A rotational ellipsoid model for solid Earth tide with high precision

Abstract

Abstract Solid Earth tide represents the response of solid Earth to the lunar (solar) gravitational force. The yielding solid Earth due to the force has been thought to be a prolate ellipsoid since the time of Lord Kelvin, yet the ellipsoid’s geometry such as major semi-axis’s length, minor semi-axis’s length, and flattening remains unresolved. Additionally, the tidal displacement of reference point is conventionally resolved through a combination of expanded potential equations and given Earth model. Here we present a geometric model in which both the ellipsoid’s geometry and the tidal displacement of reference point can be resolved through a rotating ellipse with respect to the Moon (Sun). We test the geometric model using 23-year gravity data from 22 superconducting gravimeter (SG) stations and compare it with the current model recommended by the IERS (International Earth Rotation System) conventions (2010), the average Root Mean Square (RMS) deviation of the gravity change yielded by the geometric model against observation is 6.47 µGal (equivalent to 2.07 cm), while that yielded by the current model is 30.77 µGal (equivalent to 9.85 cm). The geometric model will greatly contribute to many application fields such as geodesy, geophysics, astronomy, and oceanography.

Keywords

• Solid Earth tide
• Geometry of ellipsoid
• Tidal displacement
• Superconducting gravity