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| Titel |
Geostatistical inversion of transient moment equations of groundwater flow |
| VerfasserIn |
M. Riva, A. Guadagnini, S. P. Neuman, E. Bianchi Janetti, B. Malama |
| Konferenz |
EGU General Assembly 2009
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 11 (2009) |
| Datensatznummer |
250023705
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| Zusammenfassung |
| We present a methodology for conditioning estimates of hydraulic heads and fluxes and their
associated uncertainty on information about transmissivity, T , and hydraulic heads, h,
collected within a randomly heterogeneous aquifer under transient conditions. Our
approach is based on recursive finite-element approximations of exact nonlocal first
and second conditional moment equations. We present a nonlinear geostatistical
inverse algorithm for transient groundwater flow that allows estimating jointly the
spatial variability of log-transmissivity, Y = ln T, the underlying variogram and its
parameters, and the variance-covariance of the estimates. Log-transmissivity is
parameterized geostatistically based on measured values at discrete locations and
unknown values at discrete “pilot points.” While prior pilot point values are obtained
by generalized kriging, posterior estimates at pilot points are obtained by history
matching of transient mean flow against values of hydraulic head collected during a
pumping test. Parameters are then projected onto a computational grid by kriging. Prior
information on hydraulic properties is included in the optimization process via a suitable
regularization term which is included in the objective function to be minimized. The
weight of the regularization term, hydraulic and unknown variogram parameters
are then estimated by maximum likelihood calibration. The main features of the
methodology are explored by means of a synthetic example. As alternative flow models we
consider (a) a second-order and (b) a lower-order closure of the mean transient flow
equation and assess the ability of these models at capturing the parameters of the
estimated log-transmissivity variogram. With the aid of formal model selection
criteria we associate each mean flow model and different sets of tested variogram
parameters with a weight, or posterior probability, representing their relative degrees
of likelihood. Our findings suggest that the weight of the regularization term is
best identified by adopting a complete second-order approximation of the mean
flow model, while predictions of Y (x) and h(x, t) only marginally benefit from a
second-order correction. Analysis based on posterior model weights based on the
Kashyap measure, KIC, sharply identify the second-order based mean flow model as
the most reliable. A unique feature of the method is its capability of providing
estimates of prediction errors of hydraulic heads and fluxes, which are calculated a
posteriori, upon solving corresponding moment equations. Our example shows that
conditioning transient flow predictions on information of both transmissivity and
hydraulic heads in general brings about a notable reduction of predictive uncertainty. |
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