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首页> 外文期刊>SIAM Journal on Applied Mathematics >ESTIMATING A GREEN'S FUNCTION FROM 'FIELD-FIELD'CORRELATIONS IN A RANDOM MEDIUM
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ESTIMATING A GREEN'S FUNCTION FROM 'FIELD-FIELD'CORRELATIONS IN A RANDOM MEDIUM

机译：从随机介质中的“ FIELD-FIELD”关联估计格林函数

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摘要

Traditional imaging methods use coherent signals as data. Here, we discuss recent developments in imaging that aim at exploiting as data incoherent noisy signals that are not associated with well-defined arrival times. Indeed, signal constituents that in a classical setting may be regarded as noise may contain important information about the medium to be imaged. We show how it is possible to use the statistics of such noisy signals, specifically, the second-order statistics, for imaging. We consider two particular situations: first, the estimation of an ("empirical") Green's function from noisy signals which can subsequently be used in imaging; second, the localization of a cluster of random sources from noisy signals (passive imaging). The analysis presented here is based on assuming a remote sensing scaling and the paraxial approximation, and it uses in part the results set forth in Papanicolaou, Ryzhik, and Solna [SIAM J. Appel. Math., 64 (2004), pp. 1133-1155] that relate to time-reversal, statistical stability, and superresolution. Robustness with respect to modeling assumptions is illustrated by considering other scaling regimes also. We demonstrate how the estimation problem and its robustness can be considered as a dual to that of time-reversal and stable superresolution. We obtain a novel analysis and foundation for the use of ambient seismic noise in body-wave (tomographic) imaging, motivated by the recent successes of surface-wave tomography using ambient seismic noise.
机译：传统的成像方法使用相干信号作为数据。在这里，我们讨论了成像的最新发展，其目的是利用与数据不相关的嘈杂信号，这些信号与明确定义的到达时间无关。实际上，在经典环境中可能被视为噪声的信号成分可能包含有关要成像介质的重要信息。我们展示了如何使用此类噪声信号的统计数据，特别是二阶统计数据进行成像。我们考虑两种特殊情况：首先，从有噪信号估计（“经验”）格林函数，然后将其用于成像;第二，定位来自噪声信号的随机源群集（无源成像）。这里提出的分析是基于假设遥感比例和近轴近似，并且部分使用了Papanicolaou，Ryzhik和Solna [SIAM J. Appel。 [Math。64（2004），pp。1133-1155]中涉及到时间反转，统计稳定性和超分辨率。关于建模假设的鲁棒性也通过考虑其他缩放方式来说明。我们演示了如何将估计问题及其鲁棒性视为时间反转和稳定超分辨率的双重问题。我们获得了在体波（断层扫描）成像中使用环境地震噪声的新颖分析方法和基础，这是由使用环境地震噪声的表面波层析成像技术的最新成功所激发的。

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