Geophysical parameterization and parameter structure identification using natural neighbors in groundwater inverse problems

A natural neighbor interpolation (NN) method based on Voronoi tessellation and Delaunay triangulation is developed for both parameter heterogeneity characterization and parameter structure identification in groundwater modeling. Honoring information from the natural neighboring basis points, NN generates a continuously distributed field. With NN, parameter structure identification seeks to identify the optimal parameter distribution in terms of the number, values, and locations of basis points. At each level of parameter structure complexity, the estimated distributed parameter is obtained by minimizing a regularized fitting residual. This is done sequentially, first by a genetic algorithm (GA) and then by a gradient-based algorithm (BFGS). In this study, sensitivity equations of state variables to both values and locations of basis points are developed for optimization as well as for parameter uncertainty analysis. The results obtained from numerical experiments show that, for a given set of head observations and point transmissivity measurements, the proposed inverse methodology successfully captures the variation of the true transmissivity field. The parameter structure complexity as represented by the parameter dimension is determined by considering the trade-off between the fitting residual and the parameter uncertainty error. An optimal parameter dimension is selected when the head fitting residual is close to the observation error and the uncertainty associated with identified transmissivity structure is acceptable.