Applied Geophysics ( IF 0.7 ) Pub Date : 2021-05-04 , DOI: 10.1007/s11770-020-0838-2 Liang Kai , Cao Dan-Ping , He Bing-Hong , Wu Guo-Chen
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 difference 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 verified 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.
中文翻译:
基于常数Q特性的粘弹性介质中波动方程的表征
粘弹性介质中的恒定Q属性假定品质因数Q不会随频率变化(即Q值与频率无关)。对于在粘弹性介质中传播的地震波,波动方程由粘弹性介质模型确定。对于恒定的Q特性,各种频域数学模型和物理流变模型之间存在等价关系。考虑到两个弹性模量和三个衰减变量,本研究将基于不同广义流变模型的24种波动方程分为6类,并推导了12种时域波动方程的具体表示形式。根据广义流变模型之间的等价关系,证明并阐明了不同波动方程之间的差异和等价关系。结果表明,高阶广义流变模型可以准确地表征地震波的衰减特性,并且在表征粘弹性介质中的色散特性方面具有优势。最后,通过对恒定Q波方程的正演模拟,验证了由Q值差异引起的地震反射特征,从而为反射地震资料中地层Q值的分析和反演提供了理论依据。结果表明,高阶广义流变模型可以准确地表征地震波的衰减特性,并且在表征粘弹性介质中的色散特性方面具有优势。最后,通过对恒定Q波方程的正演模拟,验证了由Q值差异引起的地震反射特征,从而为反射地震资料中地层Q值的分析和反演提供了理论依据。结果表明,高阶广义流变模型可以准确地表征地震波的衰减特性,并且在表征粘弹性介质中的色散特性方面具有优势。最后,通过对恒定Q波方程的正演模拟,验证了由Q值差异引起的地震反射特征,从而为反射地震资料中地层Q值的分析和反演提供了理论依据。