CT-UNet: Curvelet transform-based component-wise deep learning framework for seismic trace interpolation

Abstract

Seismic data may suffer from missing traces due to economic and environmental constraints as well as equipment malfunctions, where regular gaps caused by receiver or streamer spacing and irregular gaps resulting from topographic limitations occur simultaneously. Such missing data degrade the reliability of subsequent processing and interpretation, making accurate interpolation essential. High-resolution reconstruction requires balanced recovery of broadband components spanning low to high frequencies; however, existing deep learning-based interpolation methods exhibit degraded performance in certain spectral regions. In this study, we propose the curvelet transform (CT)-UNet, a deep learning interpolation method that leverages CT-based frequency- and directional-component separation to improve reconstruction balance across frequency bands, particularly under high-rate, regular undersampling conditions. The proposed method applies the uniform discrete CT (UDCT) to decompose input data into low-frequency and high-frequency components with multi-resolution and directional characteristics, trains specialized U-Net models for each component, and reconstructs the final result through inverse transformation. Performance was evaluated on synthetic data (Society of Exploration Geophysicists/European Association of Geoscientists and Engineers Salt Model) and field data (Mobil Amplitude Versus Offset Viking Graben Line 12) by comparing to f–x interpolation, Constrained Diffusion-Driven Deep Image Prior, a standard U-Net, a parameter-matched U-Net-Wide, and the wavelet-based wavelet transform-UNet. An exploratory experiment on irregular missing and a structural compatibility analysis of the UDCT level configuration were also conducted. Results show that CT-UNet improves reconstruction quality across the tested missing conditions, with the clearest gains observed under high-rate regular undersampling and the 70% irregular missing scenario. Shot-level analysis further supports its advantage in challenging cases, particularly for synthetic 80%, field 75%, field 80%, and 70% irregular missing conditions. The advantage is especially pronounced in recovering curvature-varying, conflicting-dip events, while structural similarity is generally maintained at a level comparable to or higher than that of the baseline methods.

Keywords

Seismic data interpolation / Curvelet transform / Deep learning / U-Net / Uniform discrete curvelet transform / Missing trace reconstruction

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