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Volume 2017 (2017), Article ID 1361289, 11 pages
Research Article

Characterization of Aquifer Multiscale Properties by Generating Random Fractal Field with Truncated Power Variogram Model Using Karhunen–Loève Expansion

1Department of Oil-Gas Field Development, College of Petroleum Engineering, China University of Petroleum, Beijing 102249, China
2State Key Laboratory of Petroleum Resources and Engineering, China University of Petroleum, Beijing 102249, China
3State Key Laboratory of Shale Oil and Gas Enrichment Mechanisms and Effective Development, Sinopec Group, Beijing 100083, China
4Department of Hydrosciences, School of Earth Sciences and Engineering, Nanjing University, Nanjing 210093, China

Correspondence should be addressed to Tongchao Nan

Received 29 June 2017; Revised 31 October 2017; Accepted 28 November 2017; Published 19 December 2017

Academic Editor: Walter A. Illman

Copyright © 2017 Liang Xue et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The traditional geostatistics to describe the spatial variation of hydrogeological properties is based on the assumption of stationarity or statistical homogeneity. However, growing evidences show and it has been widely recognized that the spatial distribution of many hydrogeological properties can be characterized as random fractals with multiscale feature, and spatial variation can be described by power variogram model. It is difficult to generate a multiscale random fractal field by directly using nonstationary power variogram model due to the lack of explicit covariance function. Here we adopt the stationary truncated power variogram model to avoid this difficulty and generate the multiscale random fractal field using Karhunen–Loève (KL) expansion. The results show that either the unconditional or conditional (on measurements) multiscale random fractal field can be generated by using truncated power variogram model and KL expansion when the upper limit of the integral scale is sufficiently large, and the main structure of the spatial variation can be described by using only the first few dominant KL expansion terms associated with large eigenvalues. The latter provides a foundation to perform dimensionality reduction and saves computational effort when analyzing the stochastic flow and transport problems.