Calibration and Reliability in Groundwater
Modelling: Credibility of Modelling
(Proceedings of ModelCARE 2007 Conference, held in
Denmark, September 2007). IAHS Publ. 320, 2008, 310-315.
Data-driven
reparameterization structure for estimation of fluid conductivity
I. berre1,2, f. clˇment3, m.
lien1,2 & t. mannseth1,2
1 Department of Mathematics, University of Bergen (UoB), Joh. Brunsgate 12, N-5008 Bergen, Norway
inga.berre@math.uib.no
2 Centre for Integrated Petroleum Research, UoB, Realfagbygget, Allˇgaten 41, N-5007 Bergen, Norway
3 INRIA-Rocquencourt, B.P. 105, 78153 Le Chesnay Cedex, France
Abstract
Estimation of a parameter field such as fluid conductivity based on dynamic
data (e.g. transient head observations) is a challenging inverse problem due to
the limited amount and quality of the available information. Reparameterization
is commonly applied to regularize the estimation by reducing the number of
unknowns in the representation of the fluid conductivity. It is, however,
difficult to select the reparameterization structure prior to estimation.
By altering the reparameterization structure adaptively during estimation, it
is possible to explicitly account for the resolving power of the data with
respect to the chosen forward operator. Using parameter-space-derivative
information, the reparameterization can be refined based on performance-measure
values for tentative structures. The performance measures approximate the
ability of a new reparameterization structure to reduce the objective-function
value. Examples are the magnitude of the objective-function gradient and a
prediction of the decreased objective function value based on a linearization
of the model response. In this paper we give a general presentation of how coarse-scale
features of a parameter field can be identified following these ideas. An
example illustrates the methodology for estimation of fluid conductivity based
solely on information from pressure data.
Key words parameter identification; reparameterization; two-phase porous-media flow