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.