1,721,042 research outputs found
Surface deformations and gravity changes caused by pressurized finite ellipsoidal cavities
Full text linkWe develop quasi-analytical solutions for the surface deformation field and gravity changes due to the pressurization of a finite (triaxial) ellipsoidal cavity in a half-space. The solution is in the form of a non-uniform distribution of triaxial point sources within the cavity. The point sources have the same aspect ratio, determined by the cavity shape, while their strengths and spacing are determined in an adaptive manner, such that the net point-source potency per unit volume is uniform. We validate and compare our solution with analytical and numerical solutions. We provide computationally efficient MATLAB codes tailored for source inversions. This solution opens the possibility of exploring the geometry of shallow magma chambers for potential deviations from axial symmetry
Dyke emplacement in fractured media: application to the 2000 intrusion at Izu islands, Japan
No full textWe use a boundary element approach to study the problem of a large, magma-filled dyke embedded in a fractured, damaged medium. The numerical simulations show that the dyke opening and the crack extension force at the dyke tip increases with increasing fracture density. We show that this behaviour can at moderate fracture densities be predicted by an effective media model. Simple analytical formulae are given for the increasing average opening of the dyke and the decreasing fracture toughness as functions of increasing fracture density. The numerical and the theoretical results are found to be in good agreement. In a first application we tested the model by using GPS deformation and seismicity data from a recent lateral magma intrusion in Izu islands, Japan. This shows that a simple comparison of the distance change and the cumulative earthquake number enables the study of the stability of the dyke intrusion. The method seems to distinguish whether the dyke opening is actively driven by magma influx or passively driven by an expansion due to fracturing
Mathematical and analogue models of fluid filled fracture propagation in layered elastic media
No full textIn order to overcome the practical impossibility of direct observation of dike propagation within the crust, we develop mathematical and analogue models to describe the physical processes involved in their dynamics.
We focus our attention on what happens when a dike approaches the boundary between two media with different rigidities. In our 2D mathematical models, a dike opens and propagates in an infinite elastic medium, made up of 2 welded half-spaces with different elastic parameters.
Dikes are modelled as boundary element fluid-filled cracks. The pressure gradient along the crack is proportional to the difference between the densities of the host rock and the fluid. We take into account the compressibility of the fluid and a variable density in order to conserve the mass of the intrusion during its motion. The mathematical model allows to set a tectonic stress field and an arbitrarily tilted boundary separating different media. The growth, arrest and direction of propagation of the crack is governed by an energetic criterion: the motion of the dike is driven by the minimization of the elastic deformation energy plus the gravitational energy. Propagation is allowed when the energy release during the motion exceeds a fracture threshold.
The output of this code gives us the path followed by the crack during the propagation, its shape and the stresses induced in the elastic medium.
Interestingly, the mathematical simulations provide a sort of refraction phenomenon, that is a sudden change in direction of propagation when the crack crosses the boundary separating different rigidities. In order to validate our mathematical results, we perform laboratory experiments of air filled cracks propagating in gelatine. Gelatine represents well an elastic medium: it is brittle at refrigerator temperature and varying the concentration of dry gel powder dissolved in water we can control its rigidity. By injecting air from the bottom of a trasparent cylinder containing the gelatine, we obtain an air filled crack, tilted with respect to the vertical and propagating upwards toward the rigidity transition surface.
The experiments confirm the main characteristics of the mathematical simulations
Effects of elastic, density and strength discontinuities on dike propagation path
No full textWe present a 2D numerical model describing dike propagation in proximity of a discontinuity in elastic parameters,
density and fracture toughness of the embedding medium. Dikes are modeled, employing the boundary
element technique, as fluid filled cracks in plane strain configuration. Dikes open and propagate in an infinite
elastic medium, made up of 2 welded half-spaces with different rigidities, densities and fracture toughness. The
pressure gradient along the crack is assumed proportional to the difference between the densities of host rock
and fluid. We take into account the compressibility of the fluid and a variable density in order to conserve the
mass of the intrusion during its motion. Our model allows to set a tectonic stress field and an arbitrarily tilted
boundary separating different media. The path followed by the crack is found by maximizing the total energy
release, given by the sum of the elastic and gravitational contributions. Propagation is allowed when the energy
release during the motion exceeds a fracture threshold. The output of this code gives the path followed by the
crack during the motion, the trend of the energy release per unit of propagation length, the dike shape, the stress
and displacement fields induced in the surrounding medium. 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 dike enters a softer medium, its path deviates toward the vertical,
if the dike enters a harder medium its path deviates away from the vertical. Even if the magma density is low
enough to provide positive buoyancy, dike may become arrested as a horizontal sill along the interface, if the
rigidity contrast is large or if the fracture toughness is lower along the interface (e.g., layers are weakly welded).
