A semianalytical solution for one-dimensional transient wave propagation in a saturated single-layer porous medium with a fluid surface layer
A semianalytical solution for one-dimensional transient wave propagation in a saturated single-layer porous medium with a fluid surface layer
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具有流体表面层的饱和单层多孔介质中一维瞬态波传播的半解析解
DOI：
10.1002/nag.2978
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发表时间：
2019
影响因子：
4
通讯作者：
Li Yongqiang
中科院分区：
文献类型：
--
作者：
Shan Zhendong;Ling Daosheng;Xie Zhinan;Jing Liping;Li Yongqiang
本文研究了一维瞬态波在具有流体表层的饱和单层多孔介质中的传播。给出了动力渗透系数kf → ∞的特殊情况的解析解和任意动力渗透系数的一般情况的半解析解。采用本征函数展开法和精细时步积分法。该解以级数形式给出，因此，可以很容易地计算具有小渗透系数的饱和多孔介质的长期动力响应。首先将非齐次边界条件转化为齐次边界条件，然后得到流固系统的特征值和正交特征函数。最后，在时域的解决方案开发。由于该模型是一维的，不考虑几何衰减，只考虑饱和多孔介质中的衰减。利用该模型可以分析不同海底类型对声波在流体层中传播的影响，这在海洋声学和海洋地震学中具有重要意义。该解也可用于验证各种数值方法的精度。
One‐dimensional transient wave propagation in a saturated single‐layer porous medium with a fluid surface layer is studied in this paper. An analytical solution for a special case with a dynamic permeability coefficientkf→ ∞ and a semianalytical solution for a general case with an arbitrary dynamic permeability coefficient are presented. The eigenfunction expansion and precise time step integration methods are employed. The solution is presented in series form, and thus, the long‐term dynamic responses of saturated porous media with small permeability coefficients can be easily computed. We first transform the nonhomogeneous boundary conditions into homogeneous boundary conditions, and then we obtain the eigenvalues and orthogonal eigenfunctions of the fluid–solid system. Finally, the solutions in the time domain are developed. As the model is one dimensional, geometric attenuation is absent, and only the attenuation in the saturated porous medium is considered. We can apply this model to analyse the influences of different seabed types on the propagation of acoustic waves in the fluid layer, which is very important in ocean acoustics and ocean seismic. This solution can also be employed to validate the accuracies of various numerical methods.