Double-phase-shift filtering method for harmonic elimination based on AR2U-Net

The double-phase-shift filtering method, which is based on the traditional pure-phase-shift filtering method, is a novel approach to harmonic elimination that can be applied to more complicated signals such as white noise and slip-sweep. Nonetheless, any type of phase-shift filtering method necessitates a relationship between the frequency of fundamental sweep and time, which may cost necessitate an enormous amount of human and physical resources to achieve inaccurate results with low efficiency. This paper combines deep learning with harmonic elimination to produce a double-phase-shift filtering method based on AR2U-Net, a type of U-Net with attention gates structure and recurrent residual blocks for improving accuracy and function while simplifying computational complexity. The input of the AR2U-Net structure in this paper is seismic data of slip-sweep signals in vibroseis, and the output is signal frequency variation with the time of the fundamental waves, which are required to eliminate the harmonic waves and adjacent signals using a double-phase-shift method to obtain the fundamental sweep. The training sets and test sets are formed by forward models, and a Log-Cosh loss function is used to monitor the process, during which the results of AR2U-Net and traditional U-Net are compared to demonstrate the eminent function of AR2U-Net. Following that, the outcomes’ Log-Cosh loss functions and accuracy are also compared to validate the conclusion. AR2U-Net, when applied to raw data and combined with the double-phase-shift method, tends to polish the filtering effects and is worth promoting.