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This paper presents a methodology to invert tracer arrival times and to incorporate travel time data in the delineation of well capture zones. Within a Bayesian framework the observed arrival times are used to obtain probability-based weights for each realization of the hydraulic conductivity field. Realizations that closely reproduce the observed arrival times are more likely to represent the "true" or real conductivity field than realizations yielding worse predictions, and are consequently characterized by a higher conditional probability. In the prediction of the capture zones the realizations are weighted by their respective probability. We combine the arrival time data with conductivity measurements and head observations to delineate stochastic capture zones. The conductivity measurements update the prior distributions specified for the unknown structural parameters of the conductivity field, and are used as conditioning data in the generation of conditional conductivity fields. The parameter values used to generate the conductivity realizations are sampled by Monte Carlo from the updated parameter distributions. The head and travel time observations are subsequently used to assign probability-based weights to the conductivity realizations by applying Bayes' theorem. The hyperparameters of the error model are assumed unknown, and their effect is accounted for by marginalization. A synthetic flow setup consisting of a single extraction well in a fully confined aquifer under a regional gradient is used to illustrate the method. We evaluate the relative worth of the different data types by introducing them sequentially in the inverse methodology. Results indicate that the different data types are complementary and that the travel time data are essential to improve the predictions of the capture zones. This is confirmed by the results for the case where uncertainty in the homogeneous porosity is accounted for.

A methodology to determine the uncertainty associated with the delineation of well capture zones in heterogeneous aquifers is presented. The log transmissivity field is modeled as a random space function and the Bayesian paradigm accounts for the uncertainty that stems from the imperfect knowledge about the parameters of the stochastic model. Unknown parameters are treated as random quantities and characterized by a prior probability distribution. Log transmissivity measurements are incorporated into Bayes' theorem, updating the prior distribution and yielding posterior estimates of the mean value and the covariance parameters of the log transmissivity. Conditional simulations of the log transmissivity field are generated using samples from the posterior distribution of the parameters, yielding samples from the predictive distribution of the log transmissivity field. The uncertainty in the model parameters is propagated to the predictive uncertainty of the capture zone by solving numerically the groundwater flow equation, followed by a semianalytical particle-tracking algorithm. The method is applied to a set of hypothetical flow fields for various sampling densities and assuming different levels of parameter uncertainty. Simulation results for all the sampling densities show no univocal relation between the predictive uncertainty of the capture zones and the level of parameter uncertainty. However, in general, the predictive uncertainty increases when parameter uncertainty is taken into account.