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对地球内部地质特征的空间描述，这些地质特征是无法以其他方式获得的，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变和动态至关重要，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，到大陆运动和造山运动模式等一阶特征起源的基本问题。该项目研究如何通过将地质知识纳入成像工具而不是仅仅依赖于标准的数学成像工具来从根本上改善地球物理成像。具体的成像目标包括洛杉矶、圣盖博和圣贝纳迪诺盆地，这些盆地对于准确界定和改进高频地震危险性计算至关重要，并将有助于确定这一具有重要社会意义地区的地震危险性。另一个目标是对黄石火山口进行成像，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。这项工作还汇集了不同社区的地球物理学家和数学家，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，因此需要仔细选择参数化和正则化，以产生合理的结果，特别是在区域和全球的长度尺度上，数据特别稀缺。块、像素或球谐函数方面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。地球物理成像的以前的改进已经被推动的进步，在解决正问题，大规模优化和不确定性量化方法的伴随方法的发展，但相对较小的进展已经取得了有效的参数化战略的发展。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Enhancement卡尔曼滤波器的同类最佳无导数优化方案。该项目重点关注两个有影响力的问题，并为团队的方法提供补充测试用例。第一个应用程序集中在几何优化的地质单元在洛杉矶，圣加布里埃尔和圣贝纳迪诺盆地，从更好的计算地震地面运动盆地内可以计算。黄石火山口的第二个应用程序允许更好地量化岩浆房体积和熔体分数估计之间的权衡，通过使用本地和对流体波层析成像的速度扰动确定。该奖项反映了NSF的法定使命，并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。

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.