Approaches and Prospects of Provenance Analysis
Provenance analysis is the most important aspect in the research of ba sins and orogene and is of great significance in studying the relative position, evolution and the interaction of the basins and orogenes. There have been various ways in provenance analysis. The paper has discussed the ways, rules an d limitations of heavy minerals, clastic rock components, fission track, sedimen tary, geochemistry and isotopic methods. It is showen that geochemistry and iso topic methods have the bright and wide uses in the future. Meanwhile, the influence structure and sedimentation such as structure uplift, erosion, chemical weathering on provenan ce can not be neglected. It is worthy to note that reasonable conclusion sho uld be drawn only through the combination of various ways of provenance analysis .
In this paper we study the multivariate ANOVA decomposition for $1$-periodic functions on the torus. In particular we use the integral projection operator that leads to the classical ANOVA decomposition. Relationships between the Fourier coefficients of the function and its ANOVA terms lead to special frequency index sets and give an understanding of the decomposition working in the frequency domain. Moreover, we consider the truncated ANOVA decomposition and provide error bounds for approximation in $\mathrm{L}_\infty$ and $\mathrm{L}_2$. We present an approximation method based on the truncated decomposition with regard to a superposition dimension $d_s$.