Nonstationary signal inversion based on shaping regularization for random noise attenuation

Abstract

Prediction filtering is one of the most commonly used random noise attenuation methods in the industry; however, it has two drawbacks. First, it assumes that the seismic signals are piecewise stationary and linear. However, the seismic signal exhibits nonstationary due to the complexity of the underground structure. Second, the method predicts noise from seismic data by convolving with a prediction error filter (PEF), which applies inconsistent noise models before and after denoising. Therefore, the assumptions and model inconsistencies weaken conventional prediction filtering’s performance in noise attenuation and signal preservation. In this paper, we propose a nonstationary signal inversion based on shaping regularization for random noise attenuation. The main idea of the method is to use the nonstationary prediction operator (NPO) to describe the complex structure and obtain seismic signals using nonstationary signal inversion instead of convolution. Different from the convolutional predicting filtering, the proposed method uses NPO as the regularization constraint to directly invert the effective signal from the noisy seismic data. The NPO varies in time and space, enabling the inversion system to describe complex (nonstationary and nonlinear) underground geological structures in detail. Processing synthetic and field data results demonstrate that the method effectively suppresses random noise and preserves seismic reflection signals for nonstationary seismic data.