Band-limited functions on a bounded spherical domain: the Slepian problem on the sphere

The Slepian problem consists of determining a sequence of functions that constitute an orthonormal basis of a subset of ℝ (or ℝ²) concentrating the maximum information in the subspace of square integrable functions with a band-limited spectrum. The same problem can be stated and solved on the sphere. The relation between the new basis and the ordinary spherical harmonic basis can be explicitly written and numerically studied. The new base functions are orthogonal on both the subspace and the whole sphere. Numerical tests show the applicability of the Slepian approach with regard to solvability and stability in the case of polar data gaps, even in the presence of aliasing. This tool turns out to be a natural solution to the polar gap problem in satellite geodesy. It enables capture of the maximum amount of information from non-polar gravity field missions. Received: 10 June 1998 / Accepted: 20 May 1999     

Measured performance of the application of EGNOS in the road traffic sector

European Geostationary Navigation Overlay Service (EGNOS) is a satellite-based system developed to improve the performance of GPS in the European region. It not only enhances the estimated positioning accuracy but also provides an integrity solution. We assess the EGNOS performance through analysis of real measurements, performed in different road user environments. We investigate the use of the integrity concept in future Global Navigation Satellite System (GNSS)-based applications in the road environment, considering both suburban and dense urban areas. The analysis is motivated by the fact that there is an increasing number of road applications, such as billing system, transportation of dangerous goods, remote tracking of trucks and snow plows, fleet management and “pay as you go” car insurances, where the system liability has to be guaranteed. The scope of the analysis is to investigate to which extent the use of the integrity concept can be used for such purpose; the assessment is based on real measurement campaigns in representative environments, providing statistical results in terms of accuracy and integrity, and in a wider sense of the feasibility of the use of EGNOS for augmenting the reliability of GNSS positioning for road applications.     

Hamiltonian perturbation theory on a manifold

This paper deals with Hamiltonian perturbation theory for systems which, like Euler-Poinsot (the rigid body with a fixed point and no torques), are degenerate and do not possess a global system of action-angle coordinates. It turns out that the usual methods of perturbation theory, which are essentially local being based on the construction of normal forms within the domain of a local coordinate system, are not immediately usable to study perturbations of these systems, since degeneracy makes impossible to control that the system does not fall into a singularity of the coordinates. To overcome this difficulty, we develop a global formulation of Hamiltonian perturbation theory, in which the normal forms are globally defined on the phase space manifold. The key for this study lies in the geometry of the fibration by the invariant tori of an integrable degenerate Hamiltonian system, which is described by some generalizations of the Liouville-Arnol'd theorem and is reviewed in the paper. As an application, we provide a global formulation of Nekhoroshev's theorem on the stability for exponentially long times.     

M4–18: the planetary nebula and its WC10 central star

We present a detailed analysis of the planetary nebula M4–18 (G146.7+07.6) and its WC10-type Wolf–Rayet (WR) central star, based on high‐quality optical spectroscopy (WHT/UES, INT/IDS, WIYN/DensPak) and imaging ( HST /WFPC2). From a non-LTE model atmosphere analysis of the stellar spectrum, we derive T _eff=31 kK,     v _∞=160 km s⁻¹ and abundance number ratios of H/He<0.5, C/He=0.60 and O/He=0.10. These parameters are remarkably similar to those of He 2–113 ([WC10]). Assuming an identical stellar mass to that determined by De Marco et al. for He 2–113, we obtain a distance of 6.8 kpc to M4–18 [ E ( B−V )=0.55 mag from nebular and stellar techniques]. This implies that the planetary nebula of M4–18 has a dynamical age of ∼3100 yr, in contrast to ≥270 yr for He 2–113. This is supported by the much higher electron density of the latter. These observations may be reconciled with evolutionary predictions only if [WC]-type stars exhibit a range in stellar masses.
Photoionization modelling of M4–18 is carried out using our stellar WR flux distribution, together with blackbody and Kurucz energy distributions obtained from Zanstra analyses. We conclude that the ionizing energy distribution from the WR model provides the best consistency with the observed nebular properties, although discrepancies remain.     

