Artificial neural networks and conditional stochastic simulations for characterization of aquifer heterogeneity

Abstract

Although it is one of the most difficult tasks in hydrology, delineation of aquifer heterogeneity is essential for accurate simulation of groundwater flow and transport. There are various approaches used to delineate aquifer heterogeneity from a limited data set, and each has its own difficulties and drawbacks. The inverse problem is usually used for estimating different hydraulic properties (e.g. transmissivity) from scattered measurements of these properties, as well as hydraulic head. Difficulties associated with this approach are issues of indentifiability, uniqueness, and stability. The Iterative Conditional Simulation (ICS) approach uses kriging (or cokriging), to provide estimates of the property at unsampled locations while retaining the measured values at the sampled locations. Although the relation between transmissivity (T) and head (h) in the governing flow equation is nonlinear, the cross covariance function and the covariance of h are derived from a first-order-linearized version of the equation. Even if the log transformation of T is adopted, the nonlinear nature between f (mean removed Ln[T]) and h still remains. The linearized relations then, based on small perturbation theory, are valid only if the unconditional variance of f is less than 1.0. Inconsistent transmissivity and head fields may occur as a result of using a linear relation between T and h. In this dissertation, Artificial Neural Networks (ANN) is investigated as a means for delineating aquifer heterogeneity. Unlike ICS, this new computational tool does not rely on a prescribed relation, but seeks its own. Neural Networks are able to learn arbitrary non-linear input-output mapping directly from training data and have the very advantageous property of generalization. For this study, a random field generator was used to generate transmissivity fields from known geostatistical parameters. The corresponding head fields were obtained using the governing flow equation. Both T and h at sampled locations were used as input vectors for two different back-propagation neural networks designed for this research. The corresponding values of transmissivities at unsampled location (unknown), constituting the output vector, were estimated by the neural networks. Results from the ANN were compared to those obtained from the (ICS) approach for different degrees of heterogeneity. The degree of heterogeneity was quantified using the variance of the transmissivity field, where values of 1.0, 2.0, and 5.0 were used. It was found that ANN overcomes the limitations of ICS at high variances. Thus, ANN was better able to accurately map the highly heterogeneous fields using limited sample points.