Quantifying the influence of pressure on the effective elastic rock properties is important for applications in rock physics and reservoir characterization. Here I investigate the relationship between effective pressure and seismic velocities by performing inversion on the laboratory-measured data from a suite of clastic, carbonate and igneous rocks, using different analytic and discrete inversion schemes. I explore the utility of a physical model that models a natural fracture as supported by asperities of varying heights, when an effective pressure deforms the tallest asperities, bringing the shorter ones into contact while increasing the overall fracture stiffness. Thus, the model is known as the ?asperity-deformation? (ADM) or ?bed-of-nails? (BNM) model. Existing analytic solutions include one that assumes the host rock is infinitely more rigid than the fractures, and one that takes the host-rock compliance into account. Inversion results indicate that although both solutions can fit the data to within first-order approximation, some systematic misfits exist as a result of using the rigid-host solution, whereas compliant-host inversion returns smaller and random misfits, yet out-of-range parameter estimates. These problems indicate the effects of nonlinear elastic deformation whose degree varies from rock to rock. Consequently, I extend the model to allow for the pressure dependence of the host rock, thereby physically interpreting the nonlinear behaviors of deformation. Furthermore, I apply a discrete grid-search inversion scheme that generalizes the distribution of asperity heights, thus accurately reproduces velocity profiles, significantly improves the fit and helps to visualize the distribution of asperities. I compare the analytic and numerical asperity-deformation models with the existing physical model of elliptical ?pennyshape? cracks with a pore-aspect-ratio (PAR) spectrum in terms of physical meaning and data-fitting ability. The comparison results provide a link and demonstrate the consistency between the use of the two physical models, making a better understanding of the microstructure as well as the contact mechanism and physical behaviors of rocks under pressure. ADM-based solutions, therefore, have the potential to facilitate modeling and interpretation of applications such as time-lapse seismic investigations of fractured reservoirs.

Afin d’améliorer la durée de vie des micro-relais MEMS ohmiques, plusieurs traitements de surface de films minces d’or sont réalisés pour augmenter leur dureté tout en conservant une résistance électrique de contact faible.Les revêtements ultrafins de ruthénium (20 à 100 nm) déposés sur l’or augmentent la dureté des surfaces de contact d’un facteur 15. L’implantation ionique de bore ou d’azote (3,5 ppm à 10 % atomique) à une profondeur de 100 nm dans le film mince d’or permet d’atteindre un gain en dureté de 75%. Le contrôle (AFM, EBSD et DRX) de la microstructure induite met en évidence le durcissement par solution solide par insertion. Mais au-delà de 1% atomique, les atomes d’azote quittent le réseau cristallin de l’or pour former des précipités de nitrure d’or.L’analyse AFM (rugosité et diamètre) des empreintes résiduelles (quelques μm²) réalisées par nano-indentation sphérique, imitant le cyclage et le fluage des surfaces de contact de ces MEMS, démontre l’apport de ces traitements de surface. De plus, leurs résistances électriques de contact, mesurées par nano-indentation instrumentée reproduisant un micro-contact identique à un dispositif réel, sont similaires à celle de l’or pur.La modélisation discrète mécanique du contact rugueux est ajustée à la mesure de la déformation mécanique de nano-rugosités en comparant les relevés topographiques réalisés par AFM avant et après nano-indentation sphérique. La comparaison entre la modélisation et la mesure de la résistance électrique de contact indique que pour les gammes de force utilisées dans les micro-relais MEMS (inférieure au mN), seule une fraction allant de 2% à 9% de la surface de contact réelle est conductrice. / Ohmic MEMS switches made by gold thin films are promising devices but their mechanical contacts are one of the critical concerns for enhancing reliability. For this reason, surface processes are investigated in this work to improve both mechanical and electrical contact resistance (ECR) of MEMS gold contacts. Ruthenium ultra-thin films (20 to 100 nm) deposited on a top of gold layer increase surface hardness by a factor of fifteen. In parallel, surface implantations of both boron (<10% atomic) or nitrogen (<0.1% atomic) into gold reveals a solid solution hardening by insertion, thus increasing the hardness of initial film by about 75% and 25%, respectively. Notably, above 0.1% atomic of nitrogen, atoms precipitate from the tetra or octahedral sites of gold inducing a decrease of hardness.Static and multi load/unload spherical nano-indentation are performed on treated gold thin films to simulate the mechanical actuation of ohmic MEMS switches. Analysis of residual imprints (about few µm²) from treated surface exhibits both minimal local deformation and adhesion forces that reduce stiction probability. In-situ measurement of ECR for treated gold by instrumented nano-indentation, reproducing the design of MEMS, is in the same range of pure gold-to-gold configuration.A new mechanical discrete model of rough contact is introduced, confronted and validated to the experimental mechanical surface deformation obtained by comparison of AFM images before and after spherical nano-indentation. An electrical discrete model is added and fitted to the ECR measurements. In ohmic MEMS switch load range (< 1 mN), the conductive area is found to be about 2% to 9% of the real contact area.