement profile changes to a single ridge centered at the fissure and the erupted lava alters the local topography a well developed rift zone owes its structure and topography to the integrated effects of many magmatic rifting events to investigate this process we compute the elastic displacements and stresses in a homogeneous two dimensional half space driven by a pressurized crack that may breach the surface a derivative graphical method permits one to estimate the three geometric parameters of the dike height inclination and depth to center and the mechanical parameter driving pressure rock stiffness from a smoothly varying displacement profile direct comparison of measured and theoretical profiles may be used to estimate these parameters even if inelastic deformation notably normal faulting creates discontinuities in the profile geological structures open cracks normal faults buckles and thrust faults form because of stresses induced by dike emplacement and fissure eruption theoretical stress states associated with dilation of a pressurized crack are used to interpret the distribution and orientation of these structures and their role in rift formation

african climate change and faunal evolution during the pliocene pleistocene abstract environmental theories of african faunal evolution state that important evolutionary changes during the pliocene pleistocene interval the last ca 5 3 million years were mediated by changes in african climate or shifts in climate variability marine sediment sequences demonstrate that subtropical african climate periodically oscillated between markedly wetter and drier conditions paced by earth orbital variations with evidence for step like 0 2 ma increases in african climate variability and aridity near 2 8 ma 1 7 ma and 1 0 ma coincident with the onset and intensification of high latitude glacial cycles analysis of the best dated and most complete african mammal fossil databases indicates african faunal assemblage and perhaps speciation changes during the pliocene pleistocene suggesting more varied and open habitats at 2 9 2 4 ma and after 1 8 ma these intervals correspond to key junctures in early hominid evolution including the emergence of our genus homo pliocene pleistocene shifts in african climate vegetation and faunal assemblages thus appear to be roughly contemporary although detailed comparisons are hampered by sampling gaps dating uncertainties and preservational biases in the fossil record further study of possible relations between african faunal and climatic change will benefit from the accelerating pace of important new fossil discoveries emerging molecular biomarker methods for reconstructing african paleovegetation changes tephra correlations between terrestrial and marine sequences as well as continuing collaborations between the paleoclimatic and paleoanthropological communities

spatial distribution of surface rock fragments along catenas in semiarid arizona and nevada usa improved techniques for estimating soil erosion by water have shown that soil surface cover is a major component in the estimate of soil loss erosion prediction models require the user to input slope gradient and soil profile descriptions if equations expressing the relations between slope gradient soil profile rock fragment content and surface rock fragment cover were embedded in these models then direct user input could be reduced field measurements of slope gradient soil profile rock fragment content surface rock fragment cover and vegetation type and cover were made on 12 soil slope complexes on catenas in southeastern arizona usa correlation analysis showed that both slope gradient and soil profile rock fragment content were significantly p 0 01 correlated to surface rock fragment cover additional analysis indicated that the combined effects of slope gradient and soil profile rock content were better defined by a soil slope factor ssf two equations were developed to estimate surface rock fragment cover a logarithmic relation using slope gradient as the independent variable and a hyperbolic equation using the ssf as the independent variable these equations were used to estimate surface rock fragment cover from a soil slope complex in southern nevada the ssfrfc equation gave better estimates of the measured surface rock fragment cover these relations developed for catenas in southeastern arizona may be site specific but they do show that a relation exists for this semiarid area and suggest that similar relations may exist in areas with similar geology and climate such as parts of africa asia australia and south america development of simple relations describing important erosion processes will improve erosion estimates while simultaneously decreasing time and costs associated with using erosion prediction models