Modeling Rayleigh wave in viscoelastic media with constant Q model using fractional time derivatives

• Published in: Journal of applied geophysics 2024-11, Vol.230, p.105544, Article 105544
• Main Authors: Fan, Jianyu, Zhu, Peimin, Cai, Wei, Xu, Zhiwei, Yuan, Yuefeng
• Format: Article
• Language: English
• Subjects: Constant-Q model; Fractional derivatives; Low-Q media; Rayleigh waves
• ISSN: 0926-9851
• DOI: 10.1016/j.jappgeo.2024.105544

The propagation of seismic waves within the near-surface weathering layers, characterized by their low-quality factors (Q), is often accompanied by strong attenuation and dispersion phenomena. Among these, the Rayleigh wave, with its sensitivity to dispersion, has proven to be a powerful tool for near-surface exploration. We propose a novel approach for simulating Rayleigh wave propagation in such low-Q media. Our method uses the time-domain fractional wave equation with memory effect, based on Kjartansson's constant-Q (CQ) model, for accurate characterization of the propagation process. To solve numerically the wave equation with the fractional derivatives, we employ a finite-difference method combined with the auxiliary differential equation-perfectly matched layer (ADE-PML) and the acoustic-elastic boundary approach (AEA). The algorithm's high computational accuracy is verified through comparison with the conventional integer-order wave equation based on the nearly constant-Q (NCQ) models in strong attenuation media. The research in this paper deepens our understanding of the propagation characteristics of Rayleigh waves in strongly weathering layers. This new method strongly supports those seismic imaging and inversion methods depending on seismic modeling, including the reverse time migration and the full waveform inversion of the internal structure of low-Q media. •A novel modeling method based on CQ model is proposed for Rayleigh waves.•AEA are introduced into the fractional derivative wave equation for free boundary.•The modeling accuracy is verified by comparing with the analytical solution.•CQ model exhibits higher modeling accuracy in strongly attenuating media than NCQ.