Seismic multiples are a serious hindrance to hydrocarbon exploration in Australia. In particular, water bottom multiples can be very difficult to attenuate. This is because there often exists a strongly reflective sea floor which gives multiples large amplitudes when compared with the primary events they overlay, and secondly, because of a widely occurring velocity inversion, which seriously reduces the effectiveness of a very important class of multiple attenuation techniques.Multiple attenuation techniques can be classified according to the characteristic of the data which is used to discriminate against the multiples in conjunction with the operation behind the demultiple process. Common multiple attenuation processes include FK demultiple, Radon Demultiple, predictive deconvolution, wave equation based demultiple procedures and the family of techniques which come under the umbrella of Surface Multiple Attenuation (SMA). All of these techniques, given the right conditions, can be very effective. They also vary in price from very cheap (FK demultiple) through to expensive (wave equation based demultiple procedures).However, despite these procedures, and fifty odd years of research, there is no effective general solution to multiple problems off the coast of Western Australia and indeed in many regions around the world.Two new wavefield transformations, Multiple MoveOut (MMO) and IsoStretch Radial Trace (ISR), have been developed in this research to precondition data prior to the removal of surface related multiples by existing techniques. These form the basis of a new multiple attenuating procedure.MMO shifts the data so that the water bottom primary event is flattened and the simple water bottom multiples are also flat and periodic. Water bottom peg leg multiples are made approximately periodic.To solve the stretch problem introduced by the MMO transform, ISR ++ / interpolates oblique traces of constant stretch, which also map constant shot emergence angles. The water bottom primary and multiple events form a stationary time series after MMO and ISR. They are then amenable to removal by autoconvolution and predictive deconvolution.The results of the new procedure are demonstrated on two case studies from offshore Western Australia. It is shown to be more effective at removing both simple and peg leg water bottom multiples than traditional techniques. Finally, it is an inexpensive procedure, which does not require velocity analysis prior to its application.

Cette thµese est consacree à l'etude d'abstractions d'ensemble de traces adaptees µa l'analyse statique et aux transformations de programmes. Cette etude a ete menee dans le cadre de l'interpretation abstraite. Dans une premiµere partie, nous proposons un cadre general permettant de definir des analyses effectuant un partitionnement des traces. Cela permet en particulier d'utiliser des proprietes definies par l'histoire des executions, pou ecrire des disjonctions de proprietes abstraites utiles lors de l'analyse statique. Ainsi, nous obtenons des analyses plus efficaces, qui sont non seulement plus precises mais aussi plus rapides. La methode a ete implementee et eprouvee dans l'analyseur de code C Astree, et on obtient d'excellents resultats lors de l'analyse d'applications industrielles de grande taille. La seconde partie est consacree au developpement de methodes permettant d'automatiser le diagnostique des alarmes produites par un analyseur tel qu'Astree. En eff en raison de l'incompletude de l'analyseur, une alarme peut, soit reveler une veritable erreur dans le programme, soit provenir d'une imprecision de l'analyse. Nous proposons tout d'abord d'extraire des slices semantiques, c'est à ire des sous-ensembles de traces du programme, satisfaisant certaines conditions ; cette technique permet de mieux caracteriser le contexte d'une alarme et peut aider, soit àprouver l'alarme fausse, soit à montrer un veritable contexte d'erreur. Ensuite, nous definissons des familles d'analyses de dependances adaptees µa la recherche d'origine de comportements anormaux dans un programme, afin d'aider µa un diagnostique plus efficace des raisons d'une alarme. Les resultats lors de l'implementation d'un prototype sont encourageants. Enfin, dans la troisiµeme partie, nous definissons une formalisation generale de la compilation dans le cadre de l'interpretation abstraite et integrons diverses techniques de compilation certifiee dans ce cadre. Tout d'abord, nous proposons une methode fondee sur la traduction d'invariants obtenus lors d'une analyse du code source et sur la verification independante des invariants traduits. Ensuite, nous formalisons la methode de preuve d'equivalence, qui produit une preuve de correction de la compilation, en prouvant l'equivalence du programme compile et du programme source. Enfin, nous comparons ces methodes du point de vue theorique et µa l'aide de resultats experimentaux.

Quantum systems with finite Hilbert space where position x and momentum p take values in Z(d) (integers modulo d) are considered. Symplectic tranformations S(2ξ,Z(p)) in ξ-partite finite quantum systems are studied and constructed explicitly. Examples of applying such simple method is given for the case of bi-partite and tri-partite systems. The quantum correlations between the sub-systems after applying these transformations are discussed and quantified using various methods. An extended phase-space x-p-X-P where X, P ε Z(d) are position increment and momentum increment, is introduced. In this phase space the extended Wigner and Weyl functions are defined and their marginal properties are studied. The fourth order interference in the extended phase space is studied and verified using the extended Wigner function. It is seen that for both pure and mixed states the fourth order interference can be obtained.

Quantum systems with finite Hilbert space where position x and momentum p take values in Z(d) (integers modulo d) are considered. Symplectic tranformations S(2¿,Z(p)) in ¿-partite finite quantum systems are studied and constructed explicitly. Examples of applying such simple method is given for the case of bi-partite and tri-partite systems. The quantum correlations between the sub-systems after applying these transformations are discussed and quantified using various methods. An extended phase-space x¿p¿X¿P where X, P ¿ Z(d) are position increment and momentum increment, is introduced. In this phase space the extended Wigner and Weyl functions are defined and their marginal properties are studied. The fourth order interference in the extended phase space is studied and verified using the extended Wigner function. It is seen that for both pure and mixed states the fourth order interference can be obtained. / Ministry of Higher Education, Sultanate of Oman

This work aims at rendering 3D scene using ray tracing. It describes advantages and disadvantages of this technology and its alternation known as distributed ray tracing. Other part deals with method from different branch, which are closely related to distributed ray tracing - constructive solid geometry and procedural texturing.

Cette thèse traite de l'intégration et de la réduction symbolique des systèmes d'équations différentielles ordinaires non-linéaires autonomes. Ces systèmes sont étudiés localement au voisinage d'un point simple ou singulier. Pour réduire ces systèmes à une forme intégrable, nous utilisons des transformations telles que les transformations quasi-monomiales, les éclatements et des constructions de formes normales. Ces méthodes permettent d'intégrer tout système à deux dimensions et des systèmes non-nilpotents à trois dimensions. Pour les systèmes nilpotents en trois dimensions et les systèmes de dimension supérieure nous rencontrons de nouvelles difficultés. La forme des cônes contenant le support de tels systèmes peut être très compliquée et cela complique l'utilisation des algorithmes introduits précédemment. Nous proposons alors une autre approche, basée sur une extension du diagramme de Newton et permettant de résoudre ces systèmes.