Estimation of near‐surface quality factors by inversion of Rayleigh‐wave attenuation coefficients

Abstract

Quality factors of near-surface materials are as important as velocities of the materials in many applications. High-frequency (≥ 2 Hz) surface-wave data are generally inverted to determine near-surface shear (S)-wave velocities, in which only phase information of surface-wave data is utilized. Amplitude information of high-frequency surface-wave data can be used to determine quality factors of near-surface materials. Given S-wave velocity, compressional (P)-wave velocity, and Rayleigh-wave phase velocities, it is feasible to solve for S-wave quality factor QS and P-wave quality factor QP (for some specific velocity models) in a layered earth model down to 30 meters below the ground surface in many settings by inverting high-frequency Rayleigh-wave attenuation coefficients. Because an inversion system of this problem is unstable, we introduce a regularization parameter to limit a model length. Based on the linear nature of the inversion system, we search for a smooth model that is a trade-off solution between data (attenuation coefficient) misfit and model (quality factor) length. Several real-world examples demonstrate that the optimal regularization parameter can be found by the L-curve method and so can a smooth model.