A Genetic Algorithm for Stochastic Inversion in Contaminant Subsurface Hydrology

Identifying the spatial distribution of hydrological properties of aquifers is a key problem in subsurface hydrology. The aquifer structure plays an important role in contaminant transport. Identifying the properties (primarily the hydraulic conductivity) is essentially an inversion problem that is ill-posed, non-unique and computationally intensive by definition. In this work, the non-uniqueness of the inverse problem is tackled via a novel Genetic Algorithm approach combined with a geostatistical method (Sequential Indicator Simulations) for construction of realizations of properties spatial distributions, which are modeled as random. The Genetic Algorithm cross-over operator is based on a novel concept of pilot-planes: daughter realizations adopt pilot-planes from one of their parents. In addition, each aquifer realization is conditioned on the geological hard data and is constructed by sampling the facies distribution, evaluated by indicator variograms. The approach is illustrated in two test cases: a synthetic two-dimensional (2D) case and an actual three-dimensional (3D) case. The results have shown the ability of the proposed approach to generate a set of realizations, where each individual exhibits minor deviations from the measurements. Further, a comparison between the proposed approach and direct (Monte Carlo) approach shows that the Genetic Algorithm was able to generate an ensemble of solutions with a better fitting of the measurements than the direct approach by a significantly reduced computational effort.