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该文讨论了如何利用伪谱法合成零偏移距记录进行结构损伤探测与偏移成像。从二维标量波动方程出发推导了不同情况下的数值计算公式。采用反周期扩展法对边界吸收问题做了有效处理,消除了边界反射产生的假象和干扰波场。用波场外推法合成得到了能适应复杂损伤形态和横向变速介质的零偏移距记录。根据波动方程分析了伪谱法的数值频散性、奇异性以及波场形态、位移、振幅、能量、动应力集中系数等力学特征,通过波动方程的位移解得到波场快照图和时间剖面图,实现了结构损伤可视化探测与识别。数值算例证明了伪谱法偏移成像的适用性。
This paper discusses how to use pseudo-spectral synthesis of zero-offset recording for structural damage detection and migration imaging. Based on the two-dimensional scalar wave equation, the numerical formulas under different conditions are deduced. The counter-cyclical expansion method is used to effectively deal with the boundary absorption problem, which eliminates the illusion and interference wave field generated by the boundary reflection. By wave field extrapolation, the zero-offset recording which can adapt to the complex damage morphology and transverse speed change medium is obtained. According to the wave equation, the numerical dispersivity and singularity of the pseudospectral method as well as the mechanical characteristics such as wave shape, displacement, amplitude, energy and dynamic stress concentration coefficient are analyzed. The wavefield snapshot and time profile are obtained by the displacement solution of the wave equation , To achieve structural damage visual detection and recognition. Numerical examples demonstrate the applicability of pseudospectral migration imaging.