TY - JOUR
T1 - Theory and generation of conditional, scalable sub-Gaussian random fields
AU - Panzeri, M.
AU - Riva, M.
AU - Guadagnini, A.
AU - Neuman, S. P.
N1 - Funding Information:
Funding from the European Union's Horizon 2020 Research and Innovation programme (Project "Furthering the knowledge Base for Reducing the Environmental Footprint of Shale Gas Development" FRACRISK'grant agreement 640979) is acknowledged. This work was supported in part through a contract between the University of Arizona and Vanderbilt University under the Consortium for Risk Evaluation with Stakeholder Participation (CRESP) III, funded by the U.S. Department of Energy. All data used in the paper will be retained by the authors for at least 5 years after publication and will be available to the readers upon request.
Publisher Copyright:
© 2016. American Geophysical Union. All Rights Reserved.
PY - 2016/3/1
Y1 - 2016/3/1
N2 - Many earth and environmental (as well as a host of other) variables, Y, and their spatial (or temporal) increments, ΔY, exhibit non-Gaussian statistical scaling. Previously we were able to capture key aspects of such non-Gaussian scaling by treating Y and/or ΔY as sub-Gaussian random fields (or processes). This however left unaddressed the empirical finding that whereas sample frequency distributions of Y tend to display relatively mild non-Gaussian peaks and tails, those of ΔY often reveal peaks that grow sharper and tails that become heavier with decreasing separation distance or lag. Recently we proposed a generalized sub-Gaussian model (GSG) which resolves this apparent inconsistency between the statistical scaling behaviors of observed variables and their increments. We presented an algorithm to generate unconditional random realizations of statistically isotropic or anisotropic GSG functions and illustrated it in two dimensions. Most importantly, we demonstrated the feasibility of estimating all parameters of a GSG model underlying a single realization of Y by analyzing jointly spatial moments of Y data and corresponding increments, ΔY. Here, we extend our GSG model to account for noisy measurements of Y at a discrete set of points in space (or time), present an algorithm to generate conditional realizations of corresponding isotropic or anisotropic random fields, introduce two approximate versions of this algorithm to reduce CPU time, and explore them on one and two-dimensional synthetic test cases.
AB - Many earth and environmental (as well as a host of other) variables, Y, and their spatial (or temporal) increments, ΔY, exhibit non-Gaussian statistical scaling. Previously we were able to capture key aspects of such non-Gaussian scaling by treating Y and/or ΔY as sub-Gaussian random fields (or processes). This however left unaddressed the empirical finding that whereas sample frequency distributions of Y tend to display relatively mild non-Gaussian peaks and tails, those of ΔY often reveal peaks that grow sharper and tails that become heavier with decreasing separation distance or lag. Recently we proposed a generalized sub-Gaussian model (GSG) which resolves this apparent inconsistency between the statistical scaling behaviors of observed variables and their increments. We presented an algorithm to generate unconditional random realizations of statistically isotropic or anisotropic GSG functions and illustrated it in two dimensions. Most importantly, we demonstrated the feasibility of estimating all parameters of a GSG model underlying a single realization of Y by analyzing jointly spatial moments of Y data and corresponding increments, ΔY. Here, we extend our GSG model to account for noisy measurements of Y at a discrete set of points in space (or time), present an algorithm to generate conditional realizations of corresponding isotropic or anisotropic random fields, introduce two approximate versions of this algorithm to reduce CPU time, and explore them on one and two-dimensional synthetic test cases.
KW - anisotropic random fields
KW - conditional simulation
KW - generalized sub-Gaussian model
KW - non-Gaussian geostatistics
KW - non-Gaussian random fields
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U2 - 10.1002/2015WR018348
DO - 10.1002/2015WR018348
M3 - Article
AN - SCOPUS:84960331281
SN - 0043-1397
VL - 52
SP - 1746
EP - 1761
JO - Water Resources Research
JF - Water Resources Research
IS - 3
ER -