ABSTRACT Dictionary learning is a successful method for random seismic noise attenuation that has been proven by some scholars. Dictionary learning–based techniques aim to learn a set of common bases called dictionaries from given noised seismic data. Then, the denoising process will be performed by assuming a sparse representation on each small local patch of the seismic data over the learned dictionary. The local patches that are extracted from the seismic section are essentially two‐dimensional matrices. However, for the sake of simplicity, almost all of the existing dictionary learning methods just convert each two‐dimensional patch into a one‐dimensional vector. In doing this, the geometric structure information of the raw data will be revealed, leading to low capability in the reconstruction of seismic structures, such as faults and dip events. In this paper, we propose a two‐dimensional dictionary learning method for the seismic denoising problem. Unlike other dictionary learning–based methods, the proposed method represents the two‐dimensional patches directly to avoid the conversion process, and thus reserves the important structure information for a better reconstruction. Our method first learns a two‐dimensional dictionary from the noisy seismic patches. Then, we use the two‐dimensional dictionary to sparsely represent all of the noisy two‐dimensional patches to obtain clean patches. Finally, the clean patches are patched back to generate a denoised seismic section. The proposed method is compared with the other three denoising methods, including FX‐decon, curvelet and one‐dimensional learning method. The results demonstrate that our method has better denoising performance in terms of signal‐to‐noise ratio, fault and amplitude preservation.

中文翻译：

---

用于抑制随机地震噪声的二维字典学习

摘要 字典学习是一种成功的随机地震噪声衰减方法，已被一些学者证明。基于字典学习的技术旨在从给定的噪声地震数据中学习一组称为字典的公共基础。然后，将通过在学习字典上的地震数据的每个小局部块上假设稀疏表示来执行去噪过程。从地震剖面中提取的局部斑块本质上是二维矩阵。然而，为了简单起见，几乎所有现有的字典学习方法都只是将每个二维块转换为一维向量。这样做会暴露原始数据的几何结构信息，导致地震结构重建能力低下，例如断层和倾角事件。在本文中，我们提出了一种用于地震去噪问题的二维字典学习方法。与其他基于字典学习的方法不同，所提出的方法直接表示二维块以避免转换过程，从而保留重要的结构信息以便更好地重建。我们的方法首先从嘈杂的地震斑块中学习二维字典。然后，我们使用二维字典稀疏表示所有嘈杂的二维补丁以获得干净的补丁。最后，干净的补丁被修补以生成去噪的地震剖面。将所提出的方法与其他三种去噪方法进行了比较，包括FX-decon、曲波和一维学习方法。