Tomographic Approach to Identify Transmissivity with Differential System Method
Publication: Journal of Hydrologic Engineering
Volume 12, Issue 6
Abstract
If two independent sets of data are available—the piezometric heads and the related source terms for two stationary flow situations, such that the hydraulic gradients are not parallel to each other—the aquifer transmissivity can be identified with the differential system method (DSM), provided that an initial value of transmissivity is given at least at one point. In field applications, it is difficult to collect two data sets that are independent throughout the aquifer, and the results depend on the location of the point where the initial value is assigned. These difficulties are reduced if several data sets are available and the differential system is obtained either by applying a least square technique to the whole ensemble of data sets, or by choosing the “best” couple of data at each point. Numerical tests on a synthetic aquifer show that both techniques yield good results and make the DSM more robust to noise on the piezometric heads than the standard DSM applied with two data sets only.
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References
Beckie, R. (1996). “Measurement scale, network sampling scale, and groundwater model parameters.” Water Resour. Res., 32, 65–76.
Bierkens, M. F. P., and van der Gaast, J. W. J. (1998). “Upscaling hydraulic conductivity: theory and examples from geohydrological studies.” Nutr. Cycling Agroecosyst., 50, 193–207.
Carrera, J. (1988). “State of art of the inverse problem applied to the flow and solute transport equations.” Groundwater flow and quality modeling, E. Custodio et al., eds., Reidel, Dordrecht, The Netherlands, 549–583.
Carrera, J., Alcolea, A., Medina, A., Hidalgo, J., and Slooten, L. J. (2005). “Inverse problems in hydrogeology.” Hydrogeol. J., 13, 206–222.
Carrera, J., and Neuman, S. P. (1986). “Estimation of aquifer parameters under transient and steady state conditions. 3: Application to synthetic and field data.” Water Resour. Res., 22, 228–242.
Cushman, J. H. (1986). “On measurement, scale, and scaling.” Water Resour. Res., 22, 129–134.
de Marsily, G. (1986). Quantitative hydrogeology-groundwater hydrology for engineers, Academic, Orlando, Fla.
Ginn, T. R., and Cushman, J. H. (1990). “Inverse methods for subsurface flow: a critical review of stochastic techniques.” Stochastic Environ. Res. Risk Assess., 4, 1–26.
Ginn, T. R., Cushman, J. H., and Houch, M. H. (1990). “A continuous-time inverse operator for groundwater and contaminant transport modeling: deterministic case.” Water Resour. Res., 26, 241–252.
Giudici, M. (2001). “Development, calibration and validation of physical models.” Geographic information systems and environmental modeling, K. C. Clarke, B. O. Parks, and M. C. Krane, eds., Prentice-Hall, Upper Saddle River, N.J., 100–121.
Giudici, M., Delay, F., Marsily, G., de Parravicini, G., Ponzini, G., and Rosazza, A. (1998). “Discrete stability of the differential system method evaluated with geostatistical techniques.” Stochastic Environ. Res. Risk Assess., 12, 191–204.
Giudici, M., Foglia, L., Parravicini, G., Ponzini, G., and Sincich, B. (2000). “A quasi three-dimensional model of water flow in the subsurface of Milano (Italy): The stationary flow.” Hydrology Earth Syst. Sci., 4, 113–124.
Giudici, M., Morossi, G., Parravicini, G., and Ponzini, G. (1995). “A new method for the identification of distributed transmissivities.” Water Resour. Res., 31, 1969–1988.
Giudici, M., and Vassena, C. (2006). “dsm. f90: A computer code for the solution of an inverse problem of ground water hydrology by the differential system method.” Comput. Geosci., 32, 1709–1719.
Gottlieb, J., and Dietrich, P. (1995). “Identification of the permeability distribution in soil by hydraulic tomography.” Inverse Probl., 11, 353–360.
Hämmerlin, G., and Hoffmann, K. H. (1991). Numerical mathematics, Springer, New York.
Liu, S., Yeh, T.-C. J., and Gardiner, R. (2002). “Effectiveness of hydraulic tomography: Sandbox experiments.” Water Resour. Res., 38, 1034–1043.
McLaughlin, D., and Townley, L. R. (1996). “A reassessment of the groundwater inverse problem.” Water Resour. Res., 32, 1131–1161.
Neuman, S. P. (1973). “Calibration of distributed parameter groundwater flow models viewed as multiple objective decision process under uncertainty.” Water Resour. Res., 9, 1006–1021.
Parravicini, G., Giudici, M., Morossi, G., and Ponzini, G. (1995). “Minimal a priori assignment in a direct method for determining phenomenological coefficients uniquely.” Inverse Probl., 11, 611–629.
Ponzini, G., and Lozej, A. (1982). “Identification of aquifer transmissivities: the comparison model method.” Water Resour. Res., 18, 597–622.
Sagar, B., Yakowitz, S., and Duckstein, L. (1975) “A direct method for the identification of the parameters of dynamic nonhomogeneous aquifers.” Water Resour. Res., 11, 563–570.
Scarascia, S., and Ponzini, G. (1972). “An approximate solution for the inverse problem in hydraulics.” Energ. Elettr., 49, 518–531.
Snodgrass, M. F., and Kitanidis, P. K. (1998). “Transmissivity identification through multidirectional aquifer stimulation.” Stochastic Environ. Res. Risk Assess., 12, 299–316.
Sun, N. Z. (1994). Inverse problems in groundwater modeling, Kluwer, Norwell, The Netherlands.
Vázquez González, R., Giudici, M., Parravicini, G., and Ponzini, G. (1997). “The differential system method for the identification of transmissivity and storativity.” Transp. Porous Media, 26, 339–371.
Yeh, T.-C. J., and Liu, S. (2000). “Hydraulic tomography: Development of a new aquifer test method.” Water Resour. Res., 36, 2095–2105.
Yeh, W.-G. W. (1986). “Review of parameter identification procedures in groundwater hydrology: The inverse problem.” Water Resour. Res., 22, 95–108.
Zimmerman, D. A., et al. (1998). “A comparison of seven geostatistically based inverse approaches to estimate transmissivities for modeling advective transport by groundwater flow.” Water Resour. Res., 34, 1373–1413.
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Published In
Journal of Hydrologic Engineering
Volume 12 • Issue 6 • November 2007
Pages: 617 - 625
Copyright
© 2007 ASCE.
History
Received: Mar 16, 2006
Accepted: Nov 30, 2006
Published online: Nov 1, 2007
Published in print: Nov 2007
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