3D seismic data denoising and reconstruction using total variation regularized nonlocal low-rank tensor decomposition

In seismic data acquisition, the recorded seismic data is often corrupted by unavoidable noises and missing traces, which has a negative impact on subsequent seismic imaging and geophysical inversion. In the past decade, low-rank tensor based methods have been proposed for high-dimensional seismic data denoising and reconstruction and have achieved good results. However, when the structure of the seismic data is somewhat complex, the low-rank based methods cannot get satisfactory result. In fact, the effective structures of seismic data can be characterized by the abundance of self-repeating patterns. Taking these characteristics into account, we model the nonlocal similar patch group as a low rank tensor of 3-order, and then propose to use the total variation regularized low-rank tensor decomposition approach to each constructed nonlocal tensor, which can characterize the low rank property of nonlocal tensor well and effectively identify the intrinsic structures of the clean seismic data to achieve seismic data denoising and reconstruction. Specifically, for each tensor formed by nonlocal similar patches, the tensor Tucker decomposition is used to describe the global correlation among all patches, and an anisotropic total variation regularization is adopted to characterize the piecewise smooth structures in and between the patches and remove Gaussian noise. At the same time, the L₁ norm regularization is used to model sparse noise, and the Frobenius norm term is further used to model heavy Gaussian noise. In order to better preserve the spatial structure of seismic data, we implement the proposed scheme in three dimensions of seismic data respectively, and finally average these three results to obtain the denoised and reconstructed seismic data. Both synthetic and field data examples show that the proposed method is capable of removing seismic noise and recover missing traces of seismic data effectively even when the structure of the seismic data is somewhat complex.