The advantage of the nonlinear mixed model and its application in typical seismically active areas in China

As an essential parameter in earthquake prediction and risk assessment research, the b-value has received extensive attention and discussion. In this study, we chose a nonlinear mixed model to fit the earthquake magnitude-frequency distribution to the China Earthquake Catalog database. The b-values calculated by this method were used to analyze and evaluate the seismic activity. This paper takes 27 seismic belts in China as the research area, collects earthquake data of magnitude 4.7 and above from 1920 to 2019 as a complete earthquake catalog, performs mixed model fitting and G-R model fitting for these 27 seismic belts, and compares the fitting effects. Taking Tibet as the test area, the earthquake catalog data from 1920 to 2019 were selected, and the nonlinear mixed model was applied to fitting the earthquake magnitude-frequency model in Tibet at 10-year intervals. Firstly, the earthquake data screened in the study area was classified and counted by magnitude and time; Secondly, the relevant variables in the nonlinear mixed model were calculated using the moment magnitude and seismic moment conversion formula. Finally, a nonlinear hybrid model was used to perform nonlinear regression analysis on the seismic data. The results show that: When low values of b occur, earthquakes occur around the corresponding periods. When b-values are low, earthquakes of large magnitude and low frequency occur. When b-values are relatively high, earthquakes of small magnitude and high frequency occur. Applying the nonlinear mixed model to the complete seismic data in China and neighboring regions enables a more comprehensive analysis of the data and overcomes the limitations of the traditional modeling method in analyzing earthquakes of high magnitude. The b-value will be calculated by rational analysis, which enhances the analysis and evaluation of seismic catalog data.