平面波在双孔隙介质中球形夹杂上的散射

Scattering of plane wave by a spherical ideal fluid inclusion in a double-porosity medium

基于拓展的Biot孔隙介质弹性理论,将波函数展开法推广应用到求解平面压缩波在双孔隙介质中单球形理想流体夹杂上的散射问题中。在低频条件下,给出了问题解析解的形式,包括位移场和应力场。由进一步的数值计算结果可知:P1波和S波的一阶谐波振幅随着基质孔隙率的增大而减小,P2波的谐波振幅则增大,而P3波的谐波振幅基本不受其影响;随着裂隙孔隙率的增大,P1波的谐波振幅逐渐减小,P3波和S波的谐波振幅增大,而对P2波的谐波振幅的影响甚微;频率越高,双孔隙介质的基质孔隙率及裂隙孔隙率对其谐波振幅的影响越显著。

By using the wave expansion method,the scattering of plane longitudinal wave by a spherical ideal fluid inclusion in double-porosity medium is investigated.The medium is described by an extended Biot's theory of poroelasticity.At low frequencies,the explicit analytical solutions for harmonic amplitude,displacement field and stress field of the problem are obtained.Numerical results show that with the increasing of the matrix porosity,the first spherical harmonic amplitudes of P1 and S waves gradually decrease,while that of P2 wave increases.With the increasing of the fracture porosity,the amplitude of P1 wave decreases,while P3 and S waves gradually increase.The matrix porosity has almost no effect on the amplitude of P3 wave and so does the fracture porosity on P2 wave.It is also shown that the higher the frequencies,the more obvious effects of the matrix and fracture porosities on the amplitude of the waves.