Response of well-aquifer systems to Earth tides

Abstract

The water level in a well open to an artesian aquifer responds to pressure-head fluctuations caused by the dilatation of the aquifer. Based on hydrologic considerations, it is shown that (1) most well-aquifer systems respond to disturbances with periods of less than several days as if the well were drilled into a medium of infinite or partially bounded extent, and (2) the representation of an aquifer as a finite cavity is unrealistic for most well-aquifer systems. The amplitude of tidal water level fluctuations in well-aquifer systems depends on the dilatation and the specific storage of the aquifer. Analysis of the dilatation caused by the earth tide is based on the assumptions that (1) the latitudinal and longitudinal strains caused by the earth tide are determined by the elastic properties of the earth as a whole and are largely independent of the elastic properties of a near surface aquifer, and (2) the vertical strain of a near surface aquifer depends on Poisson's ratio (or the Lame constants) for the aquifer and the latitudinal and longitudinal strains. The tidal dilatation can be computed from equilibrium tide theory provided that Poisson's ratio is known. The amplitude of the tidal dilatation produced by the large semidiurnal wave, M2, is approximately 1 × 10−8. It is not unusual to have earth-tide fluctuations in wells corresponding to M2 with an amplitude of 1 to 2 cm. The fact that tidal water-level fluctuations depend upon the specific storage of the aquifer explains the variation in amplitude which troubled others. The specific storage and the porosity of the aquifer can be computed from an analyses of earth-tide fluctuations if Poisson's ratio for the aquifer is known. Computations of specific storage and porosity are presented for three artesian wells for which tidal harmonic analysis of hydrograph data was published by Melchior. The results of these calculations appear to be better than one might reasonably expect.