Decompaction weakening and channeling instability in ductile porous media: Implications for asthenospheric melt segregation

Abstract

We propose that a mechanical flow channeling instability, which arises because of rock weakening at high fluid pressure, facilitates segregation and transport of asthenospheric melts. To characterize the weakening effect, the ratio of the matrix viscosity during decompaction to that for compaction is treated as a free parameter R in the range 1 to 10 −6 . Two‐dimensional numerical simulations with this rheology reveal that solitary, vertically elongated, porosity waves with spacing on the compaction length scale δ initiate from miniscule porosity perturbations. By analogy with viscous compaction models we infer that in the absence of far‐field stress, the three‐dimensional expression of the waves is as pipe‐like structures of radius δ , a geometry that increases fluid fluxes by a factor of ∼1/ R . The waves grow by draining fluid from the background porosity but leave a wake of elevated porosity that localizes subsequent flow. Wave amplitudes grow linearly with time, increasing by a factor of R −3/8 in the time required to drain the porosity a distance of ∼ δ . Dissipation of gravitational potential energy by the waves has the capacity to enhance growth rates through melting. Maximum wave speeds are ∼40 times the speed of fluid flow through the unperturbed matrix. Such waves may provoke the elastic response necessary to nucleate, and localize the melt necessary to sustain, more effective transport mechanisms. The formulation introduces no melting effects and is applicable to fluid flow and localization problems in ductile porous media in general.