含噪声数据反演的概率描述

根据贝叶斯理论给出了对含噪声地球物理数据处理的具体流程和方法,主要包括似然函数估计和后验概率计算.我们将数据向量的概念扩展为数据向量的集合,通过引入数据空间内的信赖度,把数据噪声转移到模型空间的概率密度函数上,即获得了反映数据本身的不确定性的似然函数.该方法由于避免了处理阶段数据空间内的人工干预,因而可以保证模型空间中的概率密度单纯反映数据噪声,具有信息保真度高、保留可行解的优点.为了得到加入先验信息的后验分布,本文提出了使用加权矩阵的概率分析法,该方法在模型空间直接引入地质信息,对噪声引起的反演多解性有很强的约束效果.整个处理流程均以大地电磁反演为例进行了展示.     

纵向和横向同时约束AVO反演

为了提高AVO(amplitude versus offset)反演结果的精度和横向连续性,本文提出了一种新的AVO反演约束方法,该方法结合贝叶斯原理和卡尔曼滤波算法实现了对反演参数纵向和横向的同时约束.文章首先结合反演参数的纵向贝叶斯先验概率约束和反演参数的横向连续性假设建立了与卡尔曼滤波算法对应的AVO反演系统的数学模型,然后将该数学模型代入卡尔曼滤波算法框架,利用卡尔曼滤波算法实现了双向约束AVO反演.二维模型测试和实际数据测试结果表明,相对于单纯的纵向贝叶斯先验概率约束,双向约束能更准确地刻画参数的横向变化,得到更准确、横向连续性更好的反演结果.     

基于频变AVO技术对多尺度裂缝内流体属性反演与识别（英文）

通过地震数据获取裂缝储藏中流体的性质并对流体类型进行识别,是地震勘探岩性反演的重要问题之一。由于地震波的速度、储层的密度等弹性参数对某些流体不具有很强的敏感性,使只依赖振幅信息进行流体识别的传统AVO方法面临困境。作为传统叠前振幅反演的一个拓展,频变AVO（FDAVO）技术进一步考虑了振幅对频率的依赖关系,将这种依赖关系与地下裂缝结构、流体填充对应起来,能带来更丰富的流体信息。利用该技术,本文提出了一种基于地震数据参数化Chapman模型的贝叶斯反演新方法（BIDCMP）,它包含两步算法,即,FDAVO反演储层的非弹性属性和贝叶斯框架下的流体识别。首先,通过匹配观测数据和模型数据,构造差函数反演裂缝储层非弹性参数。随后,在贝叶斯框架下,使用马尔科夫随机场（MRF）作为先验模型,联合多参数场识别流体。本方法在计算过程中,除综合考虑了弹性参数场、测井资料等常规信息外,还特别地加人了第一步中反演得的非弹性参数的约束,从而充分利用了流体粘性差异,最后在最大后验概率（MAP）准则下输出最佳岩性一流体识别结果。分别对合成地震记录和模拟岩性—流体剖面验证本文方法的有效性,结果证明本文方法获得的流体识别结果准确可信。     

Joint AVO inversion in the time and frequency domain with Bayesian interference

Amplitude variations with offset or incident angle (AVO/AVA) inversion are typically combined with statistical methods, such as Bayesian inference or deterministic inversion. We propose a joint elastic inversion method in the time and frequency domain based on Bayesian inversion theory to improve the resolution of the estimated P- and S-wave velocities and density. We initially construct the objective function using Bayesian inference by combining seismic data in the time and frequency domain. We use Cauchy and Gaussian probability distribution density functions to obtain the prior information for the model parameters and the likelihood function, respectively. We estimate the elastic parameters by solving the initial objective function with added model constraints to improve the inversion robustness. The results of the synthetic data suggest that the frequency spectra of the estimated parameters are wider than those obtained with conventional elastic inversion in the time domain. In addition, the proposed inversion approach offers stronger antinoising compared to the inversion approach in the frequency domain. Furthermore, results from synthetic examples with added Gaussian noise demonstrate the robustness of the proposed approach. From the real data, we infer that more model parameter details can be reproduced with the proposed joint elastic inversion.     

