Geostatistical inversing for large-contrast transmissivity fields

The estimation of field parameters, such as transmissivity, is an important part of groundwater modeling. This work deals with the quasilinear geostatistical inverse approach to the estimation of the transmissivity fields from hydraulic head measurements. The standard quasilinear approach is an iterative method consisting of successive linearizations. We examine a synthetic case to evaluate the basic methodology and some modifications and extensions. The first objective is to evaluate the performance of the quasilinear approach when applied to strongly heterogeneous (or high-contrast) transmissivity fields and, when needed, to propose improvements that allow the solution of such problems. For large-contrast cases, the standard quasilinear method often fails to converge. However, by introducing a derivative-free line search as a polishing step after each Gauss-Newton iteration, we have found that convergence can be practically assured. Another issue is that the quasilinear procedure, which uses linearization about the best estimate to evaluate estimation variances, may lead to inaccurate estimation of the variance of the estimated variable. Our numerical results suggest that this may not be a particularly serious problem, though it is hard to say whether this conclusion will apply to other cases. Nevertheless, since the quasilinear approach is an approximation, we propose a potentially more accurate but computer-intensive Markov Chain Monte Carlo (MCMC) procedure based on conditional realizations generated through the quasilinear approach and accepted or rejected according to the Metropolis-Hastings algorithm. Six transmissivity fields with increasing contrast were generated and one thousand conditional realizations were computed for each studied case. The MCMC procedure proposed in this work gives an overall more accurate picture than the quasilinear approach but at a considerably higher computational cost.