【摘要】 马尔科夫链蒙特卡洛方法(MCMC)是一种启发式的全局寻优算法.它在贝叶斯框架下,利用已有资料进行约束,既可使最优解满足参数的统计特性,又通过融入的先验信息,提高解的精度;寻优过程可跳出局部最优,得到全局最优解.利用MCMC方法,可以得到大量来自于后验概率分布的样本,不仅可以得到每个未知参数的估计值,而且可以得到与之相关的各种不确定性信息.此外,由于算法并不是利用有单一最优解的目标函数,所以结果对初始值的依赖不强.通过对简单一维层状介质模型的处理,和实际资料的应用,说明利用基于Metropolis-Hastings算法的MCMC方法进行地震反演,通过对解空间的随机搜索能够得到较好的效果.更多还原

【Abstract】 Markov Chain Monte Carlo method is a heuristic global optimization method.In the Bayesian framework,the optimal solution meets the statistical properties of the parameters with the constraints of data(eg.seismic data,well log);the accuracy of solution is improved with the prior information joined in;optimization process can jump out of local optimum,and ultimately obtain the global optimal solution.Using MCMC methods,we draw a large number of samples from the posterior distribution function.With these samples,we obtain not only the estimates of each unknown variable,but also various types of uncertainty information associated with the estimation.In addition,because of not making use of a objective functions with single optimal solution,the results obtained with MCMC method are independent of the choice of initial values. By testing a 1D layered model and the application of real seismic data in South China,shows the MCMC method based on Metropolis-Hastings algorithm is available and can obtain good results by random searching solution space.更多还原