Stochastic simulation of transmissivity fields conditional to both transmissivity and piezometric data 2. Demonstration on a synthetic aquifer

Abstract

In the first paper of this series a methodology for the generation of transmissivity fields conditional to both transmissivity and piezometric head data was presented. This methodology, termed the self-calibrated approach, consists of two steps: first, the generation of a seed transmissivity field conditioned only to transmissivity data, and second, the perturbation of the seed field up until the piezometric head data are reproduced. The methodology is now demonstrated on a set of controlled numerical experiments carried out on synthetic aquifers. The objective of these experiments is not just to show that the methodology works, but also to explore its robustness under different situations. A total of 12 experiments have analyzed the performance of the method as a function of: (i) the log 10 T transmissivity variance (from 0.2 to 2.0); (ii) the number of log 10 T conditioning data (from 10 to 30); (iii) the number of piezometric head data (from 30 to 90); (iv) the number of master points (from 25 to 1000); (v) the magnitude of allowed departure of the final T field from the seed field (up to four times the kriging standard deviation). In all cases, the method was able to generate transmissivity fields conditional to both transmissivity and head measurements, at the same time preserving the spatial variability of the transmissivity field. It was found that the performance of the method increases with both the number of log 10 T data and the number of master points, whereas it decreases as either the log 10 T variance or the number of piezometric head data increases.