A Combined Non-linear Model For Earthquake Magnitude-frequency Distribution Characterization

The magnitude-frequency distribution is an important aspect in the analysis of the distribution of earthquakes and disaster assessment. Earthquakes are of singularity process as they occur in a narrow space and time interval with massive energy release,show complexity and non-linear properties. So, it is difficult to model the magnitude-frequency distribution with a simple power-law model or an exponential function. In the present paper,a combined non-linear model is derived to describe earthquake magnitude-frequency distribution: This combined non-linear model combining power-law 、 exponential 、 inverse exponential and Gaussian functions with five parameters and can be utilized either as separate and combined solutions to generate various commonly used distributions,such as power-law distribution and gamma distribution,which can be used in various background regions.In the paper,we have establish a complete and homogeneous earthquake catalog for each seismic regionalization. As the data comes from different agencies such as ISC and NEIC,the magnitude is expressed in different types,regression equations derived from the catalogues are used to covert the complied magnitudes to unified moment magnitude. The completeness of the catalogues are carefully studied using the maximum curvature method to determine the minimum critical magnitude.The combined model in this paper is superior to using the ordinary G-R model demonstrated by the seismic regionalization catalogues. We analysis the spatial distribution of parameter b,in general,b reflect earthquake activity level and is meaningful in earthquake disaster prediction.