Innovative Butterfly-Compressed Microlocal Hadamard-Babich Integrators for Large-Scale High-Frequency Wave Modeling and Inversion in Variable Media

用于可变介质中大规模高频波建模和反演的创新型蝶形压缩微局域 Hadamard-Babich 积分器

• 批准号: 2309534
• 负责人: Jianliang Qian
• 金额: $ 29万
• 依托单位: Michigan State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-08-01 至 2026-07-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2309534&HistoricalAwards=false
• 关键词: Innovative; Butterfly; Compressed; Microlocal; Hadamard

This project develops and implements innovative fast algorithms for large-scale wave modeling and inversion. Waves are ubiquitous, for example, wireless signals are communicated in the form of electromagnetic waves, and ultrasound CT imaging is based on propagation of acoustic waves. In fact, wave simulation is a fundamental, growing technology in a variety of disciplines ranging from synthetic aperture radar, sonar, geophysical resources exploration, medical imaging, submarine detection, remote sensing and electronics to microscopy and nanotechnology. Developing fast algorithms for these fields and applications will serve the national interest very well in many aspects, such as advancing national health by providing fast algorithms for medical imaging and advancing national energy security by helping the U.S. petroleum industry maintain its edge in oil and gas exploration. One of the most challenging problems in computational wave propagation is how to carry out large-scale high frequency wave simulation efficiently and accurately, and the investigator will develop new fast butterfly-compressed integrator to address this crucial objective. To expand the educational impacts, the project will integrate the scientific discoveries with a series of short courses so that graduate students can be trained on the latest scientific tools. Interdisciplinary hands-on training will be developed for both undergraduate and graduate students, with an emphasis on increasing the diversity and participation of under-represented groups of students for STEM education.The project will design novel fast butterfly-compressed microlocal Hadamard-Babich (HB) integrators for large-scale high-frequency acoustic, electromagnetic, and elastic wave modeling and inversion motivated by industrial and military applications. The targeted problems for this scientific computing project are large-scale wave modeling and inverse problems with big data sets. The aimed model equations include high-frequency Helmholtz equations, Maxwell's equations, and elastic wave equations in inhomogeneous media in the presence of caustics. This project will foster breakthrough innovations in at least three theoretical and computational aspects. First, the new butterfly-compressed HB integrators will meet significant scientific challenges in large-scale high-frequency wave modeling and inversion in the presence of caustics. Second, significant advances will be made in developing novel butterfly compression and HB integrators for PDE-based Eulerian microlocal analysis and computational wave propagation. The new fast HB integrator is capable of producing uniform asymptotic solutions beyond caustics. Third, new butterfly-compressed HB integrators will provide efficient tools for many wave-related applications in inhomogeneous media, such as seismic imaging and inversion. New butterfly-compressed microlocal HB integrators will be developed for the first time for these applications. The new methodology generated by the project will have broad impacts on multiple scientific fields in both mathematics and engineering applications and will significantly improve the simulation capacities of large-scale wave propagation.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

该项目开发并实施了用于大规模波浪建模和反演的创新快速算法。波无处不在，例如无线信号以电磁波的形式进行通信，超声CT成像基于声波的传播。事实上，波浪模拟是一种基础的、不断发展的技术，涉及合成孔径雷达、声纳、地球物理资源勘探、医学成像、潜艇探测、遥感和电子学、显微镜和纳米技术等各个学科。为这些领域和应用开发快速算法将在许多方面很好地服务于国家利益，例如通过为医学成像提供快速算法来促进国民健康，通过帮助美国石油工业保持在石油和天然气勘探方面的优势来促进国家能源安全。计算波传播中最具挑战性的问题之一是如何高效、准确地进行大规模高频波模拟，研究人员将开发新型快速蝶形压缩积分器来解决这一关键目标。为了扩大教育影响，该项目将把科学发现与一系列短期课程相结合，以便研究生能够接受最新科学工具的培训。将为本科生和研究生开展跨学科实践培训，重点是增加 STEM 教育中代表性不足的学生群体的多样性和参与度。该项目将设计新型快速蝴蝶压缩微局域 Hadamard-Babich (HB) ）积分器，用于工业和军事应用推动的大规模高频声波、电磁波和弹性波建模和反演。该科学计算项目的目标问题是大规模波浪建模和大数据集的反问题。目标模型方程包括存在焦散的非均匀介质中的高频亥姆霍兹方程、麦克斯韦方程和弹性波方程。该项目将至少在三个理论和计算方面促进突破性创新。首先，新型蝶形压缩 HB 积分器将在存在焦散的情况下应对大规模高频波建模和反演方面的重大科学挑战。其次，在开发用于基于偏微分方程的欧拉微局域分析和计算波传播的新型蝶形压缩和 HB 积分器方面将取得重大进展。新的快速 HB 积分器能够产生超越焦散的统一渐近解。第三，新型蝶形压缩HB积分器将为非均匀介质中许多与波相关的应用提供有效的工具，例如地震成像和反演。新的蝶形压缩微局域 HB 积分器将首次针对这些应用而开发。该项目产生的新方法将对数学和工程应用等多个科学领域产生广泛影响，并将显着提高大规模波传播的模拟能力。该奖项体现了NSF的法定使命，经评估认为值得支持利用基金会的智力优势和更广泛的影响审查标准。