Thesis: When an earthquake occurs, the wave field generated by the fault propagates through the earth crust then with in surfaces geological layers before reaching the earth's surface. In order to understand how these seismic waves propage from the fault till surface buildings or structures, it is possible to use numerical simulations of the wave propagation. This research project focuses particularly on the physical phenomena that take place within the superficial geological layers while taking into account the spatial variability of soil properties, non-linear behaviors and complex basin geometries