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The receiver function (RF) is a widely used crustal imaging technique. In principle, it assumes relatively noise-free traces that can be used to target receiver-side structures following source deconvolution. In practice, however, mode conversions and reflections may be severely degraded by noisy conditions, hampering robust estimation of crustal parameters. In this study, we use a sparsity-promoting Radon transform to decompose the observed RF traces into their wavefield contributions, that is, direct conversions, multiples, and incoherent noise. By applying a crustal mask on the Radon-transformed RF, we obtain noise-free RF traces with only Moho conversions and reflections. We demonstrate, using a synthetic experiment and a real-data example from the Sierra Nevada, that our approach can effectively denoise the RFs and extract the underlying Moho signals. This greatly improves the robustness of crustal structure recovery as exemplified by subsequent H-k stacking. We further demonstrate, using a station sitting on loose sediments in the Upper Mississippi embayment, that a combination of our approach and frequency-domain filtering can significantly improve crustal imaging in reverberant settings. In the presence of complex crustal structures, for example, dipping Moho, intracrustal layers, and crustal anisotropy, we recommend caution when applying our proposed approach due to the difficulty of interpreting a possibly more complicated Radon image. We expect that our technique will enable high-resolution crustal imaging and inspire more applications of Radon transforms in seismic signal processing. [ABSTRACT FROM AUTHOR]

The investigation of upper mantle structure beneath the US has revealed a growing diversity of discontinuities within, across, and underneath the sub‐continental lithosphere. As the complexity and variability of these detected discontinuities increase—for example, velocity increase/decrease, number of layers and depth—it is hard to judge which constraints are robust and which explanatory models generalize to the largest set of constraints. Much work has been done to image discontinuities of interest using S‐waves that convert to P‐waves (or top‐side reflected SS waves). A higher resolution method using P‐to‐S scattered waves is preferred but often obscured by multiply reflected waves trapped in a shallower layer, limiting the visibility of deeper boundaries. Here, we address the interference problem and re‐evaluate upper mantle stratification using filtered P‐to‐S receiver functions (Ps‐RFs) interpreted using unsupervised machine‐learning. Robust insight into upper mantle layering is facilitated with CRISP‐RF: Clean Receiver‐Function Imaging using Sparse Radon Filters. Subsequent sequencing and clustering organizes the polarity‐filtered Ps‐RFs into distinct depth‐based clusters. We find three types of upper mantle stratification beneath the old and stable continental US: (a) intra‐lithosphere discontinuities (paired or single boundary), (b) transitional discontinuities (single boundary or with a top layer), and (c) sub‐lithosphere discontinuities. Our findings contribute a more nuanced understanding of mantle discontinuities, offering new perspectives on the nature of upper mantle layering beneath continents. Plain Language Summary: Early investigations of the mantle rocks in the US indicate intricate layering. However, uncertainties remain regarding the origins of these structures. Here, we re‐examine mantle rock stratification using a fine‐resolution approach. We use short waves that improve our ability to identify the depth of thin layers and sharp transitions in rock properties. Until now, these methods haven't been used due to interference with waves trapped in the near‐surface layers. We address this problem with machine learning and the CRISP‐RF (Clean Receiver Function Images Using Sparse Radon‐Filters) method. CRISP‐RF filters out the waves trapped in the crust and machine learning reveals spatially coherent patterns. Underneath the stable continents, we find evidence for different types of rock layering: (a) reflectors within cold stiff rocks (b) reflectors at depth ranges where the rocks become warmer and flow more readily, and (c) reflectors at depths farther down in the upper mantle. Our approach enables the test of hypotheses about the origins of upper mantle layering beneath continents. Key Points: Upper mantle stratification is constrained using Clean Receiver‐function Imaging using Sparse Radon Filters and machine learningStratification is classified into intra‐lithospheric, transitional and sub‐lithosphericHigh‐resolution constraints allow the evaluation of different causal models [ABSTRACT FROM AUTHOR]

Seismic interrogation of the upper mantle from the base of the crust to the top of the mantle transition zone has revealed discontinuities that are variable in space, depth, lateral extent, amplitude and lack a unified explanation for their origin. Improved constraints on the detectability and properties of mantle discontinuities can be obtained with P-to-S receiver function (Ps-RF) where energy scatters from P to S as seismic waves propagate across discontinuities of interest. However, due to the interference of crustal multiples, uppermost mantle discontinuities are more commonly imaged with lower resolution S-to-P receiver function (Sp-RF). In this study, a new method called CRISP-RF (Clean Receiver-function Imaging using SParse Radon Filters) is proposed, which incorporates ideas from compressive sensing and model-based image reconstruction. The central idea involves applying a sparse Radon transform to effectively decompose the Ps-RF into its underlying wavefield contributions, that is direct conversions, multiples, and noise, based on the phase moveout and coherence. A masking filter is then designed and applied to create a multiple-free and denoised Ps-RF. We demonstrate, using synthetic experiment, that our implementation of the Radon transform using a sparsity-promoting regularization outperforms the conventional least-squares methods and can effectively isolate direct Ps conversions. We further apply the CRISP-RF workflow on real data, including single station data on cratons, common-conversion-point stack at continental margins and seismic data from ocean islands. The application of CRISP-RF to global data sets will advance our understanding of the enigmatic origins of the upper mantle discontinuities like the ubiquitous mid-lithospheric discontinuity and the elusive X-discontinuity. [ABSTRACT FROM AUTHOR]