A Variation Method for Acoustic Wave Imaging of Two Dimensional Targets
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摘要: 研究二维目标声波成像的新方法.首先根据Green函数理论导出一个关于波数扰动函数和波场的积分方程组;然后通过对该方程组求变分,寻求波数扰动函数微小变化和散射场微小变化之间的关系,得到反演方程;最后对几个典型目标进行模拟识别,考察了方法的收敛速度、收敛精度、抗噪性能及对复杂目标的适应能力.识别结果表明,本文方法对定量无损检测技术具有理论和应用价值.Abstract: A new way of acoustic wave imaging was investigated. By using the Green function theory a system of integral equations, which linked wave number perturbation function with wave field, was firstly deduced. By taking variation on these integral equations an inversion equation, which reflected the relation between the little variation of wave number perturbation function and that of scattering field, was further obtained. Finally, the perturbation functions of some identical targets were reconstructed, and some properties of the novel method including converging speed, inversion accuracy and the abilities to resist random noise and identify complex targets were discussed. Results of numerical simulation show that the method based on the variation principle has great theoretical and applicable value to quantitative nondestructive evaluation.
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