Groundwater Responses to Earth Tides: Evaluation of Analytical Solutions Using Numerical Simulation

Harmonic Earth tide components in well water levels have been used to estimate hydraulic and geomechanical subsurface properties. However, the robustness of various methods based on analytical solutions has not been established. First, we review the theory and examine the latest analytical solution used to relate well water levels to Earth tides. Second, we develop and verify a novel numerical model coupling hydraulics and geomechanics to Earth tide strains. Third, we assess subsurface conditions over depth for a range of realistic properties. Fourth, we simulate the well water level response to Earth tide strains within a 2D poroelastic layered aquifer system confined by a 100 m thick aquitard. We find that the non-linear inversion of analytical solutions to match two observations (amplitudes and phases) to multiple unknown parameters is sensible to the initial guess. We reveal that undrained, confined conditions are necessary for the analytical solution to be valid. This occurs for the dominant M2 frequency at depths >50 m and requires specific storage at constant strain of Sϵ ≥ 10−6 m−1, hydraulic conductivity of the aquitard of kl ≤ 5 ⋅ 10−5 ms−1 and aquifer of ka ≥ 10−4 ms−1. We further illustrate that the analytical solution is valid in unconsolidated systems, whereas consolidated systems require additional consideration of the Biot modulus. Overall, a priori knowledge of the subsurface system supports interpretation of the groundwater response. Our results improve understanding of the effect of Earth tides on groundwater systems and its interpretation for subsurface properties.