Collaborative Research: Wave Computations in Phase-Space

合作研究：相空间波计算

• 批准号: 1017062
• 负责人: Laurent Demanet
• 金额: $ 0.83万
• 依托单位: Massachusetts Institute of Technology
• 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: 2009-10-01 至 2010-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1017062&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.

主要提案：DMS- 0707921PI: Demanet， Laurent机构：斯坦福大学非主要提案：DMS-0708014 pi: Ying， Lexing机构：德克萨斯大学奥斯汀分校标题：合作研究：相空间波计算摘要地震成像领域目前面临着一个重大的计算挑战，因为反演算法的能力增长速度慢于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浪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中重新审视平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)利用相空间分割、几何下采样、方向插值和随机采样的低秩矩阵逼近等技术，提出了傅里叶积分算子（FIO）的高效算法；(2)在上述FIO算法的基础上，利用假微分符号的旅行时间、分离和随机采样等相流方法，提出了具有光滑系数的线性双曲偏微分方程的高效算法；(3)基于上述FIO算法和成像算子运动学的高维压缩技术，提出了地震成像中的Kirchhoff偏移高效算法。在单独的努力中，pi将探索更一般的物理兴趣情况，如相位放大和多路径，为此将需要新的想法。对反射地震学中新的、有效的反演方法的需求直接推动了所提出的研究。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（例如关于地幔中的对流现象），(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，提供操作代码并在地球物理界传播思想。另外，透射电子显微镜是另一个曲线断层成像问题，所提出的算法将为新的、准确的反演方法提供新的前景，并在生物学和医学成像中应用。