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Stochastic Interpolation of Aquifer Properties Using Fractional Lévy Motion
Author(s) -
Painter Scott
Publication year - 1996
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/95wr03485
Subject(s) - permeability (electromagnetism) , interpolation (computer graphics) , mathematics , fractional brownian motion , mathematical optimization , geology , computer science , motion (physics) , statistics , brownian motion , artificial intelligence , genetics , membrane , biology
This paper describes a new technique for conditional simulation of aquifer properties in unobserved regions. The technique utilizes a recently introduced model for heterogeneity based on the Lévy‐stable family of probability distributions to achieve a higher degree of realism than is possible with Gaussian‐based techniques. Specifically, permeability and porosity variations are modeled using fractional Lévy motion. A new algorithm for producing fractional Lévy motion conditioned to match known data is introduced. Two‐dimensional simulations using actual permeability measurements as input demonstrate that this algorithm produces random fields with the specified properties. Simulations using a subset of a detailed permeability map of an outcrop as input illustrate how the new method can be used to estimate important flow and transport properties and to quantify uncertainties in these estimates.