Extension of the solution of Kepler's equation to high eccentricities

The classic Lagrange's expansion of the solutionE(e, M) of Kepler's equation in powers of eccentricity is extended to highly eccentric orbits, 0.6627 ... <e<1. The solutionE(e, M) is developed in powers of (e–e*), wheree* is a fixed value of the eccentricity. The coefficients of the expansion are given in terms of the derivatives of the Bessel functionsJ _n (ne). The expansion is convergent for values of the eccentricity such that |e–e*|<(e*), where the radius of convergence (e*) is a positive real number, which is calculated numerically.     

Crustal xenoliths from Calbuco Volcano,Andean Southern Volcanic Zone: implications for crustal composition and magma-crust interaction

Crustal xenoliths in the 1961 andesite flow of Calbuco Volcano, in the southern Southern Volcanic Zone (SSVZ) of the Andes, consist predominantly of pyroxene granulites and hornblende gabbronorites. The granulites contain plagioclase+pyroxene+magnetite±amphibole, and have pronounced granoblastic textures. Small amounts of relict amphibole surrounded by pyroxene-plagioclase-magnetite-glass symplectites are found in some specimens. These and similar textures in the gabbronorites are interpreted as evidence of dehydration melting. Mineral and bulk rock geochemical data indicate that the granulites are derived from an incompatible trace element depleted basaltic protolith that underwent two stages of metamorphism: a moderate pressure, high temperature stage accompanied by melting and melt extraction from some samples, followed by thermal metamorphism after entrainment in the Calbuco andesite lavas. High _Nd ^T values (+4.0 to +8.6), Nd-isotope model ages of 1.7–2.0 Ga, and trace element characteristics like chondrite normalized La/Yb< and La/Nb1 indicate that the protoliths were oceanic basalts. Similar oceanic metabasalts of greenschist to amphibolite facies are found in the Paleozoic metamorphic belt that underlies the Chilean coastal ranges. Mineral and bulk rock compositions of the gabbronorite xenoliths indicate that they are cognate, crystallizing from the basaltic andesite magma at Calbuco. Crystallization pressures for the gabbros based on total Al contents in amphibole are 6–8 kbar. These pressures point to middle to lower crustal storage of the Calbuco magma. Neither granulite nor gabbro xenoliths have the appropriate geochemical characteristics to be contaminants of Calbuco andesites, although an ancient sedimentary contaminant is indicated by the lava compositions. The presence of oceanic metabasaltic xenoliths, together with the sedimentary isotopic imprint, suggests that the lower crust beneath the volcano is analogous to the coastal metamorphic belt, which is an accretionary complex of intercalated basalts and sediments that formed along the Paleozoic Gondwanan margin. If this is the case, the geochemical composition of the lower and middle crust beneath the SSVZ is significantly different from that of most recent SSVZ volcanic rocks.     

HP–LT Variscan metamorphism in the Cubito-Moura schists (Ossa-Morena Zone, southern Iberia)

Multi-equilibrium thermobarometry shows that low-grade metapelites (Cubito-Moura schists) from the Ossa–Morena Zone underwent HP–LT metamorphism from 340–370 °C at 1.0–0.9 GPa to 400–450 °C at 0.8–0.7 GPa. These HP–LT equilibriums were reached by parageneses including white K mica, chlorite and chloritoid, which define the earliest schistosity (S₁) in these rocks. The main foliation in the schists is a crenulation cleavage (S₂), which developed during decompression from 0.8–0.7 to 0.4–0.3 GPa at increasing temperatures from 400–450 °C to 440–465 °C. Fe³⁺ in chlorite decreased greatly during prograde metamorphism from molar fractions of 0.4 determined in syn-S₁ chlorites down to 0.1 in syn-S₂ chlorites. These new data add to previous findings of eclogites in the Moura schists indicating that a pile of allochtonous rocks situated next to the Beja-Acebuches oceanic amphibolites underwent HP–LT metamorphism during the Variscan orogeny. To cite this article: G. Booth-Rea et al., C. R. Geoscience 338 (2006).     

A way to synchronize models with seismic faults for earthquake forecasting: Insights from a simple stochastic model

Numerical models are starting to be used for determining the future behaviour of seismic faults and fault networks. Their final goal would be to forecast future large earthquakes. In order to use them for this task, it is necessary to synchronize each model with the current status of the actual fault or fault network it simulates (just as, for example, meteorologists synchronize their models with the atmosphere by incorporating current atmospheric data in them). However, lithospheric dynamics is largely unobservable: important parameters cannot (or can rarely) be measured in Nature. Earthquakes, though, provide indirect but measurable clues of the stress and strain status in the lithosphere, which should be helpful for the synchronization of the models.The rupture area is one of the measurable parameters of earthquakes. Here we explore how it can be used to at least synchronize fault models between themselves and forecast synthetic earthquakes. Our purpose here is to forecast synthetic earthquakes in a simple but stochastic (random) fault model. By imposing the rupture area of the synthetic earthquakes of this model on other models, the latter become partially synchronized with the first one. We use these partially synchronized models to successfully forecast most of the largest earthquakes generated by the first model. This forecasting strategy outperforms others that only take into account the earthquake series. Our results suggest that probably a good way to synchronize more detailed models with real faults is to force them to reproduce the sequence of previous earthquake ruptures on the faults. This hypothesis could be tested in the future with more detailed models and actual seismic data.     

