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

该项目将侧重于地震层析成像，通过研究自然地震或人工震源产生的各种地震数据来了解地球的子结构。该研究具有重要的实际应用价值，可用于裂缝基岩的表征、寻找油气矿床等。该项目将研究地震层析成像的理论基础和应用。这一结果也将用于医学成像应用，如肿瘤检测。调查人员将为研究生提供培训机会，特别是那些来自代表性不足群体的研究生。该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域）的数学理论和实际反演方法架起桥梁，对为实际地震学研究奠定坚实的理论基础具有积极作用。研究人员将引入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速度，并将其应用于全球和区域地震学。研究人员还将对反射走时数据的地震层析成像计算方法进行收敛分析。这包括分析一些用于解决高维优化问题的深度学习方法。研究将涉及理论方面，如唯一性和稳定性，和应用，包括重建算法和数值实现。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.