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

该项目将专注于地震层析成像，通过研究天然地震或人工震源产生的各种地震数据来了解地球的亚结构。该研究在裂隙基岩特征识别、油气藏寻找等方面具有重要的实际应用价值。该项目将研究地震层析成像的理论基础和应用。这一结果也将在医学成像应用中发挥作用，例如检测肿瘤。研究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。这项研究将为传输和反射地震学中产生的基本模型，包括井间模型和有障碍的域，搭建数学理论和实用反演方法的桥梁，将对为实际地震学研究奠定坚实的理论支柱产生积极影响。研究人员将介绍从传输的旅行时间数据中恢复各向同性地震波速的严格统计反演方法，并将其应用于全球和区域地震学。研究人员还将对利用反射旅行时数据进行地震层析成像的计算方法进行收敛分析。这包括分析解决高维优化问题的一些深度学习方法。这项研究将涉及理论方面，如唯一性和稳定性，以及应用，包括重建算法和数值实现。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.