LEARNING THE DECISION-RELEVANT PROBABILITY, NOT THE STATE: A DEEP-LEARNING SURROGATE FOR TRANSIENT WELLHEAD PROTECTION AREAS
Probabilistic delineation of wellhead protection areas usually treats uncertain aquifer properties by propagating ensembles of hydraulic-conductivity fields under steady-state flow. In practice, seasonal variations in regional flow and pumping continually shift the area that supplies water to a well. Reliable protection therefore requires two uncertainty measures: how often a location lies within the capture zone for a given geological realization, and how uncertain this is across realizations. Fully transient Monte Carlo simulation to resolve both is computationally expensive.
We develop a deep learning surrogate for the decision-relevant time–frequency response. For each hydraulic-conductivity realization, the surrogate predicts the fraction of the seasonal cycle that a location x lies within the transient capture zone. Ground-truth maps are generated by transient reverse random-walk particle tracking under periodic forcing. An attention U-Net is trained on paired hydraulic-conductivity and capture-frequency fields. Unlike conventional subsurface surrogates that approximate heads, velocities, or transport states, our framework directly learns the quantity needed for reliability-based capture-zone delineation.
For new hydraulic-conductivity realizations, the surrogate evaluates transient capture-frequency responses in a fraction of the time required by the high-fidelity model, enabling large Monte Carlo propagation of geological uncertainty. Applying a temporal-reliability threshold to each predicted yields binary protection maps that are aggregated over realizations to obtain deterministic protection areas for a specified geological-reliability level. Comparison with the reference model shows that the surrogate reproduces these protection areas with very high agreement. The method makes joint geo-temporal uncertainty propagation computationally feasible by learning the transient capture-frequency response directly instead of emulating the physical state sequence