Impact of Geometric Effects on Near-Surface Green's Functions
Résumé
This article investigates the impact of 2D and 3D geometric effects (i.e., topography and nonhorizontal-layering effects) on Green's functions and spectral ratios inside vertical arrays by using numerical simulations. All simulations are carefully performed by a spectral-element method of order six and are valid in the frequency range 0.05-10 Hz. Analysis reveals that a surface-to-downhole spectral ratio is a very sensitive physical variable with respect to problem's geometry; and, consequently, it should be analysed with care. We found that a small change in the waveform relative to the 1D theory can strongly affect the resonant modes. For the configuration of our 2D and 3D wave propagation problems, we show the cause of this sensitivity is mainly due to the downhole Green's function that is more affected by the geometry than the free surface Green's function. As a result, both amplitude and frequency of a resonant mode can deviate from the 1D theory because of 2D/3D geometric effects. We also found the amplitude of resonant modes was mostly lower relative to the 1D theory because of geometric scattering. As a consequence, the quality factors inverted so far from spectral ratios based on 1D theory are expected to be underestimated. Because the resonant frequencies are also affected by geometric effects, the S-wave velocity of soil layers inverted from 1D theory can be biased as well. For example, we show that the fundamental frequencies computed around small hills sometimes underestimate, sometimes overestimate the fundamental frequency of a 1D problem