Abstract: Earth's magnetic field is generated through the dynamo action in the liquid outer core. Using observational data from geomagnetic satellites and observatories, we can construct geomagnetic models that describe spatial and temporal variations of the core field. Due to the limited temporal and spatial resolution of observations and incomplete parameterization of the model, the inversion problem of geomagnetic field modeling is non-unique. Therefore, we need to incorporate regularization constraints based on prior information to alleviate the non-uniqueness of the inversion problem for geomagnetic modeling. For the core field, the non-uniqueness of modeling inversion manifests in the temporal variations of the field. Studies on the influence of regularization can help us build more reliable core field models, especially on how to suppress artificial secular variations through regularizations. In this study, we construct a series of models based on different regularization parameters within the framework of CHAOS modeling to explore the impact of regularization on the core field modeling. Our results indicate that it is necessary to use regularization constraints for the core field modeling based solely on satellite data. By comparing models with different regularization intensities of the third time derivative of the core field, we show that regularization of the third time derivative with appropriate intensity can effectively suppress artificial signals caused by overfitting of the model to observational data. However, too strong regularizations will reduce the temporal resolution of small-scale secular variations.