The problem of identifying an obstacle (scatterer) in the form of a cavity in a 2D geophysical medium is considered. This is posed as an inverse wave problem, where the location of the cavity is sought based on measurements of the elastic waves recorded by sensors located at certain points in the domain. The sensor measurements are noisy, and are generated synthetically as a first step. The inverse problem is solved by seeking the minimum of a specially designed cost functional, based on a computational time reversal (TR) procedure, where waves are radiated back in time from the sensors. The cost functional is defined to measure, for each scatterer candidate in the search space, the quality of the refocusing of the backward‐propagating waves on the given wave source at the end of the TR process. While the basic idea has appeared in previous publications, here it is applied to a 2D heterogeneous geophysical model (albeit a relatively simple one), and is enhanced by using several auxiliary techniques. These include (a) an “augmentation” technique, which is used to strengthen the coherent information (and thus to weaken the noncoherent information) by solving an elliptic problem at each time step; (b) experimentation with both instantaneous (impact) sources and time‐harmonic sources of finite duration; (c) combining the identification results of several sources and several source wavelengths to enhance identification; (d) reducing the size of the search space by a special “zooming in” technique; and (e) defining a performance index to assess the method's success and to provide a measure of confidence in the identification result in each specific case. Several numerical experiments are presented that demonstrate the performance of the proposed schemes. The sensitivity of the identification process to various parameters of the scatterer, the measurements, and the medium is investigated.

中文翻译：

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二维地球物理介质中散射体识别的增强计算时间反演方法

考虑了在二维地球物理介质中以空腔的形式识别障碍物（散射体）的问题。这被提出为逆波问题，其中基于由位于域中某些点处的传感器记录的弹性波的测量结果来寻找空腔的位置。传感器的测量结果很嘈杂，并且是第一步的综合结果。通过基于计算时间逆转（TR）程序寻求特殊设计的成本函数的最小值来解决反问题，在逆过程中，波会从传感器及时反射回去。定义成本函数是为了在搜索过程结束时，针对搜索空间中的每个散射候选物，测量后向传播波在给定波源上的重新聚焦质量。尽管基本思想已经出现在以前的出版物中，但在这里将其应用于二维异质地球物理模型（尽管是相对简单的模型），并通过使用多种辅助技术进行了增强。其中包括：（a）一种“增强”技术，该技术用于通过在每个时间步求解椭圆问题来增强相干信息（从而削弱非相干信息）；（b）对有限持续时间的瞬时（冲击）源和时谐源进行实验; （c）结合多个光源和多个光源波长的识别结果，以增强识别能力；（d）通过一种特殊的“放大”技术来缩小搜索空间的大小；（e）定义性能指标以评估该方法' 的成功，并为每种特定情况下的鉴定结果提供可信度。提出了几个数值实验，证明了所提出的方案的性能。研究了识别过程对散射体，测量值和介质各种参数的敏感性。