Corrections stemming from the non-osculating character of the Andoyer variables used in the description of rotation of the elastic Earth

We explore the evolution of the angular velocity of an elastic Earth model, within the Hamiltonian formalism. The evolution of the rotation state of the Earth is caused by the tidal deformation exerted by the Moon and the Sun. It can be demonstrated that the tidal perturbation to spin depends not only upon the instantaneous orientation of the Earth, but also upon its instantaneous angular velocity. Parameterizing the orientation of the Earth figure axis with the three Euler angles, and introducing the canonical momenta conjugated to these, one can then show that the tidal perturbation depends both upon the angles and the momenta. This circumstance complicates the integration of the rotational motion. Specifically, when the integration is carried out in terms of the canonical Andoyer variables (which are the rotational analogues to the orbital Delaunay variables), one should keep in mind the following subtlety: under the said kind of perturbations, the functional dependence of the angular velocity upon the Andoyer elements differs from the unperturbed dependence (Efroimsky in Proceedings of Journées 2004: Systèmes de référence spatio-temporels. l’Observatoire de Paris, pp 74–81, 2005; Efroimsky and Escapa in Celest. Mech. Dyn. Astron. 98:251–283, 2007). This happens because, under angular velocity dependent perturbations, the requirement for the Andoyer elements to be canonical comes into a contradiction with the requirement for these elements to be osculating, a situation that parallels a similar antinomy in orbital dynamics. Under the said perturbations, the expression for the angular velocity acquires an additional contribution, the so called convective term. Hence, the time variation induced on the angular velocity by the tidal deformation contains two parts. The first one comes from the direct terms, caused by the action of the elastic perturbation on the torque-free expressions of the angular velocity. The second one arises from the convective terms. We compute the variations of the angular velocity through the approach developed in Getino and Ferrándiz (Celest. Mech. Dyn. Astron. 61:117–180, 1995), but considering the contribution of the convective terms. Specifically, we derive analytical formulas that determine the elastic perturbations of the directional angles of the angular velocity with respect to a non-rotating reference system, and also of its Cartesian components relative to the Tisserand reference system of the Earth. The perturbation of the directional angles of the angular velocity turns out to be different from the evolution law found in Kubo (Celest. Mech. Dyn. Astron. 105:261–274, 2009), where it was stated that the evolution of the angular velocity vector mimics that of the figure axis. We investigate comprehensively the source of this discrepancy, concluding that the difference between our results and those obtained in Ibid. stems from an oversimplification made by Kubo when computing the direct terms. Namely, in his computations Kubo disregarded the motion of the tide raising bodies with respect to a non-rotating reference system when compared with the Earth rotational motion. We demonstrate that, from a numerical perspective, the convective part provides the principal contribution to the variation of the directional angles and of length of day. In the case of the x and y components in the Tisserand system, the convective contribution is of the same order of magnitude as the direct one. Finally, we show that the approximation employed in Kubo (Ibid.) leads to significant numerical differences at the level of a hundred micro-arcsecond.     

Meteorites at Meridiani Planum provide evidence for significant amounts of surface and near‐surface water on early Mars

Abstract– Six large iron meteorites have been discovered in the Meridiani Planum region of Mars by the Mars Exploration Rover Opportunity in a nearly 25 km‐long traverse. Herein, we review and synthesize the available data to propose that the discovery and characteristics of the six meteorites could be explained as the result of their impact into a soft and wet surface, sometime during the Noachian or the Hesperian, subsequently to be exposed at the Martian surface through differential erosion. As recorded by its sediments and chemical deposits, Meridiani has been interpreted to have undergone a watery past, including a shallow sea, a playa, an environment of fluctuating ground water, and/or an icy landscape. Meteorites could have been encased upon impact and/or subsequently buried, and kept underground for a long time, shielded from the atmosphere. The meteorites apparently underwent significant chemical weathering due to aqueous alteration, as indicated by cavernous features that suggest differential acidic corrosion removing less resistant material and softer inclusions. During the Amazonian, the almost complete disappearance of surface water and desiccation of the landscape, followed by induration of the sediments and subsequent differential erosion and degradation of Meridiani sediments, including at least 10–80 m of deflation in the last 3–3.5 Gy, would have exposed the buried meteorites. We conclude that the iron meteorites support the hypothesis that Mars once had a denser atmosphere and considerable amounts of water and/or water ice at and/or near the surface.     