Density discontinuities by themselves do not provide the same effect: dikes arrest near the neutral buoyancy
level without deviating from the initial direction of propagation. A density discontinuity in presence of an elastic
discontinuity, changes the “refraction” angle and the depth of dike arrest. Gravitational energy plays a major role
during propagation; in particular, in proximity of a rigidity discontinuity, this role is enhanced by the shift of
the center of mass due to changes of dike shape. Mathematical results were validated by laboratory experiments
performed injecting tilted air-filled cracks through gelatin layers with different rigidities
A quantitative study of the mechanisms governing dike propagation, dike arrest and sill formation,
No full textDikes and sills are the moving building blocks of the plumbing system of volcanoes and play a fundamental role in the accretionary processes of the crust. They nucleate, propagate, halt, resume propagation, and sometimes change trajectory with drastic implications for the outcome of eruptions (Sigmundsson et al., 2010). Their dynamics is still poorly understood, in particular when different external influencing factors are interacting. Here we apply a boundary element model to study dike and sill formation, propagation and arrest in different scenarios. We model dikes as finite batches of compressible fluid magma, propagating quasi-statically in an elastic medium, and calculate their trajectories by maximising the energy release of the magma-rock system. We consider dike propagation in presence of density layering, of density plus rigidity layering, of a weakly welded interface between
layers, under the action of an external stress field (of tectonic or topographic origin). Our simulations predict sill formation in several situations: i) when a horizontal weak interface is met by a propagating dike; ii) when a sufficiently high compressive tectonic environment is experienced by the ascending dike and iii) in case a dike, starting below a volcanic edifice, propagates away from the topographic load with a low dip angle. We find that dikes halt and stack when they become negatively buoyant and when they propagate with low overpressure at their upper tip toward a topographic load. Neutral buoyancy by itself cannot induce dikes to turn into sills, as previously suggested
Critical Fluid Injection Volumes for Uncontrolled Fracture Ascent
Full text linkHydrofracturing is a routine industrial technique whose safety depends on fractures remaining confined within the target rock volume. Both observations and theoretical models show that, if the fluid volume is larger than a critical value, pockets of fluid can propagate large distances in the Earth's crust in a self-sustained, uncontrolled manner. Existing models for such critical volumes are unsatisfactory; most are two-dimensional and depend on poorly constrained parameters (typically the fracture length). Here we derive both analytically and numerically in three-dimensional scale-independent critical volumes as a function of only rock and fluid properties. We apply our model to gas, water, and magma injections in laboratory, industrial, and natural settings, showing that our critical volumes are consistent with observations and can be used as conservative estimates. We discuss competing mechanisms promoting fracture arrest, whose quantitative study could help to assess more comprehensively the safety of hydrofracturing operations
Buoyancy-driven fracture ascent: Experiments in layered gelatine
No full textLaboratory 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
Mechanical modeling of pre-eruptive magma propagation scenarios at calderas
Full text linkSimulating magma propagation pathways requires both a well-calibrated model for the stress state of the volcano and models for dike advance within such a stress field. Here, we establish a framework for calculating computationally efficient and flexible magma propagation scenarios in the presence of caldera structures. We first develop a three-dimensional (3D) numerical model for the stress state at volcanoes with mild topography, including the stress induced by surface loads and unloading due to the formation of caldera depressions. Then, we introduce a new, simplified 3D model of dike propagation. Such a model captures the complexity of 3D magma trajectories with low running time, and can backtrack dikes from a vent to the magma storage region. We compare the new dike propagation model to a previously published 3D model. Finally, we employ the simplified model to produce shallow dike propagation scenarios for a set of synthetic caldera settings with increasingly complex topographies. The resulting synthetic magma pathways and eruptive vent locations broadly reproduce the variability observed in natural calderas
What Drives the Lateral Versus Vertical Propagation of Dikes? Insights From Analogue Models
No full textVolcanic eruptions are usually fed by dikes. Understanding how crustal inhomogeneities and topographic loads control the direction (lateral/vertical) and extent (propagation/arrest) of dikes is crucial to forecast the opening of a vent. Many factors, including buoyancy, crustal layering, and topography, may control the vertical or lateral propagation of a dike. To define a hierarchy between these factors, we have conducted analogue models, injecting water (magma analogue) within gelatin (crust analogue). We investigate the effect of crustal layering (both rigidity and density layering), topography, magma inflow rate, and the density ratio between host rock and magma. Based on the experimental observations and scaling considerations, we suggest that rigidity layering (a stiffer layer overlying a weaker one) and topographic gradient favor predominantly lateral dike propagation; inflow rate, density layering, and density ratio play a subordinate role. Conversely, a softer layer overlying a stiffer one favors vertical propagation. Our results highlight the higher efficiency of a stiff layer in driving lateral dike propagation and/or inhibiting vertical propagation with respect to the Level of Neutral Buoyancy proposed by previous studies
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