标题： 从多频相位或无相位远场模式中识别双层介质中的声源 显示英文标题

标题： Identifying an acoustic source in a two-layered medium from multi-frequency phased or phaseless far-field patterns

摘要： 本文提出了一种方法，用于从在上半球上测量的多频段相位或无相位远场模式重建位于双层介质中的声源。 两介质之间的界面假定为平坦且无限，而源则埋藏在下半空间中。 在有相位的情况下，提出了一种傅里叶方法，基于远场测量来识别源。 该方法假设源具有紧支集，并可以通过傅里叶基函数的和来表示。 通过利用不同频率的远场模式，可以确定源的傅里叶系数，从而实现其重建。 对于相位信息不可用的情况，开发了一种相位恢复公式以恢复相位信息。 该公式利用了远场模式通过保持相位信息的线性算子与源相关这一事实。 通过开发适当的相位恢复算法，可以恢复相位信息。 一旦恢复了相位，就可以采用傅里叶方法来恢复源函数。 进行了二维和三维的数值实验，以验证所提出方法的性能。 显示英文摘要

摘要： This paper presents a method for reconstructing an acoustic source located in a two-layered medium from multi-frequency phased or phaseless far-field patterns measured on the upper hemisphere. The interface between the two media is assumed to be flat and infinite, while the source is buried in the lower half-space. In the phased case, a Fourier method is proposed to identify the source based on far-field measurements. This method assumes that the source is compactly supported and can be represented by a sum of Fourier basis functions. By utilizing the far-field patterns at different frequencies, the Fourier coefficients of the source can be determined, allowing for its reconstruction. For the case where phase information is unavailable, a phase retrieval formula is developed to retrieve the phase information. This formula exploits the fact that the far-field patterns are related to the source through a linear operator that preserves phase information. By developing a suitable phase retrieval algorithm, the phase information can be recovered. Once the phase is retrieved, the Fourier method can be adopted to recover the source function. Numerical experiments in two and three dimensions are conducted to validate the performance of the proposed methods.