applied the Markov chains in AI inversion and pointed out the Markov chains can fill in a portion of the low-frequency gap that is absent in most algorithms. It not only uses the data of impedance, but also applies the distribution of impedance, thus the MCMC method based on MH is widely adopted in AI inversion. The Monte Carlo Markov Chain method (MCMC) based on Metropolis–Hastings sampling (MH) builds a stable Markov Chain to approximate distribution of impedance. The results reveal that the proposed method can improve the efficiency and resolution of impedance inversion than other methods. Finally, we use the Marmousi2 data and field data to test the proposed method based on GMHDD and other methods based on traditional MH. Moreover, combining GMHDD and MCMC, we propose a novel Bayesian AI inversion method based on GMHDD.

To reduce the sampling range and improve the efficiency, we apply the statistical information of AI to the sampling function and build a Gaussian MH sampling with data driving (GMHDD) approach to the sampling function. The parameter ignores the statistical information of AI that expands sampling range and reduces the inversion efficiency and resolution. However, the sampling function of the traditional MH sampling is a fixed parameter distribution. The Markov chain Monte Carlo (MCMC) method based on Metropolis–Hastings (MH) sampling is a popular approach in solving seismic acoustic impedance (AI) inversion problem, as it can improve the inversion resolution by statistical prior information.

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