Ck-Reconstruction of Surfaces from Partial Data

In this paper, we study the problem of constructing a smooth approximant of a surface defined by the equation z = f(x ₁, x ₂), the data being a finite set of patches on this surface. This problem occurs, for example, after geophysical processing such as migration of time-maps or depth-maps. The usual algorithms to solve this problem are picking points on the patches to get Lagrange's data or trying to get local junctions on patches. But the first method does not use the continuous aspect of the data and the second one does not perform well to get a global regular approximant (C ¹ or more). As an approximant of f, a discrete smoothing spline belonging to a suitable piecewise polynomial space is proposed. The originality of the method consists in the fidelity criterion used to fit the data, which takes into account their particular aspect (surface's patches): the idea is to define a function that minimizes the volume located between the data patches and the function, and which is globally C ^k. We first demonstrate the new method on a theoretical aspect and numerical results on real data are given.     

The granite hosted gold deposit of Moulin de Chéni (Saint-Yrieix district,Massif Central,France): petrographic,structural, fluid inclusion and oxygen isotope constraints

The Moulin de Chéni orogenic gold deposit is the only granite-hosted deposit of the Saint-Yrieix district, French Massif Central. It occurs in 338±1.5 Ma-old peraluminous leucogranites and is characterized by intense microfracturing and bleaching of the granite in relation to pervasive sulfide crystallization. Formation of quartz veins and gold deposition occurred in two successive stages: an early mesozonal stage of quartz-sulfide (Fe-As-S) deposition, usually devoid of gold and a late epizonal stage of base metal and gold deposition. Both stages postdate peak metamorphism and granite intrusion. The genesis of the deposit is the result of four successive fluid events: (1) Percolation of aqueous-carbonic metamorphic fluids under an assumed lithostatic regime of 400–450 °C, at a maximum depth of 13 km; (2) Formation of the main quartz lodes with coeval K-alteration and introduction of As and S from aqueous-carbonic fluids percolating along regional faults. Arsenopyrite and pyrite deposition was linked to the alteration of Fe-silicates into K-feldspar and phengite at near-constant iron content in the bulk granite. Temperature was similar to that of the preceding stage, but pressure decreased to 100–50 MPa, suggesting rapid uplift of the basement up to 7.5 km depth; (3) The resulting extensional tectonic leads to the deposition of gold, boulangerite, galena and sphalerite in brecciated arsenopyrite and pyrite from aqueous fluids during a mixing process. Temperature and salinity decrease from 280 to 140 °C and 8.1 wt% eq. NaCl to 1.6 wt% eq. NaCl, respectively; (4) Sealing of the late fault system by barren comb quartz which precipitated from dilute meteoric aqueous fluids (1.6 wt% eq. NaCl to 0.9 wt% eq. NaCl) under hydrostatic conditions at 200–150 °C.Editorial handling: B. Lehmann     

Assessing anthropogenic impacts on limited water resources under semi-arid conditions: three-dimensional transient regional modelling in Jordan

Both increasing aridity and population growth strongly stress freshwater resources in semi-arid areas such as Jordan. The country’s second largest governorate, Irbid, with over 1 million inhabitants, is already suffering from an annual water deficit of 25 million cubic meters (MCM). The population is expected to double within the next 20 years. Even without the large number of refugees from Syria, the deficit will likely increase to more then 50 MCM per year by 2035 The Governorate’s exclusive resource is groundwater, abstracted by the extensive Al Arab and Kufr Asad well fields. This study presents the first three-dimensional transient regional groundwater flow model of the entire Wadi al Arab to answer important questions regarding the dynamic quality and availability of water within the catchment. Emphasis is given to the calculation and validation of the dynamic groundwater recharge, derived from a multi-proxy approach, including (1) a hydrological model covering a 30-years dataset, (2) groundwater level measurements and (3) information about springs. The model enables evaluation of the impact of abstraction on the flow regime and the groundwater budget of the resource. Sensitivity analyses of controlling parameters indicate that intense abstraction in the southern part of the Wadi al Arab system can result in critical water-level drops of 10 m at a distance of 16 km from the production wells. Moreover, modelling results suggest that observed head fluctuations are strongly controlled by anthropogenic abstraction rather than variable recharge rates due to climate changes.     

