三角图的原理、快速绘制以及在砂岩分类中的应用  

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

作　　者：单云鹏 王红军[1] 张良杰[1] 白振华[1] 苏朋辉 赫英旭 孟维康 刘航宇 程木伟[1] SHAN YunPeng;WANG HongJun;ZHANG LiangJie;BAI ZhenHua;SU PengHui;HE YingXu;MENG WeiKang;LIU HangYu;CHENG MuWei(Research Institute of Petroleum Exploration&Development,PetroChina,Beijing 100083,China;Bohai Petroleum Research Institute,Tianjin Branch of CNOOC,Tianjin 300459,China;Engineering Technology Branch of Energy Development Co.,Ltd.,CNOOC,Tianjin 300452,China;School of Earth and Space Sciences,Peking University,Beijing 100871,China)

机构地区：[1]中国石油勘探开发研究院,北京100083 [2]中海石油(中国)有限公司天津分公司渤海石油研究院,天津300459 [3]中海油能源发展股份有限公司工程技术分公司,天津300452 [4]北京大学地球与空间科学学院,北京100871

出　　处：《沉积学报》2022年第4期1095-1108,共14页Acta Sedimentologica Sinica

基　　金：中国石油天然气集团公司技术攻关项目(2021DJ33)。

摘　　要：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 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 tech⁃nique 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 trian⁃gle 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.

关 键 词：三角图读值规则 三角图投点公式 砂岩分类图版 Excel与Origin及Grapher成图对比 VBA编程代码 

分 类 号：P618.13[天文地球—矿床学]