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 O₁ (25.82‐hour period) and M₂ (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 O₁ phase shift is subject to large uncertainty, while the computed M₂ phase shift is substantially more accurate. Based on an assumed storage coefficient range of 10⁻⁴ to 10⁻⁶, the estimated transmissivity range is 8 × 10⁻⁶ to 2 × 10 ⁻⁵ 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.