A frequency-domain beamforming procedure for extracting Rayleigh wave attenuation coefficients and small-strain damping ratio from 2D ambient noise array measurements

The small-strain damping ratio plays a crucial role in assessing the response of soil deposits to earthquake-induced ground motions and general dynamic loading. The damping ratio can theoretically be inverted for after extracting frequency-dependent Rayleigh wave attenuation coefficients from wavefields collected during surface wave testing. However, determining reliable estimates of in situ attenuation coefficients is much more challenging than achieving robust phase velocity dispersion data, which are commonly measured using both active-source and ambient-wavefield surface wave methods. This article introduces a new methodology for estimating frequency-dependent attenuation coefficients through the analysis of ambient noise wavefield data recorded by two-dimensional (2D) arrays of surface seismic sensors for the subsequent evaluation of the small-strain damping ratio. The approach relies on the application of an attenuation-specific wavefield conversion and frequency-domain beamforming. Numerical simulations are employed to verify the proposed approach and inform best practices for its application. Finally, the practical efficacy of the proposed approach is showcased through its application to field data collected at a deep, soft soil site in Logan, Utah, USA, where phase velocity and attenuation coefficients are extracted from surface wave data and then simultaneously inverted to develop deep shear wave velocity and damping ratio profiles.