Probabilistic inversion for compressional modulus and shear modulus based on QA-MCMC algorithm with joint probability distribution

Abstract

Compressional modulus and shear modulus play an important role in the reservoir prediction and fluid identification. Based on an optimized Markov chain Monte Carlo (MCMC) method in the Bayesian framework, we propose a probabilistic approach of utilizing seismic aptitudes to estimate compressional modulus and shear modulus. Conventional MCMC method is not efficient for prestack inversion due to the complex model parameter space. In order to accelerating the running speed of MCMC and improving the stability of Markov chain, we have developed a novel algorithm called “Quantum Annealing- Markov chain Monte Carlo algorithm (QA-MCMC) with joint probability distribution”. We derive an improved acceptance probability expression to reduce unnecessary model update in burn-in phase, and utilize joint probability distribution (JPD) to reduce the sampling space of inverted properties. Following a Bayesian framework, we generate the posterior probability distribution function and employ the improved MCMC algorithm to solve the inversion problem to estimate compressional modulus and shear modulus from prestack or angle stack gathers. The method is validated through the tests on the 1D model, 2D model and real data.