Résumé
Different applications of linear elasticity in structural geology are presented in this thesis through the development of three types of numerical computer codes. The first one uses forward modeling to study displacement and perturbed stress fields around complexly faulted regions. We show that incorporating inequality constraints, such as static Coulomb friction, enables one to explain the angle of initiation of jogs in extensional relays. Adding heterogeneous material properties and optimizations, such as parallelization on multicore architectures and complexity reduction, admits more complex models. The second type deals with inverse modeling, also called parameter estimation. Linear slip inversion on faults with complex geometry, as well as paleo-stress inversion using a geomechanical approach, are developed. The last type of numerical computer code is dedicated to restoration of complexly folded and faulted structures. It is shown that this technique enables one to check balanced cross-sections, and also to retrieve fault chronology. Finally, we show that this code allows one to smooth noisy 3D interpreted faulted and folded horizons using geomechanics.