The chemical composition of solar-type stars in comparison with that of the Sun

The question whether the solar chemical composition is typical for solar-type stars is analysed by comparing the Sun with different stellar samples, including a sample of stars with very similar parameters, solar twins. Although typical in terms of overall metallicity for stars of solar age and galactic orbit, the solar atmosphere is found to have abundances, as compared with solar twins, that indicate that its gas has once been affected by dust formation and dust separation. It is concluded that this may be related to the formation of the solar planetary system and its special properties.     

Stability and chemical equilibrium of amphibole in calc-alkaline magmas: an overview, new thermobarometric formulations and application to subduction-related volcanoes

This work focuses on a rigorous analysis of the physical–chemical, compositional and textural relationships of amphibole stability and the development of new thermobarometric formulations for amphibole-bearing calc-alkaline products of subduction-related systems. Literature experimental results (550–1,120°C, <1,200 MPa, −1 ≤ ΔNNO ≤ +5), H₂O–CO₂ solubility models, a multitude of amphibole-bearing calc-alkaline products (whole-rocks and glasses, representing 38 volcanoes worldwide), crustal and high-P (1–3 GPa) mantle amphibole compositions have been used. Calcic amphiboles of basalt-rhyolite volcanic products display tschermakitic pargasite (37%), magnesiohastingsite (32%) and magnesiohornblende (31%) compositions with aluminium number (i.e. Al# = ^[6]Al/Al_T) ≤ 0.21. A few volcanic amphiboles (~1%) show high Al# (>0.21) and are inferred to represent xenocrysts of crustal or mantle materials. Most experimental results on calc-alkaline suites have been found to be unsuitable for using in thermobarometric calibrations due to the high Al# (>0.21) of amphiboles and high Al₂O₃/SiO₂ ratios of the coexisting melts. The pre-eruptive crystallization of consistent amphiboles is confined to relatively narrow physical–chemical ranges, next to their dehydration curves. The widespread occurrence of amphiboles with dehydration (breakdown) rims made of anhydrous phases and/or glass, related to sub-volcanic processes such as magma mixing and/or slow ascent during extrusion, confirms that crystal destabilization occurs with relatively low T–P shifts. At the stability curves, the variance of the system decreases so that amphibole composition and physical–chemical conditions are strictly linked to each other. This allowed us to retrieve some empirical thermobarometric formulations which work independently with different compositional components (i.e. Si^*, Al_T, Mg^*, ^[6]Al^*) of a single phase (amphibole), and are therefore easily applicable to all types of calc-alkaline volcanic products (including hybrid andesites). The Si^*-sensitive thermometer and the fO₂–Mg^* equation account for accuracies of ±22°C (σ_est) and 0.4 log units (maximum error), respectively. The uncertainties of the Al_T-sensitive barometer increase with pressure and decrease with temperature. Near the P–T stability curve, the error is <11% whereas for crystal-rich (porphyritic index i.e. PI > 35%) and lower-T magmas, the uncertainty increases up to 24%, consistent with depth uncertainties of 0.4 km, at 90 MPa (~3.4 km), and 7.9 km, at 800 MPa (~30 km), respectively. For magnesiohornblendes, the ^[6]Al^*-sensitive hygrometer has an accuracy of 0.4 wt% (σ_est) whereas for magnesiohastingsite and tschermakitic pargasite species, H₂O_melt uncertainties can be as high as 15% relative. The thermobarometric results obtained with the application of these equations to calc-alkaline amphibole-bearing products were finally, and successfully, crosschecked on several subduction-related volcanoes, through complementary methodologies such as pre-eruptive seismicity (volcano-tectonic earthquake locations and frequency), seismic tomography, Fe–Ti oxides, amphibole–plagioclase, plagioclase–liquid equilibria thermobarometry and melt inclusion studies. A user-friendly spreadsheet (i.e. AMP-TB.xls) to calculate the physical–chemical conditions of amphibole crystallization is also provided.     

