Fractional Laplace model for hydraulic conductivity

[1] Based on an examination of K data from four different sites, a new stochastic fractal model, fractional Laplace motion, is proposed. This model is based on the assumption of spatially stationary ln(K) increments governed by the Laplace PDF, with the increments named fractional Laplace noise. Similar behavior has been reported for other increment processes (often called fluctuations) in the fields of finance and turbulence. The Laplace PDF serves as the basis for a stochastic fractal as a result of the geometric central limit theorem. All Laplace processes reduce to their Gaussian analogs for sufficiently large lags, which may explain the apparent contradiction between large-scale models based on fractional Brownian motion and non-Gaussian behavior on smaller scales.

[1]  D. Applebaum.  Stable non-Gaussian random processes , 1995, The Mathematical Gazette.

[2]  Lynn C. Sparling,et al.  Scale dependence of tracer microstructure: PDFs, intermittency and the dissipation scale , 2001 .

[3]  S. Painter.  Statistical Characterization of Spatial Variability in Sedimentary Rock , 2003 .

[4]  Harihar Rajaram,et al.  Stochastic fractal‐based models of heterogeneity in subsurface hydrology: Origins, applications, limitations, and future research questions , 2004 .

[5]  Fred J. Molz,et al.  An efficient, three-dimensional, anisotropic, fractional Brownian motion and truncated fractional Levy motion simulation algorithm based on successive random additions , 2003 .

[6]  E. Antonova,et al.  Intermittency of magnetospheric dynamics through non‐Gaussian distribution function of PC‐index fluctuations , 2003 .

[7]  Scott L. Painter,et al.  Fractional Lévy motion as a model for spatial variability in sedimentary rock , 1994 .

[8]  A. T. Walden,et al.  The nature of the non-Gaussianity of primary reflection coefficients and its significance for deconvolution , 1986 .

[9]  D. Percival,et al.  Analyzing exact fractal time series: evaluating dispersional analysis and rescaled range methods. , 1997, Physica A.

[10]  Scott L. Painter,et al.  Flexible scaling model for use in random field simulation of hydraulic conductivity , 2001 .

[11]  Samuel Kotz,et al.  The Laplace Distribution and Generalizations: A Revisit with Applications to Communications, Economics, Engineering, and Finance , 2001 .

[12]  M. Taqqu,et al.  Stable Non-Gaussian Random Processes : Stochastic Models with Infinite Variance , 1995 .

[13]  Libchaber,et al.  Transitions to turbulence in helium gas. , 1987, Physical review. A, General physics.

[14]  Scott L. Painter,et al.  Evidence for Non‐Gaussian Scaling Behavior in Heterogeneous Sedimentary Formations , 1996 .

[15]  Passive scalar fluctuations with and without a mean gradient: A numerical study. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[16]  Fred J. Molz,et al.  How well are hydraulic conductivity variations approximated by additive stable processes , 2001 .

[17]  S. P. Neuman.  Universal scaling of hydraulic conductivities and dispersivities in geologic media , 1990 .

[18]  G. K. Boman,et al.  A fractal‐based stochastic interpolation scheme in subsurface hydrology , 1993 .

[19]  David A. Benson,et al.  Subordinated advection‐dispersion equation for contaminant transport , 2001 .

[20]  D. Benson,et al.  Fractional Dispersion, Lévy Motion, and the MADE Tracer Tests , 2001 .

[21]  F. Molz,et al.  Sedimentology and Fractal-Based Analysis of Permeability Data, John Henry Member, Straight Cliffs Formation (Upper Cretaceous), Utah, U.S.A. , 2004 .

[22]  Krzysztof Podgórski,et al.  LOG-LAPLACE DISTRIBUTIONS , 2003 .

[23]  B. Baeumer.  Permeability Field Generation Based On Fractional Integration and the Effect on Long-Term Solute Dispersion , 2003 .