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

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.