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 M$_2$ frequency at depths >50 m and requires specific storage at constant strain of S$_ϵ$ ≥ 10$^{−6}$ m$^{−1}$, hydraulic conductivity of the aquitard of k$_l$ ≤ 5 ⋅ 10$^{−5}$ ms$^{−1}$ and aquifer of k$_a$ ≥ 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

Multifactor analysis of specific storage estimates and implications for transient groundwater modelling

Specific storage (S$_S$) has considerable predictive importance in the modelling of groundwater systems, yet little is known about its statistical distribution and dependency on other hydrogeological characteristics. This study provides a comprehensive overview and compiles 430 values of S$_S$ from 183 individual studies, along with complementary hydrogeological information such as estimation methods, lithology, porosity, and formation compressibility. Further evaluation of different approaches to determine and utilize S$_S$ values for numerical groundwater modelling, along with the scale and source of uncertainty of different measurement methods, was carried out. Overall, S$_S$ values range across six orders of magnitude (from 3.2 × 10$^{–9}$ to 6 × 10$^{–3}$ m$^{–1}$) with a geometric mean of 1.1 × 10$^{–5}$ m$^{–1}$ and the majority (> 67%) of values are in the order of 10$^{–5}$ and 10$^{–6}$ m$^{–1}$. High S$_S$ values of ~10$^{–4}$ m$^{–1}$ were reported for glacial till and sandy lithologies, particularly for shallow and thin strata where leakage may obscure the estimation of S$_S$. A parallel assessment of 45 transient regional-scale groundwater models reveals a disconnect between findings of this study and the way S$_S$ is treated in practice, and that there is a lack of foundational S$_S$ data to conduct quantitative uncertainty analysis. This study provides the first probability density functions of S$_S$ for a variety of lithology types based on the field and laboratory tests collated from the literature. Log transformed S$_S$ values follow a Gaussian/normal distribution which can be applied to evaluate uncertainties of modelling results and therefore enhance confidence in the groundwater models that support decision making

Comparing methods of barometric efficiency characterisation for specific storage estimation

Groundwater responses to barometric pressure fluctuations are characterized using the concept of barometric efficiency (BE). For semiconfined and confined aquifers, BE values can be used to provide efficient, low-cost estimates of specific storage. This study compares, for the first time, eight existing methods of BE estimation. Comparisons were undertaken using data from the Peel region of Western Australia. Fourier analysis and regression deconvolution methods were used to estimate aquifer confinement status. The former approach was found to be robust and provided a quantitative basis for spatial comparisons of the degree of confinement. The latter approach was confounded by the presence of diurnal and/or semidiurnal signals. For wells at which semiconfined or confined responses were identified, frequency and time domain methods were used to estimate BE values. Most BE estimation methods were similarly confounded by diurnal and/or semidiurnal signals, with the exception of the Acworth et al. (2016) method. Specific storage values calculated from BE values were order-of-magnitude consistent with the results of four historical pumping tests. The methods implemented in this research provide efficient, low-cost alternatives to hydraulic testing for estimating aquifer confinement, as well as the BE and specific storage of semiconfined and confined aquifers. The frequency and duration of observations required by these methods are minimal; for example, typically requiring a minimum of four observations per day over a four month period. In some locations they may allow additional insights to be derived from existing groundwater hydrograph data

In situ estimation of subsurface hydro-geomechanical properties using the groundwater response to semi-diurnal Earth and atmospheric tides

Subsurface hydro-geomechanical properties crucially underpin the management of Earth\u27s resources, yet they are predominantly measured on core samples in the laboratory while little is known about the representativeness of in situ conditions. The impact of Earth and atmospheric tides on borehole water levels is ubiquitous and can be used to characterise the subsurface. We illustrate that disentangling the groundwater response to Earth (M₂) and atmospheric tidal (S₂) forces in conjunction with established hydraulic and linear poroelastic theories leads to a complete determination of the whole hydro-geomechanical parameter space for unconsolidated systems. Further, the characterisation of consolidated systems is possible when using literature estimates of the grain compressibility. While previous field investigations have assumed a Poisson\u27s ratio from literature values, our new approach allows for its estimation under in situ field conditions. We apply this method to water level and barometric pressure records from four field sites with contrasting hydrogeology. Estimated hydro-geomechanical properties (e.g. specific storage; hydraulic conductivity; porosity; shear, Young\u27s, and bulk moduli; Skempton\u27s and Biot–Willis coefficients; and undrained or drained Poisson\u27s ratios) are comparable to values reported in the literature, except for consistently negative drained Poisson\u27s ratios, which is surprising. Our results reveal an anisotropic response to strain, which is expected for heterogeneous (layered) lithological profiles. Closer analysis reveals that negative Poisson\u27s ratios can be explained by in situ conditions differing to those from typical laboratory core tests and the small strains generated by Earth and atmospheric tides. Our new approach can be used to passively, and therefore cost-effectively, estimate subsurface hydro-geomechanical properties representative of in situ conditions and it improves our understanding of the relationship between geological heterogeneity and geomechanical behaviour

