论文标题
使用声波成像裂纹网络的定性指标函数
Qualitative indicator functions for imaging crack networks using acoustic waves
论文作者
论文摘要
我们考虑了从测量的多静态远场数据产生的声波生成的多静态远场数据中嵌入裂纹网络的问题。我们提出了两种新型方法，可以看作是线性采样型方法的扩展，并提供了对局部裂纹密度敏感的指标函数。第一种方法使用多个频率数据来计算与人为嵌入的局部障碍相关的光谱特征。第二种方法还利用了合并人造背景但使用单个频率的数据的想法。指标函数是使用与差分采样方法相似的概念构建的：将内部传输问题的解决方案与具有嵌入式裂纹的内部包含的解决方案进行比较。在合成示例上测试并讨论了该方法的性能，并将数值结果与使用经典分解方法获得的结果进行了比较。
We consider the problem of imaging a crack network embedded in some homogeneous background from measured multi-static far field data generated by acoustic plane waves. We propose two novel approaches that can be seen as extensions of linear sampling-type methods and that provide indicator functions which are sensitive to local cracks densities. The first approach uses multiple frequencies data to compute spectral signatures associated with artificially embedded localized obstacles. The second approach also exploits the idea of incorporating an artificial background but uses data for a single frequency. The indicator function is built using a similar concept as for differential sampling methods: compare the solution of the interior transmission problem for healthy inclusion with the one with embedded cracks. The performance of the methods is tested and discussed on synthetic examples and the numerical results are compared with the ones obtained using the classical factorization method.