基于贝叶斯方法的二维大地电磁尖锐边界反演研究

针对常规大地电磁（Magnetotelluric,MT）反演方法对电阻率异常体边界不太敏感的问题,本文尝试基于贝叶斯理论开展二维大地电磁电阻率尖锐边界反演研究.在反演中,模型参数由边界位置及内部电阻率组成,通过贝叶斯理论将模型参数与数据相联系,采用Markov Chain Monte Carlo（MCMC）的Metropolis-Hastings（MH）方法对后验概率密度函数（Posteriori Probability Density,PDD）进行采样.采样过程中无罚值函数约束,完全以数据自身所包含的信息对模型进行约束,同时与有限约束进行比较,并考虑不同起始采样点对结果的影响.以接受率为参考,用模型算例说明MH方法中建议分布函数选择的重要性.当模型参数间相关性较弱时,使用边缘概率分布对采样结果进行分析.该方法能给出模型参数的分布范围,并给出该模型参数范围对应的数据范围.通过与已知模型的对比及数据拟合情况分析检验了该反演方法的有效性.该方法有助于提高大地电磁尖锐边界反演的分辨能力.     

基于地质统计先验信息的储层物性参数同步反演

本文提出的储层物性参数同步反演是一种高分辨率的非线性反演方法,该方法综合利用岩石物理和地质统计先验信息,在贝叶斯理论框架下,首先通过变差结构分析得到合理的变差函数,进而利用快速傅里叶滑动平均模拟算法（Fast Fourier TransformMoving Average,FFT-MA）和逐渐变形算法（Gradual Deformation Method,GDM）得到基于地质统计学的储层物性参数先验信息,然后根据统计岩石物理模型建立弹性参数与储层物性参数之间的关系,构建似然函数,最终利用Metropolis算法实现后验概率密度的抽样,得到物性参数反演结果。并将此方法处理了中国陆上探区的一块实际资料,本方法的反演结果具有较高的分辨率,与测井数据吻合度较高;由于可以直接反演储层物性参数,避免了误差的累积,大大减少了不确定性的传递,且计算效率较高。     

频率域航空电磁数据变维数贝叶斯反演研究

传统的梯度反演方法已经广泛应用于频率域航空电磁数据处理中,然而此类方法受初始模型影响较大,且容易陷入局部极小.为解决这一问题,本文采用改进的变维数贝叶斯反演方法实现航空电磁数据反演.该方法根据建议分布对反演模型进行随机采样,并依据接受概率筛选合理的候选模型,最终获得反演模型的概率分布和不确定度信息.为解决贝叶斯反演方法对深部低阻层反演效果不佳的问题,本文通过引入合理加权系数,调整对反演模型约束强度,在很大程度上改善了反演效果.通过对模型统计方法进行改进,在遵循原有模型采样方法和接受标准的基础上,将满足数据拟合要求的模型纳入统计范围,削弱不合理模型对统计结果的干扰.本文最后通过对含有高斯噪声的理论数据和实测数据进行反演,并与Occam反演结果进行对比,验证了该方法的有效性.     

基于统计岩石物理模型的各向异性页岩储层参数反演

提出了各向异性页岩储层统计岩石物理反演方法.通过统计岩石物理模型建立储层物性参数与弹性参数的定量关系,使用测井数据及井中岩石物理反演结果作为先验信息,将地震阻抗数据定量解释为储层物性参数、各向异性参数的空间分布.反演过程在贝叶斯框架下求得储层参数的后验概率密度函数,并从中得到参数的最优估计值及其不确定性的定量描述.在此过程中综合考虑了岩石物理模型对复杂地下介质的描述偏差和地震数据中噪声对反演不确定性的影响.在求取最大后验概率过程中使用模拟退火优化粒子群算法以提高收敛速度和计算准确性.将统计岩石物理技术应用于龙马溪组页岩气储层,得到储层泥质含量、压实指数、孔隙度、裂缝密度等物性,以及各向异性参数的空间分布及相应的不确定性估计,为页岩气储层的定量描述提供依据.     

