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。本建议的重点是发展一个综合的理论来分析（随机）环境噪声源产生的随机介质中的波（逆）散射问题。特别是，研究人员对这种波的测量分析很感兴趣，如果（多重）散射发生在一个域的内部，而测量是在其边界上进行的。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正交奇点组成的混合模型中，建立了联合相干和非相干波散射的分析框架（“非相干”一词被慎重使用；如果环境震源与产生的场之间的相位关系是确定的，许多人更愿意用“扩散”一词）；(2)设计互相关及其他功能，以及相关灵敏度图，统计稳定地解决各种（随机）模型参数的变化。本项目开发从“噪声”中提取信息的方法。这个想法是在噪声产生的数据中观察高阶统计模式。作为一个例子，想象一下通过分析从墙壁反射的噪声来估计到墙壁的距离，而不是通过分析相干信号的延迟回波。在该项目中考虑了更为复杂的情况，即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。这些技术将应用于遥感、医学成像和利用环境噪声源的地震成像；调查人员将把重点放在后者。随着理论的改进，研究人员可以开发出逆散射工具，这些工具有可能彻底改变地下结构和过程（例如，流动、震动、地震发生）的表征，在空间尺度上与区域研究（例如，地壳和上地幔岩石圈的结构和微地震活动；危害）和碳氢化合物生产（能源）相关。该结果可进一步用于监测co2的固存。最近投入使用的大型密集传感器阵列为探索新的理论见解提供了前所未有的机会，以揭示迄今为止尚未探索的地下复杂性。

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.