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Linear functional minimization for inverse modeling
Author(s) -
BarajasSolano D. A.,
Wohlberg B. E.,
Vesselinov V. V.,
Tartakovsky D. M.
Publication year - 2015
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 - 10.1002/2014wr016179
Subject(s) - hydraulic conductivity , piecewise , estimator , inverse problem , nonlinear system , maximum a posteriori estimation , minification , algorithm , estimation theory , computer science , mathematical optimization , mathematics , geology , mathematical analysis , physics , maximum likelihood , statistics , quantum mechanics , soil science , soil water
We present a novel inverse modeling strategy to estimate spatially distributed parameters of nonlinear models. The maximum a posteriori (MAP) estimators of these parameters are based on a likelihood functional, which contains spatially discrete measurements of the system parameters and spatiotemporally discrete measurements of the transient system states. The piecewise continuity prior for the parameters is expressed via Total Variation (TV) regularization. The MAP estimator is computed by minimizing a nonquadratic objective equipped with the TV operator. We apply this inversion algorithm to estimate hydraulic conductivity of a synthetic confined aquifer from measurements of conductivity and hydraulic head. The synthetic conductivity field is composed of a low‐conductivity heterogeneous intrusion into a high‐conductivity heterogeneous medium. Our algorithm accurately reconstructs the location, orientation, and extent of the intrusion from the steady‐state data only. Addition of transient measurements of hydraulic head improves the parameter estimation, accurately reconstructing the conductivity field in the vicinity of observation locations.