A stochastic framework for the analysis of tidal effects in heterogeneous coastal aquifers

Tidal phenomena in surface water bodies may affect groundwater levels in contiguous aquifers. These effects may be manifested in oscillations of the water levels or piezometric heads in observation bores or in cyclic discharges at aquifer boundaries, although such observations may also be produced by other forcings. Observations of oscillations can be used to make inferences about the physical properties of the aquifers involved, based on the governing equations for the propagation of pressure disturbances with distance from the tidal boundaries. Most theories for tidal propagation focus on homogeneity or at least simple models of heterogeneity, and neglect the treatment of stochastic influences of random heterogeneity on the tidal responses within the aquifer porous medium. The focus of this work is to develop a theoretical framework for predicting the spatial statistics of tidal responses in randomly heterogeneous aquifers governed by linear groundwater flows, and to provide theoretical calculations of spatial responses in model systems. Comments are provided on the applicability of the results to field sites with a previously published data set for a fluvial aquifer.