Application of Mathematical Inversion Theory in Geophysics

Abstract

Under complex geological conditions and multi-source observation backgrounds, geophysical inversion problems exhibit strong nonlinearity, non-uniqueness of solutions, and high parameter dimensionality, which impose higher adaptability requirements on mathematical inversion theory. This study systematically explores the mathematical foundations and numerical implementation pathways of geophysical inversion, covering the classification structure of inversion problems, commonly used algorithms, the forward–inversion collaborative mechanism, and regularization strategies. It further analyzes the development trends of multi-physical field integration, data-driven modeling, and dynamic inversion. The study points out that inversion structures integrating physical constraints and intelligent methods significantly enhance the stability and accuracy of solutions, promoting the evolution of geophysical modeling toward multi-scale integration and intelligent optimization.