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Numerical modeling has been carried out in a 2-D cylindrical shell domain toquantify the evolution of a primordial dense layer around the core–mantleboundary. Effective buoyancy ratio, Beff was introduced to characterizethe evolution of the two-layer thermo-chemical convection in the Earth'smantle. Beff decreases with time due to (1) warming of the compositionallydense layer, (2) cooling of the overlying mantle, (3) eroding of the dense layerthrough thermal convection in the overlying mantle and (4) diluting of the denselayer through inner convection. When Beff reaches the instability point,Beff = 1, effective thermo-chemical convection starts, and the mantlewill be mixed (Beff = 0) over a short time period. A parabolic relationship wasrevealed between the initial density difference of the layers and the mixingtime. Morphology of large low-shear-velocity provinces and resultsfrom seismic tomography and normal mode data suggest a value ofBeff ≥ 1 for the mantle

Effective buoyancy ratio: a new parameter for characterizing thermo-chemical mixing in the Earth's mantle