A new method for random noise attenuation in seismic data based on anisotropic fractional-gradient operators

• We introduce an anisotropic fractional-gradient operator.
• We propose a new model based on the anisotropic fractional-gradient operator.
• We derive the Euler–Lagrange equation for solving the proposed model.
• We apply the new model to random noise removal in seismic data.
• Experiment results show the advantages of our method over the existing methods.

In this paper, we first introduce an anisotropic fractional-gradient operator, from which, we propose a new method for random noise attenuation of seismic data. Then we derive the Euler–Lagrange equation for solving the proposed minimization problem and present the corresponding numerical algorithm. Finally, we apply our proposed method to the random noise attenuation for synthetic and real seismic sections. In addition, we also provide the selection strategies of the parameters involved in our proposed method. The theoretical analysis and experimental results indicate that our method can enhance the coherence of seismic events in the horizontal direction and preserve the texture structure and detailed useful information in the vertical direction while improving the signal-to-noise ratio. This provides a reliable basis for seismic data interpretation.