Adaptive Variable Time Fractional Anisotropic Diffusion Filtering for Seismic Data Noise Attenuation: Fid-Bau Portal

Adaptive Variable Time Fractional Anisotropic Diffusion Filtering for Seismic Data Noise Attenuation

Zhou, Qingbao

Seismic records are often contaminated with various kinds of noise, which makes it very difficult to distinguish the expected geological features. In this paper, we introduce a novel adaptive variable time fractional-order anisotropic diffusion equation for seismic data noise removal and strongly oriented structure enhancement. Since the time fractional-order differential equation interpolates a parabolic equation and a hyperbolic equation, the solution benefits both of these approaches. The presented differential equation can be written as a Volterra integral equation, and its well-posedness can be guaranteed for all time. We employ a structure tensor to analyze the flow-like texture characteristic which is typical in seismic data. Then, the diffusion process is guided reasonably by a diffusion tensor based on the structure tensor analysis which allows real anisotropic behavior comparing to the classical scalar diffusion approach. In reference to the numerical implementation, we utilize the predictor-corrector algorithm to solve the Volterra integral equation which provides high-order numerical precision jointly with good stability property. Finally, numerical experiments involved with synthetic and prestacked real seismic data are presented. The obtained results demonstrate that the noise is effectively removed, and the coherent seismic events that express some important geological structures are not only preserved but significantly enhanced.