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Blind source separation for groundwater pressure analysis based on nonnegative matrix factorization
Author(s) -
Alexandrov Boian S.,
Vesselinov Velimir V.
Publication year - 2014
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 - 10.1002/2013wr015037
Subject(s) - hydrogeology , non negative matrix factorization , geostatistics , matrix decomposition , inverse problem , matrix (chemical analysis) , computer science , aquifer , cluster analysis , blind signal separation , data set , set (abstract data type) , algorithm , geology , groundwater , channel (broadcasting) , artificial intelligence , mathematics , spatial variability , statistics , physics , geotechnical engineering , mathematical analysis , computer network , eigenvalues and eigenvectors , materials science , composite material , quantum mechanics , programming language
Abstract The identification of the physical sources causing spatial and temporal fluctuations of aquifer water levels is a challenging, yet a very important hydrogeological task. The fluctuations can be caused by variations in natural and anthropogenic sources such as pumping, recharge, barometric pressures, etc. The source identification can be crucial for conceptualization of the hydrogeological conditions and characterization of aquifer properties. We propose a new computational framework for model‐free inverse analysis of pressure transients based on Nonnegative Matrix Factorization (NMF) method for Blind Source Separation (BSS) coupled with k ‐means clustering algorithm, which we call NMF k . NMF k is capable of identifying a set of unique sources from a set of experimentally measured mixed signals, without any information about the sources, their transients, and the physical mechanisms and properties controlling the signal propagation through the subsurface flow medium. Our analysis only requires information about pressure transients at a number of observation points, m , where m ≥ r , and r is the number of unknown unique sources causing the observed fluctuations. We apply this new analysis on a data set from the Los Alamos National Laboratory site. We demonstrate that the sources identified by NMF k have real physical origins: barometric pressure and water‐supply pumping effects. We also estimate the barometric pressure efficiency of the monitoring wells. The possible applications of the NMF k algorithm are not limited to hydrogeology problems; NMF k can be applied to any problem where temporal system behavior is observed at multiple locations and an unknown number of physical sources are causing these fluctuations.

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