Compressive Sensing Seismic Signal Processing Method in 3-D Radon Domain—Part II: Compressive Sensing Seismic Near-Surface Noise Adaptive Suppression Method in 3-D Conical Radon Domain

The theory of compressed sensing (CS), offering a novel perspective beyond the Nyquist-Shannon sampling theorem, has garnered significant attention from geophysicists. It enables the reconstruction of ideal high-density seismic signals using cost-effective random undersampling, provided that the seismic signals can be sparsely represented. However, the near-surface noise challenges the sparse representation of seismic reflection signals. To suppress near-surface noise and achieve a better sparse representation of seismic reflection signals within the CS framework, this article develops a method for CS-based near-surface noise suppression, centered on 3-D conical Radon transform (CRT) combined with the CS theory. First, this study introduces the 3-D CRT into seismic signal processing, exploiting the “conical surface” characteristic of near-surface noise in 3-D CMP records. A method for extracting seismic signals and suppressing noise in the 3-D conical Radon domain is proposed. Subsequently, an adaptive filtering strategy is integrated with the 3-D CRT to develop a method for adaptive near-surface noise suppression in the 3-D conical Radon domain. Finally, combining CS theory, adaptive filtering strategies, and the 3-D Radon transform, this article proposes a method for adaptive near-surface noise suppression in the 3-D conical Radon domain based on CS. Numerical examples demonstrate that the integration of the CS random undersampling framework, adaptive filtering strategies, and the 3-D CRT significantly mitigates the impact of near-surface noise on seismic reflection signal reconstruction within the CS framework. This effectively addresses the issue of the 3-D CRT’s unsuitability for near-surface noise suppression within the CS framework.