Surface temperature differences between minerals in crystalline rocks: Implications for granular disaggregation of granites through thermal fatigue

Thermal expansion differences between minerals within rocks under insolation have previously been assumed to drive breakdown by means of granular disaggregation. However, there have been no definitive demonstrations of the efficacy of this weathering mechanism. Different surface temperatures between minerals should magnify thermal expansion differences, and thus subject adjacent minerals to repeated stresses that might cause breakdown through fatigue failure. This work confirms the existence of surface temperature differences between minerals in granitic rocks under simulated short-term temperature fluctuations so as to discriminate their potential for initiating granular disaggregation. The influence of colour, as a surrogate for albedo, and crystal size, as a function of thermal mass are specifically identified because of their ease of quantification. Four rock types with a range of these properties were examined, and subjected to repeated short-term temperature cycles by radiative heating and cooling under laboratory conditions. Results show that while albedo is the main control for overall and individual maximum temperatures, crystal size is the main factor controlling higher temperature differences between minerals. Thus, stones with large differences of mineral sizes can undergo magnified stresses due to thermal expansion differences.     

Cenozoic tectonic events at the border of the Paraná Basin, São Paulo, Brazil

In the last decade, even in areas that had been considered tectonically stable, a great amount of Cenozoic, including the Quaternary period, structural data have been collected throughout Brazil. The main goal of this study is to describe the Cenozoic structures and tectonic evolution of an area that is located at the border of the Paraná Basin in the state of São Paulo.The research methods consisted of the analysis of: (1) brittle structure data, mainly conjugate fractures and fault slip data; (2) lineaments traced on air photos and TM Landsat and radar images; and (3) a second-order base surface map.The study area, during the Cenozoic, has been affected by five strike–slip tectonic events, which generated mainly strike–slip faults, and secondarily normal and reverse ones. The events were named, from the oldest to the youngest, E1-NE, E2-EW, E3-NW, E4-NS, and E5-NNE; and the maximum principal stresses σ1 strike approximately NE–SW, E–W, NW–SE, N–S, and NNE–SSW, respectively. Event E2-EW seems to have been contemporaneous with the deposition of the Rio Claro Formation, the most important Cenozoic deposit of probable Neogenic age, and also to have controlled the distribution of its deposits. Event E3-NW was the strongest one in the area, as is pointed out by structural data, and the maximum principal stress σ1 of event E5-NNE is partially concordant with the orientation of σH-max of well break-out data in the Paraná Basin, suggesting a Neotectonic activity for this event. Finally, discontinuities parallel and correlated to the directions of strike–slip faults of the Cenozoic events seem to have actively controlled the sculpturing of the relief in the study area.     

Screening model for volatile pollutants in dual porosity soils

This paper develops mass fraction models for transport and fate of agricultural pollutants in structured two-region soils. Mass fraction index models, based on a semi-infinite domain solution, are derived that describe leaching at depth, vapor losses through soil surface, absorption, and degradation in the dynamic- and stagnant-water soil regions. The models predict that leaching is the result of the combined effect of the upward vapor-phase transport relative to downward advection, residence time relative to half-life, dispersion, and lateral diffusive mass transfer. Simulations show that leached fraction of volatile compounds does not always decrease monotonically with increased residence time relative to the pollutant half-life, as a result of complex interactions among the different physical and biochemical processes. The results show that leaching, volatilization, and degradation losses can be affected significantly by lateral diffusive mass transfer into immobile-water regions and advection relative to dispersion (i.e. Peclet number) in the mobile-water regions. It is shown that solute diffusion into the immobile phase and subsequent biochemical decay reduces leaching and vapor losses through soil surface. Potential use of the modified leaching index for the screening of selected pesticides is illustrated for different soil textures and infiltration rates. The analysis may be useful to the management of pesticides and the design of landfills.     

Mixing, sediment accumulation and focusing using 210Pb and 137Cs

The Portil lagoon is a natural freshwater reservoir located at the southwest of Spain, near the coast. In its surroundings an important tourist complex has been developed since the earlier 1970s. This has resulted in increased loads of nutrients, specially during summer months. In order to evaluate the impact from humans on the lagoon caused by anthropogenic activities, we have determined vertical profiles of excess ²¹⁰Pb and ¹³⁷Cs in a sediment core taken from its bottom. Vertical profile of excess ²¹⁰Pb seems to indicate that the sediment core was affected by large-scale mixing processes. Nevertheless this possibility was ruled out based on the shape of the ¹³⁷Cs vertical distribution after modelling the ¹³⁷Cs profile considering large-scale mixing. The chronology developed from ²¹⁰Pb and ¹³⁷Cs has allowed us to calculate the temporal evolution of the mass sedimentation rate during the last century. This mass sedimentation rate increased in 1973: from 0.08(2) g cm^-2 a^-1 in the period 1900-1973 to 0.17(5) g cm^-2 a^-1 in the period 1973-1995. This increase could be related to land-movements in the drainage area and to permitted sewage inputs into the lagoon, both with its origin in the growing/running of the surrounding tourist complex.     

Aquatic hydrocarbon distributions in the Seine estuary: Biogenic polyaromatics and n-alkanes

Dissolved and particulate hydrocarbons of biogenic origin were investigated for the first time in surface waters along the Seine River and its estuary. They comprise n-alkanes (n-ALKs) and diagenetic polycyclic aromatic hydrocarbons (PAHs). Samples were collected in three different sections of the estuary: the riverine zone, the mixing zone, and the marine zone. At the river mouth, two mooring stations were used for the collection of samples over tidal cycles. Total particulate n-ALK concentrations ranged from 31 ng 1^?1 to 2,918 ng 1^?1, or 5 μg g^?1 dry ng 1^?1, or 2 μg g^?1 of SM. Concentrations varied with the SM load and could be related to sedimentation and estuarine mixing. The sources of the n-ALKs were different in each zone of the estuary. The dissolved n-ALKs displayed lower concentrations than the particulate phase, varying from 136 ng 1^?1 to 344 ng 1^?1, while biogenic dissolved PAHs were almost absent.