## 1 Introduction  
Skarn is a type of metamorphic rock primarily formed by contact metasomatism [1]. Swedish geologists initially coined the term \"skarn\" to refer to a green, calcic siliceous rock mainly composed of minerals such as garnet, pyroxene, hornblende, feldspar and epidote. The process of skarn mineralization is frequently linked with the concentration of metallic elements, leading to the formation of skarn-type deposits [1, 2]. Skarn-type depositshave a long geological history and manifest in various forms, including Fe-Cu(Au)-Mo polymetallic deposits, which are among the primary sources of iron, copper, molybdenum and related platinum group element mineral resources in China [3; 4; 5; 6]. During the process of skarn formation through contact metasomatism, the composition, physical-chemical conditions and evolution of ore-forming fluids play a crucial role in controlling the mineralization enrichment and ore grades [2]. Activation, migration and precipitation processes of ore-forming elements are the key to understanding the mineralization mechanisms and processes of skarn-type deposits [7]. Accurately defined boundaries of a skarn deposit can precisely constrain the ore-forming model, provide information on mineralization distance and guide mineral exploration. Additionally, it can determine variations in ore grades, distribution, rock characteristics, etc. [8]. Previous studies on skarn deposits have been relatively extensive and a fairly complete model of skarn formation has been established [2]. In skarn formed by magmatic processes, those formed within the rock body are called inner skarn, while those formed in the surrounding rocks are called outer skarn. Worldwide studies indicate that the inner zone is generally less developed in the skarn [1; 2; 3]. Outer skarn is characterized by the presence of numerous skarn minerals, which are also the primary sites of skarn-type deposit formation. Microscopically, inner skarn may contain remnants of original minerals such as feldspar and mica, whereas outer skarn does not show any trace of the original minerals. However, some weak outer skarn still retains the characteristics of the original rock, which can often cause interference [9]. Moreover, compared to intrusive rocks, carbonate surrounding rocks are less likely to preserve the characteristics of the original rock. For example, in the Antamina skarn deposit in Peru, the vein-like outer skarn is often mistaken for inner skarn [8]. In certain deposits such as Qiaoxiahala, late-stage overprinting influenced the classification and interpretation of the deposit type in earlier years [10]. From a geochemical perspective, there are significant differences in the whole-rock major and trace elements between the inner and outer skarn [8; 11]. Generally, inner skarn contains higher levels of high-field-strength elements (HFSE) and heavy REEs such as Ti, Sc, Nb, Y, Lu and Dy [8]. However, skarn has complex compositions and can be affected by many factors such as water-rock reactions and supergene weathering, making the whole-rock major and trace element analysis process cumbersome and costly. Moreover, the previous research is unable to explain the control factors responsible for the significant differentiation of HFSE and HFEEs between inner and outer skarn [8]. Discrimination methods based on whole-rock major and trace elements also require more typical skarn profiles to validate their accuracy. Due to the complexity of the skarnization process and the superimposed reformation, previous studies often faced the problem of insufficient representativeness of the selected samples [1; 8]. At present, most research on skarn is based on only whole-rock [8; 11; 12; 13] or single-mineral analysis [14; 15; 16; 17]. There is relatively a lack of research on how to determine the skarn contact zone. There is also a lack of work that combines the analysis of single minerals (such as garnet, pyroxene, etc.)