Collaborative Research: Wave Computations in Phase-Space

合作研究：相空间波计算

• 批准号: 0708014
• 负责人: Lexing Ying
• 金额: $ 15.47万
• 依托单位: University of Texas at Austin
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-07-01 至 2011-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0708014&HistoricalAwards=false
• 关键词: Collaborative; Research; Wave; Computations; Phase

Lead Proposal: DMS - 0707921PI: Demanet, Laurent Institution: Stanford UniversityNon-Lead Proposal: DMS-0708014PI: Ying, Lexing Institution: University of Texas at AustinTitle: Collaborative Research: Wave Computations in Phase-SpaceABSTRACTThe field of seismic imaging is currently facing a major computational challenge, because the capabilities of inversion algorithms grow at a slower pace than the volume of acquired data. Success of inversion typically hinges on the practicality of solving wave or hyperbolic equations, or proper approximations thereof, on a massive computational scale. To this end, the PIs propose to revisit computational wave propagation in smooth media, in two and three space dimensions, in order to bring the complexity down to asymptotically linear in the size of the initial data, up to log factors and reasonable constants. In this low-complexity regime, precomputations involving the Green's function become the main focus of the numerical effort. To this end, the PIs propose to design, implement, test and analyze the following numerical methods: (1) an efficient algorithm for Fourier Integral Operators (FIO), using techniques such as phase-space partitionings, geometric downsamplings, directional interpolation, and low rank matrix approximations via random sampling, (2) an efficient algorithm for linear hyperbolic PDE with smooth coefficients, based on the above algorithm for FIO, and also using techniques such as the phase-flow method for travel times, separation and random samplings of pseudodifferential symbols, and specialquadratures that exploit the microlocal geometry of wave propagation, and (3) an efficient algorithm for Kirchhoff migration in seismic imaging, based on the above algorithm for FIO, and also on a high-dimensional compression technique for the kinematics of the imaging operator. In a separate effort, the PIs will explore more general situations of physical interest such as phase blowups and multipathing, for which new ideas will be required.The proposed research is directly motivated by the need for new, efficient inversion methods in reflection seismology. In turn, improved seismic imaging techniques (1) could help discover new physics and settle existing debates in geophysics (for instance concerning convection phenomena in the Earth's mantle), and (2) could provide a better map of the Earth's upper crust, for industrial exploration purposes. The PIs plan on working closely with seismologists in the later phases of the project, to deliver operational codes and disseminate ideas in the geophysics community. Alternatively, transmission electron microscopy is another curvilinear tomography imaging problem for which the proposed algorithms will provide a fresh outlook towards novel, accurate inversion methods, with applications in biology and medical imaging.

主导提案：DMS - 0707921PI：Demanet, Laurent 机构：斯坦福大学非主导提案：DMS-0708014PI：Ying，Lexing 机构：德克萨斯大学奥斯汀分校标题：协作研究：相空间中的波计算摘要地震成像领域目前面临着重大的计算挑战，因为反演算法的能力 增长速度慢于所获取数据量的增长速度。反演的成功通常取决于在大规模计算规模上求解波动方程或双曲方程或其适当近似的实用性。为此，PI 建议在二维和三维空间维度重新审视光滑介质中的计算波传播，以便将复杂性降低到初始数据大小的渐近线性，直至对数因子和合理的常数。在这种低复杂度的情况下，涉及格林函数的预计算成为数值工作的主要焦点。为此，PI 建议设计、实现、测试和分析以下数值方法：(1) 一种高效的傅里叶积分算子 (FIO) 算法，使用相空间分区、几何下采样、定向插值和通过随机采样的低秩矩阵逼近等技术，(2) 一种针对平滑线性双曲 PDE 的高效算法 系数，基于上述 FIO 算法，并使用诸如走时相流法、伪微分符号的分离和随机采样以及利用波传播的微局域几何的特殊求积等技术，以及 (3) 地震成像中基尔霍夫偏移的有效算法，基于上述算法 FIO，以及用于成像算子运动学的高维压缩技术。在另一项工作中，PI 将探索更普遍的物理兴趣情况，例如相位爆炸和多路径，为此需要新的想法。本项研究的直接动机是反射地震学中对新的、高效的反演方法的需求。反过来，改进的地震成像技术（1）可以帮助发现新的物理学并解决地球物理学中现有的争论（例如有关地幔中的对流现象），（2）可以为工业勘探目的提供更好的地球上地壳地图。 PI 计划在项目的后期阶段与地震学家密切合作，在地球物理学界提供操作规范并传播想法。另外，透射电子显微镜是另一个曲线断层扫描成像问题，所提出的算法将为新颖、精确的反演方法提供新的前景，并应用于生物学和医学成像。