Identification of Aquifer Transmissivity with Multiple Sets of Data Using the Differential System Method

  • M. Giudici
  • G. A. Meles
  • G. Parravicini
  • G. Ponzini
  • C. Vassena
Conference paper
Part of the IFIP International Federation for Information Processing book series (IFIPAICT, volume 202)


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.


Inverse problems porous media multiple data sets 


  1. [1]
    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.Google Scholar
  2. [2]
    G. Chavent. Analyse fonctionnelle et identification de coefficients répartis dans les équations aux dérivées partielles. Thése d’etat, Fac. des Science de Paris, 1971.Google Scholar
  3. [3]
    Y. Emsellem, G. de Marsily. An automatic solution for the inverse problem. Water Resour. Res. 7:1264–1283, 1971.Google Scholar
  4. [4]
    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, 1CrossRefGoogle Scholar
  5. [5]
    M. Giudici, G. Morossi, G. Parravicini, G. Ponzini. A new method for the identification of distributed transmissivities. Water Resour. Res. 31:1969–1988, 1995.CrossRefGoogle Scholar
  6. [6]
    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.MATHCrossRefGoogle Scholar
  7. [7]
    S. Liu, T.-C. J. Yeh, R. Gardiner. Effectiveness of hydraulic tomography: Sandbox experiments Water Resour. Res. doi:10.1029/2001WR000338, 2002.Google Scholar
  8. [8]
    R.W. Nelson. In place measurement of permeability in heterogeneous media, 1, Theory of a proposed method. J. Geophys. Res. 65:1753–1760, 1960.Google Scholar
  9. [9]
    R.W. Nelson. In place measurement of permeability in heterogeneous media, 2, Experimental and computational considerations. J. Geophys. Res. 66:2469–2478, 1961.Google Scholar
  10. [10]
    R.W. Nelson. Condition for determining areal permeability distribution by calculation. Soc. Pet. Eng. J. 2:223–224, 1962.Google Scholar
  11. [11]
    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.MATHMathSciNetCrossRefGoogle Scholar
  12. [12]
    G. Ponzini, A. Lozej. Identification of aquifer transmissivities: the comparison model method. Water Resour. Res. 18:597–622, 1982.Google Scholar
  13. [13]
    G.R. Richter. An inverse problem for the steady state diffusion equation. SIAM J. Math. Anal. 41:210–221, 1981.MATHCrossRefGoogle Scholar
  14. [14]
    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.Google Scholar
  15. [15]
    S. Scarascia, G. Ponzini. An approximate solution for the inverse problem in hydraulics. L’Energia Elettrica 49:518–531, 1972.Google Scholar
  16. [16]
    M.F. Snodgrass, P.K. Kitanidis. Transmissivity identification through multi-directional aquifer stimulation. Stochastic Hydrol. and Hydraul. 12:299–316, 1998.MATHCrossRefGoogle Scholar
  17. [17]
    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.CrossRefGoogle Scholar
  18. [18]
    W.-G. W. Yeh. Review of parameter identification procedures in groundwater hydrology: the inverse problem. Water Resour. Res. 22:95–108, 1986.CrossRefGoogle Scholar
  19. [19]
    T.-C. J. Yeh, S. Liu. Hydraulic tomography: Development of a new aquifer test method. Water Resour. Res. 36:2095–2105, 2000.CrossRefGoogle Scholar

Copyright information

© International Federation for Information Processing 2006

Authors and Affiliations

  • M. Giudici
    • 1
  • G. A. Meles
    • 1
  • G. Parravicini
    • 2
  • G. Ponzini
    • 1
  • C. Vassena
    • 1
  1. 1.Dipartimento di Scienze della TerraUniversità degli Studi di MilanoMilanoItaly
  2. 2.Dipartimento di FisicaUniversità degli Studi di MilanoMilanoItaly

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