Articles | Volume 28, issue 4
https://doi.org/10.5194/hess-28-1041-2024
© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/hess-28-1041-2024
© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Technical note
| 
29 Feb 2024
Technical note |
| 29 Feb 2024
| 29 Feb 2024
Technical note: Analytical solution for well water response to Earth tides in leaky aquifers with storage and compressibility in the aquitard
French Red Cross, 4 rue Diderot, Paris, France
Hydrogeology Lab, UMR EMMAH, University of Avignon, 74 rue Louis Pasteur, Avignon, France
Agnès Rivière
Geosciences Department, Mines Paris – PSL, 75272 Paris, France
Jean-Michel Vouillamoz
PhYRev lab, Univ. Grenoble Alpes, IRD, CNRS, INRAE, Grenoble INP, IGE, 38000 Grenoble, France
Gabriel C. Rau
School of Environmental and Life Sciences, The University of Newcastle, Callaghan, Australia
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Cited articles
Agnew, D. C.: SPOTL: Some programs for ocean-tide loading, SIO technical report, Scripps Institution of Oceanography, UC San Diego, California, https://escholarship.org/uc/item/954322pg (last access: 22 February 2024), 2012.
Allègre, V., Brodsky, E. E., Xue, L., Nale, S. M., Parker, B. L., and Cherry, J. A.: Using earth-tide induced water pressure changes to measure in situ permeability: A comparison with long-term pumping tests, Water Resour. Res., 52, 3113–3126, 2016.
Barker, J. A.: A generalized radial flow model for hydraulic tests in fractured rock, Water Resour. Res., 24, 1796–1804, 1988.
Bastias Espejo, J. M., Rau, G. C., and Blum, P.: Groundwater responses to Earth tides: Evaluation of analytical solutions using numerical simulation, J. Geophys. Res.-Sol. Ea., 127, e2022JB024771, https://doi.org/10.1029/2022JB024771, 2022.
Batlle-Aguilar, J., Cook, P. G., and Harrington, G. A.: Comparison of hydraulic and chemical methods for determining hydraulic conductivity and leakage rates in argillaceous aquitards, J. Hydrol., 532, 102–121, https://doi.org/10.1016/j.jhydrol.2015.11.035, 2016.
Bower, D. R.: Bedrock fracture parameters from the interpretation of well tides, J. Geophys. Res.-Sol. Ea., 88, 5025–5035, 1983.
Bredehoeft, J. D.: Response of well-aquifer systems to earth tides, J. Geophys. Res., 72, 3075–3087, 1967.
Burbey, T. J., Hisz, D., Murdoch, L. C., and Zhang, M.: Quantifying fractured crystalline-rock properties using well tests, earth tides and barometric effects, J. Hydrol., 414, 317–328, 2012.
Butler Jr., J. J. and Tsou, M. S.: Pumping-induced leakage in a bounded aquifer: An example of a scale-invariant phenomenon, Water Resour. Res., 39, 1344, https://doi.org/10.1029/2002WR001484, 2003.
Carr, P. A. and Van Der Kamp, G. S.: Determining aquifer characteristics by the tidal method, Water Resour. Res., 5, 1023–1031, 1969.
Cartwright, N., Nielsen, P., and Perrochet, P.: Influence of capillarity on a simple harmonic oscillating water table: Sand column experiments and modelling, Water Resour. Res., 41, W08416, https://doi.org/10.1029/2005WR004023, 2005.
Cutillo, P. A. and Bredehoeft, J. D.: Estimating aquifer properties from the water level response to Earth tides, Groundwater, 49, 600–610, 2011.
De Marsily G.: Quantitative hydrogeology, Academic, San Diego, CA, ISBN 0-12-208915-4, 1986.
de Pasquale, G., Valois, R., Schaffer, N., and MacDonell, S.: Contrasting geophysical signatures of a relict and an intact Andean rock glacier, The Cryosphere, 16, 1579–1596, https://doi.org/10.5194/tc-16-1579-2022, 2022.
Domenico, P. A. and Schwartz, F. W.: Physical and chemical hydrogeology, 2nd edn., Wiley, Chichester, UK, ISBN 978-0-471-59762-9, 1998.
Fuentes-Arreazola, M. A., Ramírez-Hernández, J., and Vázquez-González, R.: Hydrogeological properties estimation from groundwater level natural fluctuations analysis as a low-cost tool for the Mexicali Valley Aquifer, Water, 10, 586, https://doi.org/10.3390/w10050586, 2018.
Gao, X., Sato, K., and Horne, R. N.: General Solution for Tidal Behavior in Confined and Semiconfined Aquifers Considering Skin and Wellbore Storage Effects, Water Resour. Res., 56, e2020WR027195, https://doi.org/10.1029/2020WR027195, 2020.
