HR: 0800h
AN: H51E-07 [Abstracts]
TI: An Extension of a Nonstationary Inversion Method with Approximation Error Analysis Applied to Hydrological Process Monitoring
AU: * Lehikoinen, A
EM: anssi.lehikoinen@uku.fi
AF: Department of Physics, University of Kuopio, P.O. Box 1627, Kuopio, 70211, Finland
AU: Huttunen, J M
EM: janne.huttunen@uku.fi
AF: Department of Physics, University of Kuopio, P.O. Box 1627, Kuopio, 70211, Finland
AU: Finsterle, S
EM: safinsterle@lbl.gov
AF: Earth Sciences Division, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, MS 90-
1116, Berkeley, CA 94720, United States
AU: Kowalsky, M B
EM: mbkowalsky@lbl.gov
AF: Earth Sciences Division, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, MS 90-
1116, Berkeley, CA 94720, United States
AU: Kaipio, J P
EM: jpkaipio@physics.uku.fi
AF: Department of Physics, University of Kuopio, P.O. Box 1627, Kuopio, 70211, Finland
AB:
We extend the previously presented methodology for imaging the evolution of electrically conductive fluids in
porous media. In that method, the nonstationary inversion problem was solved using Bayesian filtering. The
method was demonstrated using a synthetically generated test case where the monitored target is a time-varying
water plume in an unsaturated porous medium, and the imaging modality was electrical resistance tomography
(ERT). The inverse problem was formulated as a state estimation problem, which is based on observation-
evolution models. As an observation model for ERT, the complete electrode model was used, and for time-
varying unsaturated flow, the Richards equation was used as an evolution model. Although the "true" evolution of
water flow was simulated using a heterogeneous permeability field, in the inversion step the permeability was
assumed to be homogeneous. This assumption leads to approximation errors that have been taken into account
by constructing a statistical model between the different realizations of the accurate and the approximate fluid flow
models. This statistical model was constructed using an ensemble of samples from the evolution model in a
way that the construction can be carried out prior to taking observations. However, the statistics of approximation
errors actually depends on observations (through the state). In this work we extend the previously presented
method so that the statistics of the approximation error are adjusted based on the observations. The basic idea of
the extension is to gather those samples from the ensemble which at the current time best represents the
observed state. We then determine the statistics of the approximation error based on these collated samples.
The extension of the methodology provides improved estimates of water saturation distributions compared to the
previously presented approaches. The proposed methodology may be extended for imaging and estimating
parameters of dynamical processes using a variety of geophysical methods. This work was supported, in part, by
the Finnish Funding Agency for Technology and Innovation (TEKES), projects 40285/05 and 40347/05, and by the
U.S. Dept. of Energy under Contract No. DE-AC02-05CH11231.
DE: 1835 Hydrogeophysics
DE: 1894 Instruments and techniques: modeling
DE: 3225 Numerical approximations and analysis (4260)
DE: 3260 Inverse theory
DE: 3275 Uncertainty quantification (1873)
SC: Hydrology [H]
MN: 2007 Joint Assembly