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Titel |
Comparison of three methods of solution to the inverse problem of groundwater hydrology for multiple pumping stimulation |
VerfasserIn |
Mauro Giudici, Davide Casabianca, Alessandro Comunian |
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 |
250105311
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Publikation (Nr.) |
EGU/EGU2015-4814.pdf |
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Zusammenfassung |
The basic classical inverse problem of groundwater hydrology aims at determining aquifer
transmissivity (T ) from measurements of hydraulic head (h), estimates or measures of
source terms and with the least possible knowledge on hydraulic transmissivity. The
theory of inverse problems shows that this is an example of ill-posed problem, for
which non-uniqueness and instability (or at least ill-conditioning) might preclude the
computation of a physically acceptable solution. One of the methods to reduce the
problems with non-uniqueness, ill-conditioning and instability is a tomographic
approach, i.e., the use of data corresponding to independent flow situations. The
latter might correspond to different hydraulic stimulations of the aquifer, i.e., to
different pumping schedules and flux rates. Three inverse methods have been analyzed
and tested to profit from the use of multiple sets of data: the Differential System
Method (DSM), the Comparison Model Method (CMM) and the Double Constraint
Method (DCM). DSM and CMM need h all over the domain and thus the first step
for their application is the interpolation of measurements of h at sparse points.
Moreover, they also need the knowledge of the source terms (aquifer recharge,
well pumping rates) all over the aquifer. DSM is intrinsically based on the use of
multiple data sets, which permit to write a first-order partial differential equation for
T , whereas CMM and DCM were originally proposed to invert a single data set
and have been extended to work with multiple data sets in this work. CMM and
DCM are based on Darcy’s law, which is used to update an initial guess of the
T field with formulas based on a comparison of different hydraulic gradients. In
particular, the CMM algorithm corrects the T estimate with ratio of the observed
hydraulic gradient and that obtained with a comparison model which shares the
same boundary conditions and source terms as the model to be calibrated, but a
tentative T field. On the other hand the DCM algorithm applies the ratio of the
hydraulic gradients obtained for two different forward models, one with the same
boundary conditions and source terms as the model to be calibrated and the other
one with prescribed head at the positions where in- or out-flow is known and h is
measured. For DCM and CMM, multiple stimulation is used by updating the T field
separately for each data set and then combining the resulting updated fields with
different possible statistics (arithmetic, geometric or harmonic mean, median, least
change, etc.). The three algorithms are tested and their characteristics and results are
compared with a field data set, which was provided by prof. Fritz Stauffer (ETH) and
corresponding to a pumping test in a thin alluvial aquifer in northern Switzerland.
Three data sets are available and correspond to the undisturbed state, to the flow
field created by a single pumping well and to the situation created by an “hydraulic
dipole”, i.e., an extraction and an injection wells. These data sets permit to test the
three inverse methods and the different options which can be chosen for their use. |
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