Study of the mantle mixing driving by plate motions

Two new quantitative terms are employed to investigate the problem of the mantle mixing in this paper,Box Replacement Degree of convective mantle mixing and pervasion degree of convective mantle mixing. The first term is to count statistically the percent of the mantle boxes that have been replaced by other mantle boxes. The second term is to evaluate the pervasion degree for a group of fine mantle elements confined in a small space. In this study we assume that there is a stable convection system in the mantle, which drives by plate motions and density distribution anomaly. In our numerical experiment the mantle is divided into 20736 boxes(5° × 5° × 300 km) and there are 2376 tracers placed on 5° × 5° grids at 100km depth and 100 km above CMB. The results show that the Box Replacement Degree of convective mantle mixing is over 80% for the whole mantle and is over 90% for upper mantle after 4 billion years. It infers that most mantle boxes have been replaced. For two groups of 1681 tracers in a small space 10° × 10° placed at the top and bottom of the mantle their pervasion degree approaches a constant and the initial tracers become widely distributed in the mantle after 3 billion years. These results infer that the Earth's mantle, excepting lithosphere and "D" layer, has been mixed very well in the past 4 billion years. There are not much initial heterogeneity boxes with a size more than 5° × 5° × 300 km present in our mantle now.