Complex wave propagation from open water bodies into aquifers: A fast analytical approach

Aquifers are of particular interest in the vicinity of rivers, lakes and coastal areas due to their extensive usage. Hydraulic properties such as transmissivity and storativity can be deduced from periodical water level fluctuations in both open water bodies and groundwater. Here, we model the effect of complex wave propagation into adjacent isotropic and homogeneous aquifers. Besides confined aquifers, we also study wave propagation in leaky aquifers and situations with flow barriers near open water bodies as encountered in harbours where sheet piling are in place. We present a fast analytical solution for the hydraulic head distribution which allows for determining the hydraulic diffusivity ($S_s/K$) of the aquifer, with low investigational efforts. We make use of the Fast Fourier Transform to decompose complex wave boundary conditions and derive solutions through superposition. Analytical solutions are verified by comparing to numerical MODFLOW models for three application examples: a tidal wave measured in the harbour of Rotterdam, a synthetic square wave and river fluctuations in the river Rhine near Lobith. We setup a parameter estimation routine to identify hydraulic diffusivity, which can be easily adapted to real observation data from piezometers. Inverse estimates show relative differences of less than $2\%$ to numerical input data. A sensitivity study further shows how to achieve reliable estimates depending on the piezometer location or other influencing factors such as resistance values of the confining layer (for leaky aquifers) and flow barriers.