Guiltinan, E. and Becker, M. W.: Measuring well hydraulic connectivity in fractured bedrock using periodic slug tests, J. Hydrol., 521, 100–107, 2015.
Hantush, M. S.: Modification of the theory of leaky aquifers, J. Geophys. Res., 65, 3713–3725, 1960.
Hsieh, P. A., Bredehoeft, J. D., and Farr, J. M.: Determination of aquifer transmissivity from Earth tide analysis, Water Resour. Res., 23, 1824–1832, 1987.
Kitagawa, Y., Itaba, S., Matsumoto, N., and Koizumi, N.: Frequency characteristics of the response of water pressure in a closed well to volumetric strain in the high-frequency domain, J. Geophys. Res., 116, B08301, https://doi.org/10.1029/2010JB007794, 2011.
Klönne, F.: Die periodischen Schwankungen des Wasserspiegels in den inundierten Kohlenschachten von Dux in der Periode, Sitzungsberichte der mathematisch-naturwissenschaftlichen Classe der Kaiserlichen Akademie der Wissenschaften, Wien, 8, 101–106, 1880.
Lai, G., Ge, H., and Wang, W.: Transfer functions of the well-aquifer systems response to atmospheric loading and Earth tide from low to high-frequency band, J. Geophys. Res.-Sol. Ea., 118, 1904–1924, 2013.
McMillan, T. C., Rau, G. C., Timms, W. A., and Andersen, M. S.: Utilizing the impact of Earth and atmospheric tides on groundwater systems: A review reveals the future potential, Rev. Geophys., 57, 281–315, 2019.
Meinzer, O. E.: Ground water in the United States, a summary of ground-water conditions and resources, utilization of water from wells and springs, methods of scientific investigation, and literature relating to the subject, (Tech. Rep. 1938–39), U.S. Department of the Interior, Geological Survey, https://doi.org/10.3133/wsp836D, 1939.
Merritt, M. L.: Estimating hydraulic properties of the Floridan aquifer system by analysis of earth-tide, ocean-tide, and barometric effects, Collier and Hendry Counties, Florida (No. 3), US Department of the Interior, US Geological Survey, https://doi.org/10.3133/wri034267, 2004.
Moench, A. F.: Transient flow to a large-diameter well in an aquifer with storative semiconfining layers, Water Resour. Res., 21, 1121–1131, 1985.
Narasimhan, T. N., Kanehiro, B. Y., and Witherspoon, P. A.: Interpretation of earth tide response of three deep, confined aquifers, J. Geophys. Res.-Sol. Ea., 89, 1913–1924, 1984.
Pacheco, F. A. L.: Hydraulic diffusivity and macrodispersivity calculations embedded in a geographic information system, Hydrol. Sci. J., 58, 930–944, 2013.
Rabinovich, A., Barrash, W., Cardiff, M., Hochstetler, D. Ls., Bakhos, T., Dagan, G., and Kitanidis, P. K.: Frequency dependent hydraulic properties estimated from oscillatory pumping tests in an unconfined aquifer, J. Hydrol., 531, 2–16, 2015.
Rahi, K. A. and Halihan, T.: Identifying aquifer type in fractured rock aquifers using harmonic analysis, Groundwater, 51, 76–82, 2013.
Renner, J. and Messar, M.: Periodic pumping tests, Geophys. J. Int., 167, 479–493, 2006.
Roeloffs, E.: Poroelastic techniques in the study of earthquake-related hydrologic phenomena, Adv. Geophys., 37, 135–195, https://doi.org/10.1016/S0065-2687(08)60270-8, 1996.
Rojstaczer, S. and Agnew, D. C.: The influence of formation material properties on the response of water levels in wells to Earth tides and atmospheric loading, J. Geophys. Res.-Sol. Ea., 94, 12403–12411, 1989.
Schweizer, D., Ried, V., Rau, G. C., Tuck, J. E., and Stoica, P.: Comparing Methods and Defining Practical Requirements for Extracting Harmonic Tidal Components from Groundwater Level Measurements, Math. Geosci., 53, 1147–1169, https://doi.org/10.1007/s11004-020-09915-9, 2021.
Sedghi, M. M. and Zhan, H.: Hydraulic response of an unconfined-fractured two-aquifer system driven by dual tidal or stream fluctuations, Adv. Water Resour., 97, 266–278, 2016.
Shen, Q., Zheming, S., Guangcai, W., Qingyu, X., Zejun, Z., and Jiaqian, H.: Using water-level fluctuations in response to Earth-tide and barometric-pressure changes to measure the in-situ hydrogeological properties of an overburden aquifer in a coalfield, Hydrogeol. J., 28, 1465–1479, https://doi.org/10.1007/s10040-020-02134-w, 2020.
