What are Mathematical Geosciences and its frontiers?

doi:10.13745/j.esf.sf.2021.1.17

Abstract

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

CLC Number:

P628

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

Figures/Tables 10

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

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

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

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

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

Fig.6 Crystallographic systems

Fig.7 Laws of distribution for geochemical elements

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

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.

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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