什么是数学地球科学及其前沿领域?

doi:10.13745/j.esf.sf.2021.1.17

摘要/Abstract

摘要：

数学地质或者数学地球科学作为一门自然科学与地球科学的交叉学科,长期以来缺乏统一的学科定义,导致了学界对该门学科的理解常常出现偏差,甚至常常不把其作为一门独立学科,一定程度上影响了学科的发展。笔者曾任国际数学地球科学学会的执行主席、副主席、主席十余年,见证和领导了国际数学地球科学学会从数学地质向数学地球科学的转变,以及学会相关的杂志、会议等名称和内容的更新。期间于2014年在学会年度报告中提出了数学地球科学的新定义和学科内涵,2018年在庆祝学会50周年的数学地球科学手册中详细论述了数学地球科学学科的定义、内涵、贡献和前缘等。本文将在以上数学地球科学新的学科体系框架下探讨数学地球科学的主要贡献、科学进展、学科前缘和科普教育。在回顾学科发展历史的基础上分析了数学地球科学与数学地质学的差异,介绍了数学地球科学在大地测量和地球物理学、板块构造理论、地球化学、沉积学、地理信息系统、矿产资源和能源预测等领域的重要贡献。从国际地球科学前缘方向分析了数学地球科学的学科前缘,介绍了定量研究地球复杂性、大数据-深度机器学习与复杂人工智能等新的学科增长点。回答诸如什么是数学地球科学?数学地球科学家对地球科学的贡献?数学地球科学是否处在地学前缘等问题。

关键词: 数学地球科学, 数学地质, 交叉学科, 学科增长点, 基础科学问题, 地球科学前缘

Abstract:

The lack of a unified definition of Mathematical Geology or Mathematical Geosciences as an interdisciplinary field of natural science, may lead to misunderstanding of the subject or not even treating it as an independent discipline. This has, to some extent, affected the development of the field of Mathematical Geosciences. As a decade-long (2004-2016) lead administrator of the International Association for Mathematical Geosciences (IAMG), the author of this paper has witnessed and led the transformation of IAMG from Mathematical Geology to Mathematical Geosciences, and has overseen the updates of the names and contents of various journals and conferences related to IAMG. In 2014, a new definition and disciplinary connotation of Mathematical Geosciences were put forward by the author in the IAMG President Forum in Newsletters. In 2018, in celebrating the 50th anniversary of IAMG, the definition, connotation, contribution, and leading-edge researches of Mathematical Geosciences were discussed in detail in the Handbook of Mathematical Geosciences. The current paper reviews the main contributions, scientific progress, frontiers, and public education of the field under the framework of the new discipline of Mathematical Geosciences. On the basis of reviewing the developmental history of the discipline, the difference between Mathematical Geosciences and Mathematical Geology is analyzed, and the significant contributions of Mathematical Geosciences to the advances in geodesy, geophysics, plate tectonics theory, geochemistry, sedimentology, geographic information system, and mineral resources and energy forecasting are introduced. The frontiers of Mathematical Geosciences are discussed from a viewpoint of the challenges in international Earth Sciences, while new growth directions of Mathematical Geosciences are proposed, such as quantitative research on the complexity of the Earth, big data, deep machine learning, and complex artificial intelligence. This paper aims to answer such questions: What is Mathematical Geosciences? What contributions are made by mathematical geoscientists to advance Earth Sciences? And, Is the discipline of Mathematical Geosciences at the forefront of Geosciences?

Key words: Mathematical Geosciences, Mathematical Geology, interdisciplinary science, growth of the disciplinary, fundamental issues of Earth science, Earth science frontiers

中图分类号:

P628

成秋明. 什么是数学地球科学及其前沿领域?[J]. 地学前缘, 2021, 28(3): 6-25.

CHENG Qiuming. What are Mathematical Geosciences and its frontiers?[J]. Earth Science Frontiers, 2021, 28(3): 6-25.

