Hierarchical organization as a diagnostic approach to volcano mechanics: Validation on Piton de la Fournaise

Grasso, Jean‐Robert; Bachèlery, Patrick

doi:10.1029/95gl01786

Cited by 37 publications

(39 citation statements)

References 32 publications

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“…Power-law distributions indicating SOC behavior in volcano eruptions are mentioned in the literature. For example this behavior was found in the eruptions, volcano-induced earthquakes, dikes, fissures, lava flows, and interflow periods of the Piton de la Fournaise volcano by Grasso and Bachélery (1995). Birkeland and Landry (2002) found evidence of frequency-size power-laws in several groups of snow avalanche paths and state that their results are consistent with SOC.…”

Section: Landslides Wildfires Volcanoes Snow Avalanches Rock-fallsupporting

confidence: 66%

Frequency distributions: from the sun to the earth

Crosby

2011

Nonlin. Processes Geophys.

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Abstract. The space environment is forever changing on all spatial and temporal scales. Energy releases are observed in numerous dynamic phenomena (e.g. solar flares, coronal mass ejections, solar energetic particle events) where measurements provide signatures of the dynamics. Parameters (e.g. peak count rate, total energy released, etc.) describing these phenomena are found to have frequency size distributions that follow power-law behavior. Natural phenomena on Earth, such as earthquakes and landslides, display similar power-law behavior. This suggests an underlying universality in nature and poses the question of whether the distribution of energy is the same for all these phenomena. Frequency distributions provide constraints for models that aim to simulate the physics and statistics observed in the individual phenomenon. The concept of self-organized criticality (SOC), also known as the "avalanche concept", was introduced by Bak et al. (1987Bak et al. ( , 1988, to characterize the behavior of dissipative systems that contain a large number of elements interacting over a short range. The systems evolve to a critical state in which a minor event starts a chain reaction that can affect any number of elements in the system. It is found that frequency distributions of the output parameters from the chain reaction taken over a period of time can be represented by power-laws. During the last decades SOC has been debated from all angles. New SOC models, as well as non-SOC models have been proposed to explain the powerlaw behavior that is observed. Furthermore, since Bak's pioneering work in 1987, people have searched for signatures of SOC everywhere. This paper will review how SOC behavior has become one way of interpreting the power-law behavior observed in natural occurring phenomenon in the Sun down to the Earth.

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Section: Landslides Wildfires Volcanoes Snow Avalanches Rock-fallsupporting

confidence: 66%

Frequency distributions: from the sun to the earth

Crosby

2011

Nonlin. Processes Geophys.

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“…A fractal set implies a scale invariance and the appearance of identical features at different scales. In real world, this scale invariance is generally bounded [Lei et al, 1993;Grasso and Bachelery, 1995]. In the present case, the lower bound lc, initially related to the microstructure of the material, decreased during the fracturing process and became undetectable at failure, i.e., below the resolution limit of 0. i mm.…”

Section: Methodsmentioning

confidence: 79%

Fracturing of ice under compression creep as revealed by a multifractal analysis

Weiss¹,

Gay²

1998

J. Geophys. Res.

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Abstract. Fracturing of freshwater granular ice up to failure under uniaxial compression creep was investigated from series of interrupted creep tests and from a multifractal analysis of the corresponding fracture patterns. At the early stages of damage corresponding to primary and secondary creep, the fracturing process is dominated by the nucleation of microcracks from stress concentrations within the material (unlike rocks, artificial freshwater ice does not contains starter flaws). Because of the crack nucleation mechanisms, the microstructure of the material (e.g., the nonfractal grain size distribution) strongly influences the organization of fracturing which is therefore nonfractal. As fracturing proceeds during tertiary creep, a hierarchical (fractal) organization of the fracturing emerges progressively over a wider scale range. At failure, this fractal organization is fully developed without detectable lower or upper bound, and the role of the initial microstructure has completely disappeared. Similarly, cracks are preferentially oriented along the compression axis at the early stages of damage, but this anisotropy vanishes as failure is approached. The simultaneity between the onset of tertiary creep and the emergence of fractal organization suggests that the acceleration of the deformation during tertiary creep is due to the cataclasis of a material which becomes granular. An important consequence of the fractal organization of fracturing is that homogenization procedures, as well as damage mechanics, developed to study the behavior of damaged materials, cannot be used to describe tertiary creep and failure. 1.IntroductionOffshore structures located in polar regions experience important forces when a moving sea-ice cover or icebergs crush against them. This problem has given rise, in the last 15th years, to an abundant literature about damage, fracturing and failure of ice under compressive loading. The dependence of the compressive failure stress on temperature, strain rate or confinement has been established for different kinds of ice (see e.g. Schulson [1990] On the other hand, the fracturing processes of other geomaterials (i.e., essentially rocks) have been largely studied from the laboratory scale to the Earth's crust scale, and one major preoccupation was to relate large-scale features to small-scale (laboratory) observations. The self-similar nature of fracturing and faulting (i.e. the appearance of identical features at different scales) has been claimed both for laboratory experiments and field observations. This scale invariance can be expressed by power law distributions of fracture or fault lengths (see, e.g., Main [1996], Grasso and Bachelery [1995] [1992] argued that the fractal properties of rock fracturing result "naturally" from basic mechanical mechanisms such as crack nucleation from initial flaws, buckling of slabs, spalling, and interactions between particles of different sizes in a granular medium. However, they considered the evolution of damage and fracturing within mater...

