Computational efficient inverse groundwater modeling using Random Mixing and Whittaker–Shannon interpolation

•Computationally efficient geostatistical inversion.•High-dimensional optimization replaced by a sequence of one-dimensional optimizations.•Guarantees a monotonic decrease of the objective function. Geostatistical inverse modeling problems can potentially be very high-dimensional and computationally...

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Bibliographic Details
Published in:Advances in water resources 2019-01, Vol.123, p.109-119
Main Authors: Hörning, S., Sreekanth, J., Bárdossy, A.
Format: Article
Language:English
Subjects:
Computer applications
Geostatistical simulation
Geostatistics
Groundwater
Groundwater flow
Interpolation
Inverse modeling
Inverse problems
Modelling
Objective function
Optimization
Random Mixing
Whittaker–Shannon interpolation
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Summary:•Computationally efficient geostatistical inversion.•High-dimensional optimization replaced by a sequence of one-dimensional optimizations.•Guarantees a monotonic decrease of the objective function. Geostatistical inverse modeling problems can potentially be very high-dimensional and computationally expensive. Using the Random Mixing approach the dimensionality can be reduced, and any optimization algorithm can be applied to solve the inverse problem in this lower dimensional space. In order to reduce computational costs the standard optimization is replaced by a sequence of one-dimensional optimizations. In this one-dimensional space a simplified calculation of the objective function using Whittaker–Shannon interpolation is carried out. This procedure requires a significantly reduced number of forward model runs and it also guarantees monotonic convergence of the objective function. A synthetic and a real world example will be used to demonstrate the procedure and to evaluate the quality of the Whittaker–Shannon interpolation in comparison to the actual objective functions.
ISSN:0309-1708
1872-9657
DOI:10.1016/j.advwatres.2018.11.012