Comparative Studies of Nonlinear Models and Their Applications to Magmatic Evolution and Crustal Growth of the Huai'an Terrane in the North China Craton

Power-law, inverse exponential and logarithmic models are widely used as empirical tools to describe anomalies in spatial and temporal geodynamic processes. However, the lack of clear interpretation of the relationships and distinctions among these models often makes their selection challenging, leaving them as empirical tools to be validated by data. This paper introduces these nonlinear functions derived from a unified differential equation, with parameters that reflect their relative nonlinearities and singularities, enabling their comparative application. By applying these functions to analyze magmatic events of the Huai'an Terrane, this study reveals two major crustal growth and reworking events between 2.6 and 1.7 Ga, each exhibiting distinctive nonlinear characteristics. The power-law function highlights strong nonlinearity and singularity during phases of intense magmatic activity, while logarithmic and exponential functions effectively characterize transitions between different tectonic processes. Geochemical data, including U-Pb zircon dating and Lu-Hf isotopic analyses, further validate the models by delineating distinct phases of crustal growth and reworking within the Trans-North China Orogen. The findings help connect the anomalies of frequency of magmatic events with the tectonic processes, providing important insights into the evolution processes of the North China Craton.