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，否则无法进入，因此构成了洞察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，从控制地震和火山活动等自然灾害的相对较短的长度和时间尺度，到大陆运动和造山模式等一级特征起源的基本问题。该项目通过将地质学知识融入成像工具，而不是仅仅依靠标准的数学成像工具，研究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，这些盆地对于准确定义和改进高频地震风险计算至关重要，并将有助于表征这一具有重要社会意义的地区的地震风险。另一个目标是对黄石火山口进行成像，在那里改进成像可以更好地了解地壳岩浆侵位和火山喷发的动力学。这项工作还将地球物理学家和数学家的不同群体聚集在一起，并支持研究生和本科生的教育。地球物理成像问题从根本上是不适定的，因此需要谨慎选择参数化和正则化才能产生合理的结果，特别是在数据特别稀缺的区域和全球范围内。块、像素或球面调和的参数化通常由数学效用驱动。这些参数化忽略了这样一个事实，即断层成像的最终目标通常是将亚表面分类为离散的结构。地球物理成像以前的改进是由正演问题的解决、大规模优化的伴随方法和不确定性量化方法的发展所推动的，但在开发有效的地球参数化战略方面进展相对较小。这项工作将用于描述地球结构的创新的几何和水平集参数化策略与基于集合卡尔曼滤波的一流的无导数优化方案相结合。该项目关注两个有影响力的问题，并提供团队方法的补充测试用例。第一个应用侧重于对洛杉矶、圣加布里埃尔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。黄石火山口的第二个应用程序允许更好地量化岩浆室体积和熔体比例估计之间的权衡，这是通过使用本地和远程地震体波层析成像的速度扰动确定的。该奖项反映了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。

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.