The Study Of Seismic Inversion Method Based On Adaptive Metropolis-markov Chain Monte Carlo

Generally, the linear inversion methods easily fall into local optimal solution in geophysical inversion problems. So the nonlinear inversion methods which can obtain the global optimal solution have been more and more important in study. Markov Chain Monte Carlo(MCMC) which is one important member of the nonlinear inversion methods gets the favour of the researchers because of its unique algorithm structure.As we know, MCMC method can effectively avoid the complex integral calculation of denominator in the Bayesian formula. But, in order to obtain Markov Chains of different objective functions, the calculation for convergence, the capacity of parameters, the speed of convergence and so on have been big obstacles which restrict MCMC method getting extensive application. The shape and the size of the proposal distribution is kown to be very crucial for the convergence of the Markov Chain. Therefore, in order to guarantee the computational efficiency, it is necessary to use appropriate proposal distribution. Based on this idea, AM(Adaptive Metropolis) algorithm arises on the basis of the M-H(Metropolis-Hastings) algorithm and AM(Adaptive Metropolis) no longer needs to determine variable proposal distribution before Markov Chain starting. It defines proposal distribution as multidimensional normal distribution of the parameter space. In the process of sampling, it adjusts recommended density(namely covariance matrix) adaptively according to the history of the Markov Chain sampling information.At fist, based on the detailed study of MCMC method’s theory and limitations, we propose a fixed step strategy. This strategy can effectively reduce lots of skills and time of the decreasing step strategy which usually is used in Metropolis-Hastings algorithm. Through the application of the model, we achieved good effect in the range of a reasonable error. Then we give a detailed description of the AM-MCMC method and improve the existing formula through the sampling situation of bimodal function. Finally the AM-MCMC method was applied to different poststack or prestack seismic inversion problem. Results showed that the method is feasible and effective...