Aquifer Characterization and Parameter Heterogeneity Estimation with a Coupled Zonation-Geostatistical Method and Natural Neighbors

Abstract

This research develops a generalized parameterization method that couples zonation and geostatistics for characterization and identification of a stochastic field. The coupled zonation-geostatistical method honors distinct pointwise measurements in a field to create a zonation structure, a kriging field, or a mixed distribution. In this study, a Voronoi tessellation (VT) is adopted to create a zonation structure of Voronoi cells over a set of sample points. VT determines the boundary, shape, and distribution of zones completely and uniquely for a given set of sample points. Other than zonation approach, this study develops a natural neighbor kriging (NNK) method that honors natural neighboring sample points for estimation. The natural neighbors of an estimation site are determined by VT. Specifically, we combine VT and NNK together as a coupled VT-NNK method by introducing a set of binary weighting coefficients to the sample points. The coupled VT-NNK method possesses greater flexibility to characterize the randomness of parameter heterogeneity and makes the best linear unbiased estimation (BLUE) over a set of binary weighting coefficients. In the numerical example, we identify transmissivity heterogeneity with coupled VT-NNK by seeking the optimal binary value of weighting coefficients such that the fitting residual of observed groundwater heads is minimized. The nonlinear binary integer minimization problem is accomplished by a genetic algorithm (GA) to obtain a near-global optimal solution. Results show that coupled VT-NNK is able to capture the non-smoothness of true heterogeneity and gives small groundwater head fitting residual.