Inversion-Based 3-D Seismic Denoising for Exploring Spatial Edges and Spatio-Temporal Signal Redundancy

Seismic data are increasingly required to be high quality for the continuous improvement of the degree of exploration. From the viewpoint of inversion, the utilization of more information is an effective way to improve the signal-to-noise ratio of seismic data. In this letter, we adopt simultaneous sparsity constraints of the first-order differences of signals along the time direction and two spatial directions, described by minimizing the Cauchy function, as a combined constraint (or regularization) term imposed on the time-domain data misfit to propose an inversion-based 3-D seismic denoising method. In this way, the redundancies among time slices and seismic sections along two spatial directions are simultaneously considered, and the edges along the spatial directions can be preserved. Through analyzing the first-order derivative of the sum of the data misfit term and the designed combined regularization term (or the objective function), we derive that the relationship between data and desired signal samples in the range of the first-order neighborhood can be expressed as a linear system with seven data-dependent coefficients. Furthermore, it can be inferred that the sparsity constraints of signal differences along different dimensional directions of 3-D data have some complementary functions of noise reduction and signal preservation. We use a 3-D synthetic data set, a 3-D real poststack data set, and a 3-D real prestack data set to determine that the proposed method is an effective amplitude-preservation denoising tool with an acceptable computational cost.