Collaborative Research: Improving the Interpretability of Tomographic Images Using Geologically Motivated Parametrizations

地球物理成像是地球科学的基石之一。层析成像技术提供了地球内部地质特征的空间描述，这是其他方式无法获得的，因此是了解地球内部结构几何形状的主要来源。这些图像对于理解地球的演化和动力学至关重要，从控制地震活动和火山活动等自然灾害的相对较短的长度和时间尺度，到诸如大陆运动和造山模式等一级特征起源的基本问题。该项目研究了将地质知识纳入成像工具，而不是仅仅依赖标准数学工具进行成像，从而从根本上改进地球物理成像的方法。具体的成像目标包括洛杉矶、圣加布里埃尔和圣贝纳迪诺盆地，这些区域对于精确定义以提高高频率地震危险计算至关重要，并将有助于表征这一社会重要地区的地震风险。另一个目标是对黄石火山口进行成像，在那里，改进的成像可以更好地了解地壳岩浆侵位和火山喷发动力学。这项工作还汇集了地球物理学家和数学家的不同社区，并支持研究生和本科生的教育。地球物理成像问题基本上是病态的，因此需要仔细选择参数化和正则化，以产生合理的结果，特别是在数据特别稀少的区域和全球长度尺度上。以块、像素或球面谐波为参数的参数化通常由数学效用驱动。这些参数化忽略了一个事实，即层析成像的最终目标通常是将地下分类为离散结构。地球物理成像以前的进步主要是由于正演问题的解决、大规模优化的伴随方法和不确定性量化方法的发展，但在开发有效的地球参数化策略方面取得的进展相对较少。这项工作融合了一种创新的几何和水平集参数化策略，用于指定地球结构，并基于集成卡尔曼滤波器的同类最佳无导数优化方案。项目集中在两个有影响的问题上，并为团队的方法提供了互补的测试用例。第一个应用侧重于对洛杉矶、圣盖博和圣贝纳迪诺盆地的地质单元进行几何优化，由此可以更好地计算盆地内的地震地面运动。在黄石火山口的第二个应用可以更好地量化岩浆房体积和熔体分数估算之间的权衡，这是通过使用本地和远震体波断层扫描的速度扰动来确定的。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。

Geophysical imaging is one of the cornerstones of the Earth Sciences. Tomographic imaging techniques provide spatial descriptions of geologic features of the interior of the Earth that are otherwise inaccessible, and thus comprises a primary source of insight into the geometry of structures inside the Earth. These images are essential to understanding the evolution and dynamics of the Earth, from the relatively short length and timescales that govern natural hazards such as seismicity and volcanism, to fundamental questions of the origins of first order features such as patterns of continental motion and mountain building. This project investigates ways to fundamentally improve geophysical imaging by incorporating geological knowledge into imaging tools rather than relying solely on standard mathematical tools for imaging. Specific imaging targets include the Los Angeles, San Gabriel and San Bernardino basins, which are essential to accurately define to improve seismic hazard calculations at high frequencies and will help characterize earthquake risk in this societally important region. Another target is imaging the Yellowstone Caldera, where improved imaging can lead to better understanding of the dynamics of crustal magma emplacement and volcanic eruption dynamics. The work also brings together diverse communities of geophysicists and mathematicians and supports the education of graduate and undergraduate students.Geophysical imaging problems are fundamentally ill-posed so careful choices of parametrization and regularization are required to produce sensible results, especially at regional and global length scales where data are particularly scarce. Parametrizations in terms of blocks, pixels or spherical harmonics are typically driven by mathematical utility. These parametrizations ignore the fact that the end goal of tomographic imaging is typically to categorize the subsurface into discrete structures. Previous improvements in geophysical imaging have been driven by advancements in the solution of forward problems, the development of adjoint methods for large scale optimization and methods for uncertainty quantification, but comparatively little progress has been made regarding development of effective parametrization strategies for the Earth. This work melds together an innovative geometric and level set parametrization strategy for specifying Earth structure with a best-in-class derivative-free optimization scheme based on the Ensemble Kalman Filter. The project focuses on two problems that are impactful and provide complementary test cases of the team's methodology. The first application focuses on geometric optimization of geological units in the Los Angeles, San Gabriel and San Bernardino basins, from which better calculations of earthquake ground motions within the basin may be calculated. A second application at Yellowstone Caldera allows better quantification of the tradeoffs between magma chamber volume and melt fraction estimates, as determined by velocity perturbations using local and teleseismic body wave tomography.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.