Seismology- and Geodesy-Based Inverse Problems Crossing Scales, with Scattering, Anisotropy and Nonlinear Elasticity

基于地震学和大地测量学的跨尺度反问题，具有散射、各向异性和非线性弹性

基本信息

批准号：
1815143
负责人：
Maarten de Hoop
金额：
$ 32万
依托单位：
William Marsh Rice University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2018
资助国家：
美国
起止时间：
2018-07-01 至 2022-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1815143&HistoricalAwards=false
关键词：
Seismology Geodesy Based Inverse Problems

项目摘要

The investigator and his collaborators study inverse problems in seismology and geodesy crossing many scales. These inverse problems are associated with systems of partial differential equations describing elastic waves and elastostatics. Their key advances in these problems pertain to reaching real earth material properties and their complex heterogeneities through the consideration of scattering, anisotropy and nonlinear elasticity. The application goal is rigorous reconstruction, hierarchically mapping Earth's interior, locally and possibly globally, honoring these material properties, in conjunction with dislocations and fault shapes encoded in co-seismic deformation. The investigator exploits important developments in novel sensor design and data acquisition. Differentiating the features representing the observed hierarchical data complexity, expected to be associated with different scattering regimes, the investigator distinguishes different types of nonlinear inverse problems. The research promises to lead to innovative technologies for interpreting the rich information contained in seismic and geodesic (Global Positioning System) data crossing scales on the one hand, and new directions in the analysis of inverse problems underpinning modern data science on the other hand. The studies benefit natural resources management including hydrofracking and geothermal energy, hazard analysis and, moreover, provide possible approaches for planetary exploration with very few sensors. They also provide keys for important further insight on how processes at the surface are coupled to processes in Earth's deep interior. The research program offers a unique interdisciplinary educational experience for the students involved giving them a much broader appreciation of the importance of novel techniques and real-life implications. The investigator and his collaborators develop a composite analysis of seismology and geodesy based inverse problems. Following the hierarchical data complexity, they (1) analyze spectral rigidity of spherically symmetric planets, and then include angular variations through perturbation and semiclassical analysis, as well as inverse problems for (Rayleigh and Stoneley) waveguide coupling at and near phase boundaries; (2) study geometric inverse problems for the local mixed geodesic ray transforms on rank-4 tensors in Riemannian geometry, (broken) geodesic ray transforms in Finsler geometry and then boundary rigidity, and with visible orientable geodesic spheres as well as the geometric inverse problem with microseismicity data; (3) analyze hyperbolic inverse boundary value problems with piecewise smooth stiffness tensors (with associated interfaces or domain partitions), partial data and improved stability estimates using unbalanced, complex optimal transport for optimization-based reconstruction; (4) study uniqueness and conditional stability for the recovery of a heterogeneous dislocation and fault shape from geodesy boundary data; and (5) develop and analyze inverse problems in nonlinear elasticity in sedimentary rocks in the presence of discontinuities using paired Lagrangian distributions and Strichartz estimates. The implicit connections between these inverse problems come into play as they probe one planet, while contributing to a deeper understanding of information content in the exponentially growing data volumes that are available through modern data enters.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.

研究者和他的合作者研究了地震学和大地测量学中跨多个尺度的反演问题。这些反问题与描述弹性波和弹性静力学的偏微分方程组相关。他们在这些问题上的关键进展涉及通过考虑散射、各向异性和非线性弹性来达到真实的地球材料特性及其复杂的异质性。应用目标是严格重建，分层绘制地球内部局部乃至全球的地图，尊重这些材料特性，并结合同震变形中编码的位错和断层形状。研究人员利用新型传感器设计和数据采集方面的重要进展。通过区分代表观察到的分层数据复杂性的特征（预计与不同的散射机制相关），研究人员区分了不同类型的非线性逆问题。该研究有望带来创新技术，一方面用于解释地震和测地线（全球定位系统）数据交叉尺度中包含的丰富信息，另一方面为支撑现代数据科学的反演问题分析提供新方向。这些研究有利于自然资源管理，包括水力压裂和地热能、危害分析，此外，还为利用很少的传感器进行行星探索提供了可能的方法。它们还为进一步了解地表过程与地球深层内部过程如何耦合提供了重要的关键。该研究项目为参与的学生提供了独特的跨学科教育体验，让他们对新技术的重要性和现实生活的影响有更广泛的认识。研究人员和他的合作者开发了基于地震学和大地测量学的反问题的综合分析。按照分层数据复杂性，他们（1）分析球对称行星的谱刚度，然后通过扰动和半经典分析包括角度变化，以及相边界处和相边界附近的（瑞利和斯通利）波导耦合的反演问题； (2) 研究黎曼几何中四阶张量上的局部混合测地射线变换、芬斯勒几何中的（破碎）测地射线变换以及边界刚度，以及可见可定向测地球体的几何反问题以及几何反问题具有微震活动数据； (3) 使用分段平滑刚度张量（具有相关接口或域分区）、部分数据和改进的稳定性估计来分析双曲逆边值问题，使用不平衡、复杂的最优传输进行基于优化的重建； (4) 研究从大地测量边界数据恢复异质位错和断层形状的唯一性和条件稳定性； (5) 使用成对拉格朗日分布和 Strichartz 估计来开发和分析存在不连续性的沉积岩非线性弹性反演问题。这些反问题之间的隐含联系在它们探测一颗行星时发挥作用，同时有助于更深入地理解通过现代数据输入获得的呈指数增长的数据量中的信息内容。该奖项反映了 NSF 的法定使命，并被认为是值得的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来获得支持。