飞行高度同时反演的固定翼航空瞬变电磁-维反演

航空电磁测量记录中,不仅感生电动势测量数据有观测误差,而且高度计测量数据也有误差,直接进行常规反演往往导致反演结果不可靠,研究飞行高度数据有误差下的反演算法具有实际意义.本文以层状模型的固定翼时间域航空电磁多分量理论响应数据为例,提出了两种针对飞行高度计记录数据有误差时的正则化反演算法,一个是自适应正则化反演方法,另一...     

Cauchy prior distribution-based AVO elastic parameter estimation via weakly nonlinear waveform inversion

Cauchy priori distribution-based Bayesian AVO reflectivity inversion may lead to sparse estimates that are sensitive to large reflectivities. For the inversion, the computation of the covariance matrix and regularized terms requires prior estimation of model parameters, which makes the iterative inversion weakly nonlinear. At the same time, the relations among the model parameters are assumed linear. Furthermore, the reflectivities, the results of the inversion, or the elastic parameters with cumulative error recovered by integrating reflectivities are not well suited for detecting hydrocarbons and fuids. In contrast, in Bayesian linear AVO inversion, the elastic parameters can be directly extracted from prestack seismic data without linear assumptions for the model parameters. Considering the advantages of the abovementioned methods, the Bayesian AVO reflectivity inversion process is modified and Cauchy distribution is explored as a prior probability distribution and the time-variant covariance is also considered. Finally, we propose a new method for the weakly nonlinear AVO waveform inversion. Furthermore, the linear assumptions are abandoned and elastic parameters, such as P-wave velocity, S-wave velocity, and density, can be directly recovered from seismic data especially for interfaces with large reflectivities. Numerical analysis demonstrates that all the elastic parameters can be estimated from prestack seismic data even when the signal-to-noise ratio of the seismic data is low.     

基于弹性阻抗的储层物性参数预测方法

储层物性参数是储层描述的重要参数,常规的基于贝叶斯理论的储层物性参数反演方法大多是通过反演获得的弹性参数进一步转换而获得物性参数,本文提出一种基于弹性阻抗数据预测储层物性参数的反演方法.该方法主要通过建立可以表征弹性阻抗与储层物性参数之间关系的统计岩石物理模型,联合蒙特卡罗仿真模拟技术,在贝叶斯理论框架的指导下,应用期望最大化算法估计物性参数的后验概率分布,最终实现储层物性参数反演.经过模型测试和实际资料的处理,其结果表明本文提出的方法具有预测精度高,稳定性强,横向连续性好等优点.     

基于随机地震反演的Russell流体因子直接估算方法

本文研究了一种基于随机地震反演的Russell流体因子直接估算方法,该方法是一种基于蒙特卡罗的非线性反演,能够有效地融合测井资料中的高频信息,提高反演结果的分辨率.本文应用贝叶斯理论框架,首先通过测井数据计算井位置处的Russell流体因子,利用序贯高斯模拟方法(sequential Gaussian simulation,SGS)得到流体因子的先验信息;然后构建似然函数;最后利用Metropolis抽样算法对后验概率密度进行抽样,得到反演的Russell流体因子.其中对每道数据进行序贯高斯模拟时,采用一种新的逐点模拟方式,具有较高的计算速度.数值试验表明:反演结果与理论模型和实际测井数据吻合较好,具有较高的分辨率,对于判识储层含流体特征具有较好的指示作用.     

Soil moisture estimation using tomographic ground penetrating radar in a MCMC–Bayesian framework

