©　2013　SEG.　In　this　paper,　we　propose　a　new　approach　devoted　to　the　denoising　and　the　enhancing　of　strongly　oriented　seismic　image.　The　approach　is　based　on　diffusion　tensor　and　fractional　time　integral　which　can　be　written　as　a　Volterra　matrix-valued　equation　when　our　method　applies　to　seismic　image.　Since　the　fractional　integral　equation　interpolates　a　linear　parabolic　equation　and　a　hyperbolic　equation,　the　solution　enjoys　intermediate　properties.　The　Volterra　equation　introduced　is　well-posed　for　all　time　t　＞　0.　Since　the　seismic　image　shows　the　typical　line-like　texture　character,　diffusion　tensor　is　introduced　to　analysis　such　features.　In　contrast　to　many　other　nonlinear　diffusion　techniques,　such　as　scalar　diffusivity,　diffusion　tensor　allows　real　anisotropic　behavior.　The　preferred　diffusion　direction　is　determined　according　to　the　eigenvectors　of　the　structure　tensor,　and　the　diffusivity　in　this　direction　is　controlled　by　the　eigenvalues.　The　coherent　seismic　events　and　some　important　geology　structures　reflected　by　them　can　be　preserved　and　enhanced　in　our　framework.　The　improvements　achieved　by　our　approach　are　illustrated　with　real　seismic　data　experiments.