Fig. 13

Testing a model of layered structure (Fig. 11b) for seismic wave velocity (modified from Karato 2014). The relations, \( \frac{\Delta V}{V}=\frac{1}{2}\frac{\phi_o}{\phi }{\left(\frac{1-\frac{M_2}{M_1}}{\sqrt{M_2/{M}_1}}\right)}^2 \) (Karato 2008) and \( \frac{M_2}{M_1}=1-A\cdot \phi \) (A = 0.067, Takei 2002) are used. The melt fraction of the melt-rich layers needs to be in a very narrow range (14 ± 1%) in order to explain the observed 5–10% velocity drop at the lithosphere-asthenosphere boundary for the net melt fraction of ϕ_o= 0.001–0.003 (Hirschmann 2010)