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为求解变速不均匀介质中波的传播问题,使用了利用瑞雷-里兹法的有限元技术。假定在地面上位移具有给定值,而在其它边界上亦满足狄里赫利边界条件。在这样条件下导出了求解波动方程的变分原理。讨论了一维和二维波动方程有限元数值解法数学原理。对变速介质模型得到了单元质量矩阵和刚度矩阵表达式。分析了数值计算结果,讨论了在变速介质中传播的地震波和过渡层反射波的动力学特征。认为介质中垂直速度梯度的存在是地震波振幅衰减的原因之一。介绍了二维介质模型数值解。计算结果支持所提出的方法。
To solve the problem of wave propagation in an inhomogeneous medium with variable speed, a finite element technique using Rayleigh-Leeds method was used. It is assumed that the displacement on the ground has a given value, while on other boundaries the boundary condition of Dirichlet is also satisfied. Under these conditions, the variational principle for solving the wave equation is derived. The mathematical principles of numerical solution of one-dimensional and two-dimensional wave equations are discussed. The mass matrix and stiffness matrix expression of the transmission medium model are obtained. The numerical results are analyzed, and the dynamic characteristics of seismic wave and transition wave reflected in the transmission medium are discussed. It is considered that the existence of vertical velocity gradient in the medium is one of the reasons for the amplitude attenuation of seismic waves. The numerical solution of two-dimensional media model is introduced. The results support the proposed method.