Temperature induced decoupling of enzymatic hydrolysis and carbon remineralization in long-term incubations of Arctic and temperate sediments

Extracellular enzymatic hydrolysis of high-molecular weight organic matter is the initial step in sedimentary organic carbon degradation and is often regarded as the rate-limiting step. Temperature effects on enzyme activities may therefore exert an indirect control on carbon mineralization. We explored the temperature sensitivity of enzymatic hydrolysis and its connection to subsequent steps in anoxic organic carbon degradation in long-term incubations of sediments from the Arctic and the North Sea. These sediments were incubated under anaerobic conditions for 24 months at temperatures of 0, 10, and 20 °C. The short-term temperature response of the active microbial community was tested in temperature gradient block incubations. The temperature optimum of extracellular enzymatic hydrolysis, as measured with a polysaccharide (chondroitin sulfate), differed between Arctic and temperate habitats by about 8-13 °C in fresh sediments and in sediments incubated for 24 months. In both Arctic and temperate sediments, the temperature response of chondroitin sulfate hydrolysis was initially similar to that of sulfate reduction. After 24 months, however, hydrolysis outpaced sulfate reduction rates, as demonstrated by increased concentrations of dissolved organic carbon (DOC) and total dissolved carbohydrates. This effect was stronger at higher incubation temperatures, particularly in the Arctic sediments. In all experiments, concentrations of volatile fatty acids (VFA) were low, indicating tight coupling between VFA production and consumption. Together, these data indicate that long-term incubation at elevated temperatures led to increased decoupling of hydrolytic DOC production relative to fermentation. Temperature increases in marine sedimentary environments may thus significantly affect the downstream carbon mineralization and lead to the increased formation of refractory DOC.     

Sulfur isotope variations from orebody to hand-specimen scale at the Mežica lead–zinc deposit, Slovenia: a predominantly biogenic pattern

The Mississippi Valley-type (MVT) Pb–Zn ore district at Mežica is hosted by Middle to Upper Triassic platform carbonate rocks in the Northern Karavanke/Drau Range geotectonic units of the Eastern Alps, northeastern Slovenia. The mineralization at Mežica covers an area of 64 km² with more than 350 orebodies and numerous galena and sphalerite occurrences, which formed epigenetically, both conformable and discordant to bedding. While knowledge on the style of mineralization has grown considerably, the origin of discordant mineralization is still debated. Sulfur stable isotope analyses of 149 sulfide samples from the different types of orebodies provide new insights on the genesis of these mineralizations and their relationship. Over the whole mining district, sphalerite and galena have δ ³⁴ S values in the range of –24.7 to –1.5‰ VCDT (–13.5 ± 5.0‰) and –24.7 to –1.4‰ (–10.7 ± 5.9‰), respectively. These values are in the range of the main MVT deposits of the Drau Range. All sulfide δ ³⁴ S values are negative within a broad range, with δ ³⁴ S _pyrite <δ ³⁴ S _sphalerite <δ ³⁴ S _galena for both conformable and discordant orebodies, indicating isotopically heterogeneous H₂S in the ore-forming fluids and precipitation of the sulfides at thermodynamic disequilibrium. This clearly supports that the main sulfide sulfur originates from bacterially mediated reduction (BSR) of Middle to Upper Triassic seawater sulfate or evaporite sulfate. Thermochemical sulfate reduction (TSR) by organic compounds contributed a minor amount of ³⁴S-enriched H₂S to the ore fluid. The variations of δ ³⁴ S values of galena and coarse-grained sphalerite at orefield scale are generally larger than the differences observed in single hand specimens. The progressively more negative δ ³⁴ S values with time along the different sphalerite generations are consistent with mixing of different H₂S sources, with a decreasing contribution of H₂S from regional TSR, and an increase from a local H₂S reservoir produced by BSR (i.e., sedimentary biogenic pyrite, organo-sulfur compounds). Galena in discordant ore (–11.9 to –1.7‰; –7.0 ± 2.7‰, n = 12) tends to be depleted in ³⁴ S compared with conformable ore (–24.7 to –2.8‰, –11.7 ± 6.2‰, n = 39). A similar trend is observed from fine-crystalline sphalerite I to coarse open-space filling sphalerite II. Some variation of the sulfide δ ³⁴ S values is attributed to the inherent variability of bacterial sulfate reduction, including metabolic recycling in a locally partially closed system and contribution of H₂S from hydrolysis of biogenic pyrite and thermal cracking of organo-sulfur compounds. The results suggest that the conformable orebodies originated by mixing of hydrothermal saline metal-rich fluid with H₂S-rich pore waters during late burial diagenesis, while the discordant orebodies formed by mobilization of the earlier conformable mineralization.     

