State Key Laboratory of Petroleum Resources and Prospecting, CNPC Key Lab of Geophysical Exploration, China University of Petroleum, 102249, Beijing, China.
Beijing Aeronautical Science and Technology Research Institute of COMAC, 102211, Beijing, China.
Sci Rep. 2017 Aug 31;7(1):10169. doi: 10.1038/s41598-017-10833-w.
In this paper, the lattice Boltzmann method (LBM) is employed to simulate wave propagation in viscous media. LBM is a kind of microscopic method for modelling waves through tracking the evolution states of a large number of discrete particles. By choosing different relaxation times in LBM experiments and using spectrum ratio method, we can reveal the relationship between the quality factor Q and the parameter τ in LBM. A two-dimensional (2D) homogeneous model and a two-layered model are tested in the numerical experiments, and the LBM results are compared against the reference solution of the viscoacoustic equations based on the Kelvin-Voigt model calculated by finite difference method (FDM). The wavefields and amplitude spectra obtained by LBM coincide with those by FDM, which demonstrates the capability of the LBM with one relaxation time. The new scheme is relatively simple and efficient to implement compared with the traditional lattice methods. In addition, through a mass of experiments, we find that the relaxation time of LBM has a quantitative relationship with Q. Such a novel scheme offers an alternative forward modelling kernel for seismic inversion and a new model to describe the underground media.
本文采用格子玻尔兹曼方法（LBM）模拟粘性介质中的波动传播。LBM 是一种通过跟踪大量离散粒子的演化状态来模拟波动的微观方法。通过在 LBM 实验中选择不同的弛豫时间，并使用谱比方法，可以揭示品质因数 Q 和 LBM 中参数τ之间的关系。在数值实验中，测试了二维（2D）均匀模型和两层模型，并将 LBM 结果与基于 Kelvin-Voigt 模型的粘弹性方程的有限差分法（FDM）计算的参考解进行了比较。由 LBM 得到的波场和振幅谱与由 FDM 得到的结果一致，这证明了具有单一弛豫时间的 LBM 的能力。与传统的格子方法相比，新方案相对简单且高效。此外，通过大量实验，我们发现 LBM 的弛豫时间与 Q 具有定量关系。这种新的方案为地震反演提供了一种替代的正演建模内核，并为描述地下介质提供了一种新的模型。
