利用声波成像裂纹网络的定性指示函数
Qualitative indicator functions for imaging crack networks using acoustic waves
摘要：
本文研究了由平面声波产生的多站远场数据对均匀背景中的裂纹网络进行成像的问题。我们提出了两种新的方法，可以被看作是线性采样型方法的扩展，并提供指示函数是敏感的局部裂纹密度。第一种方法使用多个频率数据来计算与人工嵌入的局部障碍物相关联的频谱特征。第二种方法也利用了结合人工背景的想法，但使用单个频率的数据。指示函数的建立使用了类似的概念，差分采样方法：比较健康的包含与嵌入裂纹的内部传输问题的解决方案。的方法的性能进行了测试和讨论合成的例子和数值结果进行了比较，使用经典的因式分解方法。
英文摘要：
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.
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