In this study, we focus on a hydrogeological inverse problem specifically targeting monitoring soil moisture variations using tomographic ground penetrating radar (GPR) travel time data. Technical challenges exist in the inversion of GPR tomographic data for handling non-uniqueness, nonlinearity and high-dimensionality of unknowns. We have developed a new method for estimating soil moisture fields from crosshole GPR data. It uses a pilot-point method to provide a low-dimensional representation of the relative dielectric permittivity field of the soil, which is the primary object of inference: the field can be converted to soil moisture using a petrophysical model. We integrate a multi-chain Markov chain Monte Carlo (MCMC)–Bayesian inversion framework with the pilot point concept, a curved-ray GPR travel time model, and a sequential Gaussian simulation algorithm, for estimating the dielectric permittivity at pilot point locations distributed within the tomogram, as well as the corresponding geostatistical parameters (i.e., spatial correlation range). We infer the dielectric permittivity as a probability density function, thus capturing the uncertainty in the inference. The multi-chain MCMC enables addressing high-dimensional inverse problems as required in the inversion setup. The method is scalable in terms of number of chains and processors, and is useful for computationally demanding Bayesian model calibration in scientific and engineering problems. The proposed inversion approach can successfully approximate the posterior density distributions of the pilot points, and capture the true values. The computational efficiency, accuracy, and convergence behaviors of the inversion approach were also systematically evaluated, by comparing the inversion results obtained with different levels of noises in the observations, increased observational data, as well as increased number of pilot points.     

Sparse Bayesian linearized amplitude-versus-angle inversion

The technique of seismic amplitude-versus-angle inversion has been widely used to estimate lithology and fluid properties in seismic exploration. The amplitude-versus-angle inversion problem is intrinsically ill-posed and generally stabilized by the use of L2-norm regularization methods but with drawback of smoothing important boundaries between adjacent layers. In this study, we propose a sparse Bayesian linearized solution for amplitude-versus-angle inversion problem to preserve the sharp geological interfaces. In this regard, a priori constraint term with two regularization functions is presented: the sparse constraint regularization and the low-frequency model information. In addition, to obtain high-resolution reflectivity estimation, the model parameters decorrelation technique combined with dipole decomposition method is employed. We validate the applicability of the presented method by both synthetic and real seismic data from the Gulf of Mexico. The accuracy improvement of the presented method is also confirmed by comparing the results with the commonly used Bayesian linearized amplitude-versus-angle inversion.     

基于L1范数的瞬变电磁非线性反演

瞬变电磁反演存在高度的非线性特征,常用的最小二乘等线性反演方法往往对初始模型高度依赖,并且极易陷入局部最优解.本文基于观测数据与模拟数据的L1范数建立目标函数,采用模拟退火非线性全局最优化方法实现瞬变电磁一维反演.初始模型完全随机产生,通过指数函数退温机制模拟系统能量最小实现迭代,通过接收概率函数评价当前模型,实现局部最优解的跳出,最终实现全局最优化求解.通过数值算例发现,无论给定的反演层数等于还是大于设计模型,都可以获得较好的反演效果,因而可以在反演初始就设计较多的层数,实现反演模型的自动拟合;同时,利用含噪声数据反演进一步验证算法的稳定性.最后,对实测数据进行了反演测试,结果与钻孔编录基本一致,表明提出的基于L1范数的模拟退火反演可用于实测数据处理.     

贝叶斯同化重力反演方法构建龙门山地壳密度模型

重力异常对地壳横向密度变化敏感,而无约束重力反演得到的密度模型其垂向分辨能力往往不理想.为了改善反演结果的垂向分辨率,本文参考已有先验分层模型,基于贝叶斯原理,提出了一种重震联合反演的新策略,可实现多种参考模型和复杂加权参数条件下的最大后验概率估计.理论模型测试结果表明,对于深度加权、多参考模型约束等多种问题,本文提出...     

空-地-井重力异常正则化协同密度反演方法

围绕综合利用空-地-井多源重力异常联合反演提升精度的目标,提出正则化协同密度反演方法,从而有效利用多维数据的横向和纵向变化特征提高反演精度,且无需先验信息的约束.此外,还提出利用奇异值谱和深度分辨率工具评价航空数据观测高度和层数对反演分辨率的影响.通过理论模型试验本文方法在空-地、地-井等不同情况下的应用效果,结果表明空-地-井重力异常正则化协同密度反演方法能获得更高分辨率、高精度的反演结果,且证明不同的钻孔位置对反演结果有较大的影响,从而可指导实际的空-地-井联合勘探.最后,利用文顿盐丘实际勘探数据进行空地和空地井重力数据协同反演,反演结果垂向分辨率明显优于地面观测数据反演结果,盐盖的顶面及中心埋深与前人研究和地质资料解释相吻合,验证了方法正确性及实用性,为推进我国空-地-井立体重磁勘探提供了重要的技术手段.     

