在地震资料反演中,反褶积是一种重要的压缩地震子波、提高薄层纵向分辨率的地震数据处理方法。由于地层为层状结构,反射系数可视作稀疏的脉冲序列,因此地震反褶积可以描述为稀疏求解问题。然而,反褶积问题通常是病态的,需要引入正则化...在地震资料反演中,反褶积是一种重要的压缩地震子波、提高薄层纵向分辨率的地震数据处理方法。由于地层为层状结构,反射系数可视作稀疏的脉冲序列,因此地震反褶积可以描述为稀疏求解问题。然而,反褶积问题通常是病态的,需要引入正则化约束以获得稳定和准确的解。本研究介绍了几种不同的正则化方法,包括L1正则化、L2正则化、Cauchy正则化以及结合L1和L2正则化的方法,给出了它们的数学模型,并着重比较了Cauchy正则化与结合L1和L2正则化的方法。通过简单的一维模型和复杂的Marmousi2 (二维)模型的实验,我们评估了这些正则化方法在稀疏脉冲反褶积中的性能表现。结果表明,结合L1和L2正则化的联合方法在噪声抑制和分辨率提升方面表现优异,能够更准确地恢复地下结构的真实反射特性。本文的研究为选择适当的正则化策略以优化地震数据的反褶积处理提供了理论支持和实用指导。In seismic data inversion, deconvolution is an important seismic data processing method that compresses seismic wavelets and improves the vertical resolution of thin layers. Due to the layered structure of the strata, the reflection coefficient can be regarded as a sparse pulse sequence, so seismic deconvolution can be described as a sparse solution problem. However, deconvolution problems are often pathological and require the introduction of regularization constraints to obtain stable and accurate solutions. This study introduces several different regularization methods, including L1 regularization, L2 regularization, Cauchy regularization, and methods combining L1 and L2 regularization. Their mathematical models are given, and the comparison between Cauchy regularization and methods combining L1 and L2 regularization is emphasized. We evaluated the performance of these regularization methods in sparse pulse deconvolution through experiments using a simple one-dimensional model and a complex Marmousi2 (two-dimensional) model. The results show that the joint method combining L1 and L2 regularization performs well in noise suppression and resolution improvement, and can more accurately restore the true reflection characteristics of underground structures. This study provides theoretical support and practical guidance for selecting appropriate regularization strategies to optimize the deconvolution processing of seismic data.展开更多
文摘随着高分辨率对地观测要求的不断提高,合成孔径雷达(Synthetic Aperture Radar,SAR)的应用将越来越广泛。针对高分辨率SAR成像存在数据量大、存储难度高、计算时间长等问题,目前常用的解决方法是在SAR成像模型中引入压缩感知(Compressed Sensing,CS)的方法降低采样率和数据量。通常使用单一的正则化作为约束条件,可以抑制点目标旁瓣,实现点目标特征增强,但是观测场景中可能存在多种目标类型,因此使用单一正则化约束难以满足多种特征增强的要求。本文提出了一种基于复合正则化的稀疏高分辨SAR成像方法,通过压缩感知降低数据量,并使用多种正则化的线性组合作为约束条件,增强观测场景中不同类型目标的特征,实现复杂场景中高分辨率对地观测的要求。该方法在稀疏SAR成像模型中引入非凸正则化和全变分(Total Variation,TV)正则化作为约束条件,减小稀疏重构误差、增强区域目标的特征,降低噪声对成像结果的影响,提高成像质量;采用改进的交替方向乘子法(Alternating Direction Method of Multipliers,ADMM)实现复合正则化约束的求解,减少计算时间、快速重构图像;使用方位距离解耦算子代替观测矩阵及其共轭转置,进一步降低计算复杂度。仿真和实测数据实验表明,本文所提算法可以对点目标和区域目标进行特征增强,减小计算复杂度,提高收敛性能,实现快速高分辨的图像重构。
文摘在地震资料反演中,反褶积是一种重要的压缩地震子波、提高薄层纵向分辨率的地震数据处理方法。由于地层为层状结构,反射系数可视作稀疏的脉冲序列,因此地震反褶积可以描述为稀疏求解问题。然而,反褶积问题通常是病态的,需要引入正则化约束以获得稳定和准确的解。本研究介绍了几种不同的正则化方法,包括L1正则化、L2正则化、Cauchy正则化以及结合L1和L2正则化的方法,给出了它们的数学模型,并着重比较了Cauchy正则化与结合L1和L2正则化的方法。通过简单的一维模型和复杂的Marmousi2 (二维)模型的实验,我们评估了这些正则化方法在稀疏脉冲反褶积中的性能表现。结果表明,结合L1和L2正则化的联合方法在噪声抑制和分辨率提升方面表现优异,能够更准确地恢复地下结构的真实反射特性。本文的研究为选择适当的正则化策略以优化地震数据的反褶积处理提供了理论支持和实用指导。In seismic data inversion, deconvolution is an important seismic data processing method that compresses seismic wavelets and improves the vertical resolution of thin layers. Due to the layered structure of the strata, the reflection coefficient can be regarded as a sparse pulse sequence, so seismic deconvolution can be described as a sparse solution problem. However, deconvolution problems are often pathological and require the introduction of regularization constraints to obtain stable and accurate solutions. This study introduces several different regularization methods, including L1 regularization, L2 regularization, Cauchy regularization, and methods combining L1 and L2 regularization. Their mathematical models are given, and the comparison between Cauchy regularization and methods combining L1 and L2 regularization is emphasized. We evaluated the performance of these regularization methods in sparse pulse deconvolution through experiments using a simple one-dimensional model and a complex Marmousi2 (two-dimensional) model. The results show that the joint method combining L1 and L2 regularization performs well in noise suppression and resolution improvement, and can more accurately restore the true reflection characteristics of underground structures. This study provides theoretical support and practical guidance for selecting appropriate regularization strategies to optimize the deconvolution processing of seismic data.