Groundwater recharge in irrigated semi-arid areas: quantitative hydrological modelling and sensitivity analysis

For semi-arid regions, methods of assessing aquifer recharge usually consider the potential evapotranspiration. Actual evapotranspiration rates can be below potential rates for long periods of time, even in irrigated systems. Accurate estimations of aquifer recharge in semi-arid areas under irrigated agriculture are essential for sustainable water-resources management. A method to estimate aquifer recharge from irrigated farmland has been tested. The water-balance-modelling approach was based on VisualBALAN v. 2.0, a computer code that simulates water balance in the soil, vadose zone and aquifer. The study was carried out in the Campo de Cartagena (SE Spain) in the period 1999–2008 for three different groups of crops: annual row crops (lettuce and melon), perennial vegetables (artichoke) and fruit trees (citrus). Computed mean-annual-recharge values (from irrigation+precipitation) during the study period were 397 mm for annual row crops, 201 mm for perennial vegetables and 194 mm for fruit trees: 31.4, 20.7 and 20.5% of the total applied water, respectively. The effects of rainfall events on the final recharge were clearly observed, due to the continuously high water content in soil which facilitated the infiltration process. A sensitivity analysis to assess the reliability and uncertainty of recharge estimations was carried out.     

The economics of boldness: equity,action, and hope

Equity is usually interpreted in terms of the concept of justice, such that an equitable share of the atmospheric space is understood in terms of past emissions. This emphasizes the collective nature of sharing the burden of mitigation and the duty to act for those who have emitted the most. An alternative is considered: the aggregate costs and benefits to all Parties that could result from both increasing the level of collective ambition and implementing a climate regime that supports bold actions across all Parties. The regional impacts and carbon flow costs across differentiated scenarios are assessed and it is argued that the majority of developing-country Parties would be better off if a high ambition outcome to which all contributed, but some more than others. Moreover, those with middle or low emissions would have proportionally more to gain (or lose) relative to the level of ambition compared to those that have had higher emissions. The climate regime should be built on the principle of common but differentiated responsibility and respective capabilities (CBDR&RC), in which all act early even if some do much more; one that accounts for justice but does not forget hope.

Policy relevance

Differing interpretations of equity and the principles of the United Nations Framework Convention on Climate Change (UNFCCC) are discussed, with a focus on how these can enhance or hinder collective action. Whilst the climate change negotiations are usually taken as games in which one party gains and another loses, and interactions are dogged by continuous conflict, it is explored instead how negotiation responses can be framed in terms of cooperation. This would emphasize the gains that could be achieved by common but differentiated collective action, which could result in a collective avoidance of impacts. The possibilities that this shift of perspective could bring are explored by comparing costs under global cooperation (or lack of it). It is found that cooperation reduces the total costs for these regions. Thus, thinking in terms of cooperation focuses the options for negotiation on the means and interpretations of the UNFCCC principles that spur action and avoid climate impacts through collective action.     

Using distributed temperature sensing (DTS) technology in acid gas injection design

The use of slickline distributed temperature sensing (SL-DTS) technology is becoming widespread due to its ease of operation and ability to acquire real-time multiple temperature traces inside the wellbore. Injection of treated acid gas (TAG)—a mixture of CO₂ and H₂S—into geologic formations has become an attractive technical and economic option for oil and gas producers and processors who are faced with regulations concerning excess sulfur and greenhouse gas emissions. Acid gas injection (AGI) into geologic formations is more economical and more flexible in dealing with varying TAG compositions than sulfur recovery units (SRUs) using the Claus process. SRUs do not achieve air quality standards and have high operation and maintenance costs. In addition, there is low demand for sulfur and sulfur disposal costs are high. The results of the analysis of SL-DTS data acquired in conjunction with step rate and pressure falloff (PFO) tests are presented in this paper. These tests were conducted to evaluate the injection potential of geologic formations. The injection zone consisted of a carbonate formation characterized by Karst features, vugs, and natural fractures. The SL-DTS data during the initial injection flow rate for the step rate test (SRT) indicated that high permeability zones accepted fluid at lower injection rates. An increasing number of discrete zones began to accept fluid as the injection rate was increased. The results of the SRT provided the fracture pressure of the formation. This information was used to design an AGI program that would avoid fracturing the formation while allowing for the required volume of TAG to be injected. The results of the PFO test provided information on the reservoir pressure and permeability and also indicated the presence of one or more hydraulic fractures. This case study of SL-DTS measurements made during a SRT and a PFO test for the design of an AGI well provides valuable insights into the potential of DTS technology and its use in AGI and carbon capture/sequestration (CCS) operations. Its findings could be applied to analyze injection potential of geological formations not only for AGI projects but also for CCS, and CO₂ enhanced oil recovery opportunities.