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，旨在设计数学知识的计算工具，用于处理大型高维地震数据集，该数据集显示沿较低维的流形显示方向结构。在过去几十年中，地震成像中发生的进展在很大程度上忽略了与数据相关的并发症，例如相干噪声，多个散射，不规则的获取几何形状和同时获得的并发性。计算谐波分析通过制定利用转换域中稀疏性的优化问题来为这些问题提供解决方案。但是，这些工具不能依赖于非常大规模的反转任务，因为它们在此类制度中没有计算有利。该项目重新审查了多尺度定向变换的数学基础，以设计设计低差额，高维体系结构，这些架构甚至对于最连续数据的反转场景也应具有竞争力。 Culprit是缺乏主流算法的可扩展性：可以解决的问题的大小比硬件功能较慢。在越来越多的应用中，需要数学家的输入来帮助工程师并应用科学家重新考虑数值代码的设计，以避免这种可扩展性的诅咒。该项目是为了退后一步，并引入了新的算法思想，以实现地震成像，该学科与将地球的地下成像有关。地震成像是能源部门的主要预测工具，用于碳氢化合物，水和地热能。它是监测水库和碳固存实验的核心。事实证明，它对地球物理学家辩论地质地幔的地质构成有用。高分辨率的地震成像也开始使陆军和空军能够检测出简易爆炸。到目前为止，所有这些远程成像问题已经成为我们这一代人将负责解决的巨大复杂的计算问题。