The respective roles of surface temperature driven feedbacks and tropospheric adjustment to CO2 in CMIP5 transient climate simulations

An overview of radiative climate feedbacks and ocean heat uptake efficiency diagnosed from idealized transient climate change experiments of 14 CMIP5 models is presented. Feedbacks explain about two times more variance in transient climate response across the models than ocean heat uptake efficiency. Cloud feedbacks can clearly be identified as the main source of inter-model spread. Models with strong longwave feedbacks in the tropics feature substantial increases in cloud ice around the tropopause suggestive of changes in cloud-top heights. The lifting of the tropical tropopause goes together with a general weakening of the tropical circulation. Distinctive inter-model differences in cloud shortwave feedbacks occur in the subtropics including the equatorward flanks of the storm-tracks. Related cloud fraction changes are not confined to low clouds but comprise middle level clouds as well. A reduction in relative humidity through the lower and mid troposphere can be identified as being the main associated large-scale feature. Experiments with prescribed sea surface temperatures are analyzed in order to investigate whether the diagnosed feedbacks from the transient climate simulations contain a tropospheric adjustment component that is not conveyed through the surface temperature response. The strengths of the climate feedbacks computed from atmosphere-only experiments with prescribed increases in sea surface temperatures, but fixed CO₂ concentrations, are close to the ones derived from the transient experiment. Only the cloud shortwave feedback exhibits discernible differences which, however, can not unequivocally be attributed to tropospheric adjustment to CO₂. Although for some models a tropospheric adjustment component is present in the global mean shortwave cloud feedback, an analysis of spatial patterns does not lend support to the view that cloud feedbacks are dominated by their tropospheric adjustment part. Nevertheless, there is positive correlation between the strength of tropospheric adjustment processes and cloud feedbacks across different climate models.     

Deformation of a young salt giant: regional topography of the Red Sea Miocene evaporites

The deformational behaviour of ‘salt giants’ during and shortly after their deposition is difficult to decipher in ocean margin settings where the original evaporites have been deeply buried and strongly mobilized. Here, we examine seismic reflection data from the Red Sea, where evaporites deposited until the end of the Miocene (~5.3 Ma), are generally covered by only 200–300 m of low‐density sediments and where the presence of an axial spreading centre allows us to observe how they have responded to a varied configuration of underlying basement. The regional morphology of the S‐reflection, representing the evaporite surface, is mapped out from seismic data from 13 cruises. The S‐reflection is locally rugged and commonly angular. It is either underlain by layered reflectivity, suggestive of layered evaporite beds, or by more transparent seismic character, suggestive of massive halite. On average, the depth of the reflection on the flanks of the axial rift systematically declines from 700 to 1100 m below sea level (mbsl) going northwards from 16 to 23°N. In the central Red Sea, the S‐reflection has 100‐ to 200‐m‐deep depressions, extending towards the coasts in places. In the southern Red Sea, the S‐reflection forms a surface at 300–800 mbsl that appears less disrupted. We suggest that the evaporites originally had a flat, horizontal surface at the end of the Miocene and have subsequently been distorted by isostatic effects and axial rifting, which in turn promoted evaporite flowage. Off‐axis evaporite depressions correspond with flows identified with multibeam sonar. Furthermore, across‐rift lows in Bouguer gravity anomalies represent valleys in the underlying basement. The off‐axis evaporite depressions overlie those valleys, as would be expected if halokinetic movements were greatest where the evaporites are locally thick, leading to deflation of the evaporite surface. The thickness of post‐Miocene sediment, also mapped out as part of this procedure, confirms the generally pelagic nature of this interval and increases on average from ~250 to 300 m from the central to the southern Red Sea, mimicking the variation in pelagic productivity observed in the present water column.     

Ar / Ar dating of high-pressure rocks from the Ligurian Alps: Evidence for a continuous subduction–exhumation cycle

We present ³⁹Ar–⁴⁰Ar dating of phengite, muscovite and paragonite from a set of mafic and metasedimentary rocks sampled from the high-pressure (HP) metaophiolites of the Voltri Group (Western Alps) and from clasts in the basal layer conglomerates from the Tertiary molasse which overlie the high-pressure basement. The white mica-bearing rocks display peak eclogitic and blueschist-facies parageneses, locally showing complex greenschist-facies replacement textures. The internal discordance of age spectra is proportional to the chemical complexity of the micas. High-Si phengites from eclogite clasts record a ³⁹Ar–⁴⁰Ar age of ca. 49 Ma for the eclogite stage and ca. 43 Ma for the blueschist retrogression; phengites from a blueschist basement sample yield an age of ca. 40 Ma; low-Si muscovite from a metasediment dates the formation of the greenschist paragenesis at ca. 33 Ma. Our data indicate that the analyzed samples reached high-pressure conditions at different times over a time-span of c.a. 10 Ma. Subduction was continuing during exhumation and blueschist retrograde re-equilibration of higher-pressure, eclogite-facies rocks. This process kept the isotherms depressed, allowing the older HP-rocks to escape thermal re-equilibration. Our results, added to literature data, fit a tectonic model of a subduction–exhumation cycle, with different tectonic slices subducted at different times from Early Eocene until the Eocene–Oligocene boundary.     

