Abstract In this paper the scattering of incident surface waves by an inclined subsurface crack in a homogenous, isotropic and linearly elastic half-space has been investigated in a two-dimensional plane strain configuration. The elastodynamic reciprocity theorem together with a virtual wave has been used to determine the amplitude of the scattered surface waves in the far field. It is found that the amplitude is in terms of the crack opening volume due to the incident surface waves. A special case of low frequency, for which the wavelength of the surface wave is sufficiently larger than the crack length, has been considered to illustrate the method. A specific expression of the amplitude has been obtained, which provides information on the angle, length and depth of the crack. It shows that the amplitude of the scattered surface wave increases first and then decreases as the crack angle changes from 0° to 90°. For the case of an inclined crack, the results of the numerical analysis together with the analytical solutions show excellent agreement when the crack length is much smaller than the wavelength. The results in this paper should be useful for the quantitative measurement of subsurface cracks.

中文翻译：

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互易定理在倾斜地下裂纹散射表面波中的应用

摘要 在本文中，在二维平面应变配置中研究了均匀、各向同性和线弹性半空间中倾斜次表面裂纹对入射表面波的散射。弹性动力学互易定理和虚拟波已被用于确定远场散射表面波的幅度。发现振幅是由于入射表面波引起的裂纹开口体积。已经考虑了低频的一种特殊情况，在这种情况下，表面波的波长远大于裂纹长度，可以用来说明该方法。已经获得了振幅的特定表达式，它提供了关于裂纹角度、长度和深度的信息。表明随着裂纹角度从0°到90°变化，散射面波的幅度先增大后减小。对于倾斜裂纹的情况，当裂纹长度远小于波长时，数值分析结果与解析解显示出极好的一致性。本文的结果对于地下裂纹的定量测量应该是有用的。