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    基于三维反褶积理论的Radon域稀疏增强算法

    A Radon-domain sparsity enhancement algorithm based on 3D deconvolution

    • 摘要: Radon变换是压制多次波、实现高精度成像的重要工具,其聚焦性的强弱会影响部分地震数据处理的效果。传统基于频率−曲率域L2范数约束的最小二乘Radon变换,受有限孔径影响,易产生剪刀状拖尾效应。而稀疏Radon变换虽通过变换域稀疏性假设获得了更高聚焦性的Radon域数据,但仍存在能量团收敛不足的问题。为此,联合地震子波与曲率方向平滑函数协同构建反褶积算子,对已有的Radon数据开展三维反褶积,基于交替方向乘子法(alternating direction method of multipliers,ADMM)的迭代求解,提出了基于三维反褶积理论的Radon域稀疏增强算法。该算法依托稀疏反演理论,通过去模糊机制在曲率维度实现能量压缩,显著提升了能量团的聚集度与分辨率。数值模拟与实测数据验证表明,相较于常规最小二乘Radon变换和时间域稀疏Radon变换,经反褶积稀疏增强处理后的Radon域能量团可辨识度得到有效提升,从而提高了多次波的识别和压制精度。

       

      Abstract: The Radon transform serves as a critical tool for multiple suppression and high-precision imaging, while its focusing capability directly affects the outcomes of seismic data processing. Conventional least-squares Radon transforms based on frequency-curvature domain L2-norm constraints tend to exhibit scissor-like trailing artifacts due to the limitation of finite aperture. Sparse Radon transforms have been developed to enhance Radon-domain focusing performance by incorporating sparsity constraints, which nevertheless face the limitation in achieving adequate convergence of energy clusters. To overcome this limitation, we propose a Radon-domain sparsity enhancement algorithm based on 3D deconvolution theory. The proposed algorithm integrates a seismic wavelet and a curvature-direction smoothing function to construct a deconvolution operator, which is then applied to 3D deconvolution of Radon-domain data within an iterative inversion framework using the alternating direction method of multipliers (ADMM). This approach compresses energy in the curvature dimension via the deblurring mechanism grounded in sparse inversion theory, thereby notably improving the concentration and resolution of energy clusters. Synthetic and field data tests demonstrate that, compared with conventional least-squares and time-domain sparse Radon transforms, the proposed deconvolution-based sparsity-enhanced method substantially improves the discriminability of Radon-domain energy clusters, leading to more accurate identification and suppression of multiple reflections.

       

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