STOCHASTIC SIMULATION OF TRANSMISSIVITY FIELDS CONDITIONAL TO BOTH TRANSMISSIVITY AND PIEZOMETRIC DATA - I - THEORY

The generation of equally likely realizations of transmissivity fields conditional to both transmissivity and piezometric data is achieved u sing an iterative technique that couples geostatistics and optimizatio n. By conditioning to both transmissivity fields and piezometric data we mean that the transmissivity held generated honours the transmissiv ity data and that the solution to the how equation reproduces the meas ured piezometric heads. By equally likely realizations we mean that al l realizations display the same patterns of spatial variability as obs erved in the field. as opposed to the transmissivity fields obtained b y interpolation or by inverse modelling which are oversmooth, unrealis tic. representations of the real field. In this regard, any realizatio n could be the real but unknown transmissivity field. To achieve this goal, first a transmissivity field is generated conditional only to th e transmissivity data, then the transmissivity field (and possibly the boundary conditions), are modified without destroying the spatial pat terns 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 a re given for finite-differences solution over an aquifer discretized i n square blocks. (C) 1997 Elsevier Science B.V.