Numerical investigation of alternative fracture stiffness measures and their respective scaling behaviours

We study the mechanical deformation of fractures under normal stress, via tangent and specific fracture stiffnesses, for different length scales using numerical simulations and analytical insights. First, we revisit an equivalent elastic layer model that leads to two expressions: the tangent stiffness is the sum of an “intrinsic” stiffness and the normal stress, and the specific stiffness is the tangent stiffness divided by the fracture aperture at current stress. Second, we simulate the deformation of rough fractures using a boundary element method where fracture surfaces represented by elastic asperities on an elastic half‐space follow a self‐affine distribution. A large number of statistically identical “parent” fractures are generated, from which sub‐fractures of smaller dimensions are extracted. The self‐affine distribution implies that the stress‐free fracture aperture increases with fracture length with a power law in agreement with the chosen Hurst exponent. All simulated fractures exhibit an increase in the specific stiffness with stress and an average decrease with increase in length consistent with field observations. The simulated specific and tangent stiffnesses are well described by the equivalent layer model provided the “intrinsic” stiffness slightly decreases with fracture length following a power law. By combining numerical simulations and the analytical model, the effect of scale and stress on fracture stiffness measures can be easily separated using the concept of “intrinsic” stiffness. We learn that the primary reason for the variability in specific stiffness with length comes from the fact that the typical aperture of the self‐affine fractures itself scales with the length of the fractures.     

Spatial distribution of soil shear-wave velocity and the fundamental period of vibration – a case study of the Saguenay region,Canada

The spatial distribution of soil shear-wave velocity and the fundamental period of vibration were selected as input parameters for the determination of potential seismic site effects in the Saguenay region, Canada. The methodology used in this study involved three clear steps. First, a 3D geological model of the surficial deposits was built taking into consideration the type, spatial distribution and thickness of the deposits. Second, representative average V_s values were determined for each of the major soil units. Finally, the average shear-wave velocity from the ground surface to bedrock (V_sav), the shear-wave velocity of the upper 30 m (V_s30) and the fundamental site resonance period (T₀) were calculated over a regular grid for the study area. The results include the spatial distribution of the fundamental site resonance period, the average shear-wave velocity in the first 30 m of the ground and the spatial distribution of National Building Code of Canada seismic soil classes for the Saguenay region.     

H and Cl isotope systematics of apatite in brecciated lunar meteorites Northwest Africa 4472, Northwest Africa 773, Sayh al Uhaymir 169, and Kalahari 009

We have investigated the H and Cl systematics in apatite from four brecciated lunar meteorites. In Northwest Africa (NWA) 4472, most of the apatites contain ～2000–6000 ppm H₂O with δD between ?200 and 0‰, except for one grain isolated in the matrix, which contains ～6000 ppm H₂O with δD of ～500–900‰. This low‐δD apatite contains ～2500–7500 ppm Cl associated with δ³⁷Cl of ～15–20‰, while the high‐δD grain contains ～2500 ppm Cl with δ³⁷Cl of ～7–15‰. In NWA 773, apatites in a first group contain ～700–2500 ppm H₂O with δD values averaging around ～0 ± 100‰, while apatites in a second group contain ～5500–16500 ppm H₂O with δD ～250 ± 50‰. In Sayh al Uhaymir (SaU) 169 and Kalahari (Kal) 009, apatites are similar in terms of their H₂O contents (～600–3000 ppm) and δD values (?100 to 200‰). In SaU 169, apatites contain ～6000–10,000 ppm Cl, characterized by δ³⁷Cl of ～5–12‰. Overall, most of the analyzed apatite grains have δD within the range reported for carbonaceous chondrites, similar to apatite analyzed in ancient (>3.9 Ga) lunar magmatic. One grain in NWA 4472 has H and Cl isotope compositions similar to apatite from mare basalts. With an age of 4.35 Ga, this grain could be a representative of the oldest known lunar volcanic activity. Finally, since numerous evolved clasts in NWA 773 formed through silicate liquid immiscibility, the apatite grains with extremely high H₂O contents, reaching pure hydroxylapatite composition, could provide insights into the effects of such process on the evolution of volatiles in lunar magmas.     

Linear stability analysis of the explicit treatment of mobilities in non-Newtonian and non-Darcy porous media flow simulation

A von Neumann stability analysis of the discretized conservation equation for single-phase porous media flows is performed, where non-Newtonian and non-Darcy effects are accounted for using a velocity (or mass flux)-dependent mobility factor. Comprehensive results in three dimensions for two low-order finite-volume discretizations typically encountered in reservoir simulation are provided, based on edge-centered and upstream cell-centered mobility calculations. It is found that common semi-implicit schemes, where the pressure gradient driving the flow is taken implicitly while the velocity-dependent mobility is evaluated explicitly, are subject to restrictions on the logarithmic derivative of mobility with respect to velocity. A remarkable new result is nevertheless obtained: for any physically acceptable strength of non-Newtonian and non-Darcy effects, there exists a stable and explicit method to evaluate the mobility, rendering the need to implement costly fully implicit schemes more difficult to justify.     

