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ABSTRACT Seismic tomography is the most abundant source of information about the internal structure of the Earth at scales ranging from a few meters to thousands of kilometers. It constrains the properties of active volcanoes, earthquake fault zones, deep reservoirs and storage sites, glaciers and ice sheets, or the entire globe. It contributes to outstanding societal problems related to natural hazards, resource exploration, underground storage, and many more. The recent advances in seismic tomography are being translated to nondestructive testing, medical ultrasound, and helioseismology. Nearly 50 yr after its first successful applications, this article offers a snapshot of modern seismic tomography. Focused on major challenges and particularly promising research directions, it is intended to guide both Earth science professionals and early-career scientists. The individual contributions by the coauthors provide diverse perspectives on topics that may at first seem disconnected but are closely tied together by a few coherent threads: multiparameter inversion for properties related to dynamic processes, data quality, and geographic coverage, uncertainty quantification that is useful for geologic interpretation, new formulations of tomographic inverse problems that address concrete geologic questions more directly, and the presentation and quantitative comparison of tomographic models. It remains to be seen which of these problems will be considered solved, solved to some extent, or practically unsolvable over the next decade. 

Abstract Increasing deployment of dense arrays has facilitated detailed structure imaging for tectonic investigation, hazard assessment and resource exploration. Strong velocity heterogeneity and topographic changes have to be considered during passive source imaging. However, it is quite challenging for ray‐based methods, such as Kirchhoff migration or the widely used teleseismic receiver function, to handle these problems. In this study, we propose a 3‐D passive source reverse time migration strategy based on the spectral element method. It is realized by decomposing the time reversal full elastic wavefield into amplitude‐preserved vector P and S wavefields by solving the corresponding weak‐form solutions, followed by a dot‐product imaging condition to get images for the subsurface structures. It enables us to use regional 3‐D migration velocity models and take topographic variations into account, helping us to locate reflectors at more accurate positions than traditional 1‐D model‐based methods, like teleseismic receiver functions. Two synthetic tests are used to demonstrate the advantages of the proposed method to handle topographic variations and complex velocity heterogeneities. Furthermore, applications to the Laramie array data using both teleseismic P and S waves enable us to identify several south‐dipping structures beneath the Laramie basin in southeast Wyoming, which are interpreted as the Cheyenne Belt suture zone and agree with, and improve upon previous geological interpretations.