National Institute of Natural Hazards, Ministry of Emergency Management of China, Beijing 100085, China.
Rev Sci Instrum. 2021 Dec 1;92(12):125108. doi: 10.1063/5.0064186.
Compressional waves in saturated porous media are relevant to many fields from oil exploration to diagnostic of human cancellous bone and can be used to interpret physical behaviors of materials. In this work, based on Biot's theory in the low frequency range, a key finding is that there exists a critical frequency of Biot's theory in the low frequency range, which determines the coincidence of the properties of Biot waves of the first and second kinds. Furthermore, we have investigated the dispersion and attenuation of the coalescence of the first and second compressional waves in the low frequency range. The coalescence of the first and second waves is strongly attenuated with a moderate phase velocity and shows the in-phase feature. In addition, acoustic wave propagation has been calculated numerically using the space-time conservation element and solution element (CESE) method. The CESE-simulated results are compared to the experimental data and to those of the classical transfer function approach. We show that the CESE scheme preserves the local and global flux conservations in the solution procedure of Biot's theory. It is found that the CESE method provides more accurate predictions of high dispersion and strong attenuation of compressional waves in the low frequency range and is well suitable for predicting compressional wave fields in saturated porous media.
饱和多孔介质中的压缩波与从石油勘探到人类松质骨诊断等多个领域都相关，可用于解释材料的物理行为。在这项工作中，基于 Biot 理论在低频范围内的研究，我们的一个重要发现是，在低频范围内存在 Biot 理论的临界频率，这决定了第一类和第二类 Biot 波性质的一致性。此外，我们还研究了低频范围内第一类和第二类压缩波的合并的频散和衰减。第一类和第二类波的合并在中等相速度下被强烈衰减，并表现出同相特征。此外，我们还使用时空守恒元与解元（CESE）方法对声波传播进行了数值计算。CESE 模拟结果与实验数据以及经典传递函数方法的结果进行了比较。结果表明，CESE 方案在 Biot 理论的求解过程中保留了局部和全局通量守恒。研究结果发现，CESE 方法在低频范围内能够更准确地预测压缩波的高频散和强衰减，非常适合预测饱和多孔介质中的压缩波场。
