『Abstract
　Chemical weathering indices are useful tools in characterizing weathering profiles and determining the extent of weathering. However, the predictive performance of the conventional indices is critically dependent on the composition of the unweathered parent rock. To overcome this limitation, the present paper introduces an alternative statistical empirical index of chemical weathering that is extracted by the principal component analysis (PCA) of a large dataset derived from unweathered igneous rocks and their weathering profiles. The PCA analysis yields two principal components (PC1 and PC2), which capture 39.23％ and 35.17％ of total variability, respectively. The extent of weathering is reflected by variation along PC1, primarily due to the loss of Na2O and CaO during weathering. In contrast, PC2 is the direction along which the projections of unweathered felsic, intermediate and mafic igneous rocks appear to be best discriminated; therefore, PC1 and PC2 represent independent latent variables that correspond to the extent of weathering and the chemistry of the unweathered parent rock. Subsequently, PC1 and PC2 were then mapped onto a ternary diagram (MFW diagram). The M and F vertices characterize mafic and felsic rock source, respectively, while the W vertex identifies the degree of weathering of these sources, independent of the chemistry of the unweathered parent rock.
　The W index has a number of significant properties that are not found in conventional weathering indices. First, the W index is sensitive to chemical changes that occur during weathering because it is based on eight major oxides, whereas most conventional indices are defined by between two and four oxides. second, the W index provides robust results even for highly weathered sesquioxide-rich samples. Third, the W index is applicable to a wide range of felsic, intermediate and mafic igneous rock types. Finally, the MFW diagram is expected to facilitate provenance analysis of sedimentary rocks by identifying their weathering trends and thereby enabling a backward estimate of the composition of the unweathered source rock.

Keywords: Chemical weathering;p Weathering index; Logratio analysis; Principal component analysis』

1. Introduction
2. Materials and methods
　2.1. Database for input
　2.2. Statistical framework
3. Results
　3.1. PCA results
　3.2. MFW diagram
4. Discussion
　4.1. Evidence of the weathering of rock-forming minerals on the MFW diagram
　4.2. Evaluation of weathering intensity using the W index
　4.3. Application of the MFW diagram in different rock types
　4.4. Implications for provenance studies
　4.5. Limitations of the MFW scheme
5. Conclusion
Acknowledgements
Appendix A. Concepts of compositional data analysis
　A.1. Simplex; a sample space of compositional data
　A.2. Logratio analysis
References