A new stochastic inference method for inversion of pre‐stack seismic data

Abstract

In a Bayesian framework, solution of an inverse problem is given by the posterior probability density (PPD) function of the model. In this paper we report on the development of a new stochastic method, named greedy annealed importance sampling (GAIS), to draw samples from PPD to provide unbiased estimates of uncertainty. The advantages of this new technique are unbiasedness and reduction in true variance obtained by searching the important regions of the posterior distribution. Traditional importance sampling and the Markov Chain Monte Carlo (MCMC) methods (Metropolis‐Hastings/Gibbs' sampler) can also yield unbiased estimates but they are computationally very slow. Multiple very fast simulated annealing (VFSA) is an approximate method but is very fast. The estimates are, however, biased. Greedy annealed importance sampling (GAIS) combines VFSA and GIS to improve the speed of a traditional importance sampling and maintain unbiasedness. We demonstrate the performance of GAIS with application to pre‐stack seismic waveform inversion of angle stack traces.