Modified equations for the determination of odd zonal harmonics

The development of the analytical theory of the motion of an artificial satellite (Berger, 1972–1975) points out the great importance of the second, third order and coupling terms between zonal harmonics. These terms have been added to the equations established byKing-Hele andCook (1968–1973) for the determination of odd zonal harmonics. This solution is compared with theirs. It satisfies all the equations much better and especially the equations relating to near-critical inclination satellites.     

Un calculateur électronique analogique pour la prévision methématique du temps

Résumé On montre d'abord que la théorie des perturbations, due à l'un de nous, conduit à une équation aux dérivées partielles pour les variations de pression au niveau de la mer. Cette même équation peut aussi être déduite par une méthode purement analytique en se basant sur quelques propriétés générales de l'intégrale de Fourier de la perturbation de pression. La méthode utilisée montre d'ailleurs que d'autres fonctions (température, vent, etc.) satisfont aussi à l'équation dont il s'agit. Cette équation de base peut être résolue dans le cas analytique et dans le cas général non analytique et les opérations mathématiques que comporte la solution (opération d'advection par un champ vectoriel horizontal, opération d'intégration pondérée suivant les méridients et son inverse) peuvent être effectuées rapidement et simultanément par l'électronique, ce qui nous a conduit à la construction d'un calculateur analogique approprié à la prévision mathématique du temps à courte et assez longue échéance.

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Summary The first part of the paper is devoted to the theory of the partial differential equation which is the mathematical foundation of the computer, as well as to the deduction of its general solution.The basic equations of our hydrodynamical theory of perturbations are first of all derived and then associated with the equations of motion and continuity, thus giving the fundamental system of the equations of the atmospheric perturbations. A new form of the kinematical condition on the sea level surface is then derived and applied to give the final equation of the pressure variations. This equation, with its advective and development terms, has two horizontal vectorial coefficients: the one is an advection vector defined as the geostrophic velocity associated with the field of the mean temperature (for a period such that the time variations of the corresponding mean are negligible compared with the variations of the observed temperature); the other coefficient is an horizontal vector having the dimensions of a length, varying as cotg , directed towards north, its streamlines being the geographical meridians.The same partial differential equation can also be deduced by a pure analytical method based on some properties of the Fourier transform of the pressure perturbation. This method also shows that other functions than pressure (temperature, wind, for instance) fulfill the same basic equation on any level surface of gravity.The solution of this equation can be written both in the analytical and in the general non analytical cases, and the second part of the paper shows that the mathematical operations appearing in its expression (advection operation by an horizontal vector field, weighted meridional intergration and its inverse) can be rapidly and simultaneously performed by electronic means, thus leading to the construction of an analogue computer for the short and extended range mathematical weather forecasting.

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Certaines parties de ce mémoire ont été communiquées le 10 Avril 1953 à la 1.ère Assemblée de la «Società Italiana di Geofisica e meteorologia» (Gênes, 10–12 Avril 1953).     

On dehydroxylation mechanisms of a biotite in vacuo and in oxygen

The dehydroxylation mechanisms of a biotite in the temperature range 300–800° C at controlled oxygen pressures were studied by infrared (IR) and Mössbauer spectroscopies. At low pressure, the lack of O₂ delays the oxidation of Fe⁺² and simultaneous loss of hydrogen but favours the loss of OH associated with octahedral vacancies in comparison with heat treatment in air. Stoichiometrical considerations based on the facts that the octahedral cations are randomly distributed and all Fe⁺² is oxidized lead to the conclusion that all the OH groups initially coordinated to Fe⁺² must be lost during the oxidation process.     

Crustal structure of the Ribeira fold belt, SE Brazil, derived from receiver functions

Crustal thicknesses previously estimated by [J. Geophys. Res. 107 (2002) 2] in SE Brazil varied from 47 km in the middle of the Paraná basin to approximately 35 km in the Ribeira fold belt. We study the crustal structure of the Ribeira belt in more detail by identifying the Ps Moho converted phase and its multiple reflection PpPms, as well as using waveform modeling of receiver functions. We use phase-weighted slant stacking to identify the Ps and PpPms arrival times, which provides the v_P/v_S beneath each station. In inverting the receiver functions, we use average crustal velocities and initial models obtained from a deep seismic refraction line, as well as data from a timed quarry blast. The crustal thickness ranges 34–42 km with a thinning trend toward the coast. Crustal thickness correlates with elevation, indicating approximate regional Airy isostasy. Along the Serra do Mar coastal range, the average crustal Poisson ratio is about 0.25. The southern part of the Mantiqueira range has a higher Poisson ratio of 0.28. Stations near the São Francisco craton have a lower Poisson ratio of 0.23.     

Monthly and annual statistical distributions of daily rainfall at the Fabra Observatory (Barcelona, NE Spain) for the years 1917–1999

Summary Three empirical distributions of the daily rainfall collected at the Fabra Observatory from 1917 to 1999 are fitted to different statistical models. The first two are designated as the distributions of cumulative amounts and cumulative times. The third distribution accounts for the time interval between two consecutive rainy days with rain amounts equalling or exceeding a threshold amount. Whereas the distribution of cumulative amounts follows an exponential model at monthly and annual scale, except for a few cases, the distribution of the cumulative times is well modelled by a Weibull function, whether monthly or annual scales are considered. The distribution of time intervals also follows a Weibull distribution for the different thresholds considered. In addition, the combination of the two first distributions leads to the normalised rainfall curve, NRC, which is also reproduced satisfactorily by a beta (type 1) distribution. It is worth mentioning that the NRCs follow the expected behaviour with respect to the coefficient of variation of daily rain amounts at monthly and annual scales. In addition, a better understanding of fluctuations and time trends affecting the daily pluviometric regime is achieved by analysing the annual NRCs. The impact of some features of this rain regime, developed for Barcelona, a crowded metropolitan area, on many human activities, may provides the focus of future interdisciplinary analyses.     

