## 3 Geochemical Classification Method on Shale  
We propose a geochemical method to classify shale into six types based on SiO\({}_{2}\), CaO, and MgO contents, values of CaO/MgO, and a weathering index named \"weathering index of granite\" (WIG). Here, the content unit of the major oxides is wt%, as is commonly used in analytical reports. However, the WIG is calculated using molecular proportions (mass fraction divided by molecular weight) of major oxides as [27]:  
\[\text{WIG}=100[\text{Na}_{2}\text{O}+\text{K}_{2}\text{O}+(\text{CaO}-10/3 \text{P}_{2}\text{O}_{5})]/(\text{Al}_{2}\text{O}_{3}+\text{TFe}_{2}\text{O}_ {3}+\text{TiO}_{2}) \tag{1}\]  
where (CaO \(-\) 10/3P\({}_{2}\)O\({}_{5}\)) is a non-negative value (if the value of (CaO \(-\) 10/3P\({}_{2}\)O\({}_{5}\)) is negative, its value is set as zero). A lower WIG value indicates a stronger weathering degree when the WIG value of the sample is lower than 120. However, the WIG value no longer reflects the weathering degree of the sample, but rather indicates that the sample contains carbonates, when the WIG value of a sample is higher than 120 [28]. The six types of the proposed geochemical classification were determined sequentially based on the following steps:  
Type 1, determined by SiO\({}_{2}\)\(\geq\) 79%, represents a siliceous component, mainly referring to components with a content of SiO\({}_{2}\) equivalent to siliceous rock, quartzite, quartz sandstone, flint rock, and feldspar quartz sandstone. Type 2, determined by SiO\({}_{2}\) ranging between 67.5 and 79%, is defined as a felsic component, mainly referring to components with a content of SiO\({}_{2}\) equivalent to feldspar sandstone, lithic sandstone, and granitic or hyloitic components. Type 3, classified by SiO\({}_{2}\) < 67.5% and WIG < 120, is defined as a silicate component, mainly referring to samples with SiO\({}_{2}\) < 67.5% and basically no carbonate components, equivalent to rocks or mudstone rich in aluminosilicates. Type 4, determined based on a content of CaO < 22%, is defined as a calcsilicate component, mainly referring to silicate components mixed with carbonate minerals, equivalent to calcareous sandstone, calcareous mudstone, or sediment mixed with calcareous and siliceous components. The value of 22 is determined based on the hypothesis that the carbonate and non-carbonate components are equal in weight percent, the carbonate minerals are equal to calcite and dolomite in molecular proportions, and the content of CaO in the non-carbonate components is ignored. Type 5 and type 6 are defined as dolomitic component and calcareous components, based on their CaO/MgO contents (CaO/MgO < 4.2 and CaO/MgO \(\geq\) 4.2 in weight percent, respectively). Type 5 mainly refers to carbonate components dominated by dolomite, while type 6 mainly refers to carbonate components dominated by calcite. The ratio value of 4.2 is determined based on the hypothesis that the molar amount of calcite and dolomite minerals in the sample is equal, and the non-carbonate forms of CaO and MgO are ignored. Through the above steps, geological materials were classified into six types with type numbers ranging from 1 to 6, and the specific conditions to determine the six types are listed in Table 1. As the type number increases from 1 to 6, the content of CaO increases, and that of SiO\({}_{2}\) decreases. Using these type numbers, a geochemical map of areal samples or a line graph on profile samples can be drawn easily with clear geochemical implications. With SiO\({}_{2}\) content as the horizontal coordinate (its variation range is 0-100%) and CaO content as the vertical coordinate (its variation range is 0-56%), the SiO\({}_{2}\)-CaO classification diagram is illustrated in Figure 1.