Simulation of seismic response in an idealized city

A noticeable feature of many earthquake-prone cities such as Kobe (Japan), Izmit (Turkey), Nice (France), Mexico City, Los Angeles etc., is that they are partially or wholly built on soft soil. A straightforward 1D analysis (which takes no account of the presence of the buildings) shows that the soft layer increases the seismic vulnerability of the city in that it is responsible for amplification of ground motion during an earthquake. However, the 1D model does not account either for the beating phenomena and very long codas in the building vibrations, nor for the large spatial variability of response, repeatedly observed in sites such as Mexico City. To analyze the possible causes of these puzzling effects, we study the action of a seismic wave on a relatively-simple structural model with both geological and man-made features. Our 2D model has three components (from bottom to top in Fig.1): a hard half space (HHS), overlaid by a soft soil layer (SL), in which are partially imbedded a set of even softer blocks (SB). HHS and SL are geological features, the set of SB, which are homogenized for the purpose of the analysis (see fig.2), is man-made and constitutes the ‘visible’ component of an idealized city. First consider the case in which the blocks are absent. Then the stress-free surface (upper boundary of the soft layer constituting the ground) is a straight horizontal line (in Fig.