Abstract:

It is convenient to investigate the gravimetry using a harmonic spheric function for the description of the distribution and thickness of the Antarctic ice sheet. The gravitational theory and the Stokes' harmonic spheric function formula were used to determine the impact of the Antarctic ice cap on the global geoid. The Antarctic ice cap is formed from the condensation of seawater vapour whose mass is equal to a layer of seawater 59 m thick of covering the earth's surface, i.e. 2.7×10¹⁹ kg. This will cause the global averaged geoid to decrease for around 23 m. The authors' computations show that the Antractic ice cap has a great impact on the global geoid, which increases (+) in some regions, but decreases (-) in other reigions. The geoid is +115 m, -37 m and +8 m at the South Pole, the 25°S parallel and the North Pole, respectively. If the Antarctic ice cap melts completely, on the rigid Earth's surface the seawater and geoid will return to its original position (and height) due to the balancing force of the fluid. Since the crust is almost in a state of isostasy, assuming that the crust is an elastic solid and the mantle is an incompressible fluid, the load of seawater will deflect the crust and drive the mantle material to flow. The material above the isostatic surface compensates mutually. If the densities of the mantle and seawater are 3270 kg/m³ and 1030 kg/m³, respectively, then the variation in the elevation of the continent is only 2.8 m with respect to the sea level after the Antarctic ice cap melts; it is not larger than that estimated by some people.It is worth noting that the above results were derived from an ideal Earth model. In the real Earth, the mantle and crust are visco elastic.

Key words: Antarctic ice sheet, geoid undulation, relative change of sea level