CDI-Type I: Collaborative Research: High-Dimensional Phase-Space Subdivisions for Seismic Imaging

CDI-Type I：协作研究：地震成像的高维相空间细分

• 批准号: 1327658
• 负责人: Lexing Ying
• 金额: $ 6.79万
• 依托单位: Stanford University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-01-01 至 2013-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1327658&HistoricalAwards=false
• 关键词: CDI; Type; Collaborative; Research; Dimensional

This award supports a research program aimed at designing mathematically-informed computational tools for processing large, high-dimensional seismic datasets that display directional structure along lower-dimensional manifolds. The progress that occurred over the past few decades in seismic imaging has largely ignored growing data-related complications, such as coherent noise, multiple scattering, irregular acquisition geometries, and simultaneous acquisition. Computational harmonic analysis provides solutions to these problems by formulating optimization problems that leverage sparsity in a transformed domain. These tools can however not be relied upon for very large scale inversion tasks, because they are not computationally advantageous in such regimes. This project revisits the mathematical underpinnings of multiscale directional transforms with a view toward designing low-redundancy, high-dimensional architectures that should be competitive for even the most data-intensive inversion scenarios.Moore's law of exponential increase in computing performance is not often matched by exponential progress in the computational sciences. The culprit is the lack of scalability of mainstream algorithms: the size of problems that can be solved grows more slowly than hardware capabilities. In increasingly many applications, the input of mathematicians is needed to help engineers and applied scientists rethink the design of numerical codes to avoid this curse of scalability. This project is an effort to take a step back and introduce new algorithmic ideas for seismic imaging, the discipline concerned with imaging the subsurface of the Earth. Seismic imaging is the energy sector's main predictive tool for hydrocarbon, water, and geothermal energy prospection. It is at the heart of monitoring techniques for reservoirs and carbon sequestration experiments. It has proved useful to geophysicists who debate the geological composition of the Earth's mantle. High-resolution seismic imaging is also starting to enable the Army and the Air Force to detect IEDs. All these remote imaging problems have by now become formidably complex computational questions that our generation will be responsible for solving.

该奖项支持一项研究计划，旨在设计数学计算工具，用于处理大型高维地震数据集，这些数据集显示沿低维流形的方向结构。过去几十年地震成像领域取得的进步在很大程度上忽略了与数据相关的日益增长的复杂性，例如相干噪声、多重散射、不规则采集几何形状和同时采集。计算调和分析通过制定利用变换域中稀疏性的优化问题来解决这些问题。然而，这些工具不能依赖于非常大规模的反演任务，因为它们在这种情况下在计算上不有利。该项目重新审视了多尺度定向变换的数学基础，着眼于设计低冗余、高维架构，即使对于数据最密集的反演场景也应该具有竞争力。计算性能指数增长的摩尔定律通常无法与计算科学的指数级进步。罪魁祸首是主流算法缺乏可扩展性：可解决问题的规模增长速度慢于硬件能力。在越来越多的应用中，需要数学家的输入来帮助工程师和应用科学家重新思考数字代码的设计，以避免这种可扩展性的诅咒。该项目旨在退后一步，为地震成像引入新的算法思想，地震成像是与地球地下成像有关的学科。地震成像是能源部门碳氢化合物、水和地热能勘探的主要预测工具。它是水库监测技术和碳封存实验的核心。事实证明，它对于争论地幔地质成分的地球物理学家很有用。高分辨率地震成像也开始帮助陆军和空军检测简易爆炸装置。所有这些远程成像问题现在都已成为我们这一代人将负责解决的极其复杂的计算问题。