Estimating Elastic Parameters from Prestack Seismic Data Using Markov Chain Monte Carlo Method

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.