Éditeur(s) : HAL CCSD SpringerOpen
Résumé : International audience
We introduce methods which seem to be a new and promising tool in hierarchical fixed-point problems. The goal of this note is to analyze the convergence properties of these new types of approximating methods for fixed-point problems. The limit attained by these curves is the solution of the general variational inequality,, where denotes the normal cone to the set of fixed point of the original nonexpansive mapping and a suitable nonexpansive mapping criterion. The link with other approximation schemes in this field is also made.
ISSN: 1687-1820

hal-00780237
https://hal.univ-antilles.fr/hal-00780237
https://hal.univ-antilles.fr/hal-00780237/document
https://hal.univ-antilles.fr/hal-00780237/file/1687-1812-2006-95453.pdf
DOI : 10.1155/FPTA/2006/95453

Éditeur(s) : HAL CCSD European Geosciences Union
Résumé : We propose to assess the error done when temperature is considered as a conservative tracer in fluviokarst studies. As a matter of fact, heat exchanges occur between karstic Conduit System (CS) and Porous Fractured Matrix (PFM) that prevents from using this approximation without caution. The conservative tracer approximation boils down to consider the cooling of CS water by PFM flow in an open thermodynamic system where the CS is bounded by an Adiabatic Wall (AW). The resulting CS water temperature contrasts with the one obtained from more complete models (CW), which also take into account heat conduction within the CS, within the PFM, and from the CS to PFM through CS a Conductive Wall. In order to assess first orders of this error, the dimensionless equations, characteristic of CS cooling by PFM, have been solved thanks to Alternate Finite Difference Implicit methods both in AW and CW configurations. Four groups of dimensionless numbers appear in the various terms of energy and mass equations among which the Peclet and Reynolds numbers depict the large morphologic and hydrologic variability of natural karstic systems. A parametric exploration of the differences between AW and CW models has then been conducted vs. Peclet numbers (Pe numbers varying from 106 to 109, at constant CS Reynolds number) and vs. Reynolds numbers (Red varying from 103 to 107, at constant Peclet number). The error curves bound finite volumes in the Peclet–Reynolds space that converge uniformly to zero for the extreme values of these parameters. However, for Peclet and Reynolds numbers characteristic of realistic fluviokarst configurations, the errors reach finite values, that give first order information assessing the error done by considering temperatures as conservative tracers. Maximum relative errors around 10−2 (in fact 0.0092) have been found varying Pe; while it remained slightly lower than 0.7 × 10−2 varying Red. An illustrative example of the temperature conservative tracer AW approximation is presented with the data obtained from the main morphologic and hydrologic properties of the Cent–Font resurgence (Hérault, France). According to the results, the error reached at the output of the fluviokarst is 0.00613 (for Pe = 1.4993 × 108 and Red = 4.2969 × 104). When rescaled to the physical domain, this error leads to a temperature difference of 1.77 K between the CW and AW configurations.
ISSN: 1812-2108

hal-01358348
https://hal.archives-ouvertes.fr/hal-01358348
https://hal.archives-ouvertes.fr/hal-01358348/document
https://hal.archives-ouvertes.fr/hal-01358348/file/hessd-11-169-2014.pdf
DOI : 10.5194/hessd-11-169-2014

Éditeur(s) : HAL CCSD
Résumé : International audience
An iterative method for solving set-valued variational inequalities is considered and its convergence properties are studied under strong monotonicity and coercivity conditions. The results obtained in this paper include, as a special case, some known results in this field.
Mathematical Inequalities & Applications

hal-00776616
https://hal.univ-antilles.fr/hal-00776616

Éditeur(s) : HAL CCSD
Résumé : International audience
We deal with a perturbed version of a Hummel-Seebeck type method to approximate a solution of variational inclusions of the form : 0 ∈ Φ(z) + F(z) where Φ is a single-valued function twice continuously Fréchet differentiable and F is a set-valued map from Rn to the closed subsets of Rn. This framework is convenient to treat in a unified way standard sequential quadratic programming, its stabilized version, sequential quadratically constrained quadratic programming, and linearly constrained Lagrangian methods (see [1]). We obtain, thanks to some semistability and another property (which is close to the hemistability) of the solution z ̄ of the previous inclusion, the local existence of a sequence that is superquadratically or cubically convergent.
ISSN: 2518-3680

