The efficiency, precision, and denoising capabilities of reconstruction algorithms are critical to seismic data processing. Based on the Fourier-domain projection onto convex sets (POCS) algorithm, we propose an inversely proportional threshold model that defines the optimum threshold, in which the descent rate is larger than in the exponential threshold in the large-coefficient section and slower than in the exponential threshold in the small-coefficient section. Thus, the computation efficiency of the POCS seismic reconstruction greatly improves without affecting the reconstructed precision of weak reflections. To improve the flexibility of the inversely proportional threshold, we obtain the optimal threshold by using an adjustable dependent variable in the denominator of the inversely proportional threshold model. For random noise attenuation by completing the missing traces in seismic data reconstruction, we present a weighted reinsertion strategy based on the data-driven model that can be obtained by using the percentage of the data-driven threshold in each iteration in the threshold section. We apply the proposed POCS reconstruction method to 3D synthetic and field data. The results suggest that the inversely proportional threshold model improves the computational efficiency and precision compared with the traditional threshold models; furthermore, the proposed reinserting weight strategy increases the SNR of the reconstructed data.
针对地面微地震资料强周期干扰和随机干扰突出的特点以及单一去噪方法无法有效压制噪声的问题,提出了基于单道奇异值分解(singular value decomposition,SVD)和振幅比的联合去噪方法。首先利用单道微地震记录构建分解矩阵,使矩阵各维具有较强的相关性,然后对分解矩阵进行奇异值分解,选取数值居中部分奇异值进行矩阵重构,以达到压制单道微地震记录强周期干扰的目的。其次采用具有伸缩特性时窗的振幅比法改善有效信号与随机噪声的统计特性差异,有效压制微地震资料中的随机噪声。理论模型数据和四川某地区地面微地震射孔资料应用结果表明,联合去噪方法有效地压制了微地震记录中的噪声,提高了资料的信噪比,在很大程度上改善了单一去噪方法无法较好突出微地震有效信号的不足,为后期微地震资料的处理与解释奠定了良好的基础。