United Nations office for outer space affairs GNSS web-pages

In this article, Dr. J.F.G. Monico introduces the on-line resources at the website of the UN Office for Outer Space Affairs, including the web-based GPS resources and their technical background information. Its purpose is to inform the reader about the data, software, electronic documents that are available on-line. This article is coordinated by Dr. Jinling Wang, University of New South Wales, Sydney. Comments and suggestions are appreciated (Jinling.Wang@unsw.edu.au).     

A numerical system to study the transport properties in the Ria de Aveiro lagoon

This work presents results from numerical modelling studies on the hydrodynamics and sediments and passive particles transport properties in Ria de Aveiro, a shallow lagoon located on the Portuguese Northwest Atlantic coast. The hydrodynamic of the lagoon was systematically studied, from both the Eulerian and Lagragian point of view, in order to understand the overall circulation in the lagoon, characterize the dynamics of its different channels and assess the transport of suspended cohesive sediments.Responsible Editor: Hans Burchard     

Electron microprobe dating of monazite substantiates ages of major geological events in the southern Brazilian shield

To obtain the chemical Th^*–Pb isochron ages and surface maps of monazite crystals in igneous and metamorphic rocks from the southern Brazilian Shield, we employ Th–U-total Pb dating by an electron probe microanalyzer. The ages of two Trans-Amazonian metamorphic events are given by a felsic, garnet-bearing granulite from the Santa Maria Chico granulitic complex. The age of the first event, at approximately 2.35 Ga, was obtained by surface mapping in a grain included in garnet. The dating of the second event, 1899±43 Ma, is in agreement with previous data obtained in zircon crystals with sensitive high-resolution ion microprobe. Other determinations belong to the Brasiliano cycle. In the São Gabriel block, an age of 643±129 Ma was obtained on monazite from a staurolite-garnet schist of the Cambaizinho Formation, whereas a staurolite-bearing schist from the Passo Feio complex yielded a 510±68 Ma age. Several units in the Dom Feliciano belt were dated, including the biotite-sillimanite gneisses of the Várzea do Capivarita complex (552±90 Ma), the sillimanite-garnet gneisses of Camboriú complex (565±77 Ma), the Três Figueiras granite (558±57 Ma), and the Plaza Itapema granite (545±55 Ma). The ages presented in this study, obtained through monazite chemical dating, are confirmed through comparison with previous data regarding zircon crystals from the same geological units.     

Uncertainty Estimate in Resources Assessment: A Geostatistical Contribution

For many decades the mining industry regarded resources/reserves estimation and classification as a mere calculation requiring basic mathematical and geological knowledge. Most methods were based on geometrical procedures and spatial data distribution. Therefore, uncertainty associated with tonnages and grades either were ignored or mishandled, although various mining codes require a measure of confidence in the values reported. Traditional methods fail in reporting the level of confidence in the quantities and grades. Conversely, kriging is known to provide the best estimate and its associated variance. Among kriging methods, Ordinary Kriging (OK) probably is the most widely used one for mineral resource/reserve estimation, mainly because of its robustness and its facility in uncertainty assessment by using the kriging variance. It also is known that OK variance is unable to recognize local data variability, an important issue when heterogeneous mineral deposits with higher and poorer grade zones are being evaluated. Altenatively, stochastic simulation are used to build local or global uncertainty about a geological attribute respecting its statistical moments. This study investigates methods capable of incorporating uncertainty to the estimates of resources and reserves via OK and sequential gaussian and sequential indicator simulation The results showed that for the type of mineralization studied all methods classified the tonnages similarly. The methods are illustrated using an exploration drill hole data sets from a large Brazilian coal deposit.     

Sediment hosted lead–zinc deposits of the Neoproterozoic Bambuí Group and correlative sequences, São Francisco Craton, Brazil: A review and a possible metallogenic evolution model

The Proterozoic sediment-hosted Zn–(Pb) sulfide and non-sulfide deposits of the São Francisco Craton, Brazil, are partially syn-diagenetic and epigenetic and were probably formed during extensional events. The majority of the deposits occur within shallow water dolomites. The Pb isotopic data of sulfides are relatively homogeneous for individual deposits and plot above the upper crust evolution curve of the Plumbotectonic model. Some of the deposits are characterized by highly radiogenic lead (²⁰⁶Pb/²⁰⁴Pb ≥ 21) originating from the highly radioactive crust of the São Francisco Craton. Pb and S isotopic data suggest the sources of metal and sulfur for the deposits to be the basement rocks and seawater sulfates in the sediments, respectively. The relatively high temperatures of formation (100 to 250 °C) and moderate salinity (3% to 20% NaCl equiv.) of the primary fluid inclusions in the sphalerite crystals suggest the participation of basinal mineralizing fluids in ore formation. The steep paleo-geothermal gradient generated by the radioactively enriched basement rocks probably assisted in heating up the circulating mineralizing fluids.