The quality of a seismic section is typically determined by the effectiveness of the frequency band: low-frequency information is advantageous for improving the quality of deep imaging, while high-frequency information helps to enhance resolution. Compressive sensing (CS) has the potential for precise spread extension. However, during the spread spectrum extension, a low signal-to-noise ratio (SNR) may lead to frequency anomalies, compensation artifacts, and issues caused by noise. In this paper, based on the theory of compressive sensing, we derive a formula for full-frequency compensation with a Shearlet denoising constraint. We analyze the effectiveness and feasibility of this method. Compared to other mathematical transforms, Shearlet exhibits superior denoising capabilities and effective signal protection. Additionally, by replacing the identity matrix in the denoising constraint with a sampling matrix, it can accurately reconstruct missing data, even when dealing with discontinuous data. To improve the accuracy and effectiveness of compensation, we perform autocorrelation calculations on the data to extend the wavelet for frequency compensation. We apply the proposed method to various field data, including thin layers, low signal-to-noise ratio regions, missing data, and gas-bearing areas. Examples demonstrate the effectiveness and applicability of the proposed method.

The reconstruction of data is a critical preliminary work in the seismic data processing. Compressed sensing (CS) has been well applied in the field of reconstruction. The key point of CS is random sampling, which converts the mutual interference alias caused by regular undersampling into lower-amplitude outside noise. But traditional sampling methods lack constraints on sampling points, emerging too much alias. Segmented random sampling (SRS) effectively controls the distance between sampling points. On the other hand, a single mathematical transformation will lead to incomplete sparse expression and bad restoration effects. Morphological component analysis (MCA) decomposes a signal into several components with outstanding morphological features to approximate the complex internal structure of data. In this paper, we found a new dictionary combination (shearlet + DCT) under the MCA framework and used the block coordinate relaxation algorithm to get the optimal solution to obtain reconstruction results. Tests of 2D data and 3D data have proved that the proposed method can get a better effect when reconstructing the SRS data.

Precise characterization of small-scale geological heterogeneities is fundamental to seismic exploration; however, its success relies heavily on high-fidelity diffraction imaging. Conventionally, weak diffraction signals are often obscured by dominant specular reflections, making robust wavefield separation a critical prerequisite for target identification. Current mainstream paradigms, primarily based on post-migration dip-domain separation, are inherently limited by their high sensitivity to velocity model inaccuracies and the significant computational overhead associated with multidimensional gather extraction. Consequently, there is a pressing need to develop high-precision pre-stack separation techniques. Nevertheless, this remains challenging due to complex wavefield interference in raw data, where conventional methods struggle to distinguish deep, weak diffractions from kinematically similar reflections, often resulting in severe residual noise or signal degradation. To address these limitations, we propose a novel framework operating in a high-dimensional 3D slowness-frequency-wavenumber (p, f, k) feature space. By leveraging the distinct topological differences between reflections and diffractions in this transformed domain, the proposed method effectively decouples interfering energy components without relying on precise velocity models. Benchmarking against synthetic and field datasets demonstrates that our approach significantly suppresses reflection leakage while preserving the structural integrity of diffracted wavefields. Results indicate that the proposed p − f − k topological separation provides a more robust and computationally efficient solution for imaging complex fractures and small-scale reservoirs.