HR: 1330h
AN: H42B-1075    [PDF]
TI: Mono- and Multi-Fractal Scalings of Air Permeability Data from Unsaturated Fractured Tuff
AU: * Hyun, Y
EM: yjhyun@snu.ac.kr
AF: Seoul National University, San 56-1, Shillim-dong, Kwanak-gu, Seoul, 151-742 Korea, Republic of
AU: Neuman, S P
EM: neuman@hwr.arizona.edu
AF: University of Arizona, 1133 E. North Campus Drive, Tucson, AZ 85721 United States
AB: Air permeabilities in unsaturated fractured tuff at the Apache Leap Research Site (ALRS) near Superior, Arizona, exhibit a pronounced scale effect. The effect appears to be consistent with a view of the permeability field as a truncated random mono-fractal [Hyun et al., 2002]. We investigate the extent to which single-hole air permeability data, obtained at the site on a nominal support scale of about 1 m, are compatible with various scaling models including fBm (fractional Brownian motion), fGn (fractional Gaussian noise), fLm (fractional Levy motion), bfLm (bounded fractional Levy motion) and UM (Universal Multifractals). We find that log permeability data have a Levy -like distribution at small lags but become Gaussian as the lag increases, corresponding to bfLm. Though this implies multiple scaling it is not consistent with the UM model, which considers a unique distribution. If one nevertheless interprets the log permeability data on the basis of UM one obtains a very small codimension, suggesting that multiple scaling is of minor consequence. Doing the same for permeabilities (as opposed to their logarithm) yields a larger codimension but is otherwise not consistent with UM. Variogram and (rescaled) range analyses of the log-permeability data yield comparable estimates of the Hurst coefficient. Rescaled range analysis shows that the data are not compatible with fGn. The data appear to be represented most closely by a truncated fBm model of log permeabilities.
DE: 1800 HYDROLOGY
DE: 1869 Stochastic processes
SC: Hydrology [H]
MN: 2003 Fall Meeting