Multistage growth of Fe–Mg–carpholite and Fe–Mg–chloritoid,from field evidence to thermodynamic modelling

We provide new insights into the prograde evolution of HP/LT metasedimentary rocks on the basis of detailed petrologic examination, element-partitioning analysis, and thermodynamic modelling of well-preserved Fe–Mg–carpholite- and Fe–Mg–chloritoid-bearing rocks from the Afyon Zone (Anatolia). We document continuous and discontinuous compositional (ferromagnesian substitution) zoning of carpholite (overall X _Mg = 0.27–0.73) and chloritoid (overall X _Mg = 0.07–0.30), as well as clear equilibrium and disequilibrium (i.e., reaction-related) textures involving carpholite and chloritoid, which consistently account for the consistent enrichment in Mg of both minerals through time, and the progressive replacement of carpholite by chloritoid. Mg/Fe distribution coefficients calculated between carpholite and chloritoid vary widely within samples (2.2–20.0). Among this range, only values of 7–11 correlate with equilibrium textures, in agreement with data from the literature. Equilibrium phase diagrams for metapelitic compositions are calculated using a newly modified thermodynamic dataset, including most recent data for carpholite, chloritoid, chlorite, and white mica, as well as further refinements for Fe–carpholite, and both chloritoid end-members, as required to reproduce accurately petrologic observations (phase relations, experimental constraints, Mg/Fe partitioning). Modelling reveals that Mg/Fe partitioning between carpholite and chloritoid is greatly sensitive to temperature and calls for a future evaluation of possible use as a thermometer. In addition, calculations show significant effective bulk composition changes during prograde metamorphism due to the fractionation of chloritoid formed at the expense of carpholite. We retrieve P–T conditions for several carpholite and chloritoid growth stages (1) during prograde stages using unfractionated, bulk-rock XRF analyses, and (2) at peak conditions using compositions fractionated for chloritoid. The P–T paths reconstructed for the Kütahya and Afyon areas shed light on contrasting temperature conditions for these areas during prograde and peak stages.     

Northern latitude chemical weathering rates: clues from the Mackenzie River Basin, Canada

The main scope of this study is to investigate parameters controlling chemical weathering rates for a large river system submitted to subarctic climate. More than 110 river water samples from the Mackenzie River system (northern Canada) have been sampled and analyzed for major and trace elements and Sr isotopic ratios in the dissolved phase. The three main morphological units are reflected in water chemistry. Rivers from the Canadian Shield are very dilute, dominated by silicate weathering (Millot et al., 2002), whereas the rivers of the Rocky and Mackenzie Mountains as well as the rivers of the sedimentary Interior Platform are dominated by carbonate weathering and are SO₄ rich. Compared to the rivers of the Mackenzie and Rocky Mountains, the rivers of the interior plains are organic, silica, and Na rich and constitute the dominant input term to the Mackenzie River mainstream. Rivers of the Canadian Shield area do not significantly contribute to the Mackenzie River system. Using elemental ratios and Sr isotopic ratios, a mathematical inversion procedure is presented that distinguishes between solutes derived from silicate weathering and solutes derived from carbonate weathering. Carbonate weathering rates are mostly controlled by runoff, which is higher in the mountainous part of the Mackenzie basin. These rates are comparable to the carbonate weathering rates of warmer areas of the world. It is possible that part of the carbonate weathering is controlled by sulfide oxidative weathering, but its extent remains difficult to assess. Conversely to what was stated by Edmond and Huh (1997), overall silicate weathering rates in the Mackenzie basin are low, ranging from 0.13 to 4.3 tons/km²/yr (Na + K + Ca + Mg), and confirm the negative action of temperature on silicate weathering rates for river basins in cold climates. In contrast to what has been observed in other large river systems such as the Amazon and Ganges Rivers, silicate weathering rates appear 3 to 4 times more elevated in the plains than in the mountainous headwaters. This contradicts the “Raymo hypothesis” (Raymo and Ruddiman, 1992). Isotopic characterization of suspended material clearly shows that the higher weathering rates reported for the plains are not due to the weathering of fine sediments produced in the mountains (e.g., by glaciers) and deposited in the plains. Rather, the relatively high chemical denudation rates in the plains are attributed to lithology (uncompacted shales), high mechanical denudation, and the abundance of soil organic matter derived from incomplete degradation and promoting crystal lattice degradation by element complexation. The three- to fourfold factor of chemical weathering enhancement between the plains and mountains is similar to the fourfold factor of enhancement found by Moulton et al. (2000) between unvegetated and vegetated watershed. This study confirms the negative action of temperature on silicate weathering for cold climate but shows that additional factors, such as organic matter, associated with northern watersheds are able to counteract the effect of temperature. This acceleration by a factor of 4 in the plains is equivalent to a 6°C increase in temperature.     

