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）资助的。该建议的重点是发展一个全面的理论来分析（逆）散射问题与波在随机介质中产生的（随机）环境噪声源。特别是，调查人员感兴趣的是，这种波的测量分析，如果（多）散射发生在一个域的内部和测量采取的边界上。里程碑包括：（1）在由宏观多尺度分量、随机微尺度分量和相干余法向奇点组成的混合模型中，联合相干波和非相干波的散射的分析框架（"不相干"一词的使用是不恰当的;如果环境地震源和产生的场之间的相位关系是确定性的，许多人更喜欢"扩散"一词）;以及（2）互相关和超越的泛函的设计，以及统计上稳定地解析各种（随机）模型参数（中的变化）的相关灵敏度图。 该项目开发了从"噪音"中提取信息的方法。这个想法是在噪声生成的数据中查看高阶统计模式。作为一个例子，想象一下通过分析从墙壁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壁的距离。在该项目中，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（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，以及有效处理上述数据的算法，以提取相关的统计信息和随后的成像。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;研究人员将重点关注后者。随着理论的改进，研究人员可以开发出具有革命性结构和过程表征潜力的逆散射工具（例如，流动、震动、地震发生），在与区域研究相关的空间尺度上（例如，地壳和上地幔岩石圈结构和微地震活动;灾害）和油气生产（能源）。研究结果可进一步应用于CO_2封存监测。最近已经开始运作的大型和密集的传感器阵列为利用新的理论见解来解开迄今为止尚未探索的地下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.