hal-01630560
https://hal.archives-ouvertes.fr/hal-01630560
DOI : 10.22606

Éditeur(s) : HAL CCSD
Résumé : International audience
This paper deals with variational inclusions of the form 0 ∈ K − f(x) − g(x) where f is a smooth function from a reflexive Banach space X into a Banach space Y , g is a function from X into Y admitting divided differences and K is a nonempty closed convex cone in the space Y . We show that the previous problem can be solved by a combination of two methods: the Newton and the Secant methods. We show that the order of the semilocal method obtained is equal to (1 + √5)/2. Numerical results are also given to illustrate the convergence at the end of the paper.
Serdica Math. J.

hal-00924150
https://hal.archives-ouvertes.fr/hal-00924150

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
We consider a variable Krasnosel'skii-Mann algorithm for approximating critical points of a prox-regular function or equivalently for finding fixed-points of its proximal mapping proxλf. The novelty of our approach is that the latter is not non-expansive any longer. We prove that the sequence generated by such algorithm (via the formula xk+1=(1−αk)xk+αkproxλkfxk, where (αk) is a sequence in (0,1)), is an approximate fixed-point of the proximal mapping and converges provided that the function under consideration satisfies a local metric regularity condition.
ISSN: 0362-546X

hal-00778175
https://hal.univ-antilles.fr/hal-00778175
DOI : 10.1016/j.na.2009.07.011

Éditeur(s) : HAL CCSD Oxford University Press (OUP)
Résumé : International audience
Iran is an active continental domain accommodating the convergence between the Arabia and Eurasia plates. In northwestern Iran, deformation between the Central Iranian block and the Caucasus domain is mainly accommodated by right lateral strike-slip on the Tabriz fault. Cities and villages, including the city of Tabriz, have been destroyed by several strong historical earthquakes (M similar to 7). In this study, we compare the slip-rates estimated from geodetic measurements (radar interferometry and UPS) with those determined by dating a geomorphological offset of an alluvial fan along the Tabriz fault. The GPS measurements along two profiles normal to the Tabriz fault suggest a slip-rate of 7.3 +/- 1.3 mm yr(-1). The persistent scatterer radar interferometry analysis of Envisat satellite archives from 2003 to 2010 shows a velocity gradient (6 +/- 3 mm yr(-1)) across the Tabriz fault in agreement with GPS results. Moreover, it reveals that most of the area located south of the Tabriz fault is affected by subsidence, and that some sections of the fault probably act as barriers to fluid migration which may have an impact on its mechanical behaviour. West of Tabriz morphotectonic investigations on an alluvial fan surface show a right-lateral cumulative offset of 320 +/- 40 m Luminescence analyses of the coarse matrix alluvial fan deposits provide an age of 46 +/- 3 ka. This yields a slip-rate comprised between 6.5 and 7.3 mm yr(-1) along this segment. These results suggest that the Late Quaternary slip-rate is in agreement with the present-day slip-rate estimated by geodetic measurements, showing no slip-rate changes during the past 45 000 yr. Short-term variations within the 45 000 yr related to temporal earthquake clustering over few seismic cycles cannot be ruled out, but if they exist, they do not affect the geodetic and the geomorphological estimates. This study is in agreement with previous ones suggesting that long-term slip-rates (i.e. averaged over several tens of seismic cycles) are consistent with geodetic estimated slip-rates (i.e. extrapolated from few years of interseismic observations), and suggests that perturbations of fault slip-rates are related to variations over few seismic cycles.
ISSN: 0956-540X

hal-00844695
https://hal.archives-ouvertes.fr/hal-00844695
https://hal.archives-ouvertes.fr/hal-00844695v2/document
https://hal.archives-ouvertes.fr/hal-00844695/file/rizza2013.pdf
DOI : 10.1093/gji/ggt041