Foliation fields and 3D cartography in geology: Principles of a method based on potential interpolation

A modeling method that takes into account known points on a geological interface and plane orientation data such as stratification or foliation planes is described and tested. The orientations data do not necessarily belong to one of the interfaces but are assumed to sample the main anisotropy of a geological formation as in current geological situations. The problem is to determine the surfaces which pass through the known points on interfaces and which are compatible with the orientation data. The method is based on the interpolation of a scalar field defined in the space the gradient in which is orthogonal to the orientations, given that some points have the same but unknown scalar value (points of the same interface), and that scalar gradient is known on the other points (foliations). The modeled interfaces are represented as isovalues of the interpolated field. Preliminary two-dimensional tests carried-out with different covariance models demonstrate the validity of the method, which is easily transposable in three dimensions.     

Une méthode globale d'estimation des températures des réservoirs alimentant les sources thermales. Exemple du Massif Central Français

A chemical model based on the equilibrium of water with quartz, albite, adularia, calcite, kaolinite or illite, and chlorite can explain the chemical composition of the main groups of hot springs in Massif Central. Temperature is the principal variable for determining this composition. Model temperatures generally agree with those given by classical cation geothermometers (t ? 135–150° C for Vichy. La Bourboule. Evaux and Châteauneuf; t ? 175–180° C for Chaudes Aigues and Saint Nectaire). The model fails to represent the composition of Mont Dore waters: the high temperatures given by classical geothermometers are considered doubtful.     

Main Species Characteristics of Phytoplankton Spring Blooms in NE Atlantic and Arctic Waters (68–80° N)

A compilation of phytoplankton species abundance data from the spring bloom along the northern Norwegian coast and in the Barents Sea shows that the quantitatively most important species are the prymnesiophyte Phaeocystis pouchetii and the common cold water to temperate diatoms Chaetoceros socialis, Skeletonema costatum sensu lato, Fragilariopsis oceanica, Thalassiosira spp., Chaetoceros furcellatus, Chaetoceros compressus, Chaetoceros debilis and Bacterosira bathyomphala. The relative abundance of diatoms and Phaeocystis varied highly and apparently stochastically between years. P. pouchetii occurred during all stages of the spring bloom and sometimes completely dominated the phytoplankton community. Along the Norwegian coast, the importance of P. pouchetii increased northwards. The species composition in coastal fjords at 70° N is surprisingly similar to that of shelf waters in the Barents Sea (up to 80° N). An exception is S. costatum sensu lato which was seldom observed in Arctic waters. Small flagellates (<10 μm) other than dinoflagellates and P. pouchetii are also important among the Barents Sea spring phytoplankton. Associations of species seem rigid over time and are dominated by C. socialis and P. pouchetii in northern waters. Biogeographical categories of spring bloom species in relation to environmental conditions are discussed.     

Ammonium in aqueous fluids to 600 °C, 1.3 GPa: A spectroscopic study on the effects on fluid properties, silica solubility, and K-feldspar to muscovite reactions

