A systematic analysis of mathematical and geophysical principles applied to the modeling of strong ground motion parameters under seismic loading conditions has been performed. The focus of the study is on one of the key characteristics of the seismic process — the peak ground acceleration (PGA), which represents a fundamental indicator of earthquake intensity. The methodological framework of the research is based on the analysis of median ground motion models that formalise the dependence of seismic impact parameters on the source characteristics, hypocentral distance, and geophysical conditions of the medium. Models of aleatory uncertainty are examined, reflecting the natural variability of ground motion parameters and ensuring the statistical correctness of model parameterisation. Particular attention is given to stochastic modeling, which allows reproducing the probabilistic distribution of strong ground motion scenarios. The application of stochastic algorithms enables the inclusion of both typical and rare extreme events, which is crucial for seismic hazard assessment. The aim of the study is to develop recommendations for the selection and application of mathematically and geophysically justified models, artificial intelligence (AI) algorithms that meet the criteria of accuracy, reliability, and reproducibility. A comparative analysis of different approaches has revealed their respective strengths and limitations, as well as identified the optimal areas of practical application. The practical significance of the research lies in the fact that properly selected and geophysical validated models improve the accuracy of ground motion prediction and enhance the efficiency of engineering calculations during the design of buildings and structures.

Keywords: earthquake, strong ground motion, peak ground acceleration, mathematical modeling, median models, stochastic modeling, artificial intelligence

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