基于全连接张量网络分解的五维地震数据重建

5D Seismic Data Reconstruction Based on Fully Connected Tensor Network Decomposition

三维地震数据采集方位已达到了五维(5-Dimension,5D)。相比于常规的三维(3-Dimension,3D)重建,5D重建能够充分利用高维数据中不同方位角、偏移距等的相关特性以及更多的空间信息特点,更准确地预测缺失道。基于阻尼降秩(Damped Rank Reduction,DRR)等的矩阵降秩方法对由5D数据频率切片构成的块Hankel矩阵进行多次奇异值分解(Singular Value Decomposition,SVD),计算效率较低。基于高阶正交迭代(High Order Orthogonal Iteration,HOOI)等的张量降秩方法对频率切片4D张量进行降秩重建,但是在强噪声和高缺失情况下重建精度不高。本文采用全连接张量网络(Fully Connected Tensor Network,FCTN)分解方法对5D数据重建,将频率切片4D张量分解成低维度张量收缩的形式。该方法无需SVD运算,而且更精确的张量分解形式可以得到更高精度的重建结果。仿真和真实地震数据实验结果表明:相比于HOOI方法,重建数据的信噪比提高了约8~9 dB;相比于DRR方法,重建数据的信噪比提高了约6~7 dB。

The acquisition position of three-dimensional seismic data has reached 5-dimension(5D).Compared with conventional 3-dimension(3D)reconstruction,5D reconstruction can make full use of the relevant characteristics of different azimuth angles and offsets in high-dimensional data as well as more spatial information characteristics to predict the missing track more accurately.The matrix rank reduction method based on damped rank reduction(DRR)was used to perform multiple singular value decomposition(SVD)on a block Hankel matrix composed of 5D data frequency slices,resulting in low computational efficiency.The tensor rank reduction method based on high-order orthogonal iteration was used for rank reduction reconstruction of frequency slices 4D tensor,but the reconstruction accuracy was not high under the conditions of strong noise and high miss.In this paper,we adopted the fully connected tensor network(FCTN)decomposition method to reconstruct the 5D data,which decomposed the frequency slice 4D tensor into the contracted form of low-dimensional tensor.The proposed method does not require SVD operation,and a more accurate tensor decomposition form can obtain higher precision reconstruction results.The results of synthetic and real seismic data experiment show that the signal to noise ratio of reconstructed data is improved by about 8~9 dB compared with HOOI method,and the signal to noise ratio of reconstructed data is improved by about 6~7 dB compared with the DRR method.