Permeability anisotropy systematically deflects fluid flow in volcanic media

Jamie Ian Farquharson 

Permeability is fundamental in volcanic systems, governing heat and mass transfer across spatial scales and controlling pressurisation of the edifice and conduit. In nature, permeability is rarely isotropic and should be treated as a second-order tensor rather than a scalar. This contribution experimentally demonstrates directional dependence of permeability in transversely isotropic volcanic tuff, highlighting a critical phenomenon: other than when measurements are made parallel or perpendicular to fabric (the structural axis n), flow is deflected away from the driving hydraulic gradient. A closed-form analytical expression is derived for the critical gradient angle β^*, which describes the hydraulic gradient orientation relative to n at which flow deflection reaches its maximum value δ^*. The angle β^* depends only on the permeability anisotropy ratio. This effect has consequences for the interpretation of volcanic fluid pathways: anisotropy can decouple surface fluid discharge from the direction of the driving pressure gradient, produce lateral offsets between subsurface sources and surface expressions, and allow permeability anisotropy to be inferred from flow trajectories. Changes in anisotropy during deformation or compaction can further significantly redirect preferential flow pathways through time.