Low-Frequency Seismic Noise Reduction Based on Deep Complex Reaction–Diffusion Model

Abstract

The low-frequency seismic noise has partially overlapping frequency band and similar waveform with seismic signals, making identification of seismic signals difficult in the seismic data at low signal-to-noise ratio (SNR). For improving the quality of seismic data, a deep complex reaction–diffusion (DCRD) model is proposed by combining the convolutional neural network (CNN) with the complex shock diffusion (CSD) which consists of a diffusion term and a shock term. By introducing a reaction term with an adjustable weight into the CSD, the CNN model can be embedded to learn the reaction term, leading to more effective signal preservation. The DCRD feeds smoothed signal components to the evolution process, by fusing the intermediate result based on low-level seismic features of data to be processed and the result of CNN model that learns deep seismic features. Moreover, the learnable reaction term facilitates the DCRD to apply effective diffusion for filtering out low-frequency seismic noise with spatiotemporally variable levels. Finally, the diffusion and shock terms in the DCRD can adjust the deviation of CNN model when the noise statistics of noisy seismic data having spatiotemporally variable levels deviate from training data, which also expand the practical application of CNN model. The DCRD is tested on synthetic and field seismic data and the results demonstrate that the DCRD achieves a great performance in suppressing low-frequency seismic noise with spatiotemporally variable levels and preserving seismic signals.