论文标题
声学波导中的逆源问题的单模式多频率分解方法
Single Mode Multi-frequency Factorization Method for the Inverse Source Problem in Acoustic Waveguides
论文作者
论文摘要
本文在声波指导中以多个频率下的单个传播模式研究了反向源问题。目的是使用采样方法提供理论上的理由和有效算法来对扩展源进行成像。与基于采样方法中空间变量的积分的现有远/近场运算符相反，基于频率变量的积分不优势介绍了多频远场操作员。该远场操作员的定义是通过结合可能的非线性分散关系的方式，这是波导中的独特功能。部署了分解方法来建立对范围支持的严格表征，这是波传播方向的源支持。还讨论了一种基于分解的采样方法。这些抽样方法可显示能够成像源的范围支持。提供了数值示例来说明采样方法的性能，包括一个示例来对一个完整的声音软块进行映像。
This paper investigates the inverse source problem with a single propagating mode at multiple frequencies in an acoustic waveguide. The goal is to provide both theoretical justifications and efficient algorithms for imaging extended sources using the sampling methods. In contrast to the existing far/near field operator based on the integral over the space variable in the sampling methods, a multi-frequency far-field operator is introduced based on the integral over the frequency variable. This far-field operator is defined in a way to incorporate the possibly non-linear dispersion relation, a unique feature in waveguides. The factorization method is deployed to establish a rigorous characterization of the range support which is the support of source in the direction of wave propagation. A related factorization-based sampling method is also discussed. These sampling methods are shown to be capable of imaging the range support of the source. Numerical examples are provided to illustrate the performance of the sampling methods, including an example to image a complete sound-soft block.
