  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 paper 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.
