Determination of aquifer transmissivity from Earth tide analysis

Abstract

The water level in an open well tapping an artesian aquifer responds to pressure head disturbance caused by Earth tide dilatation of the aquifer. Because a finite amount of time is needed for water to flow into and out of the well, there exists a phase shift (or time lag) between the tidal dilatation of the aquifer and the water level response in the well. We derive an analytical solution that expresses the phase shift as a function of the aquifer transmissivity, storage coefficient, well radius, and the period of the harmonic disturbance. This solution is rather insensitive to the storage coefficient. Thus if the phase shift is known for a harmonic disturbance, the transmissivity can be calculated given a rough estimate of the storage coefficient. Theoretical analysis shows that a significant phase shift may be present even if the disturbance is slowly varying, as in the case of Earth tides. This opens the possibility of estimating aquifer transmissivity from water level records that show Earth tide fluctuations. A case study, using data from a site near Parkfield, California, is presented to illustrate application of the theory. Phase shifts of the O• (25.82hour period) and M 2 (12.42-hour period) tidal constituents are chosen for analysis because they are free of systematic contamination by fluctuations in barometric pressure. A brief error analysis suggests that the computed O x phase shift is subject to large uncertainty, while the computed M 2 phase shift is substantially more accurate. Based on an assumed storage coefficient range of 10 -• to 10 -6, the estimated transmissivity range is 8 x 10 -6 to 2 x 10 -• m2/s. While hydraulic tests have not been performed to validate these estimates, the range is consistent with the transmissivity value determined by other investigators from analysis of the water level response to an earthquake.

Pahute Mesa Well Development and Testing Analyses for Wells ER-20-8 and ER-20-4, Nevada National Security Site, Nye County, Nevada, Revision 0

“…Of the three, N 2 typically has a poor signal to noise ratio, leaving only O 1 and M 2 signals remaining. Most studies (Hsieh et al, 1987;Merritt, 2004;Cutillo and Bredehoeft, 2011) analyze only these two frequencies when estimating aquifer properties from water-level response to earth-tide forcings. Thus, this analysis was also based only on the O 1 and M 2 signals, ignoring the K 1 , S 2 , and N 2 frequencies.…”

“…Thus, this analysis was also based only on the O 1 and M 2 signals, ignoring the K 1 , S 2 , and N 2 frequencies. Source: Hsieh et al, 1987 Appendix D…”

“…The low-pass filter used for this analysis is based on Godin (1972) and is recommended by Hsieh et al (1987) and Kilroy (1992). The low pass filter consists of a series of moving averaging operations and can be written mathematically as A 24 A 24 A 25 /(242425) where A n /n is a moving average that takes the average of n consecutive data points and assigns it to time k + (n-1)/2, where k is the time of the first data point considered.…”

“…Thus, Hsieh et al (1987) and Cutillo and Bredehoeft (2011) Table D.1-1, which shows that the tidal constituents of interest all have periodicities greater than 12 hours.) For this analysis, a continuous period of record (without any gaps in data) is required.…”

“…The assumption of only vertical deformation was later relaxed by Rojastaczer and Agnew (1989), who derived expressions relating porosity and specific storage to the amplitude ratio of earth-tide-induced areal strain and the corresponding water-level response. Hsieh et al (1987) derived theoretical relations for transmissivity and storage based on amplitude ratio and phase lags for harmonic components of earth tides and water levels. Another approach, given by Bernard and Delay (2008), relied on spectral analysis of the auto-and cross-correlation function between barometric, water level, and earth-tide time series.…”