Anti-Noise Full-Frequency Expansion for Seismic Data With Compressed Sensing

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 article, based on the theory of CS, 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. In addition, 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 SNR regions, missing data, and gas-bearing areas. Examples demonstrate the effectiveness and applicability of the proposed method.