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在实际的地球物理数据采集工作中,会因为多方面的客观原因导致数据缺失,对缺失数据进行插值重构是地球物理数据处理和解释的基础问题。基于地球物理数据自身或在变换域内的稀疏性,将地球物理数据的重构转化为稀疏优化问题可提高数据重构的精确度与稳定性。本文建立了LO范数最小化的地球物理数据稀疏重构模型,针对不同规模、不同特征的地球物理数据引入了两种不同类型的LO范数最小优化问题的近似求解算法,即基于LO范数最小化的迭代再加权最小二乘算法与具有快速收敛性的快速迭代硬阈值法。理论分析与数值试验表明,将迭代再加权最小二乘算法应用到位场数据重构中可发挥其收敛速度快,计算时间短,精度高的优势,而快速迭代硬阈值法更适合处理地震数据,相对于传统的迭代硬阈值法计算效率有了很大的提高。
In actual geophysical data acquisition, data will be missing due to many objective reasons. Interpolating and reconstructing missing data is the basic issue of geophysical data processing and interpretation. Based on the sparsity of geophysical data itself or in the transform domain, the reconstruction of geophysical data into a sparse optimization problem can improve the accuracy and stability of data reconstruction. In this paper, a sparse reconstruction model of geophysical data with LO norm minimization is established. Two different types of approximate algorithms for minimizing LO norm minimization problems are introduced for geophysical data of different scales and different characteristics. Minimized Iterative Reweighted Least Squares Algorithm and Fast Iterative Hard Threshold Method with Fast Convergence. The theoretical analysis and numerical experiments show that the iterative reweighted least squares algorithm can be used to reconstruct the field data, which has the advantages of fast convergence speed, short computation time and high accuracy. However, the fast iterative hard-thresholding method is more suitable for seismic data processing. Compared with the traditional iterative hard threshold calculation efficiency has been greatly improved.