单相与多相介质中弹性波波速相关问题对比研究

Comparative study on wave velocity related problems of elastic waves in mono-phase and multi-phase media

从单相介质到双相及三相多孔介质,通过研究Rayleigh波波速与体波波速之间的关系,得到了3种介质下半空间表面Rayleigh波存在所需满足的条件,以及分析了其理论求解过程之间的联系与差异。对由两种不同定义式得到的平面弹性波传播速度进行了理论分析,并以双相多孔介质为例,通过数值计算直观地对两者进行了比较,结果表明:(1)对于快纵波(P1)和剪切波(S),两种传播速度随频率的变化曲线(即弥散曲线)重叠;(2)对于慢纵波(P2)和Rayleigh波,两条弥散曲线分离,两种传播速度在数值上存在一定差异;(3)两者随频率的变化趋势基本一致。弹性波波数虚部与实部的比值的数值计算结果验证了上述结论。

From mono-phase media to two-phase and three-phase porous media, through studying the relation between Rayleigh wave velocity and Body waves velocities,the conditions for the existence of the Rayleigh waves at the half-space surface of those three kinds of media are obtained. Moreover, the connection and difference among their theoretical solving processes are analyzed. The two kinds of elastic wave propagation velocities achieved by different definition formulas are compared theoretically. Taking two-phase porous medium as an example,numerical calculations are conducted in order to intuitively compare those two propagation velocities. The numerical results show that：（1） for the fast compressional wave （P1） and shear wave （S）, the variation curves of the two propagation velocities with frequency, known as dispersion curves,overlap each other;（2） For the slow compressional wave （P2） and Rayleigh waves,the two dispersion curves separate from each other, which means that discrepancy exists between the values of the two propagation velocities;（3） The variation trends of the two propagation velocities with frequency are basical-ly coincident. Finally, the numerical results of the ratio between the imaginary part and the real part of wave number verify those findings.