A mathematical model developed by Zhang et al. [Modeling wave propagation in cracked porous media with penny-shaped inclusions. Geophys. 2019;84(4):1–11. doi:10.1190/GEO2018-0487.1] for wave motion in a cracked porous solid with penny-shaped inclusions is solved for the propagation of harmonic plane waves. The solution is obtained in the form of Christoffel equations. The solution of Christoffel equations demonstrates the existence of four (three longitudinal and one transverse) waves in the cracked porous solid. The behavior of the considered medium is dissipative as both host medium and inclusions are filled with the same viscous fluid. So, all the waves are inhomogeneous in nature. A finite non-dimensional parameter is used to represent the inhomogeneity character of an inhomogeneous wave. The phenomenon of reflection is investigated in two situations (i.e. sealed and opened surface pores) at the stress-free plane surface of a cracked porous solid. Further, the partition of incident energy is calculated in the form of an energy matrix. A numerical example is taken to discuss the effects of various properties on the partition of incident energy. The conservation of incident energy at each angle of incidence is prevailed in both situations.

张等人开发的数学模型。[模拟具有便士形夹杂物的破裂多孔介质中的波传播。地球物理学。2019;84(4):1-11。doi:10.1190/GEO2018-0487.1] 求解带有便士形夹杂物的破裂多孔固体中的波动，以解决谐波平面波的传播问题。该解以 Christoffel 方程的形式获得。Christoffel 方程的解表明在破裂的多孔固体中存在四个（三个纵向和一个横向）波。所考虑的介质的行为是耗散的，因为宿主介质和夹杂物都充满了相同的粘性流体。所以，所有的波在本质上都是不均匀的。一个有限的无量纲参数用于表示非均匀波的非均匀性特征。在裂纹多孔固体的无应力平面上，在两种情况下（即密封和开放的表面孔隙）研究了反射现象。此外，入射能量的划分以能量矩阵的形式计算。举一个数值例子来讨论各种性质对入射能量分配的影响。在这两种情况下，每个入射角的入射能量守恒都是普遍存在的。