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    Seismic tomography is a cornerstone of geophysics and has led to a number of important discoveries about the interior of the Earth. However, seismic tomography remains plagued by the large number of unknown parameters in most tomographic applications. This leads to the inverse problem being underdetermined and requiring significant non-geologically motivated smoothing in order to achieve unique answers. Although this solution is acceptable when using tomography as an explorative tool in discovery mode, it presents a significant problem to use of tomography in distinguishing between acceptable geological models or in estimating geologically relevant parameters since typically none of the geological models considered are fit by the tomographic results, even when uncertainties are accounted for. To address this challenge, when seismic tomography is to be used for geological model selection or parameter estimation purposes, we advocate that the tomography can be explicitly parametrized in terms of the geological models being tested instead of using more mathematically convenient formulations like voxels, splines or spherical harmonics. Our proposition has a number of technical difficulties associated with it, with some of the most important ones being the move from a linear to a non-linear inverse problem, the need to choose a geological parametrization that fits each specific problem and is commensurate with the expected data quality and structure, and the need to use a supporting framework to identify which model is preferred by the tomographic data. In this contribution, we introduce geological parametrization of tomography with a few simple synthetic examples applied to imaging sedimentary basins and subduction zones, and one real-world example of inferring basin and crustal properties across the continental United States. We explain the challenges in moving towards more realistic examples, and discuss the main technical difficulties and how they may be overcome. Although it may take a number of years for the scientific program suggested here to reach maturity, it is necessary to take steps in this direction if seismic tomography is to develop from a tool for discovering plausible structures to one in which distinct scientific inferences can be made regarding the presence or absence of structures and their physical characteristics.

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  2. Abstract

    The proliferation of dense arrays promises to improve our ability to image geological structures at the scales necessary for accurate assessment of seismic hazard. However, combining the resulting local high‐resolution tomography with existing regional models presents an ongoing challenge. We developed a framework based on the level‐set method that infers where local data provide meaningful constraints beyond those found in regional models ‐ for example the Community Velocity Models (CVMs) of southern California. This technique defines a volume within which updates are made to a reference CVM, with the boundary of the volume being part of the inversion rather than explicitly defined. By penalizing the complexity of the boundary, a minimal update that sufficiently explains the data is achieved. To test this framework, we use data from the Community Seismic Network, a dense permanent urban deployment. We inverted Love wave dispersion and amplification data, from the Mw 6.4 and 7.1 2019 Ridgecrest earthquakes. We invert for an update to CVM‐S4.26 using the Tikhonov Ensemble Sampling scheme, a highly efficient derivative‐free approximate Bayesian method. We find the data are best explained by a deepening of the Los Angeles Basin with its deepest part south of downtown Los Angeles, along with a steeper northeastern basin wall. This result offers new progress toward the parsimonious incorporation of detailed local basin models within regional reference models utilizing an objective framework and highlights the importance of accurate basin models when accounting for the amplification of surface waves in the high‐rise building response band.

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