One-dimensional to three-dimensional density distribution functions and their applications in visualized big data analysis: Exemplified by picritic basalt and some other rocks

In this paper, the calculation methods and visualization schemes of density distribution functions of different dimensions are proposed to solve the problem of difficulties in analysis and comparison of rock sample data with different orders of magnitude and different measurement errors. Data mining based on the GEOROC and PETDB databases by using the three-dimensional density distribution function of SiO₂, total alkali and MgO index as well as the t-distribution random neighborhood embedding visualization method revealed that picritic basalt is similar to oceanite and ankaramite, while picrate is similar to intrusive olivine gabbro and ferropicrate. Comparisons between two-dimensional density distribution function and cumulative density contour visualization were used to analyze the data distribution of different rocks on TAS and Si-Mg maps and the core area of data concentration. It is found that the SiO₂ content of magnesium-rich picrite is higher than that of picrite basalt in general distribution. The core area of picrite is mainly located in the B area of TAS diagram, which is contrary to the traditional view that SiO₂=45% is used as the boundary between basic and ultramafic rocks.