Fractional anisotropic gradient based filtering for random noise attenuation of seismic data

Motivated by the fact that the fractional derivative operators in existing fractional gradient are unable to separately act on input signals in the horizontal and vertical directions, we first introduce the concept of fractional anisotropic gradient in this paper. Based on this concept, we propose a new denoising model, derive the Euler-Lagrange equation for this new model and present the corresponding numerical algorithm. Finally, we apply our proposed method to the random noise attenuation for real seismic profiles. The theoretical analysis and experimental results indicate that our method can preferably enhance the lateral continuity of seismic events and preserve the line-like texture characters and useful detail information in the vertical direction while improving the signal-to-noise ratio. This provides a reliable basis for seismic data interpretation.