Abstract
The mass balance equation for stationary flow in a confined aquifer and the phenomenological Darcy’s law lead to a classical elliptic PDE, whose phenomenological coefficient is transmissivity, T, whereas the unknown function is the piezometric head. The differential system method (DSM) allows the computation of T when two “independent” data sets are available, i.e., a couple of piezometric heads and the related source or sink terms corresponding to different flow situations such that the hydraulic gradients are not parallel at any point. The value of T at only one point of the domain, x0, is required. The T field is obtained at any point by integrating a first order partial differential system in normal form along an arbitrary path starting from x0. In this presentation the advantages of this method with respect to the classical integration along characteristic lines are discussed and the DSM is modified in order to cope with multiple sets of data. Numerical tests show that the proposed procedure is effective and reduces some drawbacks for the application of the DSM.
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J. Carrera, S.P. Neuman. Estimation of aquifer parameters under transient and steady-state conditions: 1, maximum likelihood method incorporating prior information. Water Resour. Res. 22:199–210, 1986.
G. Chavent. Analyse fonctionnelle et identification de coefficients répartis dans les équations aux dérivées partielles. Thése d’etat, Fac. des Science de Paris, 1971.
Y. Emsellem, G. de Marsily. An automatic solution for the inverse problem. Water Resour. Res. 7:1264–1283, 1971.
T.R. Ginn, J.H. Cushman, M.H. Houch. A continuous me inverse operator for ground-water and contaminant transport modeling: deterministic case. Water Resour. Res. 26:241–252, 1
M. Giudici, G. Morossi, G. Parravicini, G. Ponzini. A new method for the identification of distributed transmissivities. Water Resour. Res. 31:1969–1988, 1995.
M. Giudici, F. Delay, G. de Marsily, G. Parravicini, G. Ponzini, A. Rosazza. Discrete stability of the Differential System Method evaluated with geostatistical techniques. Stochastic Hydrol. and Hydraul. 12:191–204, 1998.
S. Liu, T.-C. J. Yeh, R. Gardiner. Effectiveness of hydraulic tomography: Sandbox experiments Water Resour. Res. doi:10.1029/2001WR000338, 2002.
R.W. Nelson. In place measurement of permeability in heterogeneous media, 1, Theory of a proposed method. J. Geophys. Res. 65:1753–1760, 1960.
R.W. Nelson. In place measurement of permeability in heterogeneous media, 2, Experimental and computational considerations. J. Geophys. Res. 66:2469–2478, 1961.
R.W. Nelson. Condition for determining areal permeability distribution by calculation. Soc. Pet. Eng. J. 2:223–224, 1962.
G. Parravicini, M. Giudici, G. Morossi, G. Ponzini. Minimal a priori assignment in a direct method for determining phenomenological coefficients uniquely. Inverse Problems 11:611–629, 1995.
G. Ponzini, A. Lozej. Identification of aquifer transmissivities: the comparison model method. Water Resour. Res. 18:597–622, 1982.
G.R. Richter. An inverse problem for the steady state diffusion equation. SIAM J. Math. Anal. 41:210–221, 1981.
B. Sagar, S. Yakowitz, L. Duckstein. A direct method for the identification of the parameters of dynamic non-homogeneous aquifers. Water Resour. Res. 11:563–570, 1975.
S. Scarascia, G. Ponzini. An approximate solution for the inverse problem in hydraulics. L’Energia Elettrica 49:518–531, 1972.
M.F. Snodgrass, P.K. Kitanidis. Transmissivity identification through multi-directional aquifer stimulation. Stochastic Hydrol. and Hydraul. 12:299–316, 1998.
R. Vàzquez Gonzàlez, M. Giudici, G. Parravicini, G. Ponzini. The differential system method for the identification of transmissivity and storativity. Transport in Porous Media 26:339–371, 1997.
W.-G. W. Yeh. Review of parameter identification procedures in groundwater hydrology: the inverse problem. Water Resour. Res. 22:95–108, 1986.
T.-C. J. Yeh, S. Liu. Hydraulic tomography: Development of a new aquifer test method. Water Resour. Res. 36:2095–2105, 2000.
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Giudici, M., Meles, G.A., Parravicini, G., Ponzini, G., Vassena, C. (2006). Identification of Aquifer Transmissivity with Multiple Sets of Data Using the Differential System Method. In: Ceragioli, F., Dontchev, A., Furuta, H., Marti, K., Pandolfi, L. (eds) Systems, Control, Modeling and Optimization. CSMO 2005. IFIP International Federation for Information Processing, vol 202. Springer, Boston, MA . https://doi.org/10.1007/0-387-33882-9_16
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DOI: https://doi.org/10.1007/0-387-33882-9_16
Publisher Name: Springer, Boston, MA
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