Accurate Decomposition of Full Waveform Sonic Data

Abstract Full waveform sonic data is typically dominated by strong direct wave mode propagating along the borehole, which obscures the weak reflected signals of interest. Therefore, accurate wave mode decomposition is an essential step in enhancing the interpretability of full waveform sonic data, particularly for applications such as velocity estimation and imaging of near-borehole structures. We propose a novel decomposition technique based on a 3D sparse Radon transform that effectively separates overlapping wave in full waveform sonic data. The proposed method first estimates the slowness of different dominant linear events in common-shot gather through semblance analysis and then compute the dip of direct wave mode in common-offset gather using structure tensor. After that, the full waveform sonic data, originally in the time-space domain, is transformed into a time–slowness–space domain using a 3D sparse Radon transform. This transformation creates a sparse, higher-dimensional representation in which different wave modes become more separable due to their distinct orientations and slowness characteristics. A mask function is then automatically constructed in the Radon domain by analyzing signal orientation in both common-shot and common-offset gathers. This enables the selection and isolation of specific wave mode components, including weak reflections and directionally distinct upgoing and downgoing reflected waves. Finally, an inverse transform reconstructs each wave component into the original time-space domain, yielding high-fidelity decomposed wavefields. Numerical tests on field monopole full waveform sonic datasets demonstrate that the proposed method significantly improves the signal-to-noise ratio (SNR) by suppressing random noise and enhancing coherent energy. Furthermore, it accurately decomposes the monopole dataset into six physically meaningful components: direct P-waves, direct S-waves, Stoneley waves, reflected waves, upgoing and downgoing reflections. This approach provides a powerful processing tool for acoustic logging interpretation and reflection imaging applications in complex subsurface environments.