波的传播及其与介质间断相互作用的数值模拟研究

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。

Numerical Modelling of Wave Propagation and Interaction

This paper investigates wave propagation and its interaction with discontinuities in media using numerical models which employ a finite difference method. The paper has two parts, the first of which considers wave propagation and scattering by simulating a compressive body source in a 2-D half-space containing a step or a slot on the surface, which represents a cliff or a rift valley that has dimensions of the order of the wavelength in the source. The second part of the paper reports a hybrid technique which combines a perturbation method and the finite difference method for wave propagation again caused by the body source in a 2-D half-space system but with a shallow surface obstacle, such as a smoothed ridge, with elastic constants slightly different from bulk material and the slops of the topography being shallow. This hybrid technique is also reported being applied to a half-space with a horizontal insert or void. Results obtained are of importance in both theoretical studies on wave propagation and interaction and applied researches on the analysis and isolation of the damage caused by seismic waves.