The behavior of ammonium, NH₄⁺, in aqueous systems was studied based on Raman spectroscopic experiments to 600 °C and about 1.3 GPa. Spectra obtained at ambient conditions revealed a strong reduction of the dynamic three-dimensional network of water with addition of ammonium chloride, particularly at small solute concentrations. The differential scattering cross section of the ν₁-NH₄⁺ Raman band in these solutions was found to be similar to that of salammoniac.The Raman band of silica monomers at ∼780 cm⁻¹ was present in all spectra of the fluid at high temperatures in hydrothermal diamond-anvil cell experiments with H₂O ± NH₄Cl and quartz or the assemblage quartz + kyanite + K-feldspar ± muscovite/tobelite. However, these spectra indicated that dissolved silica is less polymerized in ammonium chloride solutions than in comparable experiments with water. Quantification based on the normalized integrated intensity of the H₄SiO₄⁰ band showed that the silica solubility in experiments with H₂O + NH₄Cl was significantly lower than that in equimolal NaCl solutions. This suggests that ammonium causes a stronger decrease in the activity of water in chloridic solutions than sodium.The Raman spectra of the fluid also showed that a significant fraction of ammonium was converted to ammonia, NH₃, in all experiments at temperatures above 300 °C. This indicates a shift towards acidic conditions for experiments without a buffering mineral assemblage. The estimated pH of the fluid was ∼2 at 600 °C, 0.26 GPa, 6.6 m initial NH₄Cl, based on the ratio of the integrated ν₁-NH₃ and ν₁-NH₄⁺ intensities and the HCl⁰ dissociation constant. The NH₃/NH₄⁺ ratio increased with temperature and decreased with pressure. This implies that more ammonium should be retained in K-bearing minerals coexisting with chloridic fluids upon high-P low-T metamorphism. At 500 °C, 0.73 GPa, ammonium partitions preferentially into the fluid, as constrained from infrared spectroscopy on the muscovite and from mass balance.The conversion of K-feldspar to muscovite proceeded much faster in experiments with NH₄Cl solutions than in comparable experiments with water. This is interpreted as being caused by enhancement of the rate-limiting alumina solubility, suggesting complexation of Al with NH₄. Nucleation and growth of mica at the expense of K-feldspar and NH₄⁺/K⁺ exchange between fluid and K-feldspar occurred simultaneously, but incorporation of NH₄⁺ into K-feldspar was distinctly faster than K-feldspar consumption.     

Le magmatisme basique calcoalcalin d'âge dévono-dinantien du nord du Massif Central,témoin d'une marge active hercynienne: arguments géochimiques et isotopiques Sr/Nd

Abstract

Samples of volcanic rocks from the main outcrops of Devono-Dinantian series in northern Massif-Central have been studied for Sr and Nd isotopes and immobile incompatible trace elements. In addition, two intrusive bodies of dioritic composition have been dated at 365 ± 3 Ma (Aydat) and 360 ± 1 Ma (Beaumont-Huriel), using the U/Pb zircon method. Together with geochemical data, these ages show that all the studied rocks belong to the same igneous episode. Based on trace element and radiogenic isotopes (⁸⁷Sr/⁸⁶Sr_i from 0,7041 to 0,7057; εNd_i from +1.5 to +5.0), the Late Devonian and Early Carboniferous igneous rocks bear distinct similarities with magmas produced in modern active margin settings. Combined with independent evidence for the occurrence of Devonian oceanic lithosphere in the northern branch of the Variscides, these geochemical affinities suggest that southward subduction of oceanic crust prevailed during the Late Devonian in northern Massif-Central. As a corollary, it appears that true continent-continent collision did not occur before Early Carboniferous times. © 2002 Éditions scientifiques et médicales Elsevier SAS. All rights reserved.     

BAKTRAK: backtracking drifting objects using an iterative algorithm with a forward trajectory model

The task of determining the origin of a drifting object after it has been located is highly complex due to the uncertainties in drift properties and environmental forcing (wind, waves, and surface currents). Usually, the origin is inferred by running a trajectory model (stochastic or deterministic) in reverse. However, this approach has some severe drawbacks, most notably the fact that many drifting objects go through nonlinear state changes underway (e.g., evaporating oil or a capsizing lifeboat). This makes it difficult to naively construct a reverse-time trajectory model which realistically predicts the earliest possible time the object may have started drifting. We propose instead a different approach where the original (forward) trajectory model is kept unaltered while an iterative seeding and selection process allows us to retain only those particles that end up within a certain time–space radius of the observation. An iterative refinement process named BAKTRAK is employed where those trajectories that do not make it to the goal are rejected, and new trajectories are spawned from successful trajectories. This allows the model to be run in the forward direction to determine the point of origin of a drifting object. The method is demonstrated using the leeway stochastic trajectory model for drifting objects due to its relative simplicity and the practical importance of being able to identify the origin of drifting objects. However, the methodology is general and even more applicable to oil drift trajectories, drifting ships, and hazardous material that exhibit nonlinear state changes such as evaporation, chemical weathering, capsizing, or swamping. The backtracking method is tested against the drift trajectory of a life raft and is shown to predict closely the initial release position of the raft and its subsequent trajectory.