Advanced

A generalization of the fractal/facies model

Molz, Fred; Kozubowski, Tom; Podgorski, Krzysztof LU and Castle, James (2007) In Hydrogeology Journal 15(4). p.809-816
Abstract
In order to generalize the fractal/facies concept presented by Lu et al. (2002), a new stochastic fractal model for ln(K) (K = hydraulic conductivity) increment probability density functions (PDFs) is presented that produces non-Gaussian behavior at smaller measurement lags and converges to Gaussian behavior at larger lags, a property that is observed in data sets. The model is based on the classical Laplace PDF and its generalizations. In analogy with its Gaussian counterparts, the new stochastic fractal family is called fractional Laplace motion (fLam) having stationary increments called fractional Laplace noise (fLan). This fractal is different because the character of the underlying increment PDFs change dramatically with lag size,... (More)
In order to generalize the fractal/facies concept presented by Lu et al. (2002), a new stochastic fractal model for ln(K) (K = hydraulic conductivity) increment probability density functions (PDFs) is presented that produces non-Gaussian behavior at smaller measurement lags and converges to Gaussian behavior at larger lags, a property that is observed in data sets. The model is based on the classical Laplace PDF and its generalizations. In analogy with its Gaussian counterparts, the new stochastic fractal family is called fractional Laplace motion (fLam) having stationary increments called fractional Laplace noise (fLan). This fractal is different because the character of the underlying increment PDFs change dramatically with lag size, which leads to lack of self-similarity and self-affinity as they are traditionally defined. Data also appear to display this characteristic. In the larger lag size ranges, however, approximate self-affinity does hold. The basic field procedure for further testing of the fractional Laplace theory is to measure ln(K) increment distributions along transects, calculate frequency distributions from the data, and compare results to various members of the auto-correlated fLan family. The variances of the frequency distributions should also change with lag size (scale) in a prescribed manner. There are mathematical reasons, such as the geometric central limit theorem, for surmising that fLam/fLan may be more fundamental than other approaches that have been proposed for modeling ln(K) frequency distributions, such as the flexible scaling model of Painter (2001). If this turns out not to be the case, then other approaches may be comparable or preferable. (Less)
Please use this url to cite or link to this publication:
author
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Facies · Fractal model · Heterogeneity · Hydraulic conductivity · Sediments
in
Hydrogeology Journal
volume
15
issue
4
pages
809 - 816
publisher
Springer
external identifiers
  • scopus:34249994617
ISSN
1431-2174
language
English
LU publication?
no
id
66a56a23-95e7-44e9-b5be-05ae3a4f1ec3 (old id 938183)
date added to LUP
2008-01-23 12:12:49
date last changed
2017-01-01 05:11:45
@article{66a56a23-95e7-44e9-b5be-05ae3a4f1ec3,
  abstract     = {In order to generalize the fractal/facies concept presented by Lu et al. (2002), a new stochastic fractal model for ln(K) (K = hydraulic conductivity) increment probability density functions (PDFs) is presented that produces non-Gaussian behavior at smaller measurement lags and converges to Gaussian behavior at larger lags, a property that is observed in data sets. The model is based on the classical Laplace PDF and its generalizations. In analogy with its Gaussian counterparts, the new stochastic fractal family is called fractional Laplace motion (fLam) having stationary increments called fractional Laplace noise (fLan). This fractal is different because the character of the underlying increment PDFs change dramatically with lag size, which leads to lack of self-similarity and self-affinity as they are traditionally defined. Data also appear to display this characteristic. In the larger lag size ranges, however, approximate self-affinity does hold. The basic field procedure for further testing of the fractional Laplace theory is to measure ln(K) increment distributions along transects, calculate frequency distributions from the data, and compare results to various members of the auto-correlated fLan family. The variances of the frequency distributions should also change with lag size (scale) in a prescribed manner. There are mathematical reasons, such as the geometric central limit theorem, for surmising that fLam/fLan may be more fundamental than other approaches that have been proposed for modeling ln(K) frequency distributions, such as the flexible scaling model of Painter (2001). If this turns out not to be the case, then other approaches may be comparable or preferable.},
  author       = {Molz, Fred and Kozubowski, Tom and Podgorski, Krzysztof and Castle, James},
  issn         = {1431-2174},
  keyword      = {Facies · Fractal model · Heterogeneity · Hydraulic conductivity · Sediments},
  language     = {eng},
  number       = {4},
  pages        = {809--816},
  publisher    = {Springer},
  series       = {Hydrogeology Journal},
  title        = {A generalization of the fractal/facies model},
  volume       = {15},
  year         = {2007},
}