Array performances for ambient vibrations on a shallow structure and consequences over Vs inversion

Valuable information about one-dimensional soil structures can be obtained by recording ambient vibrations at the surface, in which the energy contribution of surface waves predominates over the one of other types of waves. The dispersion characteristics of surface waves allow the retrieval of the shear-wave velocity as a function of depth. Microtremor studies are usually divided in two stages: deriving the dispersion (or auto-correlation) curve from the recorded signals and inverting it to obtain the site velocity profile. The possibility to determine the dispersion curve over the adequate frequency range at one site depends on the array aperture and on the wavefield spectra amplitude that can be altered by filtering effects due to the ground structure. Microtremors are usually recorded with several arrays of various apertures to get the spectral curves over a wide frequency band, and different methods also exist for processing the raw signals. With the objective of defining a strategy to achieve reliable results for microtremor on a shallow structure, we analyse synthetic ambient vibrations (vertical component) simulated with 333 broadband sources for a 25-m deep soil layer overlying a bedrock. The first part of our study is focused on the determination of the reliable frequency range of the spectral curves (dispersion or auto-correlation) for a given array geometry. We find that the wavenumber limits deduced from the theoretical array re sponse are good estimates of the valid spectral curve range. In the second part, the spectral curves are calculated with the three most popular noise-processing techniques (frequency–wavenumber, high-resolution frequency–wavenumber and spa tial auto-correlation methods) and inverted indi vidually in each case. The inversions are performed with a tool based on the neighbour hood algorithm that offers a better estimation of the global uncertainties than classical linearised methods, especially if the solution is not unique. Several array apertures are necessary to construct the dispersion (auto-correlation) curves in the appropriate frequency range. Considering the final velocity profiles, the three tested methods are almost equivalent, and no significant advantage was found for one particular method. With the chosen model, all methods exhibit a penetration limited to the bedrock depth, as a consequence of the filtering effect of the ground structure on the vertical component, which was observed in numerous shallow sites.