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| Titel |
Variogram-based inversion of time-lapse electrical resistivity data: development and application to a thermal tracing experiment |
| VerfasserIn |
Thomas Hermans, Frédéric Nguyen |
| Konferenz |
EGU General Assembly 2015
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 17 (2015) |
| Datensatznummer |
250106549
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| Publikation (Nr.) |
 EGU/EGU2015-6225.pdf |
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| Zusammenfassung |
| Electrical resistivity tomography (ERT) has become a popular imaging methodology in a
broad range of applications given its large sensitivity to subsurface parameters and its relative
simplicity to implement. More particularly, time-lapse ERT is now increasingly used for
monitoring purposes in many contexts such as water content, permafrost, landslide, seawater
intrusion, solute transport or heat transport experiments.
Specific inversion schemes have been developed for time-lapse data sets. However, in
contrast with static inversions for which many techniques including geostatistical, minimum
support or structural inversion are commonly applied, most of the methodologies for
time-lapse inversion still rely on non-physically based spatial and/or temporal smoothing of
the parameters or parameter changes.
In this work, we propose a time-lapse ERT inversion scheme based on the difference
inversion scheme. We replace the standard smoothness-constraint regularization operator by
the parameter change covariance matrix. The objective function can be expressed
as
Ïdiff(δm ) = /¥Wd [d - d0 + f(m0)- f(m )]/¥2 + λ /¥/¥C-δ0m.5δm /¥/¥2
where Wd is the data weighting matrix, d and d0 are the data sets corresponding to the
considered time-step and to the background, f() is the forward operator, m and m0 are the
models corresponding to the considered time-step and to the background, δm is the
parameter change (resistivity), Cδm is the parameter change covariance matrix and λ the
regularization parameter. This operator takes into account the correlation between changes in
resistivity at different locations through a variogram computed using independent data (e.g.,
electromagnetic logs). It may vary for subsequent time-steps if the correlation length is
time-dependent.
The methodology is first validated and compared to the standard smoothness-constraint
inversion using a synthetic benchmark simulating the injection of a conductive tracer into a
homogeneous aquifer inducing changes in resistivity values of known correlation length. We
analyze the influence of the assumed correlation length on inversion results. Globally, the
method yields better results than the traditional smoothness constraint inversion. Even if a
wrong correlation length is assumed, the method performs as well as the smoothness
constraint since the regularization operator balances the weight given to the model constraint
functional in the objective function.
Then the methodology is successfully applied to a heat injection and pumping experiment
in an alluvial aquifer. The comparison with direct measurements in boreholes (temperature
loggers and distributed temperature sensing optic fibres) shows that ERT-derived
temperatures and breakthrough curves image reliably the heat plume through time
(increasing part of the curve, maximum and tail are correctly retrieved) and space (lateral
variations of temperature are observed) with less spatial smoothing than standard
methods.
The development of new regularization operators for time-lapse inversion of ERT data is
necessary given the broad range of applications where ERT monitoring is used. In many
studies, independent data are available to derive geostatistical parameters that can be
subsequently used to regularize geophysical inversions. In the future, the integration of
spatio-temporal variograms into existing 4D inversion schemes should further improve ERT
time-lapse imaging. |
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