Abstract. Scaling in fracture systems has become an active field of research in the last 25 years motivated by practical applications in hazardous waste disposal, hydrocarbon reservoir management, and earthquake hazard assessment. Relevant publications are therefore spread widely through the literature. Although it is recognized that some fracture systems are best described by scale-limited laws (lognormal, exponential), it is now recognized that power laws and fractal geometry provide widely applicable descriptive tools for fracture system characterization. A key argument for power law and fractal scaling is the absence of characteristic length scales in the fracture growth process. All power law and fractal characteristics in nature must have upper and lower bounds. This topic has been largely neglected, but recent studies emphasize the importance of layering on all scales in limiting the scaling characteristics of natural fracture systems. The determination of power law exponents and fractal dimensions from observations, although outwardly simple, is problematic, and uncritical use of analysis techniques has resulted in inaccurate and even meaningless exponents. We review these techniques and suggest guidelines for the accurate and objective estimation of exponents and fractal dimensions. Syntheses of length, displacement, aperture power law exponents, and fractal dimensions are found, after critical appraisal of published studies, to show a wide variation, frequently spanning the theoretically possible range. Extrapolations from one dimension to two and from two dimensions to three are found to be nontrivial, and simple laws must be used with caution. Directions for future research include improved techniques for gathering data sets over great scale ranges and more rigorous application of existing analysis methods. More data are needed on joints and veins to illuminate the differences between different fracture modes. The physical causes of power law scaling and variation in exponents and fractal dimensions are still poorly understood. INTRODUCTIONThe study of fracture systems (terms in italic are defined in the glossary, after the main text) has been an active area of research for the last 25 years motivated to a large extent by the siting of hazardous waste disposal sites in crystalline rocks, by the problems of multiphase flow in fractured hydrocarbon reservoirs, and by earthquake hazards and the possibility of prediction. Here we define a fracture as any discontinuity within a rock mass that developed as a response to stress. This comprises primarily mode I and mode II fractures. In mode I fracturing, fractures are in tensile or opening mode in which displacements are normal to the discontinuity walls (joints and many veins). Faults correspond to mode II fractures, i.e., an in-plane shear mode, in which the displacements are in the plane of the discontinuity. Fractures exist on a wide range of scales from microns to hundreds of kilometers, and it is known that throughout this scale range they have a sign...

We present experiments and numerical simulations dealing with the growth of faults in thin brittle/ductile systems to understand deformation modes in the continental lithosphere. Experiments were uniaxial shortening of layers of dry sand and silicone putties of various viscous resistances. For large strength ratios between the brittle and ductile layers (R>5-10), the deformation localizes into two shear bands; the fault pattern is created before reaching 10% shortening, and has fractal dimensions varying between 1.6 and 1.8. For small strength ratios (R<5-10), deformation never localizes; the fault pattern is homogeneous with a trivial dimension of 2, and grows continuously during deformation. The transition between localized and homogeneous deformation occurs when the mechanical resistance of brittle layers is 5-10 times larger than the resistance of ductile layers. This transition was also investigated by means of electrical analog simulations. A fuse network, which represents an elasto-brittle layer, is coupled with a capacitor layer which models strain-rate dependent fluids. An AC potential is applied and the fuses progressively burned out until they form a connected network. The AC-potential frequency, f, is a tuning parameter similar to the applied strain rate in experiments. A critical frequency is obtained marking a transition between a localization mode where the density of burned fuses decreases as the system size increases, and a delocalization mode where the density of burned fuses remains constant with increasing system size. The scaling dependency of the fracture process, as well as the critical frequency, are consistent with experimental results. Available information on the rheology of the continental lithosphere shows that this mechanical transition is bracketed by the possible range of brittle-toductile strength ratios. (-50-100 km) is a good candidate for this scale [England and Jackson, 1989]. At lengths larger than •,, the instabilities, such as stress enhancement around crack tips, are considered mechanically negligible. Definition of the homogenization scale requires a detailed analysis of the deformation pattern which is not possible with available data. An attempt to examine •, was made by Davy et al. [1990] by assuming scaling laws for fault lengths and densities; however their results lead to the question of whether such a homogenization scale exists.Key observations that may resolve this debate concern the degree to which the lithosphere deforms homogeneously or within localized zones over several thousand kilometers. Such observations are possible where horizontal motions involve large continental blocks, as displayed by the India-Asia collision where the eastern boundary (Pacific border) is made up of oceanic subduction zones and may be considered as a free boundary [Tapponnier and Molnar, 1976]. The deformation localization in large wrench faults, as proposed by Tapponnier and coauthors, is certainly too a simplification of the deformation and distributed deformation has been record...

The composition and origin of continental crust is in part constrained by evidence preserved in exhumed arc crustal sections. The Bonanza arc on Vancouver Island, Canada, is a Jurassic-aged arc crust section exhumed in the Eocene. We use Al-in-hornblende geobarometry of felsic plutons in the Bonanza arc to assess the depths of crystallization of its exposed arc crust. Plutons of the unfoliated Island Plutonic Suite are emplaced as sheets at depths of 2-10 km within a stratigraphy of Devonian to Triassic supracrustal rocks. The West Coast Complex is more generally strained, and intrudes below the pre-Jurassic supracrustals at depths of 10-18 km. Previous work shows that rare ultramafi c units within the West Coast Complex crystallized at depths of 14-26 km.The Bonanza arc crustal section has a present structural thickness of at least 15 km. The average composition for each arc component (volcanic and plutonics) when apportioned into the crustal section derived by stratigraphy and hornblende barometry, shows the bulk composition of the entire arc is basaltic andesite (56% SiO 2 , Mg/Mg + Fe (Mg#) = 50), not unlike some estimates for bulk continental crust. Although only vestiges of ultramafi c rocks occur in the Bonanza arc today, a signifi cant component (6-20 km) of this rock type must have been present in the section for the bulk arc to have been a melt in equilibrium with mantle olivine, and may have been lost by foundering or tectonic thinning.