

Joint threedimensional 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 finitedifference 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. 
AD Tools ADIFOR 
BibTeX
@ARTICLE{
Rath2006Jtd,
author = "V. Rath and A. Wolf and H. M. B{\"u}cker",
title = "Joint threedimensional inversion of coupled groundwater flow and heat transfer based
on automatic differentiation: Sensitivity calculation, verification, and synthetic examples",
journal = "Geophysical Journal International",
pages = "453466",
doi = "http://dx.doi.org/10.1111/j.1365246X.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 finitedifference 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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