Reliable Multimodal Attenuation Estimation of Surface Waves Using Diffuse Ambient Noise: Theory and Applications

Seismic ambient noise often lacks the ideal diffuse characteristics required to reliably reconstruct surface wave empirical Green's functions, particularly in terms of amplitude information for attenuation estimation. Conventional methods, such as long-time stacking and coherency measurements, rely on assumptions that the ensemble average exhibits diffuse wavefield properties and that only the fundamental surface wave mode is present. To overcome these limitations, we propose an advanced method for multimodal surface wave attenuation estimation. This approach incorporates diffuseness quantification and excludes non-diffuse waveform segments to improve coherency reliability. Additionally, we derive a theoretical expression for the multiple-mode noise field, with multimodal coherency represented as a weighted superposition of individual mode coherences. The theory is applied to isolated target modes in the frequency-wavenumber domain using spatially windowed frequency-Hankel transform pairs. We validate the method using synthetic diffuse noise data and subsequently apply it to a subset of the USArray and a quasi-linear array in the Tarim Basin. The proposed method not only strengthens the robustness of fundamental mode attenuation estimation but also enables the estimation of higher-mode attenuation. These reliable multimodal attenuation estimates can significantly improve the robustness of $Q$-value tomography, thereby advancing our understanding of Earth's interior.