A spatial autocorrelation method for estimating Rayleigh-wave attenuation coefficients from microtremor array measurements

The velocity and attenuation structures of near-surface soils play an important role in controlling earthquake ground motions. While numerous passive techniques have been developed for estimating velocity structure, practical methods for estimating attenuation from microtremor array measurements remain limited. We developed a spatial autocorrelation (SPAC) method for estimating Rayleigh-wave attenuation coefficients using an attenuation-aware formulation of the SPAC coefficient. A theoretical analysis of directional aliasing showed that attenuation estimation requires denser azimuthal sampling than conventional phase-velocity estimation, motivating the use of a regular heptagonal array. The method uses a two-stage procedure in which initial estimates of phase velocity and the attenuation coefficient are obtained using a first-order approximation and then refined by fitting the complex SPAC coefficient. Synthetic data analyses demonstrated that the proposed method can recover attenuation coefficients under ideal conditions and clarified how directional aliasing, record length and sensitivity to attenuation affect the estimates. Comparison with a beamforming-based method showed that the proposed method is less sensitive to wavefield directionality and can be applied at longer wavelengths relative to the array size. The method was further validated using microtremor-like waveforms generated by independent P--SV wave-propagation simulations. Finally, a preliminary application to field microtremor records yielded attenuation coefficients that were broadly consistent across array sizes and with values expected from existing empirical attenuation relationships. These results demonstrate the applicability of the proposed method to passive estimation of Rayleigh-wave attenuation.