Technical note: Disentangling the groundwater response to Earth and atmospheric tides to improve subsurface characterisation

The groundwater response to Earth tides and atmospheric pressure changes can be used to understand subsurface processes and estimate hydraulic and hydro-mechanical properties. We develop a generalised frequency domain approach to disentangle the impacts of Earth and atmospheric tides on groundwater level responses. By considering the complex harmonic properties of the signal, we improve upon a previous method for quantifying barometric efficiency (BE), while simultaneously assessing system confinement and estimating hydraulic conductivity and specific storage. We demonstrate and validate this novel approach using an example barometric and groundwater pressure record with strong Earth tide influences. Our method enables improved and rapid assessment of subsurface processes and properties using standard pressure measurements

Comparing Methods and Defining Practical Requirements for Extracting Harmonic Tidal Components from Groundwater Level Measurements

The groundwater pressure response to the ubiquitous Earth and atmospheric tides provides a largely untapped opportunity to passively characterize and quantify subsurface hydro-geomechanical properties. However, this requires reliable extraction of closely spaced harmonic components with relatively subtle amplitudes but well-known tidal periods from noisy measurements. The minimum requirements for the suitability of existing groundwater records for analysis are unknown. This work systematically tests and compares the ability of two common signal processing methods, the discrete Fourier transform (DFT) and harmonic least squares (HALS), to extract harmonic component properties. First, realistic conditions are simulated by analyzing a large number of synthetic data sets with variable sampling frequencies, record durations, sensor resolutions, noise levels and data gaps. Second, a model of two real-world data sets with different characteristics is validated. The results reveal that HALS outperforms the DFT in all aspects, including the ability to handle data gaps. While there is a clear trade-off between sampling frequency and record duration, sampling rates should not be less than six samples per day and records should not be shorter than 20 days when simultaneously extracting tidal constituents. The accuracy of detection is degraded by increasing noise levels and decreasing sensor resolution. However, a resolution of the same magnitude as the expected component amplitude is sufficient in the absence of excessive noise. The results provide a practical framework to determine the suitability of existing groundwater level records and can optimize future groundwater monitoring strategies to improve passive characterization using tidal signatures

Comparing Methods and Defining Practical Requirements for Extracting Harmonic Tidal Components from Groundwater Level Measurements

The groundwater pressure response to the ubiquitous Earth and atmospheric tides provides a largely untapped opportunity to passively characterize and quantify subsurface hydro-geomechanical properties. However, this requires reliable extraction of closely spaced harmonic components with relatively subtle amplitudes but well-known tidal periods from noisy measurements. The minimum requirements for the suitability of existing groundwater records for analysis are unknown. This work systematically tests and compares the ability of two common signal processing methods, the discrete Fourier transform (DFT) and harmonic least squares (HALS), to extract harmonic component properties. First, realistic conditions are simulated by analyzing a large number of synthetic data sets with variable sampling frequencies, record durations, sensor resolutions, noise levels and data gaps. Second, a model of two real-world data sets with different characteristics is validated. The results reveal that HALS outperforms the DFT in all aspects, including the ability to handle data gaps. While there is a clear trade-off between sampling frequency and record duration, sampling rates should not be less than six samples per day and records should not be shorter than 20 days when simultaneously extracting tidal constituents. The accuracy of detection is degraded by increasing noise levels and decreasing sensor resolution. However, a resolution of the same magnitude as the expected component amplitude is sufficient in the absence of excessive noise. The results provide a practical framework to determine the suitability of existing groundwater level records and can optimize future groundwater monitoring strategies to improve passive characterization using tidal signatures