Abstract
The conventional Markov chain Monte Carlo (MCMC) method is limited to the selected shape and size of proposal distribution and is not easy to start when the initial proposal distribution is far away from the target distribution. To overcome these drawbacks of the conventional MCMC method, two useful improvements in MCMC method, adaptive Metropolis (AM) algorithm and delayed rejection (DR) algorithm, are attempted to be combined. The AM algorithm aims at adapting the proposal distribution by using the generated estimators, and the DR algorithm aims at enhancing the efficiency of the improved MCMC method. Based on the improved MCMC method, a Bayesian amplitude versus offset (AVO) inversion method on the basis of the exact Zoeppritz equation has been developed, with which the P- and S-wave velocities and the density can be obtained directly, and the uncertainty of AVO inversion results has been estimated as well. The study based on the logging data and the seismic data demonstrates the feasibility and robustness of the method and shows that all three parameters are well retrieved. So the exact Zoeppritz-based nonlinear inversion method by using the improved MCMC is not only suitable for reservoirs with strong-contrast interfaces and long-offset ranges but also it is more stable, accurate and anti-noise.
Highlights
Inversion of reflection coefficients extracted from amplitudes of seismic waves can provide estimates of significant reservoir parameters
We adopt an improved Markov chain Monte Carlo (MCMC) method, combining the adaptive Metropolis (AM) algorithm based on the global adaptive strategy (Haario et al 2001)
The delayed rejection (DR) algorithm based on the local adaptive strategy (Green and Mira 2001) to speed up the convergence of
Summary
Inversion of reflection coefficients extracted from amplitudes of seismic waves can provide estimates of significant reservoir parameters. Combining the PP and PS information based on a least-squares approach, Lu et al (2015) developed a method of nonlinear joint pre-stack inversion for the P- and S-wave velocities and the density. This paper is devoted to the nonlinear inversion of the exact reflection coefficients RPP based on the exact Zoeppritz equation to obtain the P- and S-velocities and density directly. We will initially introduce the improved MCMC method combining the AM and DR algorithm, and discuss the Bayesian AVO nonlinear inversion method to obtain the P- and S-velocities and density directly by using the exact Zoeppritz equation, and estimate the uncertainty of AVO inversion results based on the logging data (Hong and Sen 2009). We end with real data case studies that illustrate the method
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