P- and S-wave velocity models of shallow dry sand formations from surface wave multimodal inversion

Abstract

Surficial formations composed of loose, dry granular materials constitute a challenging target for seismic characterization. They exhibit a peculiar seismic behavior, characterized by a nonlinear seismic velocity gradient with depth that follows a power-law relationship, which is a function of the effective stress. The P- and S-wave velocity profiles are then characterized by a power-law trend, and they can be defined by two power-law exponents [Formula: see text] and two power-law coefficients [Formula: see text]. In case of depth-independent Poisson’s ratio, the P-wave velocity profile can be defined using the [Formula: see text] power-law parameters and Poisson’s ratio. Because body wave investigation techniques (e.g., P-wave tomography) may perform ineffectively on such materials because of high attenuation, we addressed the potential of surface-wave method for a reliable seismic characterization of shallow formations of dry, uncompacted granular materials. We took into account the dependence of seismic wave velocity on effective pressure and performed a multimodal inversion of surface-wave data, which allowed the [Formula: see text] and [Formula: see text] profiles to be retrieved. The method requires the selection of multimodal dispersion curve points referring to surface-wave frequency components traveling within the granular media formation and their inversion for the S-wave power-law parameters and Poisson’s ratio. We have tested our method on a synthetic dispersion curve and applied it to a real data set. In both cases, the surficial layer was made of loose dry sand. The test on the synthetic data set confirmed the reliability of the proposed procedure because the thickness and the [Formula: see text], [Formula: see text] profiles of the sand layer were correctly estimated. For the real data, the outcomes were validated by other geophysical measurements conducted at the same site and they were in agreement with similar studies regarding loose sand formations.