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Abstract Imaging of Earth’s interior has led to a large number of successful discoveries of plausible structures and associated geophysical processes. However, due to the limitations of geophysical data, Earth imaging has many trade-offs between the underlying features, and most approaches apply smoothing to reduce the effect of such trade-offs. Unfortunately, this smoothing often results in blurry images that are not clear enough either to infer the geologic processes of interest or to make quantitative inferences about the various geologic properties. Here, we first summarize some of the basic issues that make Earth imaging so difficult and explain how Earth imagers must choose between more open-ended discovery-oriented goals and more specific, scientific-inference-oriented goals. We discuss how the choice of the optimal imaging framework depends crucially on the desired goal, and particularly on whether plausible discovery or inference is the desired outcome. We argue that as Earth imaging has become more mature, sufficiently many plausible structures have been imaged that it is becoming more crucial for Earth imaging to serve the inference goal and would benefit from an inference-oriented imaging framework, despite the additional challenges in posing imaging problems in this manner. Examples of inference-oriented imaging frameworks are provided and contrasted with discovery-oriented frameworks. We discuss how the success of the various frameworks depends critically on the data quality and suggest that a careful balance must be struck between the ambition of the imager and the reality of the data. If Earth imaging is to move beyond presenting qualitatively plausible structures, it should move toward making quantitative estimates of the underlying geologic processes inferred through a self-consistent framework. 

SUMMARY 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. 

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.