Exploring the Effects of Anisotropic Aquifer Transmissivity on the Water Level Response to Earth Tides

Abstract:

The response of water level to Earth tides provides a unique probe to determine the in-situ aquifer transmissivity. The water level in an open well tapping an aquifer responds to the Earth tidal forcing with a phase lag. The phase lag between the water level oscillation and imposed tidal forcing is due to the finite time is needed for pore pressure to readjust and drive water to flow into and out of the well. The phase lag is a direct observation, and it is a key parameter to determine the transmissivity of the aquifer. Usually, people convert the phase lag information to an effective transmissivity using Hsieh et at. analytical solution (1987) by assuming the aquifer is confined, isotropic, homogeneous, infinite in lateral extent and of uniform thickness. However, the estimated transmissivity heavily relies on the assumption of an isotropic aquifer which is not true in reality. Anisotropic transmissivity would bias the interpretation of the phase lag information. Our study explores the phase response of water level to the semidiurnal Earth tide for different ratio of transmissivity in x and y directions by using the finite element method software Comsol. We find the estimated effective transmissivity is the lower bound of the transmissivity in fast direction for the same phase lag. We also find that the numerically determined phase lag can be predicted as a function of an effect transmissivity, and the effect transmissivity T can be expressed as T=(T_y*T_x^1.4)^0.4, where T_y is the transmissivity is slow direction, and T_x is the transmissivity in fast direction. Effective transmissivity is a combination weight between transmissivity in low and fast directions, and the transmissivity in fast direction would be the dominate parameter controlling the phase response. This empirical function may provide a way to estimate the range of transmissivity and anisotropic effects for the observed phase lag.