基金项目：国家自然科学基金项目(41172302,40672196)

摘要：提出了N维阵的概念和常用的几种定义和运算，包括N维阵的加减、方括号乘法和Hadamard积，给出了其性质及相应的说明；指出立体阵是N维阵的一个特例。N维阵方法的优势在于对多维数据表示更加简洁，理论分析较方便。最后，通过江绍拼合带中西段CuZnAbAgSnAs元素组合异常研究和浙西地区铜多金属矿成矿预测，说明了N维阵在实际问题应用中的方法及步骤。N维阵在处理地学多维数据方面有着重要的应用前景。

关键词：数学地质；N维阵；方括号乘法；Hadamard积；立体阵；元素组合；成矿预测

中图分类号：P628；O189.12文献标志码：A

Study of Ndimensional Matrices and Its Application in Geology

SHEN Wei

(State Key Laboratory of Geological Processes and Mineral Resources, China University of

Geosciences, Beijing 100083, China)

Abstract: A new basic concept of Ndimensional matrices was presented by the cubic matrices conception. The definition and arithmetic （including addsubtract, bracket multiplication and Hadamard product） of Ndimensional matrices were studied and proved. The cubic matrices was a special case of Ndimensional matrices. The multidimensional data were expressed more brief and facility in theoretical analysis by the method of Ndimensional matrices. The geological examples, which included the research on CuZnAbAgSnAs element combination anomalies in the middlewest of JiangshanShaoxing matching belt and the metallogenic prediction of copper polymetallic ore in the western of Zhejiang, were given to illustrate the method and procedure of Ndimensional matrices in geological application.The method of Ndimensional matrices is considered as a good tool in exploration and forecast.

Key words: mathematical geology; Ndimensional matrices; bracket multiplication; Hadamard product; cubic matrices; element combination; metallogenic prediction

0引言

在地学研究中，经常遇到多维数据，例如对于许多复杂的地质现象，要考虑全局范围各个方向的平稳性，即区别各向同性或各向异性分布规律，同时它们包含多个因变量和层次，每个因变量和层次具有不同的统计特征，必须用多变量与多个参数（即多维数据信息）来描述，才能全面刻画其特征。在矿床预测研究中经常遇到以下难题：矿质运移及其空间展布具有多维性；矿床演变与控矿构造具有多层次、多阶段性等［19］。目前，对于地质模型研究常用方法有非线性逻辑回归模型、多维对数线性模型、多维标度法和数量化理论等［1011］，但这些方法主要用于处理二维数据，因此，提出和研究处理多维数据的新方法是非常必要的［12］。N维阵概念的提出和应用，为研究多维数据提供了一个有力的工具。笔者提出了N维阵的概念、常用的几种定义和运算，包括N维阵的加减、方括号乘法和Hadamard积，同时研究了其性质，认为N维阵在处理地学多维数据中有重要应用前景。……