A Proposal for Research in Waves in Random Media and Applications

随机介质中的波研究及其应用的提案

• 批准号: 9971972
• 负责人: George Papanicolaou
• 金额: $ 29.4万
• 依托单位: Stanford University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-08-15 至 2003-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9971972&HistoricalAwards=false
• 关键词: Proposal; Research; Waves; Random; Media

Papanicolaou9971972 The goal of this project is to develop and use analyticaland computational methods for geophysical wave propagation. Theinvestigator and his colleagues have developed two generaltheories: one based around radiative transport for elastic wavepropagation in the crustal waveguide, and the other based onwaves in nearly layered random media. The mathematical issuesinvolved in radiative transfer are (i) the derivation of boundaryconditions (ii) the introduction and use of good Monte Carlomethods (iii) the solution of realistic inverse problems forparameter identification. In the case of nearly layered media animportant mathematical issue is the robustness of wavelocalization, known to hold for perfectly layered random media.Another direction of study is the assessment of the effect ofrandom inhomogeneities on time reversal imaging, called wavemigration in geophysics. The mathematical analysis requires timedomain statistics for time reversed pulses, which have to beconstructed by Fourier analysis. Theoretical explanations areprovided for the increased resolution in time reversal imagingdue to the inhomogeneities. Geophysical wave propagation, the propagation of seismicwaves in the earth's crust for example, requires mathematicalmodeling at several levels depending on the accuracy and theresolution required. It is impossible to simulate numericallyseismic wave propagation over a few hundreds of kilometers of theearth's crust while taking into account the detailedinhomogeneities in the earth's crust. Radiative transport theorycan be used very effectively and at much lower computationalcost, and it can provide estimates for the codas (tails) ofseismograms with enough accuracy to interpret and analyze manycontinental seismic events. The project provides the mathematicalmethodology and infrastructure for using radiative transport ingeophysical problems. The investigator looks carefully at what isneeded to deal with discontinuities and interfaces in the crustalenvironment, what is needed for large scale imaging from surfaceseismic measurements, what is needed for assessing the waveguideeffects that appear in long distance seismic wave propagation,and what is needed for the effective numerical simulation of longdistance seismic wave propagation.

Papanicolaou9971972该项目的目标是开发和使用分析和计算方法进行地球物理传播。 TheInvestigator及其同事开发了两个通用理论：一种基于地壳波导中弹性传输的辐射传输，而另一个基于几乎分层的随机培养基中的另一个基于Onwaves。 辐射传递中涉及的数学问题是（i）边界条件的推导（ii）引入和使用良好的蒙特卡洛动物（iii）逼真的逆问题的解决方案FORPAMETER标识。 在几乎分层的媒体动画问题的情况下，众所周知的是小波钙化的鲁棒性，它具有完美分层的随机介质。另一个研究方向是评估兰多姆不均匀性对时间反向成像的影响，称为地球物理学中称为波浪级。 数学分析需要时间逆转脉冲的计时统计统计，这些脉冲必须通过傅立叶分析来构造。 理论上的解释是为了增加时间逆转成像事件的分辨率提高到不均匀性。 地球物理波传播（例如，地壳中地震中的传播）需要根据所需的准确性和解决方案进行数学模型。 在考虑到地壳中详细的植物性时，不可能在数百公里的theearth的地壳上模拟数字观察波传播。 辐射传输理论可以非常有效地使用，并且在较低的计算结果下，它可以以足够的准确性来解释和分析许多企业地震事件的观察图（尾巴）的估计值。 该项目提供了使用辐射运输的植物物理问题的数学方法和基础设施。 研究人员仔细研究了甲壳环境中的不连续性和界面所需要的内容，从表面震荡的测量中进行大型成像所需的内容，评估在长距离地震波传播中出现的波导效应所需的需要的是什么，以及有效的长期模拟的长期模拟波动的数值模拟所需的是什么。