Résumé : Dans cette thèse nous présentons dans un premier temps une nouvelle notion de différentiabilité généralisée pour les applications multivoques, faisant intervenir des applications positivement homogènes: la H-différentiabilité. Nous étudions la stabilité de cette notion en utilisant la convergence de Fischer, d'abord dédiée aux ensembles mais que nous avons adaptée aux applications multivoques. Nous nous intéressons ensuite à l'étude de la dépendance continue des ensembles de points fixes d'une application multivoque contractante par rapport aux données. Finalement nous analysons la convergence d'une méthode d'approximations successives de type forward-backward splitting, des zéros de la somme de deux opérateurs multivoques non monotones, jouissants notamment de propriétés de pseudo H-différentiabilité
In this thesis we present at first a new concept of generalized differentiation for setvalued mappings, involving positively homogeneous applications: the H-differentiability. We study the stability of this notion by using Fischer convergence,firstly dedicated to sets but which we have adapted to set-valued mappings. We establish the continuous dependence of fixed points sets of set-valued contraction and finally we study the convergence of a forward-backward splitting method for approximating the zeros of the sum of two non-monotone set-valued mappings, notably using properties of pseudo H-differentiability.

http://www.theses.fr/2011AGUY0490/document

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
The Gibraltar arc, spans a complex portion of the Africa-Eurasia plate boundary marked by slow oblique convergence and intermediate and deep focus seismicity. The seemingly contradictory observations of a young extensional marine basin surrounded by an arcuate fold-and-thrust belt, have led to competing geodynamic models (delamination and subduction). Geophysical data acquired in the past decade provide a test for these models and support a narrow east-dipping, subduction zone. Seismic refraction studies indicate oceanic crust below the western Gulf of Cadiz. Tomography of the upper mantle reveals a steep, east-dipping high P-wave velocity body, beneath Gibraltar. The anisotropic mantle fabric from SKS splitting shows arc-parallel "fast directions", consistent with toroidal flow around a narrow, westward retreating subducting slab. The accompanying WSW advance of the Rif-Betic mountain belt has constructed a thick pile of deformed sediments, an accretionary wedge, characterized by west-vergent thrust anticlines. Bathymetric swath‐mapping images an asymmetric embayment at the deformation front where a 2 km high basement ridge has collided. Subduction has slowed significantly since 5 Ma, but deformation of recent sediments and abundant mud volcanoes suggest ongoing activity in the accretionary wedge. Three possible origins for this deformation are discussed; gravitational spreading, overall NW-SE convergence between Africa and Iberia and finally a WSW tectonic push from slow, but ongoing roll-back subduction. In the absence of arc volcanism and shallow dipping thrust type earthquakes, evidence in favor of present-day subduction can only be indirect and remains the object of debate. Continued activity of the subduction offers a possible explanation for great (M > 8.5) earthquakes known to affect the area, like the famous 1755 Great Lisbon earthquake. Recent GPS studies show SW motion of stations in N Morocco at velocities of 3-6 mm/yr indicating the presence of an independent block, a "Rif-Betic-Alboran" microplate, situated between Iberia and Africa.
ISSN: 0040-1951

insu-00769762
https://hal-insu.archives-ouvertes.fr/insu-00769762
DOI : 10.1016/j.tecto.2012.08.038

Résumé : Cette thèse est consacrée à la résolution d'un problème fondamental de l'analyse variationnelle qu'est la recherchede zéros d'opérateurs maximaux monotones dans un espace de Hilbert. Nous nous sommes tout d'abord intéressés au cas de l'opérateur somme étendue de deux opérateurs maximaux monotones; la recherche d'un zéro de cet opérateur est un problème dont la bibliographie est peu fournie: nous proposons une version modifiée de l'algorithme d'éclatement forward-backward utilisant à chaque itération, l'epsilon-élargissement d'un opérateur maximal monotone,afin de construire une solution. Nous avons ensuite étudié la convergence d'un nouvel algorithme de faisceaux pour construire ID zéro d'un opérateur maximal monotone quelconque en dimension finie. Cet algorithme fait intervenir une double approximation polyédrale de l'epsilon-élargissement de l'opérateur considéré
This thesis is devoted to solving a basic problem of variational analysis which is the search of zeros of maximal monotone operators in a Hilbert space. First of aIl, we concentrate on the case of the extended som of two maximal monotone operators; the search of a zero of this operator is a problem for which the bibliography is not abondant: we purpose a modified version of the forward-backward splitting algorithm using at each iteration, the epsilon-enlargement of a maximal monotone operator, in order to construet a solution. Secondly, we study the convergence of a new bondie algorithm to construet a zero of an arbitrary maximal monotone operator in a finite dimensional space. In this algorithm, intervenes a double polyhedral approximation of the epsilon-enlargement of the considered operator