The STAGES view of red spirals and dusty red galaxies: mass-dependent quenching of star formation in cluster infall

We investigate the properties of optically passive spirals and dusty red galaxies in the A901/2 cluster complex at redshift ∼0.17 using rest-frame near-ultraviolet–optical spectral energy distributions, 24-μm infrared data and Hubble Space Telescope morphologies from the STAGES data set. The cluster sample is based on COMBO-17 redshifts with an rms precision of  σ _cz ≈ 2000 km s⁻¹  . We find that 'dusty red galaxies' and 'optically passive spirals' in A901/2 are largely the same phenomenon, and that they form stars at a substantial rate, which is only four times lower than that in blue spirals at fixed mass. This star formation is more obscured than in blue galaxies and its optical signatures are weak. They appear predominantly in the stellar mass range of  log  M _*/M_⊙=[10, 11]  where they constitute over half of the star-forming galaxies in the cluster; they are thus a vital ingredient for understanding the overall picture of star formation quenching in clusters. We find that the mean specific star formation rate (SFR) of star-forming galaxies in the cluster is clearly lower than in the field, in contrast to the specific SFR properties of blue galaxies alone, which appear similar in cluster and field. Such a rich red spiral population is best explained if quenching is a slow process and morphological transformation is delayed even more. At  log  M _*/M_⊙ < 10  , such galaxies are rare, suggesting that their quenching is fast and accompanied by morphological change. We note that edge-on spirals play a minor role; despite being dust reddened they form only a small fraction of spirals independent of environment.     

A metrologic method of anomaly field amplitude bottom reduction in undersampled geomagnetic marine surveys

We show the results obtained by means of a seabed reduction technique on the intensity of geomagnetic anomaly fields applied to a synthetic case and then to the real case of a geomagnetic survey of eastern Ligurian Sea (Italy). The eastern Ligurian Sea has very intense short waves anomaly fields and a sea bed that varies greatly in depth. As a result the geomagnetic space signal is characterized by a very large spectral content; in these conditions it is not possible to obtain a full sampled marine survey and vertical continuation analytic procedures and standard numerical bottom reduction based on a single vertical incremental parameter, whichever is applicable, fails to give accurate results. The present technique, which has been fine-tuned over 4 years of experimentation in environmental researchs, aims to provide a simple and efficient means to reduce the distortion of geomagnetic anomalies field caused by the variation of distance between survey plane and magnetic outcrop source position. The compensation procedure is based on evaluation, by comparison of two measurements carried out at different altitudes, of the mean vertical increment typical of each anomaly field principal frequency component bands. The component anomaly fields are then corrected by application of the corresponding vertical increments and lastly, the anomaly geomagnetic field reduced to the sea-bed is computed as Inverse Fourier Transform of a spectrum built as synthesis of the component anomaly fields' spectra. The results obtained have shown a notable increase in definition of anomaly field intensity without the production of appreciable distortions or false geomagnetic echoes. This revised version was published online in November 2006 with corrections to the Cover Date.     

Profondità ipocentrali e coefficienti di assorbimento per zone Etnee

Riassunto Si discutono le diverse formule che permettono il calcolo, con i dati macrosismici, delle profondità ipocentrali dei terremoti e dei coefficienti di assorbimento delle zone interessate. Si indicano delle modifiche, nella conduzione dei calcoli richiesti dalla formula delKövesligethy, apportanti notevoli semplificazioni ai calcoli stessi. In base ai metodi indicati vengono studiati i terremoti della regione etnea e particolarmente di quella orientale. Per le profondità ipocentrali i valori ottenuti, compresi fra 0.1 e 2.5 Km, confermano le idee che si hanno sulla genesi dei terremoti della zona. Per i coefficienti di assorbimento invece i risultati, compresi fra 0.03 e 0.35, hanno permesso, di trovare una legge di variazione del coefficiente stesso con la profondità, legge che per la bassa regione orientale ha l'espressione seguente: (x)=0.27e ^–3.5x.

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Summary They discuss the various formulae which enable to calculate, by means of the macrosismical data, the ipocentral earthquake depths and the absorption coefficients. They propose some modifications in the calculus required by theKövesligethy formula, which simplify considerably these calculations. On the basis of the indicated methods, the earthquakes of the Aetna area, especially those of the eastern side, are examined. The values obtained for the ipocentral depths, comprised between 0.1 and 2.5 Km, confirm the opinion they have on the origin of the earthquakes of this area. On the contrary the results for the absorption coefficients comprised between 0.03 and 0.35 enabled to find a variation law of this coefficient with the depth. For the low eastern region this law has the following form: (x)=0.27e ^–3.5x.