Apparent motion as hyperacuity phenomenon under low two-point spatial resolution

Abstract

In this study, we analyze the acceleration time histories data at the Belleplaine (Guadeloupe, French West Indies) vertical array, recorded between 2008 and 2014, to evaluate the seismic response of sediments. First, we apply seismic interferometry by deconvolution method to compute the in-situ shear wave velocity between the sensor at the surface and the two shallow sensors located at GL-15m and GL-39m depth. The efficiency of this method is discussed by studying the variability of the velocity profile obtained and comparing with the in-situ geophysical survey of the site. Computed strains between sensors remain very weak, lower than 10−5, meaning that nonlinearities are not expected for these events. Moreover, the small dispersion of shear wave velocities values deduced from seismic interferometry may be related to the elastic behavior of the soil column. Furthermore, the transfer functions between each sensor combination are inverted to obtain a new velocity profile compatible with the geological knowledge of the site. The lag times calculated by seismic interferometry are then used to constrain random perturbations of the inverted velocity profile, allowing to study the variability of the 1D soil response. Since recorded motion has a PGA less than 10 cm/s2 in the dataset, we numerically predict the nonlinear response of the site using strong motion from a worldwide dataset. Furthermore, we study the ratio between the PGV and the medium shear velocity as a proxy showing the development of shear deformation during strong motion. Finally, using strong motion events from a worldwide dataset, we numerically predict the nonlinear response of the site based on shear wave velocity variation and the strain proxy computed by the particle velocity versus shear wave velocity ratio. We conclude that seismic interferometry by deconvolution is a robust and accurate solution to help extracting the shear wave velocity profile and to monitor the soil nonlinear response. This technique can be used when strong earthquakes will be recorded at this experimental site in order to track and assess nonlinear effects in the soil column.