A theoretical framework for estimating Rayleigh wave attenuation based on the spatial autocorrelation method

Abstract The velocity and attenuation structures of near-surface soils play a critical role in controlling ground motions at the Earth’s surface, often exerting an influence disproportionate to their thinness. While numerous passive, in-situ techniques exist for estimating velocity structure, constraining attenuation remains challenging. In this study, we revised the theoretical foundation of the spatial autocorrelation (SPAC) method, originally developed for velocity structure estimation, and formulated an attenuation-aware SPAC coefficient as a theoretical basis for attenuation estimation. Calculations for a representative near-surface model revealed that attenuation effects are expressed in the imaginary part of the attenuation-aware SPAC coefficient. Synthetic data analyses further demonstrated that, while the imaginary part is sensitive to directional aliasing, it remains robust against stochastic and incoherent noise. The effect of directional aliasing was found to be mitigated by increasing the number of observation points, as in the conventional SPAC method.