Modeling of Well-Level Tides Based on Poroelastic Tidal Deformation Theory for a Layered Spherical Earth

Objectives Observations of well-level, with low cost, has been utilized in different dynamic processes such as tides, air pressure loading and earthquakes and inversion of aquifer parameters, which shows great scientific importance of studying well-level change and its mechanisms. Tidal variation of well-level is one of dominant components of well-level changes, which is the response of the well level to Earth's deformation due to tide generating force exerted by the Moon, the Sun and other planets. Since the current theory for well-level tides is simple, it is necessary to better understand the mechanisms and characteristics of well-level tides.

Methods Unlike the traditional tidal theory of well-level for the half-space model, here we apply the poroelastic model for a layered spherical Earth, which considers the elasto-gravitational deformation and solid-fluid coupling effect of the Earth materials, to study the phenomenon of well-level tides according to Pascal's law. Therefore, the boundary value problem of the poroelastic deformation of the Earth is solved with the boundary condition results from tide generating force.

Results The tidal Love numbers are computed and the well-level tides are modeled. The results show that the magnitude of well-level tides can reach tens of centimeters with a phase lag in the range from about -150° to -180°, as compared to the tide generating force. The amplitude and phase are both highly dependent on permeability coefficient of the aquifer. If the permeability is small enough, the tidal response of the well-level approaches to that of the undrained status, for which excess pore pressure is simply linear with the volumetric strain. The amplitude decreases with respect to the increasing permeability coefficient while it increases with respect to the increasing depth of the well.

Conclusions The amplitude of the well-level tides dependent not on whether the aquifer is confined or unconfined but on the magnitude of the permeability coefficient. It is noted that the effect of the well screen is not considered, which might affect the numerical results. Nevertheless, this effect decrease with the decreasing radius of the well.