基于精确Zoeppritz方程的贝叶斯叠前地震随机反演

doi:10.11720/wtyht.2024.2572

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摘要

基于精确Zoeppritz方程的叠前地震反演方法在面向低信噪比地震资料的应用时仍然存在较大挑战。马尔科夫链蒙特卡洛(Markov chain Monte Carlo,MCMC)模拟是一种启发式的全局寻优算法,是实现叠前弹性参数非线性反演的有效途径。常规基于MCMC算法的叠前反演采用高斯分布来刻画弹性参数的统计特征,在应用于复杂岩性储层时有较大的局限性。同时,由于地下模型参数空间巨大以及地震数据中噪声等因素的影响,MCMC对弹性参数后验概率分布的搜索过程极易受到局部极值的影响,这使得基于MCMC的叠前反演较难获得稳定、准确的结果。本文针对实际复杂储层及低信噪比地震资料条件下基于精确Zoeppritz方程的叠前反演问题,提出了一种改进的MCMC弹性参数反演方法。该方法首先利用低频模型约束,将待反演参数转换为模型参数的扰动量,从而降低后验概率分布的复杂度;其次,通过对似然函数取对数,并利用低频模型来约束地震正演过程;最后,利用基于随机子空间采样的多链算法对叠前非线性反演问题进行全局寻优,以避免采样过程过早地收敛到局部极值。低信噪比模拟数据和实际数据的测试表明,本文所提方法能够获得更加准确、稳定的弹性参数反演结果,并且能够对反演结果给出可信、定量的不确定性估计。

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	牛丽萍
	胡华锋
	周单
	郑晓东
	耿建华

关键词 ： Zoeppritz方程, 贝叶斯理论, 叠前反演, MCMC, 不确定性

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.

Key words： Zoeppritz equation Bayesian theory prestack inversion MCMC uncertainty

收稿日期: 2022-11-25 修回日期: 2023-10-19 出版日期: 2024-02-20

ZTFLH:

P631.4

基金资助:中国科学院战略性先导科技专项(A类)“深层油气储层地球物理分布预测”(XDA14010203);国家自然科学基金企业创新发展联合基金“海相深层油气富集机理与关键工程技术基础研究”(U19B6003)

作者简介: 牛丽萍(1993-),工程师,博士,2021年毕业于同济大学地球物理学专业,从事储层预测与描述方法的研究工作。Email:niulp.swty@sinopec.com

引用本文:

牛丽萍, 胡华锋, 周单, 郑晓东, 耿建华. 基于精确Zoeppritz方程的贝叶斯叠前地震随机反演[J]. 物探与化探, 2024, 48(1): 77-87.
NIU Li-Ping, HU Hua-Feng, ZHOU Dan, ZHENG Xiao-Dong, GENG Jian-Hua. Bayesian prestack seismic stochastic inversion based on the exact Zoeppritz equation. Geophysical and Geochemical Exploration, 2024, 48(1): 77-87.

链接本文:

https://www.wutanyuhuatan.com/CN/10.11720/wtyht.2024.2572 或 https://www.wutanyuhuatan.com/CN/Y2024/V48/I1/77

Fig.1 对弹性参数扰动量的随机采样流程

Fig.2 弹性参数的测井曲线及其低频模型

Fig.3 弹性参数的交会及利用高斯混合分布拟合得到的概率密度等值线

Fig.4 弹性参数扰动量的交会及利用高斯分布拟合得到的概率密度等值线

Fig.5 模拟地震角道集
a—无噪声;b—信噪比为3

Fig.6 含噪声地震数据的弹性参数反演结果

Fig.7 收敛性指标 $R^$ 随迭代次数的变化

Fig.8 时间为1 630 ms处弹性参数扰动量的后验统计直方图

Fig.9 时间为1 672 ms处弹性参数扰动量的后验统计直方图

Fig.10 叠加地震剖面

Fig.11 不同CDP位置处的实际地震角道集

Fig.12 低频模型
a—纵波速度;b—横波速度;c—密度

Fig.13 测井位置处弹性参数扰动量的交会及其高斯分布拟合结果

Fig.14 弹性参数的反演剖面
a—纵波速度;b—横波速度;c—密度

Fig.15 W1井的反演结果
a—纵波速度;b—横波速度;c—密度;d—井旁地震角道集

Fig.16 W2井的反演结果
a—纵波速度;b—横波速度;c—密度;d—井旁地震角道集

Fig.17 弹性参数的后验标准差
a—纵波速度; b—横波速度; c—密度

Fig.18 不同CDP位置处收敛性指标 $R^$ 随迭代次数的变化

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