Collaborative Research: Stochastic and Multiscale Analysis of Ambient-Noise Generated Scattered Waves and Imaging

该奖项是根据2009年《美国复苏和再投资法案》(公法111-5)提供资金的。这一建议的重点是发展一种全面的理论来分析由(随机)环境噪声源产生的随机介质中的波的(逆)散射问题。特别是，研究人员感兴趣的是，如果(多次)散射发生在区域内部，并且测量是在其边界上进行的，则对这种波的测量进行分析。里程碑包括：(1)由宏观多尺度分量、随机微尺度分量和相干正交奇点组成的混合模型中联合相干和非相干波散射的分析框架(有意使用“非相干”一词；如果环境地震震源和所产生的场之间的相位关系是确定性的，许多人倾向于使用“扩散”一词)；以及(2)互相关泛函及以外函数的设计，以及相关的敏感性图，在统计上稳定地解决各种(随机)模型参数的变化。这个项目开发了从“噪音”中提取信息的方法。这个想法是为了研究噪声产生的数据中的高阶统计模式。例如，设想通过分析墙外反射的噪声而不是通过分析相干信号的延迟回波来估计到墙的距离。在这个项目中，考虑了更复杂的情况，其中噪声产生的波在测量之前已经通过复杂的(随机)介质传播。研究人员将开发新的技术来描述受这种介质影响的波，此外还将开发有效地以数字方式处理上述数据以提取相关统计信息和后续成像的算法。这些将在遥感、医学成像和使用环境噪声源的地震成像中得到应用；研究人员将重点放在后者上。有了改进的理论，研究人员可以开发反散射工具，这些工具有可能在与区域研究有关的空间尺度上彻底改变地下结构和过程的特征(例如流动、震动、地震成因)(例如地壳和上地幔岩石圈的结构和微震活动；灾害)和碳氢化合物生产(能源)。研究结果可进一步应用于CO_2封存监测。最近投入使用的大型密集传感器阵列为利用新的理论见解揭开地下迄今尚未探索的复杂性提供了前所未有的机会。

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5). The focus of this proposal is the development of a comprehensive theory to analyze (inverse) scattering problems with waves in random media generated by (random) ambient noise sources. In particular, the investigators are interested in the analysis of measurements of such waves if the (multiple) scattering takes place in the interior of a domain and the measurements are taken on its boundary. Milestones include: (1) an analysis framework for the scattering of jointly coherent and incoherent waves in a mixed model consisting of a macro multi-scale component, a random microscale component and coherent conormal singularities (the word ``incoherent'' is used advisedly; many would prefer the term ``diffuse'' if the phase relation between source of ambient seisms and the field that is generated is deterministic); and (2) the design of functionals of cross correlations and beyond, and associated sensitivity maps statistically stably resolving (changes in) the various (random) model parameters. This project develops methods for extracting information from ``noise''. The idea is to look at higher order statistical patterns in noise-generated data. As an example, imagine to estimate the distance to a wall by analyzing noise reflected off the wall rather than by analyzing the delayed echo of a coherent signal. In the project much more complicated situations are considered in which noise generated waves have propagated through a complex (random) medium before they are measured. The investigators will develop new techniques for describing waves that are affected by such a medium, in addition to algorithms that effectively process the mentioned data numerically to extract relevant statistical information and subsequent imaging. These will have applications in remote sensing, medical imaging and seismic imaging using ambient noise sources; the investigators will focus on the latter. With improved theory the investigators can develop inverse scattering tools that have the potential to revolutionize the characterization of structures and processes (e.g., flow, tremors, seismogenesis) in the subsurface, on spatial scales relevant for regional studies (e.g., structure and microseismic activity of crust and upper mantle lithosphere; hazards) and hydrocarbon production (energy). The results can furthermore be applied to monitoring CO_2 sequestration. Large and dense sensor arrays that have become operative recently provide unprecedented opportunities for exploiting new theoretical insights to unravel, hitherto unexplored, complexities in the subsurface.