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
Two splitting procedures for solving equilibrium problems involving the sum of two bifunctions are proposed and their convergence is established under mild assumptions.
Journal of Mathematical Analysis and applications

hal-00779982
https://hal.univ-antilles.fr/hal-00779982
DOI : 10.1016/j.jmaa.2009.06.005

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
Most of the plate boundaries are activated obliquely with respect to the direction of far field stresses, as roughly only 8% of the plate boundaries total length shows a very low obliquity (ranging from 0 to 10°, sub-orthogonal to the plate displacement). The obliquity along plate boundaries is controlled by (i) lateral rheological variations within the lithosphere and (ii) consistency with the global plate circuit. Indeed, plate tectonics and magmatism drive rheological changes within the lithosphere and consequently influence strain localization. Geodynamical evolution controls large-scale mantle convection and plate formation, consumption, and re-organization, thus triggering plate kinematics variations, and the adjustment and re-orientation of far field stresses. These geological processes may thus result in plate boundaries that are not perpendicular but oblique to the direction of far field stresses. This paper reviews the global patterns of obliquity along plate boundaries. Using GPlate, we provide a statistical analysis of present-day obliquity along plate boundaries. Within this framework, by comparing natural examples and geological models, we discuss deformation patterns and kinematics recorded along oblique plate boundaries.
ISSN: 0040-1951

hal-01467188
https://hal.archives-ouvertes.fr/hal-01467188
DOI : 10.1016/j.tecto.2016.05.033

Éditeur(s) : HAL CCSD
Résumé : The Lesser Antilles is an area of high volcanic and earthquake activity, characterized by a 1000 km convergence zone resulting from the Atlantic plate subduction under the Caribbean plate with a slow convergent motion (2 cm/year). With five years of available data, the CDSA data base presents a more homogeneous vision of Lesser Antilles arc seismicity and allows detecting low seismic activity zones, in the north near the Virgin Islands, and in the south between St-Lucia and Grenada. The accuracy improvements of location is used to better study the relationship between tectonic structures and seismicity, to better define the subduction slab geometry, and to analyse the spatial variations of the Gutenberg-Richter law b-value. Concerning the 21 november 2004 Les Saintes earthquake, EMS98 intensities in Les Saintes islands were evaluated from an individual request and hypocenter relocalisations of the Les Saintes earthquake and the biggest aftershock of 14 february 2005 were made using a method of master/slave in order to contrain the seismic source of the mainchock. As seismic hazard assessment depends from strong ground motion generated by earthquakes, the last part of this work concerns modeling accelerometric records of the Les Saintes earthquakes, combining a composite source model with an empirical Green Function technique. In our study, we used Les Saintes aftershocks as Empirical Green Function.
L'arc des Petites Antilles situé sur la bordure nord-est de la plaque Caraïbe, résulte d'un phénomène de subduction, les plaques américaines plongeant sous celle de la Caraïbe avec une vitesse de 2 cm/an. Les Antilles Françaises représentent la région française où le risque sismique est le plus important. Ce travail dont l'objectif est d'améliorer la connaissance de l'aléa sismique dans les Antilles Françaises, repose sur les données du Réseau Accélérométrique Permanent (RAP) et sur celles du « Centre de Données des Antilles Françaises ». L'analyse de ces données permet de mieux contraindre la sismicité de l'arc. Deux zones de très faible sismicité sont mises en évidence : au nord près des Iles Vierges et au sud entre Sainte-Lucie et Grenade. D'autres points sont aussi résolus : imagerie de la subduction le long de l'arc, relations entre la sismicité superficielle et la tectonique active, variations de la pente (b-value) de la loi de Gutenberg-Richter. Le séisme majeur du 21 novembre 2004 Mw=6.3 est au cœur des deux derniers chapitres. Plusieurs aspects y sont présentés : macrosismicité avec l'évaluation d'intensités EMS98 obtenues du dépouillement de formulaires individuels recueillis pour les Iles des Saintes, et relocalisation par la méthode de maître/esclave du choc principal et de sa plus forte réplique du 14 février 2005, de façon à mieux contraindre l'imagerie de la source du choc principal, étape primordiale pour la dernière partie portant sur la modélisation des signaux du choc principal des Saintes. Nous tentons dans cette dernière partie de modéliser les enregistrements de mouvements forts avec une approche semi-empirique en se basant sur un modèle stochastique large-bande et proposons l'utilisation de plusieurs Fonctions de Green Empiriques (FGE) sélectionnées parmi les répliques du séisme des Saintes.
https://tel.archives-ouvertes.fr/tel-00409021

