Stochastic simulation of transmissivity fields conditional to both transmissivity and piezometric data—I. Theory

• Published in: Journal of hydrology (Amsterdam) Vol. 203; no. 1; pp. 162 - 174
• Main Authors: Jaime Gómez-Hernánez, J., Sahuquillo, Andrés, Capilla, JoséE.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 31.12.1997
• Subjects: Geostatistics; groundwater flow; saturated flow; Self-calibrated algorithm; Stochastic hydrogeology; Stochastic inversion; stochastic processes; Stochastic hydrogeology; Stochastic inversion; Geostatistics; Self-calibrated algorithm
• ISSN: 0022-1694; 1879-2707
• DOI: 10.1016/S0022-1694(97)00098-X

The generation of equally likely realizations of transmissivity fields conditional to both transmissivity and piezometric data is achieved using an iterative technique that couples geostatistics and optimization. By conditioning to both transmissivity fields and piezometric data we mean that the transmissivity field generated honours the transmissivity data and that the solution to the flow equation reproduces the measured piezometric heads. By equally likely realizations we mean that all realizations display the same patterns of spatial variability as observed in the field, as opposed to the transmissivity fields obtained by interpolation or by inverse modelling which are oversmooth, unrealistic, representations of the real field. In this regard, any realization could be the real but unknown transmissivity field. To achieve this goal, first a transmissivity field is generated conditional only to the transmissivity data, then the transmissivity field (and possibly the boundary conditions), are modified without destroying the spatial patterns of variability of transmissivity until the piezometric data are also honoured. The methodology is presented for steady-state flow in a confined two-dimensional aquifer. The details of the implementation are given for finite-differences solution over an aquifer discretized in square blocks.