Implicit expansion rate of the Earth in global plate motions

Based on eight published plate motion models, we separately estimated the net area changes of tectonic plates and the area change of the solid Earth surface over geological time using the Euler vectors of plates with determined boundaries. Then, under the context of a currently expanding Earth, we inferred the change rate of the Earth’s mean radius from the estimated net area changes. The results show that the total increases and decreases in the areas of different plates cannot be compensated. Specifically, the area of the Northern Hemisphere decreases while that of the Southern Hemisphere increases, but the net area of the solid Earth surface slightly increases in th computing period(0.01 Ma). For the latest NNRMORVEL56 plate motion model, the area of the Southern Hemisphere increases by 7802 km2 while the area of the Northern Hemisphere decreases by 7711 km^2. This indicates a net area increase of 91 km2 in the solid Earth surface corresponding to an expansion rate of 0.06 mm/a for the Earths mean radius.This result coincides with the slow rate of expansion derived from geodetic measurements and geophysical modeling.