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| Bayesian prestack seismic stochastic inversion based on the exact Zoeppritz equation |
NIU Li-Ping1( ), HU Hua-Feng1, ZHOU Dan1, ZHENG Xiao-Dong2, GENG Jian-Hua3,4,5 |
1. SINOPEC Geophysical Research Institute Co.,Ltd.,Nanjing 211103,China
2. Research Institute of Petroleum Exploration and Development,PetroChina,Beijing 100083,China
3. State Key Laboratory of Marine Geology,Tongji University,Shanghai 200092,China
4. School of Ocean and Earth Science,Tongji University,Shanghai 200092,China
5. Research Center for Marine Resources,Tongji University,Shanghai 200092,China |
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Abstract The prestack seismic inversion method based on the exact Zoeppritz equation is challenged by seismic data with low signal-to-noise ratios(SNRs).The Markov chain Monte Carlo(MCMC) simulation is a heuristic global optimization algorithm that can achieve effective prestack nonlinear inversion of elastic parameters.The conventional MCMC-based prestack inversion method,which characterizes the statistical properties of elastic parameters via the Gaussian distribution,has significant limitations when applied to complex lithologic reservoirs.Besides,due to the influence of the huge parameter space of subsurface models and the noise in seismic data,the MCMC search process for the posterior probability distribution of elastic parameters is very sensitive to local extrema,making it difficult to obtain stable and accurate results from MCMC-based prestack inversion.This study proposed an improved MCMC-based elastic parameter inversion method to address the challenges faced by the prestack inversion based on the exact Zoeppritz equation under the conditions of actual complex reservoirs and seismic data with low SNRs.First,the method reduced the complexity of the posterior probability distribution by transforming the parameters to be inverted into the perturbations of the model parameters using a low-frequency model (LFM) constraint.Then,the seismic forward modeling process was constrained by taking the logarithm of the likelihood function and utilizing an LFM.Finally,a multi-chain algorithm based on random subspace sampling was employed to perform global optimization for the prestack nonlinear inversion problems,thus avoiding premature convergence of the sampling process to local extrema.As indicated by the tests on the simulated data with low SNRs and the actual data,the method proposed in this study can yield more accurate and stable inversion results while providing credible and quantitative uncertainty estimates for the inversion results.
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Received: 25 November 2022
Published: 26 February 2024
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Flow chart of stochastic sampling for the elastic parameter perturbations
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Real well logs of elastic parameters and the corresponding LFMs
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Crossplots of the elastic parameters and the corresponding probability density contours obtained by fitting with Gaussian mixture distributions
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Crossplots of elastic parameter perturbations and the corresponding probability density contours obtained by fitting with Gaussian distributions
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The synthetic seismic angle gathers
a—no noise;b—S/N is 3
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The inversion results of the elastic parameters with noisy seismic data
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R ^ with the number of iterations
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The variation of convergence diagnostic with the number of iterations
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Statistical histogram of the sampling results for the elastic parameter perturbations at time 1630 ms
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Statistical histogram of the sampling results for the elastic parameter perturbations at time 1672 ms
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Poststack seismic section
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Actual seismic angle gathers at different CDP
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Low-frequency model
a—P-velocity;b—S-velocity;c—density
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Crossplots of elastic parameter perturbations at well locations and the corresponding probability density contours obtained by fitting with Gaussian distributions
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Inverted results of elastic parameters
a—P-velocity;b—S-velocity;c—density
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Inverted results at well W1
a—P-velocity;b—S-velocity;c—density;d—the seismic angle gather at well
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Inverted results at well W2
a—P-velocity;b—S-velocity;c—density;d—the seismic angle gather at well
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Post standard deviation of elastic parameters
a—P-velocity;b—S-velocity and;c—density
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R ^ with the number of iterations at different CDP
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The variation of convergence diagnostic with the number of iterations at different CDP
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