White noise attenuation of seismic trace by integrating variational mode decomposition with convolutional neural network

Seismic noise attenuation is an important step in seismic data processing. Most noise attenuation algorithms are based on the analysis of time-frequency characteristics of the seismic data and noise. We have aimed to attenuate white noise of seismic data using the convolutional neural network (CNN). Traditional CNN-based noise attenuation algorithms need prior information (the "clean" seismic data or the noise contained in the seismic) in the training process. However, it is difficult to obtain such prior information in practice. We assume that the white noise contained in the seismic data can be simulated by a sufficient number of user-generated white noise realizations. We then attenuate the seismic white noise using the modified denoising CNN (MDnCNN). The MDnCNN does not need prior clean seismic data nor pure noise in the training procedure. To accurately and efficiently learn the features of seismic data and band-limited noise at different frequency bandwidths, we first decomposed the seismic data into several intrinsic mode functions (IMFs) using variational mode decomposition and then apply our denoising process to the IMFs. We use synthetic and field data examples to illustrate the robustness and superiority of our method over the traditional methods. The experiments demonstrate that our method can not only attenuate most of the white noise but it also rejects the migration artifacts.