图/表 10

图1 数学地球科学是自然科学与地球科学融合形成交叉学科,采用数学、计算机和数据解决地球科学问题

Fig.1 Schematic diagrams showing the relationship between natural sciences and Earth science (left) and how Mathematical Geosciences works (right)

图2 地球几何形状的数学模型——椭球地球

Fig.2 The mathematical model of the geometric shape of the Earth as an ellipsoid

图3 多重分形插值(引自文献[15]) (A)—de Wijs’的玻利维亚铅锌矿剖面Zn元素含量;(B)—局部奇异性分析方法(LSA)计算的Zn元素的局部奇异性指数;(C)—多重分形Kriging插值结果(黄色拟合线)与传统滑动平均的结果(红色拟合线)对比,蓝色点为实际测量结果。

Fig.3 Multifractal IDW—a new data interpolation method incorporating spatial association and local singularity. Adapted from [15].

图4 (A)刚性体在球面旋转可由Euler轴和角度来表示;(B)Euler向量定理解释洋中脊、俯冲带、转换断层的共轭关系[17];(C)太平洋板块与北美板块俯冲区域的洋中脊、俯冲带、转换断层的共轭关系

Fig.4 (A) Euler geometry applied to plate tectonics; (B) Explanation of the conjugate relationship among the mid-ocean ridge,subduction zone and transformation fault according to Euler vector theorem (adapted from [17]); (C) Map showing the conjugate relationship among mid-ocean ridge,subduction zone and transform faults in the Pacific and North America subduction zones

图5 McKenzie建立的洋中脊热流扩散模型[18] (A)—模型参数、初始条件、边界条件;(B)—McKenzie模型的理论结果与实际测量存在显著差距,反映洋中脊由于热流对流可能损失热流;(C)—成秋明[20]采用他提出的分形密度取代了McKenzie模型中的岩石圈密度,显著改善了理论结果与实际测量结果的拟合度(黑线)。

Fig.5 The heat flow model by McKenzie for mid-ocean ridge. Adapted from [18].

图6 矿物结晶学体系 (A)—晶体对称性(symmetry);(B)—晶体体系(crystal systems);(C)—魏斯晶面指数或者米勒晶面指数(Weiss indices or Miller indices)。

Fig.6 Crystallographic systems

图7 地球化学元素分布定律 (A)—基于正态或者对数正态分布区分地球化学异常与地球化学背景;(B)—成矿元素异常显示空间自相似性,服从幂律(power-law)分布,具有分形自相似规律[32];(C)—多重分形模型[15,33]。

Fig.7 Laws of distribution for geochemical elements

图8 云南兰坪—金顶地区S-A方法Zn异常与背景分解 (A)—原始水系沉积物地球化学数据;(B)—新圈定的五处具有等间距、串珠状、自相似分布的铜铅锌找矿靶区(1998年笔者与云南省地质调查院(局)签订数据保密协议,成果未公开发表,但在国内外多次学术会议进行交流,经勘探新发现了五宝山、菜子地矿床)。

Fig.8 Application of the spectral energy density-area (S-A) method to Zn anomaly and related background analyses in the Lanping-Jinding district in Yunnan Province

图9 分形几何-分形密度-分形动力学机制 (A)—从正常几何以及几何体密度(左图)到从分形几何以及分形几何体密度(右);(B)—产生分形密度(质量密度、能量密度、热量密度等)的几种奇异性地质过程;(C)—产生分形密度和奇异性的几种机制:相变、自组织临界性、多重级联-循环和混沌机制。

Fig.9 Fractal geometry, density and mechanism. (A) Concepts of fractal density; (B) Possible geological processes that may generate fractal density; (C) Mechanisms of fractal density generation.

图10 地球科学、数学与计算机科学交叉支撑地学信息、地学大数据、地学人工智能应用

Fig.10 Interdisciplinary relationships of various natural science fields related to geo-data science (upper diagram), and the realm of machine learning where various mathematical subjects support its development

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