“…After that study was published, many followed a similar approach, either tracking preset heterogeneities (e.g. Davies, 2002;Zhong and Hager, 2003;Nakagawa and Tackley, 2004), or having the chemical heterogeneities emerge via melting during the calculation at fixed melting zones (Walzer and Hendel, 1999;Davies, 2002;Huang and Davies, 2007a, b, c), moving melting zones that follow force-balanced plates or imposed plate motions (Brandenburg and van Keken, 2007a, b;Brandenburg et al, 2008), or freely moving melting location via a melting phase diagram (De Smet et al, 1998;Van Thienen et al, 2004;Xie and Tackley, 2004a, b;Nakagawa et al, 2009Nakagawa et al, , 2010.…”