Characterization for wave equations in viscoelastic media based on the constant Q property*

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Abstract The constant Q property in viscoelastic media assumes that the quality factor Q does not change with frequency (i.e., the Q value is independent of the frequency). For seismic waves propagating in viscoelastic media, the wave equation is determined by the viscoelastic media model. Equivalence relations exist between various frequency domain mathematical models and physical rheological models for the constant Q property. Considering two elastic moduli and three attenuation variables, 24 kinds of wave equations based on different generalized rheological models are divided into six classes in this study, and the 12 kinds of specific representation for the wave equations in the time domain are derived. On the basis of the equivalence relations between the generalized rheological models, the diff erence and equivalence relation between different wave equations are proven and clarified. Results show that the high-order generalized rheological model can accurately characterize the attenuation characteristics of seismic waves and has advantages in characterizing the dispersion characteristics in viscoelastic media. Lastly, the seismic reflection characteristics caused by the difference of Q value are verifi ed by the forward modeling of the constant Q wave equation in this study, thereby providing a theoretical basis for the analysis and inversion of the formation Q value from reflection seismic data.

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Key words： viscoelastic media constant Q wave equation seismic wave attenuation rheology theory

Received: 2019-12-20;

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This work was supported by National Natural Science Foundation of China (No. 41774137) and 111 project (No. B18055),and the Fundamental Research Funds for the Central Universities (No. 19CX02002A).

Corresponding Authors: Cao Dan-Ping (Email: caodp@upc.edu.cn)
E-mail: caodp@upc.edu.cn

About author: Liang Kai received his Ph.D.(2009)degrees in geological resources and geological engineering from China University of Petroleum (East China). Now he is a lecturer of the same university, and his main research interests are the seismic wave propagation, and forward modeling in complex media. Email: liangkai@upc.edu.cn Communication author: Cao Danping received his M.S. (2004) and Ph.D.(2009) degrees in applied geophysics from China University of Petroleum (East China). Now he is a professor of the same university, and his main research interests are the numerical modeling of seismic waves, seismic inversion, and reservoir prediction. Email: caodp@upc.edu.cn

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. Characterization for wave equations in viscoelastic media based on the constant Q property*[J]. APPLIED GEOPHYSICS, 2020, 17(4): 561-575.

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