Abstract
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. However, the sampling function of the traditional MH sampling is a fixed parameter distribution. The parameter ignores the statistical information of AI that expands sampling range and reduces the inversion efficiency and resolution. 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. Moreover, combining GMHDD and MCMC, we propose a novel Bayesian AI inversion method based on GMHDD. Finally, we use the Marmousi2 data and field data to test the proposed method based on GMHDD and other methods based on traditional MH. The results reveal that the proposed method can improve the efficiency and resolution of impedance inversion than other methods.
Highlights
Acoustic impedance (AI) is an important rock property that relates closely to lithology and porosity [1,2]
We apply the statistical information of acoustic impedance (AI) to the sampling function through a Gaussian distribution and build a Gaussian MH sampling with data driving (GMHDD)
The proposed method based on GMHDD
Summary
Acoustic impedance (AI) is an important rock property that relates closely to lithology and porosity [1,2]. In AI inversion, the Bayesian AI forward model was proposed This model uses the posterior probability density function (PDF) and the prior PDF to represent the seismic data and the prior knowledge of rock property and combines the posterior and prior PDF and builds a maximum likelihood estimation problem to represent the AI inversion problem. The sampling functions of the aforementioned methods are fixed parameter distributions This approach ignores the statistical information of AI which can further improve the efficiency and resolution of inversion result. The results show the proposed method based on GMHDD outperforms the other methods based on traditional MH in efficiency and accuracy
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