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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，通过研究自然地震或人工地震源产生的各种地震数据，了解地球的下部结构。这一研究在实际中有重要的应用，如描述断裂基岩，寻找油气藏。该项目将涉及地震层析成像的理论基础和应用。这些结果也将在医学成像应用中有用，例如肿瘤的检测。研究人员将为研究生提供培训机会，特别是来自代表性不足群体的研究生，研究将为透射和反射地震学中出现的基本模型（包括井间模型和障碍物域）的数学理论和实用反演方法架起桥梁，这将对奠定坚实的理论基础，为实际地震学研究奠定坚实的理论基础产生积极影响。研究人员将介绍严格的统计反演方法，从传输的走时数据中恢复各向同性地震波的速度，并应用于全球和区域地震学。调查人员还将对利用反射走时数据进行地震层析成像的计算方法进行收敛性分析。这包括分析一些用于解决高维优化问题的深度学习方法。该研究将解决两个理论方面，如唯一性和稳定性，和应用，包括重建算法和数值implementations.This奖项反映了NSF的法定使命，并已被认为是值得通过评估使用基金会的智力价值和更广泛的影响审查标准的支持。