基于张量环分解的三维地震数据重建方法

3D seismic data reconstruction based on tensor ring decomposition

地震数据处理一直是地震学研究的热点,地震数据重建是地震数据处理中不可或缺的一环。本研究提出一种基于张量环分解的三维地震数据重建方法。通过张量环分解将大的三维数据转换成小的三维数据的乘积,利用张量环隐空间的低秩结构对张量环因子施加低秩约束,在使用交替方向乘子法和增广拉格朗日函数求解过程中对张量环因子进行核范数正则化和奇异值分解,通过循环多线性乘积将小的三维数据恢复为大的三维数据,最终获得三维地震数据重建结果。仿真数据和真实数据的实验结果表明,与正交矩阵追踪汉克尔重建方法和数据驱动紧致框架方法相比,本方法具有更好的重建效果和计算效率。

Seismic data processing has always been a hot spot in seismology research,and seismic data reconstruction is an indispensable part of seismic data processing.In this paper,a 3D seismic data reconstruction method based on tensor ring decomposition was proposed.Tensor ring decomposition was applied to convert large 3D data into a product of small 3D data.The TR factor was constrained by the low-rank structure of the latent space of the tensor ring.The nuclear norm regularization and singular value decomposition of the TR factor were carried out in the solution process by using the alternating direction multiplier method and the augmented Lagrangian function.The small 3D data was recovered into large 3D data through the cyclic multilinear product and the data reconstruction results were obtained.The experimental results of simulation data and field data show that the proposed method has better reconstruction performance and computational efficiency compared with the orthogonal matrix pursuit Hankel reconstruction method and the data-driven tight frame method.