## 1 Introduction  
The continental crust is characterized by an andesitic to dactile bulk composition [1; 2; 3], but its origin is still a controversial issue ([4; 5] and references therein). It is widely accepted that, at least since the Phanerozoic, the growth of the continental crust has occurred at convergent margins based on the obvious trace element similarity between the continental crust and arc magmas (enriched in Pb and depleted in Nb, Ta, and Ti). According to this, the differentiation of arc magmas should play an important role in the formation of the continental crust [3; 6; 7]. However, compared with the andesitic composition of the continental crust, the partial melting of the sub-arc mantle wedge produces mainly basaltic melts [2; 8]. Therefore, deciphering the evolution of arc magmas is significant in understanding the formation of the continental crust. Minerals record the petrogenesis and evolution of igneous rocks, such as phenocryst assemblages in lavas or minerals in plutons [9]. However, crystals in magma are rarely composed of a single crystal population but are composed of a combination of phenocrysts, xenocrysts, antecrysts, and microcrysts [10]. The information recorded by these crystalsprovides a window for timescales of magmatism, contamination, and magma mixing or recharging, degassing, and magma plumbing histories [11]. Amphibole crystallization plays a critical role during arc magma differentiation [12; 13; 14], responsible for the chemical diversity of igneous rocks in plutons. But amphibes rarely present as a phenocryst phase in arc lavas and eruptive pyroclastic rocks due to their instability at low pressures [15; 16], which is regarded as a cryptic fractional crystallization phase [12; 13; 17]. However, without the significant nucleation and growth of amphibe grains, this cryptic fractionation will produce evolved melts with La/Yb and Dy/Yb \"amphibole sponge\" signatures. Some minerals, such as amphibes and garnets, rarely exist as phenocrysts in arc lavas and can also participate in controlling the differentiation trend of magma [18]. At the same time, crystal assemblage in volcanic rocks may not match the liquid line of descent of the magma in which phenocrysts are often not equilibrated with the matrix [19]. The stability condition of amphibes in volcanic rocks sometimes is more rigorous compared with other common phenocrysts (e.g., olivine, pyroxene, etc.). Therefore, it is more common to find abundant amphibes in arc root complexes, cumulates, and cognate xenoliths in arc lava. Natural samples for revealing the mechanism of amphibe differentiation in magmas have been reported in the Adamello Batholith, Central Alps, Italy [20; 21]; the Chelan Complex, Washington Cascades [22]; and the Cuijiu Complex and Daggyai Co pluton, Eastern Gangdese Batholith, southern Tibet [23; 24; 25]. Most ultramafic-mafic arc complexes are considered cumulates formed through fractional crystallization [17; 22; 26]. Amphibole-rich cumulates are formed by nucleation, growth, and settling from parent liquids [12] or reactions between early crystallized phases (e.g., olivine and clinopyroxene) and interstitial melts in a closed system [19; 27]. There are two genetic models for cumulates with textural and chemical heterogeneities. The first model argues that the amphibe cumulates are products of polybaric fractional crystallization of the same parent melt in a closed system; that is, the primitive calc-alkaline basaltic magma crystallizes the cumulus phases in the deep crust and then rises to the shallow crust along with continuous crystallization, resulting in the textural heterogeneity of intrusive rocks [23; 28; 29; 30]. The other model proposes that the cumulates form through a rock-melt reaction in an open system. The precursory olivine and clinopyroxene react with the permeable melt unbalanced with later nonequilibrium liquid to form amphibes [14; 20; 21; 31].