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| Titel |
Efficient Geostatistical Inversion under Transient Flow Conditions in Heterogeneous Porous Media |
| VerfasserIn |
Ole Klein, Olaf A. Cirpka, Peter Bastian, Olaf Ippisch |
| Konferenz |
EGU General Assembly 2014
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 16 (2014) |
| Datensatznummer |
250091832
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| Publikation (Nr.) |
 EGU/EGU2014-6146.pdf |
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| Zusammenfassung |
| The assessment of hydraulic aquifer parameters is important for the evaluation of
anthropogenic impacts on groundwater resources. The distribution of these parameters
determines flow paths and solute travel times and is therefore critical for the successful design
and deployment of remediation schemes at contaminated sites. Direct measurement of these
properties is not possible, making indirect observations through dependent quantities and
parameter estimation a necessity.
The geostatistical approach characterizes these hydraulic parameters without
predetermined zonation. The parameter fields are treated as stochastic processes, optionally
incorporating a priori information in the probability distribution. Maximizing the likelihood
of the parameters with regard to the given observations yields a parameter estimate with high
spatial resolution.
This approach naturally leads to nonlinear least squares optimization problems, namely
objective functions of the form
L(Y ) = 1(Y ′)TQ -Y1YY ′ + 1[F(Y) - z]T Q-z1z [F(Y )- z],
2 2
where Y are the parameters, Y ′ their deviations from the a priori estimate, QY Y their
covariance matrix, z the measurements, Qzz their covariance matrix and F the forward
model mapping parameters to observations. In theory, this objective function may be
minimized using standard gradient-based techniques like Gauss-Newton. Due to the typically
high number of parameters, however, this is not practical. Let nY be the number of
parameters and nz the number of observations. Then QY Y and its inverse are both dense
nY xnY matrices, and the sensitivity matrix Hz := -z--Y is a nz xnY matrix that has to
be assembled using forward or adjoint model runs.
Specialized schemes have been developed to reduce the dimensionality of the problem
and avoid the high cost of handling products with QY Y -1. This enables efficient inversion in
the case of a moderate number of observations as encountered in stationary inversion,
where the cost of assembling Hz is in a reasonable range. Transient inversion,
however, requires time series of measurements and therefore typically leads to a large
number of observations, and under these circumstances the existing methods become
unfeasible.
We present an extension of the existing inversion methods to instationary flow regimes.
Our approach uses a Conjugate Gradients scheme preconditioned with the prior covariance
matrix QY Y to avoid both multiplications with QY Y -1 and the explicit assembly of Hz.
Instead, one combined adjoint model run is used for all observations at once. As the
computing time of our approach is largely independent of the number of measurements used
for inversion, the presented method can be applied to large data sets. This facilitates
the treatment of applications with variable boundary conditions (nearby rivers,
precipitation).
We integrate the geostatistical inversion method into the software framework DUNE,
enabling the use of high-performance-computing techniques and full parallelization.
Feasibility of our approach is demonstrated through the joint inversion of several synthetic
data sets in two and three dimensions, e.g.estimation of hydraulic conductivity using
hydraulic head values and tracer concentrations, and scalability of the new method is
analyzed. A comparison of the new method with existing geostatistical inversion approaches
highlights its advantages and drawbacks and demonstrates scenarios in which our scheme can
be beneficial. |
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