三角图的原理、快速绘制以及在砂岩分类中的应用

三角图广泛用于砂岩分类，但个别高引用率文献论证公式的过程繁琐甚至推导出现错误。为系统阐述三角图的原理与制作，在确定三角图的读图规则后，进行平面几何推导，指出并修正了前人推导过程中的逻辑性错误，最后使用Excel成图与商业软件Origin及Grapher的三角图进行对比。结果表明，等边三角形与等腰三角形的投点方式存在差异，但两种图版可以进行变形操作而相互转化，三角形的侧边能否作为坐标轴以及纵坐标的绝对长度能否代表石英的含量取决于三角形的形态。商业软件的图版难以满足需求，建议以Excel使用等腰三角形的投点方式，结合地质绘图软件进行制图。为降低工作量，可以使用本文所编写的VBA代码，快速绘制砂岩分类三角图。

The Principle and Fast Drawing of Ternary Plots and Their Application in Sandstone Classification

The ternary plot method is widely used in geological industries， especially in sandstone classification. However， many researchers do not appear to have a deep understanding of its principle. Demonstrations of the technique in individual much-cited publications are cumbersome， and even wrongly derived in some cases. This study systematically derives the principle of ternary plots from plane geometry， and how to read them. The errors of logic in the derivation by previous authors are pointed out and corrected. Finally， a comparison of ternary plots generated by Excel， Origin and Grapher software shows distinctions in the projection methods using an equilateral triangle or an isosceles triangle， and demonstrates that the plots transform each other if incorrectly operated. The shape of the triangle determines whether the side of the triangle is viewed as the ordinate axis， and whether the absolute length of the ordinate represents the quartz content. Templates provided by Origin or Grapher do not satisfy oilfield requirements. The isosceles triangle projection method in Excel is recommended， combined with geological mapping software for mapping. To reduce the workload， the VBA code written in this paper can be used to quickly draw a ternary plot for sandstone classification.