Application of Mathematics in Modeling and Analysis of Geophysical Phenomena

Geophysical phenomena exhibit highly nonlinear, multiscale, and multiphysics coupling characteristics, and their modeling and analysis heavily rely on the rigorous structure of mathematical methods and the adaptability of computational strategies. With the growth of observational data and the increasing complexity of modeling requirements, geophysical models are transitioning from analytical expressions to high-dimensional numerical simulations integrated with intelligent algorithms. Focusing on the critical role of mathematics in geophysical modeling, this study systematically explores the mathematical structural characteristics of geophysical systems, the modeling mechanisms of typical phenomena, and the applicable pathways of tools such as multiscale analysis, high-order computation, and machine learning in data processing. The results show that mathematics is not only the core language for characterizing the behavior of Earth systems but also an important bridge connecting physical processes, observational data, and predictive mechanisms, providing solid support for the modeling and understanding of complex natural systems.