  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.
