Seismic data are often undersampled owing to physical or financial limitations. However, complete and regularly sampled data are becoming increasingly critical in seismic processing. In this paper, we present an efficient two-dimensional (2D) seismic data reconstruction method that works on texture-based patches. It performs completion on a patch tensor, which folds texture-based patches into a tensor. Reconstruction is performed by reducing the rank using tensor completion algorithms. This approach differs from past methods, which proceed by unfolding matrices into columns and then applying common matrix completion approaches to deal with 2D seismic data reconstruction. Here, we first re-arrange the seismic data matrix into a third-order patch tensor, by stacking texture-based patches that are divided from seismic data. Then, the seismic data reconstruction problem is formulated into a low-rank tensor completion problem. This formulation avoids destroying the spatial structure, and better extracts the underlying useful information. The proposed method is efficient and gives an improved performance compared with traditional approaches. The effectiveness of our patch tensor-based framework is validated using two classical tensor completion algorithms, low-rank tensor completion (LRTC), and the parallel matrix factorization algorithm (TMac), on both synthetic and field data experiments.

中文翻译：

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使用面片张量完成的二维地震数据重建

由于物理或财务方面的限制，地震数据经常被抽样不足。但是，完整和定期采样的数据在地震处理中变得越来越重要。在本文中，我们提出了一种有效的二维（2D）地震数据重建方法，该方法可用于基于纹理的斑块。它对面片张量执行补全，然后将基于纹理的面片折叠成张量。通过使用张量完成算法降低秩来执行重建。该方法不同于以往的方法，后者通过将矩阵展开为列，然后应用常见的矩阵完成方法来处理2D地震数据重建。在这里，我们首先通过堆叠从地震数据中分割出来的基于纹理的补丁，将地震数据矩阵重新排列为三阶补丁张量。然后，将地震数据重建问题表述为低秩张量完成问题。这种表述避免了破坏空间结构，并更好地提取了潜在的有用信息。与传统方法相比，所提出的方法是有效的并且提供了改进的性能。在合成和现场数据实验中，使用两种经典的张量完成算法，低秩张量完成（LRTC）和并行矩阵分解算法（TMac）验证了我们基于补丁张量的框架的有效性。与传统方法相比，所提出的方法是有效的并且提供了改进的性能。在合成和现场数据实验中，使用两种经典的张量完成算法，低秩张量完成（LRTC）和并行矩阵分解算法（TMac）验证了我们基于补丁张量的框架的有效性。与传统方法相比，所提出的方法是有效的并且提供了改进的性能。在合成和现场数据实验中，使用两种经典的张量完成算法，低秩张量完成（LRTC）和并行矩阵分解算法（TMac）验证了我们基于补丁张量的框架的有效性。