【作者】 王爽；

【导师】 巩向博；

【作者基本信息】 吉林大学 ， 地球探测与信息技术， 2024， 硕士

【摘要】 在地震勘探中,地震数据的高精度反演与成像对地下油气储层的精准探测具有重要意义。近年来,随着计算能力的提升以及地震采集技术的发展,最小二乘逆时偏移与全波形反演方法以其能够获取高分辨率的复杂地下图像的优势在实际应用中得到了快速发展。然而,常规的最小二乘逆时偏移与全波形反演方法仍面临着诸多挑战。在最小二乘逆时偏移与全波形反演方法中,通常通过最小化观测数据和合成地震数据之间的差异来搜索最佳拟合模型。目前大多数问题的研究都集中在如何高效准确地获取最佳拟合模型上。然而,由于缺少关键的不确定性信息,很难客观地评估和解释获取的地下模型,特别是对于获取的地下小尺度结构来说。观测数据的噪声、正演模拟的计算误差及不准确的速度模型等都会导致获取的地下反射率模型或物性参数出现误差。与确定性反演方法不同,贝叶斯方法通过计算出的后验分布提取未知参数的统计特性。给定观测数据与模型空间的先验分布,就可以获取模型空间上的后验分布,从而量化反演模型的不确定性,这种不确定性反映了反演得到的模型参数的置信度。随着反演方法和计算技术的发展,不确定性量化,特别是在根据贝叶斯推论来估计与地震反问题相关的模型不确定性,在地震反问题的求解中展现出了广泛的应用前景。本文的主要研究成果为含不确定性量化的贝叶斯逆时偏移与全波形反演研究,主要做了以下两个方面的研究工作:(1)使用了基于贝叶斯推论的迭代反演方法来量化逆时偏移的成像不确定性。通过Born近似的线性正演算子(逆时偏移算子的伴随算子)显示计算了基于格林函数的灵敏度矩阵。通过在目标函数内加入包含模型与数据不确定性信息协方差矩阵进行迭代反演获得模型空间的最大后验解。模型迭代过程的同时,通过显示灵敏度矩阵计算后验协方差矩阵,量化了最大后验解的不确定性。在频率域中,使用迭代扩展卡尔曼滤波器方法迭代模型以加快收敛。贝叶斯逆时偏移方法可以提供其不确定性显著低于初始不确定性的偏移图像和它的不确定性估计。除此之外,我们还验证了贝叶斯逆时偏移方法对速度模型的敏感性。(2)由于后验协方差的高维性,很难通过直接分析后验协方差矩阵来获取其中的模型不确定性信息。通过构建基于Tikhonov正则化的目标函数,利用Lanczos方法与随机奇异值分解(SVD)等方法对先验预处理Hessian进行低阶近似计算后验协方差矩阵,在降低了计算的内存要求同时,可以有效的对全波形反演结果的不确定性进行量化。更多还原

【Abstract】 In seismic exploration,high-precision inversion and imaging of seismic data are of significant importance for the accurate detection of underground oil and gas reservoirs.In recent years,with the advancement of computational capabilities and seismic acquisition techniques,the advantages of least squares reverse time migration(LSRTM)and full waveform inversion(FWI)in obtaining high-resolution complex underground images have led to rapid development in practical applications.However,conventional LSRTM and FWI still face numerous challenges.In LSRTM and FWI methods,the optimal fitting model is typically sought by minimizing the difference between observed data and synthetic seismic data.Most research efforts currently focus on efficiently and accurately obtaining the optimal fitting model.However,due to the lack of crucial uncertainty information,it is challenging to objectively evaluate and interpret the obtained underground models,especially for small-scale structures.Noise in observed data,computational errors in forward modeling,and inaccurate velocity models can all lead to errors in the obtained underground reflectivity models or physical property parameters.Unlike deterministic inversion methods,Bayesian methods extract statistical characteristics of unknown parameters through the computed posterior distribution.Given observed data and prior distributions in model space,the posterior distribution on model space can be obtained,thus quantifying the uncertainty of inversion models.This uncertainty reflects the confidence in the obtained model parameters.With the development of inversion methods and computational techniques,uncertainty quantification,particularly in estimating model uncertainty associated with seismic inverse problems based on Bayesian inference,demonstrates wide application prospects in solving seismic inverse problems.The main research achievements of this paper focus on Bayesian reverse time migration and full waveform inversion with uncertainty quantification.The following two aspects of research work are mainly carried out:(1)The use of iterative inversion methods based on Bayesian inference to quantify the imaging uncertainty of reverse time migration.Sensitivity matrices based on Green’s functions are computed through Born approximation of the linear forward operator(adjoint operator of reverse time migration).By incorporating covariance matrices containing model and data uncertainty information into the objective function for iterative inversion,the maximum a posteriori solution in model space is obtained.During the model iteration process,posterior covariance matrices are quantified through the computed sensitivity matrices,quantifying the uncertainty of the maximum a posteriori solution.In the frequency domain,an iterative extended Kalman filter method is used to iterate the model to accelerate convergence.Bayesian reverse time migration can provide migration images with uncertainty estimates significantly lower than the initial uncertainty.In addition,we also validate the sensitivity of Bayesian reverse time migration to velocity models.(2)Due to the high dimensionality of posterior covariances,it is difficult to directly analyze model uncertainty information contained therein.By constructing an objective function based on Tikhonov regularization,low-order approximations of posterior covariance matrices are computed through preprocessed Hessian using methods such as Lanczos and random singular value decomposition(SVD).This effectively quantifies the uncertainty of full waveform inversion results while reducing memory requirements for computations.更多还原