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

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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.