Episodic tremor and slip (ETS) along the subduction interface takes place where there is abundant evidence for elevated, near-lithostatic pore pressures, at sufficiently great depths (30-45 km) that chemical dehydration reactions must act as their dominant source. We simulate fluid and heat flow while tracking the location of a vertically oriented, one-dimensional column of material as it subducts through the slow slip and tremor zone. The material in the column is transformed through a pressure-dependent and temperature-dependent dehydration reaction that we describe with a generalized nonlinear kinetic rate law. Column deformation is largely dominated by viscous creep, with a closure rate that depends linearly on porosity. This behavior causes the dehydration reaction to generate traveling porosity waves that transport increased fluid pressures within the slow slip region. To explore the possibility that the observed periodicity of slow slip and tremor in subduction zones can be explained by the migration of such porosity waves, we derive a dispersion relation that accurately describes our numerical results. We also obtain an expression for how the thickness of the dehydrating layer is expected to vary as a function of the parameters in the reaction rate law. Although the amplitudes of pore pressure perturbations rival those that are produced by known external forcings (e.g., tides or passing surface waves), our analysis suggests that given reasonable estimates of rock viscosity, permeabilities in the range 6.5x10-15 to 5x10-10m2 are required for porosity wave trains to form at periods comparable to those of slow slip and tremor.
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