Simultaneous Reconstruction and Denoising of Extremely Sparse 5-D Seismic Data by a Simple and Effective Method

5-D data is the original recorded form in the 3-D seismic acquisition, which includes sufficient information from all five dimensions. However, environmental and economic logistic difficulties often severely impact the data acquisition geometry, leading to raw data with missing traces and strong contaminating random noise. This deficiency often causes troubles in subsequent processing. Thus, an efficient interpolation and denoising method is required to recover useful signals. Unfortunately, practical applications of many existing reconstruction algorithms are limited by their intensive computational cost when applied to the 5-D data. Additionally, the stability of these algorithms is also challenged by complex geological structures, which often degrades the reconstruction performance. To seek solutions to the aforementioned problems, we design a simple and effective framework for fast reconstruction and denoising of undersampled 5-D seismic data via a two-step process. First, we prepare the initial model from the original recordings by constructing a 3-D gather at each common offset point. This step effectively interpolates the missing traces in 3-D common offset gathers by exploiting the data coherency in the adjacent areas (i.e., nearby mid-points). In the second step, the processed 5-D data is reorganized into 3-D common midpoint gathers, with each of them further sorted into a 2-D section according to absolute offset values. Then a conventional 2-D processing algorithm (e.g., F-X prediction, wavelet thresholding, or multichannel singular spectrum analysis) is invoked to filter the obtained 2-D section. The proposed workflow has a low overall computational cost and preserves signal fidelity. We use this framework to simultaneously denoise and interpolate the low-quality and extremely sparse seismic data. The synthetic and field examples both demonstrate the superb performance of the proposed framework in comparison with conventional methods.