Sun, X., Shi, Z., and Xiang, Y.: Frequency dependence of in-situ transmissivity estimation of well-aquifer systems from periodic loadings, Water Resour. Res., 56, e2020WR027536, https://doi.org/10.1029/2020WR027536, 2020.
Thomas, A., Fortin, J., Vittecoq, B., and Violette, S.: Earthquakes and Heavy Rainfall Influence on Aquifer Properties: A New Coupled Earth and Barometric Tidal Response Model in a Confined Bi‐Layer Aquifer, Water Resour. Res., 59, e2022WR033367, https://doi.org/10.1029/2022WR033367, 2023.
Valois, R., Vouillamoz, J. M., Lun, S., and Arnout, L., Assessment of water resources to support the development of irrigation in northwest Cambodia: a water budget approach, Hydrol. Sci. J., 62, 1840–1855, 2017.
Valois, R., Vouillamoz, J. M., Lun, S., and Arnout, L.: Mapping groundwater reserves in northwestern Cambodia with the combined use of data from lithologs and time-domain-electromagnetic and magnetic-resonance soundings, Hydrogeol. J., 26, 1187–1200, 2018.
Valois, R., Rau, G. C., Vouillamoz, J. M., and Derode, B.: Estimating hydraulic properties of the shallow subsurface using the groundwater response to Earth and atmospheric tides: a comparison with pumping tests, Water Resour. Res., 58, e2021WR031666, https://doi.org/10.1029/2021WR031666, 2022.
Valois, R., Derode, B., Vouillamoz, J. M., Valerie Kotchoni, D. O., Lawson, M. A., and Rau, G. C.: Use of atmospheric tides to estimate the hydraulic conductivity of confined and semi-confined aquifers, Hydrogeol. J., 31, 2115–2128, 2023.
Valois, R.: Remival/CambodiaData-for-leaky-and-compressible-aquiatrd: Aquifer with compressible and storing aquitard (Earth-tide), Zenodo [data set and code], https://doi.org/10.5281/zenodo.10695947, 2024.
Van Everdingen, A. F.: The skin effect and its influence on the productive capacity of a well, J. Petrol. Geol., 5, 171–176, 1953.
Vouillamoz, J. M., Sokheng, S., Bruyere, O., Caron, D., and Arnout, L.: Towards a better estimate of storage properties of aquifer with magnetic resonance sounding, J. Hydrol., 458, 51–58, 2012.
Vouillamoz, J. M., Valois, R., Lun, S., Caron, D., and Arnout, L.: Can groundwater secure drinking-water supply and supplementary irrigation in new settlements of North-West Cambodia?, Hydrogeol. J., 24, 195–209, 2016.
Wang, C. Y., Doan, M. L., Xue, L., and Barbour, A. J.: Tidal response of groundwater in a leaky aquifer – Application to Oklahoma, Water Resour. Res., 54, 8019–8033, https://doi.org/10.1029/2018WR022793, 2018.
Wang, H. F.: Theory of linear poroelasticity with applications to geomechanics and hydrogeology, (Vol. 2), Princeton University Press, ISBN 9780691037462, 2000.
Wen, Z., Zhan, H., Huang, G., and Jin, M.: Constant-head test in a leaky aquifer with a finite-thickness skin, J. Hydrol., 399, 326–334, 2011.
Young, A.: Tidal phenomena at inland boreholes near Cradock, T. Roy. Soc. S. Afr., 3, 61–106, 1913.
Zhang, H., Shi, Z., Wang, G., Sun, X., Yan, R., and Liu, C.: Large earthquake reshapes the groundwater flow system: Insight from the water-level response to earth tides and atmospheric pressure in a deep well, Water Resour. Res., 55, 4207–4219, 2019a.
Zhang, S., Shi, Z., and Wang, G.: Comparison of aquifer parameters inferred from water level changes induced by slug test, earth tide and earthquake – A case study in the three Gorges area, J. Hydrol., 579, 124169, https://doi.org/10.1016/j.jhydrol.2019.124169, 2019b.
Short summary
Characterizing aquifer systems is challenging because it is difficult to obtain in situ information. They can, however, be characterized using natural forces such as Earth tides. Models that account for more complex situations are still necessary to extend the use of Earth tides to assess hydromechanical properties of aquifer systems. Such a model is developed in this study and applied to a case study in Cambodia, where a combination of tides was used in order to better constrain the model.
Characterizing aquifer systems is challenging because it is difficult to obtain in situ...