http://www.theses.fr/2012AGUY0548/document

Éditeur(s) : HAL CCSD American Geophysical Union
Résumé : International audience
We report measurements of long-period P wave polarization (P pol) in Australia and Tahiti made by combining modeling of the polarization deviation and harmonic analysis. The analysis of the deviation of the horizontal polarization of the P wave as a function of event back azimuth may be used to obtain information about (1) sensor misorientation, (2) dipping discontinuities, (3) seismic anisotropy, and (4) velocity heterogeneities beneath a seismic station. The results from harmonic analysis and a grid search using Snell's law suggest the presence of a dipping seismic discontinuity beneath stations CTAO and CAN in Australia. These results are consistent with published receiver function studies for these stations. The P pol fast axis orientation is close to the N–S absolute plate motion direction at station TAU (Tasmania), which may be due to plate-motion-driven alignment of olivine crystals in the asthenosphere. Interestingly, measurements of SKS splitting at Tahiti (French Polynesia) show an apparent isotropy, whereas an inversion of P pol observations at PPTL seismic station located in Tahiti suggests the presence of two anisotropic layers. The fast axis azimuth is oriented E–W in the upper layer, and it is close to the NW–SE orientation in the lower layer. Since P pol orientations are used for real-time earthquake locations, especially in poorly instrumented areas such as the South Pacific, we show that the bias from anisotropy and sensor misorientation determined here can be corrected to improve the location accuracy, which yields fundamental data for rapid location necessary for effective tsunami warning.
ISSN: 2169-9313

hal-01389113
http://hal.univ-reunion.fr/hal-01389113
http://hal.univ-reunion.fr/hal-01389113/document
http://hal.univ-reunion.fr/hal-01389113/file/Fontaine_Ppol_JGR2009.pdf
DOI : 10.1029/2008JB005709

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
We propose an extended forward-backward algorithm for approximating a zero of a maximal monotone operator which can be split as the extended sum of two maximal monotone operators. We establish the weak convergence in average of the sequence generated by the algorithm under assumptions similar to those used in classical forward-backward algorithms. This provides as a special case an algorithm for solving convex constrained minimization problems without qualification condition.
Journal of Mathematical Analysis and applications

hal-00761657
https://hal.archives-ouvertes.fr/hal-00761657
ARXIV : 1212.0523
DOI : 10.1016/j.jmaa.2013.02.022

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
A forward-backward inertial procedure for solving the problem of finding a zero of the sum of two maximal monotone operators is proposed and its convergence is established under a cocoercivity condition with respect to the solution set.
ISSN: 0377-0427

hal-00780778
https://hal.univ-antilles.fr/hal-00780778
https://hal.univ-antilles.fr/hal-00780778/document
https://hal.univ-antilles.fr/hal-00780778/file/10.1.1.12.4189.pdf
DOI : 10.1016/S0377-0427(02)00906-8

Éditeur(s) : HAL CCSD American Geophysical Union
Résumé : International audience
We report measurements of long-period P wave polarization (P-pol) in Australia and Tahiti made by combining modeling of the polarization deviation and harmonic analysis. The analysis of the deviation of the horizontal polarization of the P wave as a function of event back azimuth may be used to obtain information about (1) sensor misorientation, (2) dipping discontinuities, (3) seismic anisotropy, and (4) velocity heterogeneities beneath a seismic station. The results from harmonic analysis and a grid search using Snell's law suggest the presence of a dipping seismic discontinuity beneath stations CTAO and CAN in Australia. These results are consistent with published receiver function studies for these stations. The P-pol fast axis orientation is close to the N-S absolute plate motion direction at station TAU (Tasmania), which may be due to plate-motion-driven alignment of olivine crystals in the asthenosphere. Interestingly, measurements of SKS splitting at Tahiti (French Polynesia) show an apparent isotropy, whereas an inversion of P-pol observations at PPTL seismic station located in Tahiti suggests the presence of two anisotropic layers. The fast axis azimuth is oriented E-Win the upper layer, and it is close to the NW-SE orientation in the lower layer. Since P-pol orientations are used for real-time earthquake locations, especially in poorly instrumented areas such as the South Pacific, we show that the bias from anisotropy and sensor misorientation determined here can be corrected to improve the location accuracy, which yields fundamental data for rapid location necessary for effective tsunami warning.
ISSN: 2169-9313

hal-00413141
https://hal.archives-ouvertes.fr/hal-00413141
https://hal.archives-ouvertes.fr/hal-00413141/document
https://hal.archives-ouvertes.fr/hal-00413141/file/FontaineetalJGR2008.pdf
DOI : 10.1029/2008JB005709