Technical Note: Analytical Solution for Well Water Response to Earth Tides in Leaky Aquifers with Storage and Compressibility in the Aquitard

Abstract. In recent years, there has been a growing interest in utilizing the groundwater response to Earth tides as a means to estimate subsurface properties. However, existing analytical models have been insufficient in accurately capturing realistic physical conditions. This study presents a new analytical solution to calculate groundwater response to Earth tide strains, including storage and compressibility of the aquitard, borehole storage and skin effects. We investigate the effects of aquifer and aquitard parameters on well water response to Earth tides at two dominant frequencies (O₁ and M₂) and compare our results with hydraulic parameters obtained from a pumping test. Inversion of the six hydro-geomechanical parameters from amplitude response and phase shift of both semi-diurnal and diurnal tides provides relevant information about aquifer transmissivity, storativity, well skin effect, aquitard hydraulic conductivity and diffusivity. The new model is able to reproduce previously unexplained observations of the amplitude and frequency responses. We emphasize the usefulness in developing relevant methodology to use the groundwater response to natural drivers for characterizing hydrogeological systems.