Parallel Semiclassical Methods for Seismic Wave Propagation, Inversion, and Data Analysis

预测地震事件，寻找隐藏的资源，加深我们对地球内部复杂性的理解，需要克服包括数学和地球物理学在内的多学科交叉科学的挑战。拟开展地震波传播、反演和数据分析的平行半经典方法开发项目，并对结果进行计算、可视化和探索，以创建地球内部结构的三维成像。具体而言，项目包括开发冻结高斯近似（FGA）来处理高对比度，非均质介质中的弹性波传播，通过构建基于FGA的代理模型来扩大粒子群方法中使用的搜索函数空间，使用全波形反演来反演背景速度，以及应用开发的数学理论和相关计算机程序来收集地震数据。这些项目将开发地震波传播、反演和数据分析的半经典方法，从而对地球整个内部结构进行定量成像，并对地震活动提供深入的了解。研究提出了一种数学系统的方法来满足地震层析成像和反演过程中减少模拟时间的要求。更广泛地说，这些新方法和模型将为计算数学提供根本性的进步，从而在地球物理领域带来实际效益，地球物理在负责任地利用资源方面发挥着重要作用。预期的结果将在其他新兴科学和工程领域得到应用，例如材料科学中的自旋转移扭矩和生物学中的大肠杆菌趋化性，这些问题也是PI一直在研究的。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。

Predicting seismic events, locating hidden resources and deepening our understanding of our planet's internal complexity require overcoming challenges from multi-interdisciplinary sciences including mathematics and geophysics. The proposed research will initiate projects to develop parallel semiclassical methods for seismic wave propagation, inversion and data analysis, with results computed, visualized and explored to create three-dimensional imaging of inner Earth structure. Specifically, the projects include development of the frozen Gaussian approximation (FGA) to handle elastic wave propagation in high-contrast, heterogeneous media, inversion of background velocity using full waveform inversion by constructing a surrogate model based on FGA to enlarge the search-function spaces used in the particle swarm method, and application of developed mathematical theory and associated computer programs to collected seismic data. The projects will develop semiclassical approaches for seismic wave propagation, inversion and data analysis, leading to quantitative imaging of our Earth's whole inner structure, and provide deep understanding of seismic activities. The research introduces a mathematically systematic way of attacking requests on reducing time of simulation in seismic tomography and inversion processes. More broadly, these new methods and models will provide fundamental advances in computational mathematics, leading to practical benefit in the field of geophysics, which plays such significant roles in responsible use of resources. The expected results will find applications in other emerging science and engineering fields such as spin-transfer torque in materials science and E. coli chemotaxis in biology, some of the problems the PI has also been working on.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.