Application Of Markov Renewal Process In The Earthquake Prediction

Earthquake disasters, inadvertently occur,which bring huge economic losses and human casualties accident. Human beings are constantly tormented with earthquake All countries in the world are researching the mechanism of earthquake occurrence, in order to forecast the earthquake much better. After decades, the research has shown that earthquake has certain regularity in a region of strong earthquake event, which has certain periodicity and repeatability. The discovery of such a rule for earthquake prediction research work provides a very good idea, it shows that people can make use of certain mathematical statistical model to describe the seismogenic period of a certain intensity earthquake and the probability of occurrence of the earthquake, in order to achieve the purpose of predicting earthquakes.Overall, there are a variety of random patterns can be applied to earthquake prediction research, and various random patterns have different characteristics: Poisson model is more suitable for smaller magnitude area. The lower frequency earthquake is,and the larger earthquake magnitude is, the higher probability of prediction and the lower probability of long-term earthquake prediction we achieve.Where the Poisson model is adopted. In the short-term prediction, the most difference between using Poisson model and using Markov model is at most40%.Semi-Markov, double Poisson, as well as cycle Poisson process and other modes require large amounts of data, so the area they apply is very limited.In the choice of mathematical model, in this paper renewal process is introduced to Markov process, forming the Markov renewal process,which is a new mathematical model. The interval time of state of the markov renewal process obeys general distribution,but the interval time of Markov process obeys exponential distribution,so the distribution function of the interval time can be a variety of combinations.This paper presents the exponential and Weibull function as mixture density function in the choice of density function.At the same time, this model in the state transition moment still has no aftereffect.So the mathematical properties of Markov renewal process is better than other mathematical model.Markov renewal process belongs to an important branch of mathematical statistics model. The model has a very extensive application in the field of statistics, biology, geography and the Internet etc. In this paper,the time interval data does not use the traditional Weibull distribution as function fitting, but usees mixed distribution function composed by Weibull distribution and exponential distribution as function fitting,which using the exponential function fitting time interval in small data and Weibull distribution fitting time interval in large data. After using the method of maximum likelihood estimation for its parameter value, we will do cross state prediction with a magnitude of two different state.We calculate the possibility of earthquake which the magnitude is above4or5occurred in the future, and gain good effect.The main work of this paper as follows:(1) This paper briefly introduces the background, significance and research status of earthquake prediction research, and introduces the advantages and disadvantages of the calculation methods and various research methods commonly used in earthquake prediction.(2) For the introduction of mathematical model, this paper introduces stochastic processes, Markov chain, Markov processes, renewal process, and finally introduces the relevant knowledge of Markov renewal process, introduces Markov renewal function, basic characteristics and its corollary, which lays a solid theoretical foundation for this paper.(3) In the aspect of data preprocessing, this paper regularly formats seismic log file of EQT format, and presents a simplified version of the aftershock elimination algorithm.(4)We take the research object sequence as a condition into consideration.The time interval data does not use the traditional Weibull distribution as function fitting, but use mixed distribution function composed by Weibull distribution and exponential distribution as function fitting,which using the exponential function fitting time interval in small data and Weibull distribution fitting time interval in large data. After using the method of maximum likelihood estimation for its parameter value, we will do cross state prediction with a magnitude of two different state.We calculate the possibility of earthquake which the magnitude is above4or5occurred in the future, and gain good effect.