tel-00409021
https://tel.archives-ouvertes.fr/tel-00409021
https://tel.archives-ouvertes.fr/tel-00409021/document
https://tel.archives-ouvertes.fr/tel-00409021/file/these_BengoubouMendy_2008.pdf

Éditeur(s) : HAL CCSD Tsing Hua University
Résumé : International audience
This paper deals with variational inclusions of the form : $0in varphi(z)+F(z)$ where $varphi$ is a single-valued function admitting a second order Fréchet derivative and $F$ is a set-valued map from $R^q$ to the closed subsets of $R^q$. In order to approximate a solution $bar z$ of the previous inclusion, we use an iterative scheme based on a multipoint method. We obtain, thanks to some semistability properties of $bar z$, local superquadratic or cubic convergent sequences
ISSN: 1607-2510

hal-00728816
https://hal.archives-ouvertes.fr/hal-00728816

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
Taking advantage of recent developments in the theory of generalized differentiation, we present an inverse mapping theorem for set-valued maps and prove its stability under small linear perturbations. Using variational convergences of set-valued mappings, we present as well an approximate version of our inverse theorem.
Journal of Mathematical Analysis and applications

hal-01023227
https://hal.archives-ouvertes.fr/hal-01023227
DOI : 10.1016/j.jmaa.2014.07.006

Éditeur(s) : HAL CCSD Hindawi Publishing Corporation
Résumé : International audience
This paper is concerned with the study of a penalization-gradient algorithmfor solving variational inequalities, namely, find x ∈ C such that Ax, y − x ≥ 0 for all y ∈ C, where A : H → H is a single-valued operator, C is a closed convex set of a real Hilbert space H. Given Ψ : H → ∪ { ∞} which acts as a penalization function with respect to the constraint x ∈ C, and a penalization parameter βk, we consider an algorithm which alternates a proximal step with respect to ∂Ψ and a gradient step with respect to A and reads as xk I λkβk∂Ψ −1 xk−1 − λkAxk−1 . Under mild hypotheses, we obtain weak convergence for an inverse strongly monotone operator and strong convergence for a Lipschitz continuous and strongly monotone operator. Applications to hierarchical minimization and fixed-point problems are also given and the multivalued case is reached by replacing themultivalued operator by its Yosida approximatewhich is always Lipschitz continuous.
ISSN: 0161-1712

hal-00776654
https://hal.univ-antilles.fr/hal-00776654
https://hal.univ-antilles.fr/hal-00776654/document
https://hal.univ-antilles.fr/hal-00776654/file/305856.pdf
DOI : 10.1155/2011/305856

Éditeur(s) : HAL CCSD Springer Verlag
Résumé : International audience
We consider a bilevel problem involving two monotone equilibrium bifunctions and we show that this problem can be solved by a simple proximal method. Under mild conditions, the weak convergence of the sequences generated by the algorithm is obtained. Using this result we obtain corollaries which improve several corresponding results in this field.
ISSN: 0925-5001

hal-00776657
https://hal.univ-antilles.fr/hal-00776657
DOI : 10.1007/s10898-009-9476-1