Lithium isotopes in island arc geothermal systems: Guadeloupe, Martinique (French West Indies) and experimental approach

We report lithium (Li) isotopic measurements in seawater-derived waters that were discharged from geothermal wells, thermal springs, and sub-marine springs located in volcanic island arc areas in Guadeloupe (the Bouillante geothermal field) and Martinique (Lamentin plain and the Diamant areas). While Li isotopic signatures of the geothermal fluids collected from deep reservoirs were found to be homogeneous for a given site, the δ⁷Li signatures for each of these reservoirs were significantly different. The first low temperature (25-250 °C) experiments of Li isotope exchange during seawater/basalt interaction confirmed that Li isotopic exchange is strongly temperature dependent, as previously inferred from natural studies. Li isotopic fractionation ranged from +19.4‰ (Δ_{solution-solid}) at 25 °C to +6.7‰ at 250 °C. These experiments demonstrated the importance of Li isotopic fractionation during the formation of Li-bearing secondary minerals and allowed us to determine the following empirical relationship between isotopic fractionation and temperature: Δ_{solution-solid} = 7847/T − 8.093. Application of experimental results and literature data to the Bouillante area suggested that geothermal water was in equilibrium at 250-260 °C. It likely has a deep and large reservoir located in the upper sheeted dike complex of the oceanic crust, just below the transition zone between andesite volcanic flows and the basaltic dikes. The upper dike section, from which Li is extracted by hydrothermal fluids, was characterized by light Li isotopic values in the rocks, indicating retention of ⁶Li by the altered rocks. For the Lamentin and Diamant areas, the geothermal fluids appeared to be in equilibrium with reservoir volcano-sedimentary rocks at 90-120 °C and 180 °C, respectively. Further evidence for this argument is provided by the fact that only the Na/Li thermometric relationship determined for sedimentary basins yielded temperature values in agreement with those measured or estimated for the reservoir fluids. This suggests the importance of a sedimentary signature in these reservoir rocks. Altogether, this study highlights that the use of Li isotopic systematics is a powerful tool for characterizing the origin of geothermal waters as well as the nature of their reservoir rocks.     

Compliance of the Parties to the Kyoto Protocol in the first commitment period

This article provides an ex post analysis of the compliance of the Parties to the Kyoto Protocol during the first commitment period (2008–2012) based on the final data for national GHG emissions and exchanges in carbon units that became available at the end of 2015. On the domestic level, among the 36 countries that fully participated in the Kyoto Protocol, only nine countries emitted higher levels of GHGs than committed and therefore had to resort to flexibility mechanisms. On the international level – i.e. after the use of flexibility mechanisms – all Annex B Parties are in compliance. Countries implemented different compliance strategies: purchasing carbon units abroad, stimulating the domestic use of carbon credits by the private sector and incentivizing domestic emission reductions through climate policies.

Overall, the countries party to the Protocol surpassed their aggregate commitment by an average 2.4 GtCO₂e yr^–1. Of the possible explanations for this overachievement, ‘hot-air’ was estimated at 2.2 GtCO₂e yr^–1, while accounting rules for land use, land-use change and forestry (LULUCF) further removed 0.4 GtCO₂e yr^–1 from the net result excluding LULUCF. The hypothetical participation of the US and Canada would have reduced this overachievement by a net 1 GtCO₂e yr^–1. None of these factors – some of which may be deemed illegitimate – would therefore on its own have led to global non-compliance, even without use of the 0.3 GtCO₂e of annual emissions reductions generated by the Clean Development Mechanism. The impact of domestic policies and ‘carbon leakage’ – neither of which is quantitatively assessed here – should not be neglected either.

Policy relevance

Given the ongoing evolution of the international climate regime and the adoption of the Paris Agreement in December 2015, we believe that there is a need to evaluate the results of the first commitment period of the Kyoto Protocol. To our knowledge there has been no overarching quantitative ex post assessment of the Kyoto Protocol based on the final emissions data for 2008–2012, which became available in late 2015. This article attempts to fill this gap, focusing on the domestic and international compliance of the Parties to the Kyoto Protocol in the first commitment period.