Quantitative interpretation of the tidal response of water levels measured in wells has long been made either with a model for perfectly confined aquifers or with a model for purely unconfined aquifers. However, many aquifers may be neither totally confined nor purely unconfined at the frequencies of tidal loading but behave somewhere between the two end members. Here we present a more general model for the tidal response of groundwater in aquifers with both horizontal and vertical flow. The model has three independent parameters: the transmissivity and storativity of the aquifer and the specific leakage of the leaking aquitard. If transmissivity and storativity are known independently, this model may be used to estimate aquitard leakage from the phase shift and amplitude ratio of water level in wells obtained from tidal analysis. We apply the model to interpret the tidal response of water level in a USGS deep monitoring well installed in the Arbuckle aquifer in Oklahoma, into which massive amount of wastewater co-produced from hydrocarbon exploration has been injected. The analysis shows that the Arbuckle aquifer is leaking significantly at this site. We suggest that the present method may be effectively and economically applied to monitor leakage in groundwater systems, which bears on the safety of water resources, the security of underground waste repositories, and the outflow of wastewater during deep injection and hydrocarbon extraction.
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