On generating conductivity fields with known fractal dimension and nonstationary increments

Fractional Brownian motion (fBm) is a stochastic process that has stationary increments with long‐range correlations and known fractal dimension. We study a multiple‐dimensional extension of fBm with nonstationary increments that allows for trends in the statistical structure while maintaining the G...

Full description

Saved in:
Bibliographic Details
Published in:Water resources research 2012-03, Vol.48 (3), p.n/a
Main Authors: O'Malley, Daniel, Cushman, John H., O'Rear, Patrick
Format: Article
Language:English
Subjects:
Brownian motion
Conductivity
Coordinate transformations
Decomposition
Fourier transforms
fractal
Fractals
Geomorphology
Groundwater
High performance computing
Hydrology
Methods
nonstationary increments
random
Random variables
Stochastic processes
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Fractional Brownian motion (fBm) is a stochastic process that has stationary increments with long‐range correlations and known fractal dimension. We study a multiple‐dimensional extension of fBm with nonstationary increments that allows for trends in the statistical structure while maintaining the Gaussian nature and fractal dimension of fBm. Two methods for simulating this extension are employed and described in detail. One approach combines Cholesky decomposition with a generalization of random midpoint displacement. The other makes repeated use of the Cholesky decomposition. The resulting fields can be employed in various geophysical settings, e.g., as log conductivity fields in hydrology and topographic elevation in geomorphology. Key Points Generating non‐stationary increment fractal fields with trends Novel numerical method The tool is multidisciplanary
ISSN:0043-1397
1944-7973
DOI:10.1029/2011WR011681