A generalization of the fractal/facies model
(2007) In Hydrogeology Journal 15(4). p.809816 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 nonGaussian 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 nonGaussian 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 selfsimilarity and selfaffinity as they are traditionally defined. Data also appear to display this characteristic. In the larger lag size ranges, however, approximate selfaffinity 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 autocorrelated 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:
http://lup.lub.lu.se/record/938183
 author
 Molz, Fred; Kozubowski, Tom; Podgorski, Krzysztof ^{LU} and Castle, James
 publishing date
 2007
 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
 14312174
 language
 English
 LU publication?
 no
 id
 66a56a2395e744e9b5be05ae3a4f1ec3 (old id 938183)
 date added to LUP
 20080123 12:12:49
 date last changed
 20170101 05:11:45
@article{66a56a2395e744e9b5be05ae3a4f1ec3, 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 nonGaussian 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 selfsimilarity and selfaffinity as they are traditionally defined. Data also appear to display this characteristic. In the larger lag size ranges, however, approximate selfaffinity 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 autocorrelated 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 = {14312174}, keyword = {Facies · Fractal model · Heterogeneity · Hydraulic conductivity · Sediments}, language = {eng}, number = {4}, pages = {809816}, publisher = {Springer}, series = {Hydrogeology Journal}, title = {A generalization of the fractal/facies model}, volume = {15}, year = {2007}, }