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

合作研究：环境噪声产生的散射波和成像的随机和多尺度分析

• 批准号: 0908450
• 负责人: Maarten de Hoop
• 金额: $ 33.75万
• 依托单位: Purdue University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-07-15 至 2012-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0908450&HistoricalAwards=false
• 关键词: Collaborative; Research; Stochastic; Multiscale; Analysis

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.

该奖项根据 2009 年美国复苏和再投资法案（公法 111-5）提供资金。该提案的重点是开发一种综合理论来分析由（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，如果（多重）散射发生在域的内部并且测量是在其边界上进行的，研究人员对分析此类波的测量结果特别感兴趣。里程碑包括：(1) 混合模型中相干波和非相干波散射的分析框架，该模型由宏观多尺度分量、随机微尺度分量和相干共正奇点组成（建议使用“非相干”一词） ；如果环境地震源和产生的场之间的相位关系是确定性的，许多人会更喜欢“扩散”一词）； (2) 互相关及其他函数的设计，以及统计上稳定地解析各种（随机）模型参数（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。这个想法是研究噪声生成数据中的高阶统计模式。举个例子，想象一下通过分析从墙壁反射的噪声而不是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。研究人员将开发新技术来描述受这种介质影响的波，以及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。这些将在使用环境噪声源的遥感、医学成像和地震成像中得到应用；研究人员将重点关注后者。通过改进的理论，研究人员可以开发逆散射工具，这些工具有可能在与区域研究相关的空间尺度上彻底改变地下结构和过程（例如流动、震动、地震发生）的表征（例如，地壳和上地幔岩石圈的结构和微震活动；危害）和碳氢化合物生产（能源）。结果还可应用于监测CO_2封存。最近投入使用的大型而密集的传感器阵列为利用新的理论见解来揭示地下迄今尚未探索的复杂性提供了前所未有的机会。