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.

Abstract. Realistic modelling of tightly coupled hydro-geomechanical processes is relevant for the assessment of many hydrological and geotechnical applications. Such processes occur in geologic formations and are influenced by natural heterogeneity. Current numerical libraries offer capabilities and physics couplings that have proven to be valuable in many geotechnical fields like gas storage, rock fracturing and Earth resources extraction. However, implementation and verification of the full heterogeneity of subsurface properties using high-resolution field data in coupled simulations has not been done before. We develop, verify and document RHEA (Real HEterogeneity App), an open-source, fully coupled, finite-element application capable of including element-resolution hydro-geomechanical properties in coupled simulations. To extend current modelling capabilities of the Multiphysics Object-Oriented Simulation Environment (MOOSE), we added new code that handles spatially distributed data of all hydro-geomechanical properties. We further propose a simple yet powerful workflow to facilitate the incorporation of such data to MOOSE. We then verify RHEA with analytical solutions in one and two dimensions and propose a benchmark semi-analytical problem to verify heterogeneous systems with sharp gradients. Finally, we demonstrate RHEA's capabilities with a comprehensive example including realistic properties. With this we demonstrate that RHEA is a verified open-source application able to include complex geology to perform scalable, fully coupled, hydro-geomechanical simulations. Our work is a valuable tool to assess challenging real-world hydro-geomechanical systems that may include different levels of complexity like heterogeneous geology and sharp gradients produced by contrasting subsurface properties.

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<p align="justify"><span lang="en-AU">Earth tides exert small gravitational variations in the subsurface which lead to pore pressure changes and water level fluctuations in groundwater monitoring wells. This groundwater response to Earth tides has been used to estimate subsurface hydraulic and geomechanical properties. However, existing approaches are based on simplifying assumptions and their reliability has not been tested for realistic conditions. To simulate how Earth tides affect the subsurface, we developed and verified a numerical model that couples hydraulic and geomechanical theories. We modelled the response of a semi-confined aquifer which exchange water with an observation well for the dominant M</span><sub><span lang="en-AU">2</span></sub><span lang="en-AU"> Earth tide component. We reveal that undrained (i.e., groundwater does not flow in response to stress) and confined (i.e., groundwater is under pressure) conditions are necessary for the analytical solution to be valid. For the M</span><sub><span lang="en-AU">2</span></sub><span lang="en-AU"> frequency we assess that this occurs at depths ≤</span><span lang="en-AU"> 50 m and requires specific storage at constant strain s<sub>ε</sub></span> ≥ 10<sup>-6 </sup><span lang="en-AU">m<sup>-1</sup>, hydraulic conductivity of the aquitard k<sub>l</sub> ≤ 5 • 10<sup>-5</sup> ms<sup>-1</sup> and aquifer k<sub>l</sub> ≥ 1 • 10<sup>-4</sup> ms<sup>-1</sup></span><span lang="en-AU">, respectively. Further, we illustrate that established analytical solutions are valid in unconsolidated systems, whereas consolidated systems require additional consideration of the compressibility ratio between the porous medium and the porous skeleton (i.e., inclusion of the Biot coefficient). Overall, we find that a priori knowledge of the subsurface system increases the reliability of the groundwater response interpretation. Our results improve understanding of the effect of Earth tides on groundwater systems and provide a framework for evaluating subsurface properties.</span></p>