USING A POWER-LAW DISTRIBUTION TO CONSTRAIN FAULT PERMEABILITIES IN AN ACTIVE NORMAL FAULT

In a previous article (Fairley and Hinds, 2004) we published an approximate distribution of hydraulic conductivities parallel to the plane of the Borax Lake fault in the Alvord Basin of southeast Oregon. The published distribution was developed on the basis of stochastic temperature simulations and a simple 1-dimensional model of advective heat and mass transport. Although our prior work provided a good initial estimate of the distribution of hydraulic properties in the Borax Lake fault, we show here that the distribution inferred by stochastic simulation failed to adequately sample the lower tail of the distribution, and therefore overestimated the actual average permeability for the fault. Here we develop a corrected distribution using the 702 measured temperature data points from the earlier study, but without recourse to stochastic simulations to estimate the remaining information; instead, we fit the measured data to a power-law distribution where frequency is proportional to temperature raised to the -5.279 power, and calculate a corrected permeability distribution using the same 1-dimensional advective transport model as in our previous work. Although a power-law distribution cannot, in theory, demonstrate a true mean value, we have calculated approximate summary statistics on the revised distribution by establishing a cut-off area of 1 m² pixels. Values of flux through the fault zone calculated using the corrected permeability distributions are lower than expected from the stochastic simulations, while estimates of the percentage of flux carried in high permeability conduits is somewhat increased over our previous estimates. Because they are scale-independent, power-law distributions provide a simple way to apply measurements to other scales of interest, and several components of fault hydraulic architecture have been suggested to follow power-law distributions (e.g., fracture densities, fracture trace lengths, flow path connectivity, etc.). The identification of a power-law distribution of permeability in the Borax Lake fault therefore has important implications for modeling fluid flow in faults, particularly if this type of distribution can be shown to hold for other hydraulically-active faults.