Bridging the Mathematical Analysis and Reconstruction Algorithms for Transmission and Reflection Seismic Tomography

连接传输和反射地震层析成像的数学分析和重建算法

基本信息

批准号：
2109116
负责人：
Hanming Zhou
金额：
$ 28万
依托单位：
University of California-Santa Barbara
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2021
资助国家：
美国
起止时间：
2021-08-15 至 2024-07-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2109116&HistoricalAwards=false
关键词：
Bridging Mathematical Analysis Reconstruction Algorithms

项目摘要

This project will focus on seismic tomography to understand the substructure of the Earth by studying various seismic data produced by natural earthquakes or artificial seismic sources. This research has important applications in practice, such as characterizing fractured bedrock, and searching for oil and gas deposits. The project will address both theoretical foundations and applications of seismic tomography. The results will also be useful in medical imaging applications such as detection of tumors. The investigators will provide training opportunities for graduate students, especially those from underrepresented groups.The research will bridge the mathematical theory and practical inversion methods for fundamental models arising in transmission and reflection seismology, including the cross-well model and domains with obstacles, which will have positive impacts on laying a solid theoretical backbone for practical seismology studies. The investigators will introduce rigorous statistical inversion methods for recovering isotropic seismic wave speed from the transmitted travel-time data, with applications to both global and regional seismology. The investigators will also conduct convergence analysis on computational methods for seismic tomography with reflection travel-time data. This includes analysis of some deep learning methods for solving high-dimensional optimization problems. The research will address both the theoretical aspect, such as uniqueness and stability, and applications, including reconstruction algorithms and numerical implementations.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.

该项目将侧重于地震层析成像，以通过研究自然地震或人工地震来源产生的各种地震数据来了解地球的亚结构。这项研究在实践中具有重要的应用，例如表征断裂的基岩以及寻找石油和天然气沉积物。该项目将解决地震层析成像的理论基础和应用。结果也将在医学成像应用中有用，例如检测肿瘤。研究人员将为研究生提供培训机会，尤其是那些人为人数不足的人群。该研究将桥接用于传播和反思地震学中基本模型的数学理论和实践反转方法，包括跨孔模型和障碍物的领域，这将对实践性的地板研究产生固体理论的积极影响。研究人员将引入严格的统计反转方法，以从传播的旅行时间数据中恢复各向同性地震波速度，并应用于全球和区域地震学。研究人员还将对具有反射旅行时间数据的地震层析成像的计算方法进行收敛分析。这包括对解决高维优化问题的一些深度学习方法的分析。这项研究将解决理论方面，例如独特性和稳定性，以及应用程序，包括重建算法和数值实现。该奖项反映了NSF的法定任务，并被认为是值得通过基金会的知识分子优点和更广泛影响的审查标准通过评估来进行评估的。