Publication: Joint three-dimensional inversion of coupled groundwater flow and heat transfer based on automatic differentiation: Sensitivity calculation, verification, and synthetic examples
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Joint three-dimensional inversion of coupled groundwater flow and heat transfer based on automatic differentiation: Sensitivity calculation, verification, and synthetic examples

- Article in a journal -
 

Area
Geophysics

Author(s)
V. Rath , A. Wolf , H. M. Bücker

Published in
Geophysical Journal International

Year
2006

Abstract
Inverse methods are useful tools not only for deriving estimates of unknown parameters of the subsurface, but also for appraisal of the thus obtained models. While not being neither the most general nor the most efficient methods, Bayesian inversion based on the calculation of the Jacobian of a given forward model can be used to evaluate many quantities useful in this process. The calculation of the Jacobian, however, is computationally expensive and, if done by divided differences, prone to truncation error. Here, automatic differentiation can be used to produce derivative code by source transformation of an existing forward model. We describe this process for a coupled fluid flow and heat transport finite-difference code, which is used in a Bayesian inverse scheme to estimate thermal and hydraulic properties and boundary conditions form measured hydraulic potentials and temperatures. The resulting derivative code was validated by comparison to simple analytical solutions and divided differences. Synthetic examples from different flow regimes demonstrate the use of the inverse scheme, and its behavior in different configurations.

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ADIFOR

BibTeX
@ARTICLE{
         Rath2006Jtd,
       author = "V. Rath and A. Wolf and H. M. B{\"u}cker",
       title = "Joint three-dimensional inversion of coupled groundwater flow and heat transfer based
         on automatic differentiation: Sensitivity calculation, verification, and synthetic examples",
       journal = "Geophysical Journal International",
       pages = "453--466",
       doi = "http://dx.doi.org/10.1111/j.1365-246X.2006.03074.x",
       abstract = "Inverse methods are useful tools not only for deriving estimates of unknown
         parameters of the subsurface, but also for appraisal of the thus obtained models. While not being
         neither the most general nor the most efficient methods, Bayesian inversion based on the calculation
         of the Jacobian of a given forward model can be used to evaluate many quantities useful in this
         process. The calculation of the Jacobian, however, is computationally expensive and, if done by
         divided differences, prone to truncation error. Here, automatic differentiation can be used to
         produce derivative code by source transformation of an existing forward model. We describe this
         process for a coupled fluid flow and heat transport finite-difference code, which is used in a
         Bayesian inverse scheme to estimate thermal and hydraulic properties and boundary conditions form
         measured hydraulic potentials and temperatures. The resulting derivative code was validated by
         comparison to simple analytical solutions and divided differences. Synthetic examples from different
         flow regimes demonstrate the use of the inverse scheme, and its behavior in different
         configurations.",
       year = "2006",
       volume = "167",
       number = "1",
       ad_area = "Geophysics",
       ad_tools = "ADIFOR"
}


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