Geostatistical approach to bayesian inversion of geophysical data: Markov chain Monte Carlo method

This paper presents a practical and objective procedure for a Bayesian inve rsion of geophysical data. We have applied geostatistical techniques such a s kriging and simulation algorithms to acquire a prior model information. T hen the Markov chain Monte Carlo (MCMC) method is adopted to infer the char acteristics of the marginal distributions of model parameters. Geostatistic s which is based upon a variogram model provides a means to analyze and int erpret the spatially distributed data. For Bayesian inversion of dipole-dip ole resistivity data, we have used the indicator kriging and simulation tec hniques to generate cumulative density functions from Schlumberger and well logging data for obtaining a prior information by cokriging and simulation s from covariogram models. Indicator approaches make it possible to incorpo rate non-parametric information into the probabilistic density function. We have also adopted the Markov chain Monte Carlo approach, based on Gibbs sa mpling, to examine the characteristics of a posterior probability density f unction and marginal distributions of each parameter. The MCMC technique pr ovides a robust result from which information given by the indicator method , that is fundamentally non-parametric, is fully extracted. We have used th e a prior information proposed by the geostatistical method as the full con ditional distribution for Gibbs sampling. And to implement Gibbs sampler, w e have applied the modified Simulated Annealing (SA) algorithm which effect ively searched for global model space. This scheme provides a more effectiv e and robust global sampling algorithm as compared to the previous study.