Non-uniqueness of reflected and transmitted waves

Abstract

Although many numerical and instrumental studies over the last decades have focused on studying the effects of subsurface geometry on seismic ground motion, it has not yet been feasible to incorporate such effects into regular engineering practice, seismic building codes, earthquake hazard assessment and risk mitigation policies. In the present work, extensive numerical analyses of the linear viscoelastic response of trapezoidal sedimentary basins are performed to investigate the sensitivity of their 2D seismic response attributes to parameters related to the geometry of the basin (width, thickness and inclination angles of lateral boundaries) and the dynamic soil properties (shear and compressional wave velocities, soil density and attenuation). Basin effects are quantified and discussed through a period-dependent “aggravation factor”, defined as the ratio between 2D and 1D acceleration response spectra at the basin surface. This aggravation factor expresses the additional effect of the 2D response at different locations along the basin with respect to the corresponding 1D response that is normally accounted for in building codes. In order to identify the maximum amplification of ground motion that can be attributed to the 2D response of the basin, the main focus is put on the maximum values of aggravation factors, as well as their spatial distribution. It is shown that above the sloping edge of the basin, maximum values of aggravation factors less than one may occur, meaning that 2D response is deamplified with respect to the corresponding 1D response, particularly for steep slopes. At the nearly constant-depth part of the basin, maximum aggravation factors strongly depend on the shape ratio of the basin, defined as the ratio of the maximum thickness of the basin to its half-width. A general increase is observed with the shape ratio and the increase is more pronounced at the central part of the basin, where for high shape ratio, i.e. deep and narrow valleys, the computed median values are as high as 1.8 and 84th percentiles around 2.3. Maximum aggravation factors are higher and exhibit a larger scattering for basins with higher values of fundamental period at the center T0,c.