Éditeur(s) : HAL CCSD Springer Verlag
Résumé : International audience
Relying on the resolvent operator method and using Nadler's theorem, we suggest and analyze a class of iterative schemes for solving multivalued quasi-variational inclusions. In fact, by considering problems involving composition of mutivalued operators and by replacing the usual compactness condition by a weaker one, our result can be considered as an improvement and a significant extension of previously known results in this field.
ISSN: 1385-1292

hal-00780762
https://hal.univ-antilles.fr/hal-00780762
https://hal.univ-antilles.fr/hal-00780762/document
https://hal.univ-antilles.fr/hal-00780762/file/10.1.1.13.5012.pdf
DOI : 10.1023/B:POST.0000023199.34934.9f

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
The island of Taiwan is located on the convergent boundary between the Philippine Sea plate and the Chinese continental margin. It offers very active mountain building and collapsing processes well illustrated by the rugged topography, rapid uplift and denudation, young tectonic landforms, active faulting and numerous earthquakes. In this paper, using simple models, we have estimated vertical movements and associated absolute gravity variations which can be expected along a profile crossing the southern part of the island and probably suffering the highest rates of rising. The two different tectonic styles proposed for the island, thin-skinned and thick-skinned, were taken into account. Horizontal and vertical movements were modeled by an elastic deformation code. Gravity variations due to these deformations are then modeled at a second step. They are dominated by plate and free-air effects, i.e. elevation of the topography, with several mu Gal yr(-1). By comparison, gravity changes generated by mass transfers are weak: maximum 0.1 mu Gal yr(-1) with the thin-skinned tectonic and 0.3 mu Gal yr(-1) with the thick-skinned tectonic. Though elastic rheology has limitations, this modeling offers interesting results on what gravity signal can be expected from the AGTO project (Absolute Gravity in the Taiwanese Orogen), which proposes to study the dynamic of these mountain ranges using absolute gravimetry (AG) and also including relative gravimetry (RG) and GPS measurements.
ISSN: 0264-3707

hal-00456035
https://hal.archives-ouvertes.fr/hal-00456035
DOI : 10.1016/j.jog.2009.09.004

Éditeur(s) : HAL CCSD
Résumé : In this note we show that the splitting scheme of Passty [7] as well as the barycentric-proximal method of Lehdili & Lemaire [4] can be used to approximate a zero of the extended sum of maximal monotone operators. When the extended sum is maximal monotone, we extend the convergence result obtained by Lehdili & Lemaire for convex functions to the case of maximal monotone operators. Moreover, we recover the main convergence results by Passty and Lehdili & Lemaire when the pointwise sum of the involved operators is maximal monotone.
https://hal.univ-antilles.fr/hal-00783905

hal-00783905
https://hal.univ-antilles.fr/hal-00783905
https://hal.univ-antilles.fr/hal-00783905/document
https://hal.univ-antilles.fr/hal-00783905/file/10.1.1.165.7044.pdf

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
Past studies have shown that high coastal uplift rates are restricted to active areas, especially in a subduction context. The origin of coastal uplift in subduction zones, however, has not yet been globally investigated. Quaternary shorelines correlated to the last interglacial maximum (MIS 5e) were defined as a global tectonic benchmark (Pedoja et al. (2011)). In order to investigate the relationships between the vertical motion and the subduction dynamic parameters, we cross-linked this coastal uplift database with the "geodynamical" databases from Heuret (2005), Conrad and Husson (2009) and Müller et al. (2008). Our statistical study shows that: [1] the most intuitive parameters one can think responsible for coastal uplift (e.g., subduction obliquity, trench motion, oceanic crust age, interplate friction and force, convergence variation, dynamic topography, overriding and subducted plate velocity) are not related with the uplift (and its magnitude); [2] the only intuitive parameter is the distance to the trench which shows in specific areas a decrease from the trench up to a distance of ~300 km; [3] the slab dip (especially the deep slab dip), the position along the trench and the overriding plate tectonic regime are correlated with the coastal uplift, probably reflecting transient changes in subduction parameters. Finally we conclude that the first order parameter explaining coastal uplift is small-scale heterogeneities of the subducting plate, as for instance subducting aseismic ridges. The influence of large-scale geodynamic setting of subduction zones is secondary.
ISSN: 0264-3707

hal-00968538
https://hal.archives-ouvertes.fr/hal-00968538
https://hal.archives-ouvertes.fr/hal-00968538/document
https://hal.archives-ouvertes.fr/hal-00968538/file/henryterraces_v2.pdf
DOI : 10.1016/j.jog.2014.04.001