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“…[1] Kagan (1992) [5] Heffer and Bevan (1990) [2] Bak and Tang (1989) [6] Power et al (1988) [3] Grasso (1993) [7] Grasso and Bachèlery (1995) [4] Barton and Zoback (1992) [8] Leary (1991) One of the largest range of scale-invariance is the distribution of dimensions and frequency of linear features ranging form microcracks, through joints and fractures, to faults and photo-lineaments documented by Heffer and Bevan (1990). This is reproduced in a modified form in Figure 3, where the distribution is nearly scale-invariant over approximately 9 orders of magnitude.…”

Section: Distributionmentioning

confidence: 99%

Shear-Wave Splitting in a Critical Crust: the Next Step

Crampin

1998

Rev. Inst. Fr. Pét.

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On pourrait avancer que l'anisotropie dans la biréfringence des ondes transversales n'a pas répondu à ses promesses initiales, à savoir ouvrir une nouvelle voie dans la compréhension des phénomènes de fissures et de contraintes dans la croûte terrestre. Dans cet article sont présentés deux développements révélés récemment, qui paraissent raviver ces premiers espoirs et apportent des opportunités nouvelles pour le contrôle, la modélisation et même la prévision des déformations (avant fracture) dans les roches microfracturées et saturées de fluides.Ainsi, un modèle de poroélasticité (APE) développé récemment concerne l'évolution sous contraintes des roches microfracturées et saturées en fluide et reproduit une large gamme de phénomènes, qui seraient autrement inexpliqués ou dissociés, et semble être une bonne approximation au premier ordre de l'évolution des roches microfracturées et saturées en fluide. Puisque les paramètres qui contrôlent à petite échelle la déformation (avant fracture) contrôlent aussi la biréfringence des ondes transversales, il apparaît que l'évolution des roches microfracturées et saturées peut être aussi directement contrôlée par cette biréfringence et que la réponse à des changements futurs peut être prédite par l'APE.Le bon usage de la modélisation de l'APE et des observations de la biréfringence des ondes transversales implique que la plupart des roches soient proches d'un stade de fracturation critique associé à une percolation limite, situation où la résistance aux contraintes transversales disparaît et où les fractures transversales peuvent se propager. Ceci corrobore une autre hypothèse concernant la mise en situation critique spontanée des roches in situ. La conséquence de cette identification est que la physique à petite échelle, qui contrôle l'ensemble du phénomène, peut maintenant être associée aux contraintes générées par les fluides baignant les fissures intergranulaires. Ceci a probablement l'avantage unique, parmi les systèmes critiques, de donner la possibilité de contrôler en chaque point les détails des déformations avant fracture et l'approche du seuil critique (dans ce cas l'approche d'une fracturation), au moyen d'observations adéquates de la biréfringence des ondes transversales.Cet article passe en revue ces développements et commente leurs conséquences et leurs applications, en particulier les conséquences sur la mise en situation critique des roches spontanément. L'étape suivante sera d'exploiter ces techniques pour modéliser, contrôler et prédire les effets de changements de conditions sur la déformation de la masse rocheuse. Copyright © 1998, Institut français du pétrole understanding cracks and stress in the crust. This paper reviews two recent related developments which appear to renew these initial hopes and provide new opportunities for monitoring, modelling, and even predicting, the (pre-fracturing) deformation of fluid-saturated microcracked rock. SHEAR-WAVE SPLITTING INA recently developed model of anisotropic poro-elasticity (APE) for the stress-induced ev...

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Hierarchical organization as a diagnostic approach to volcano mechanics: Validation on Piton de la Fournaise

Cited by 37 publications

References 32 publications

Frequency distributions: from the sun to the earth

Frequency distributions: from the sun to the earth

Fracturing of ice under compression creep as revealed by a multifractal analysis

Shear-Wave Splitting in a Critical Crust: the Next Step

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