Hu Ning, Wang Maofa, Qiu Baochun, Tao Yuanhong
Marine Technology and Equipment Research Center, Hangzhou Dianzi University, Hangzhou 310018, China.
School of Sciences, Zhejiang University of Science and Technology, Hangzhou 310023, China.
Materials (Basel). 2022 Jan 28;15(3):1020. doi: 10.3390/ma15031020.
The fractional-order differential operator describes history dependence and global correlation. In this paper, we use this trait to describe the viscoelastic characteristics of the solid skeleton of a viscoelastic two-phasic porous material. Combining Kjartansson constant Q fractional order theory with the BISQ theory, a new BISQ model is proposed to simulate elastic wave propagation in a viscoelastic two-phasic porous material. The corresponding time-domain wave propagation equations are derived, and then the elastic waves are numerically simulated in different cases. The integer-order derivatives are discretised using higher-order staggered-grid finite differences, and the fractional-order time derivatives are discretised using short-time memory central differences. Numerical simulations and analysis of the wave field characterisation in different phase boundaries, different quality factor groups, and multilayered materials containing buried bodies are carried out. The simulation results show that it is feasible to combine the constant Q fractional-order derivative theory with the BISQ theory to simulate elastic waves in viscoelastic two-phasic porous materials. The combination can better describe the viscoelastic characteristics of the viscoelastic two-phasic porous materials, which is of great significance for further understanding the propagation mechanism of elastic waves in viscoelastic two-phasic porous materials and viscoelastic two-phasic porous materials containing buried bodies. This paper provides a theoretical forward simulation for fine inversion and reconstruction of layer information and buried body structure in viscoelastic two-phasic porous materials.
分数阶微分算子描述了历史依赖性和全局相关性。在本文中，我们利用这一特性来描述粘弹性双相多孔材料固体骨架的粘弹性特征。将Kjartansson常数Q分数阶理论与BISQ理论相结合，提出了一种新的BISQ模型来模拟弹性波在粘弹性双相多孔材料中的传播。推导了相应的时域波传播方程，然后在不同情况下对弹性波进行了数值模拟。整数阶导数采用高阶交错网格有限差分进行离散，分数阶时间导数采用短时记忆中心差分进行离散。对不同相边界、不同品质因子组以及含埋藏体多层材料中的波场特征进行了数值模拟和分析。模拟结果表明，将常数Q分数阶导数理论与BISQ理论相结合来模拟粘弹性双相多孔材料中的弹性波是可行的。这种结合能够更好地描述粘弹性双相多孔材料的粘弹性特征，对于进一步理解弹性波在粘弹性双相多孔材料以及含埋藏体粘弹性双相多孔材料中的传播机制具有重要意义。本文为粘弹性双相多孔材料中层信息和埋藏体结构的精细反演与重建提供了理论正演模拟。
