SHAKEN AND STIRRED: A COMBINED REACTION-DIFFUSION AND RANDOM RATE MODEL FOR THE TEMPORAL EVOLUTION AND EARTHQUAKE-INDUCED HYDRODYNAMICS OF SILICATE MINERAL WEATHERING

The time dependency of silicate mineral weathering has been explored in the literature in terms of processes and features that are intrinsic and extrinsic to the mineral [1]. However, although the advent of sophisticated reactive transport models has allowed for coupling increasingly complex reaction and transport processes [2,3], a simple and fundamental understanding of the temporal evolution of weathering is lacking. Here, we propose that a purely deterministic approach may not be sufficient given the inherent differences in reactivity over space and time. Therefore, we explore how a combined reaction-diffusion and random rate model – informed by a stochastic distribution of weathering rates K (T^-1) – might be able to explain not only the temporal evolution but also the hydrodynamics of weathering during earthquakes; the latter being purportedly described by time-dependent property permeability (L²). Preliminary model results show that (1) an increase in dimensionless quantity βr_p, where β is the diffusion length (L^-1) and r_p is the distance between pores (L), leads to a decrease in minimum reaction rate with time from the relation K_min ∝ e^-βrp/r_p ; (2) at a given porosity, a time-dependent decrease in reactivity arises as permeability decreases due to decreasing pore size (and therefore increasing r_p), which in turn may be related to the time-dependent feedback between dissolution and precipitation; (3) while permeability is lower in older soils, transient stresses as during earthquakes [4], may induce more efficient "declogging" of pores in these soils than in younger soils due to higher hydrodynamic viscous shear stress, thereby, resulting in a coseismic change in stream discharge Q; and (4) subsequent weathering beyond t~K_min^-1 exhibits a fall in rates, marking the cessation of logarithmic decay possibly due to dissolution-precipitation feedback.

[1] White and Brantley (2003), Chem. Geol. 202, 479.

[2] Lichtner P.C. (1996), Mineralogical Society of America, 1-81.

[3] Maher K., Steefel C.I., White A.F. and Stonestrom D.A. (2009), Geochim. Cosmochim. Acta 73, 2804-2831.

[4] Manga M., Beresnev I., Brodsky E. E., Elkhoury J. E., Elsworth D., Ingebritsen S. E., Mays D.C., and Wang C.Y. (2012), Rev. Geophys., 50, RG2004.