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本文用有限差分法模拟研究二维空间中波的传播、散射及其与介质间断的相互作用。文章第一部分运用所模拟的纵波波源讨论了半无限空间表面台阶地形或槽形裂隙所造成的波的散射。这些间断可模拟具有波长量级的悬崖或狭谷。第二部分用差分法与扰动法结合而成的混合法处理半无限空间表面有另一种物质构成的表面浅障碍时波的传播,以模拟山脊、堑沟等地形的影响。此混合法也被用于讨论半无限空间内含有水平夹层或孔隙的问题。所得研究结果对波的传播及其与介质间断的相互作用的理论研究和地震波破坏效应的分析和隔离等应用研究有一定的意义。
In this paper, the finite difference method is used to simulate and study the wave propagation and scattering in two-dimensional space and its interaction with the medium discontinuity. The first part of the paper discusses the scattering of waves caused by surface landform or groove cracks in a semi-infinite space using the simulated longitudinal wave source. These discontinuities can simulate cliffs or valleys with wavelength orders. In the second part, the mixed method of difference method and perturbation method is used to deal with the propagation of shallow obstacles on the surface of semi-infinite space, which simulates the influence of topography such as ridges and depressions. This mixing method is also used to discuss the problem of horizontal interlayers or pores in a semi-infinite space. The obtained results have certain significance for the theoretical study of the wave propagation and its interaction with the medium interruption and the analysis and isolation of seismic wave damage effects.