Éditeur(s) : HAL CCSD Météo et Climat
Résumé : International audience
Le premier volet du projet Cyprim vise à mieux identifier les précurseurs des cyclogenèses et des précipitations intenses en région méditerranéenne. Cet article en présente les principaux résultats. Il est question des ingrédients météorologiques à l'origine de ces systèmes, de la grande à la mésoéchelle, des causes des fortes intensités, localisations et parfois stationnarité des récipitations associées. Le coeur de l'article présente des méthodes d'identification des anomalies de tourbillon potentiel liées à l'occurrence d'événements précipitants intenses et dresse une climatologie de ces anomalies. Les perspectives d'exploitation de cette information pour améliorer la qualité des prévisions sont évoquées. ENGLISH VERSION: The first part of the CYPRIM project (Cyclogenesis and intense precipitations in the Mediterranean region) aims at a better identification of the precursor structures of cyclogenesis and heavy precipitation in the Mediterranean region. This article presents the main results. It mentions the meteorological ingredients from which these systems originate from the large to themesoscale, the reasons for large intensities, the localization and sometimes stationarity of the associated precipitations. The heart of the article shows methods for identifiying potential vorticity anomalies involved in the occurrence of heavy precipitation events and sets up a climatology of these anomalies.The perspectives of the usefulness of this information for improving forecast quality are discussed.
ISSN: 0026-1181

insu-00448250
https://hal-insu.archives-ouvertes.fr/insu-00448250
DOI : 10.4267/2042/28828

Éditeur(s) : HAL CCSD Springer Verlag
Résumé : International audience
Selected high-resolution seismic-reflection profiles and multibeam bathymetry acquired along the convergent Ecuador margin during the ATACAMES cruise on onboard the R/V L’Atalante (Jan.15–Feb.18, 2012) allow a preliminary evaluation of the neotectonic development and stratigraphic evolution of the margin based on the sismo-stratigraphic analysis of Quaternary sediment preserved on the margin shelf and upper slope. We present three major preliminary results. (1) The evolution of the Esmeraldas, Guayaquil and Santa Elena canyons. The head of the Esmeraldas canyon is the location of a continuous significant sediment transport. The Guayaquil canyon shows several episodes of deposition and incision. Aggrading sedimentation pattern in the canyon records several changes in relative sea-level. The subsidence of the Gulf of Guayaquil probably contributes to the good preservation of the canyon filling stages. The Santa Elena canyon is controlled by a SW–NE trending normal fault. (2) Variations of sediment accumulation and relative vertical motions are shown along-strike the shelf edge. Offshore the uplifted Manta peninsula, a pronounced subsidence of the shelf edge is documented by sedimentary clinoforms that have deposited in a morphological reentrant, and have migrated upslope testifying of a local subsidence meanwhile the adjacent La Plata Island area underwent uplift. In the Esmeraldas canyon area, a local uplift of the shelf is documented. (3) Two neotectonic fault systems with a possible transcurrent component are imaged across the shelf edge and upper margin slope offshore Jama, and Cape Galera. This possible transcurrent motion could be related to the reactivation of ancient faults of the upper plate by the subduction. These preliminary results indicate that the ATACAMES data set has a strong potential to evaluate the spatial and temporal contribution of tectonic and climate changes on the structural development and stratigraphic evolution of the Ecuador continental margin.
ISSN: 0025-3235

insu-01131151
https://hal-insu.archives-ouvertes.fr/insu-01131151
DOI : 10.1007/s11001-014-9231-y