NDLI: A generalization of the fractal/facies model

Content Provider	Springer Nature Link
Author	Molz, Fred J. Kozubowski, Tomasz J. Podgórski, Krzysztof Castle, James W.
Copyright Year	2007
Abstract	In order to generalize the fractal/facies concept, a new stochastic fractal model for ln(K) increment probability density functions (PDFs) is presented that produces non-Gaussian behavior at smaller lags and converges to Gaussian at larger lags. The model is based on the classical Laplace PDF. The new stochastic fractal family is called fractional Laplace motion (fLam) having stationary increments called fractional Laplace noise (fLan). This fractal is different from other fractals because the character of the underlying increment PDFs changes dramatically with lag size, which leads to lack of self-similarity. Data also appear to display this characteristic. In the larger lag size ranges, 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 appropriate fLan family members. 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.Afin de généraliser le concept fractale/faciès, un nouveau modèle fractal stochastique est présenté pour les fonctions de densité de probabilité (FDP) d’accroissement de ln(K); il présente des comportements non-gaussiens pour des petits décalages et converge vers le gaussien pour des décalages plus grands. Le modèle est basé sur la FDP classique de Laplace. La nouvelle famille fractale stochastique est appelée mouvement fractionnaire laplacien (fLam) et présente des accroissements stationnaires appelés bruit fractionnaire laplacien (fLan). Ce fractal est différent d’autres fractals car le caractère des FDP d’accroissement sous-jacentes change considérablement avec la grandeur du décalage, ce qui conduit à un manque d’auto-similarité. Les données semblent également présenter cette caractéristique. Pour la gamme des décalages plus grands, une auto-affinité approximative a lieu. La procédure de base pour des tests supplémentaires sur la théorie du fractionnaire laplacien consiste à mesurer les distributions d’accroissement de ln(K) le long de coupes transversales, à calculer les distributions de fréquence des données et à comparer les résultats aux membres de famille de fLan appropriés. Les variances des distributions de fréquence devraient également changer avec la grandeur du décalage (échelle) suivant une méthode imposée. Il y a des raisons mathématiques, tel que le théorème géométrique de la limite centrale, qui permettent de soupçonner que l’approche fLam/fLan puisse être plus fondamentale que d’autres approches qui ont été proposées pour modéliser les distributions de fréquence de ln(K).Con objeto de generalizar el concepto de facies/fractales se presenta un nuevo modelo de fractales estocásticos para funciones de densidad de probabilidad (FDPs) del incremento ln (K) el cual produce un comportamiento no-Gaussiano en intervalos pequeños y converge en intervalos mayores. El modelo se basa en la clásica FDP Laplace. La nueva familia de fractales estocásticos se denomina señal de Laplace fraccionaria (fLam) teniendo incrementos estacionales denominados ruido de Laplace fraccionario (fLan). Este fractal es diferente de otros fractales porque el tipo de cambio del incremento subyacente en la FDP ocurre dramáticamente con el tamaño del intervalo, lo cual conduce a falta de auto-similaridad. Los datos también parecer mostrar esta característica. En los rangos con tamaño del intervalo más grandes se manifiesta auto-afinidad aproximada. El procedimiento básico de campo para evaluación posterior de la teoría de Laplace fraccionada es medir las distribuciones del incremento de ln(K) a lo largo de cortes transversales, calcular distribuciones de frecuencia para los datos, y comparar resultados para miembros de familia fLan apropiados. Las varianzas de las distribuciones de frecuencia también deberían de cambiar con el tamaño del intervalo (escala) de una manera prescrita. Existen razones matemáticas, tal como el teorema del límite central geométrico, para suponer que fLam/fLan puede ser más fundamental que otros enfoques que han sido propuestos para modelizar las distribuciones de frecuencia de ln (K).
Starting Page	809
Ending Page	816
Page Count	8
File Format	PDF
ISSN	14312174
Journal	Hydrogeology Journal
Volume Number	15
Issue Number	4
e-ISSN	14350157
Language	English
Publisher	Springer-Verlag
Publisher Date	2007-01-16
Publisher Institution	International Association of Hydrogeologists
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Facies Fractal model Heterogeneity Groundwater hydraulics Geostatistics Waste Water Technology Water Pollution Control Water Management Aquatic Pollution Geology Hydrogeology
Content Type	Text
Resource Type	Article
Subject	Earth and Planetary Sciences Water Science and Technology

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