基于姿态变化的航空频率域电磁法仪器偏置实时校正方法研究

磁偶极子的航空频率域电磁法仪器在飞行测量的过程中由于仪器偏置的存在,且仪器偏置会随着外部气压、温度等环境因素以及收发线圈晃动的影响而呈现非线性变化,使得观测数据出现误差,因此需要对仪器偏置进行校正.而传统的在测线飞行前后将仪器抬至高空的"零场值"标定方法具有成本高、受测区环境影响大以及采用线性插值获取测线飞行过程中仪器偏置的精度低等缺点.本文根据仪器偏置与仪器姿态角变化无关的特性,通过测得仪器的姿态角信息,在满足重叠偶极子模型的条件下,实现对仪器偏置的高精度实时校正.模型仿真结果表明,在30m常规飞行高度下,该方法实时测得的仪器偏置精度接近于110m高空测得的精度;校正后仪器偏置的绝对误差与理论二次场的比值即相对误差小于5%,满足反演大地电导率的精度要求.该方法不仅减少了飞行的工作量,降低了飞行成本和飞行难度,而且可更加精确地获得测线飞行过程中仪器偏置的非线性变化值,提高航测数据的观测精度.     

基于模型降阶的贝叶斯方法在三维重力反演中的实践

三维重力反演是地质工作者了解地球深部构造,认知地下结构的重要手段.按照反演单元划分,三维重力反演有离散多面体(Discrete)反演和网格节点(Voxels)反演两种方式.离散多面体反演由于易于吸收先验地质信息得到的理论场能够很好地拟合观测场,因此,在实际重力反演中更受欢迎.目前离散多面体重力反演中初始模型的建立方法繁杂不一,实际应用受到很大的限制.本文本着充分挖掘利用先验信息和重力观测数据得到丰富可靠的反演结果这一原则,以离散多面体反演技术为基础,改进建模过程.在初始模型的建立中,吸收贝叶斯算法优势,采用隐马尔科夫链改善朴素贝叶斯方法的分类效果,通过最大似然函数算法求解,再采取模型降阶技术,固定所建模型中几何体的形态或密度,达到在几何体形态(x,y,z)、密度(σ)和重力值(g)五个参数中降低维数目的,从而减小高维不确定性和正演的计算量,由此反演计算的地质体密度和分布范围相对更准确,更利于重现重力模型结构.通过单位球体和任意形态几何体模拟实验,以及安徽省泥河矿区三维重力反演实践,得到非常接近实际的密度或重力值,大幅提高了三维重力反演的精度和效率,说明该方法是有效、实用的.     

Bayesian inversion of joint SH seismic and seismoelectric data to infer glacier system properties

In glacial studies, properties such as glacier thickness and the basement permeability and porosity are key to understand the hydrological and mechanical behaviour of the system. The seismoelectric method could potentially be used to determine key properties of glacial environments. Here we analytically model the generation of seismic and seismoelectric signals by means of a shear horizontal seismic wave source on top of a glacier overlying a porous basement. Considering a one-dimensional setting, we compute the seismic waves and the electrokinetically induced electric field. We then analyse the sensitivity of the seismic and electromagnetic data to relevant model parameters, namely depth of the glacier bottom, porosity, permeability, shear modulus and saturating water salinity of the glacier basement. Moreover, we study the possibility of inferring these key parameters from a set of very low noise synthetic data, adopting a Bayesian framework to pay particular attention to the uncertainty of the model parameters mentioned above. We tackle the resolution of the probabilistic inverse problem with two strategies: (1) we compute the marginal posterior distributions of each model parameter solving multidimensional integrals numerically and (2) we use a Markov chain Monte Carlo algorithm to retrieve a collection of model parameters that follows the posterior probability density function of the model parameters, given the synthetic data set. Both methodologies are able to obtain the marginal distributions of the parameters and estimate their mean and standard deviation. The Markov chain Monte Carlo algorithm performs better in terms of numerical stability and number of iterations needed to characterize the distributions. The inversion of seismic data alone is not able to constrain the values of porosity and permeability further than the prior distribution. In turn, the inversion of the electric data alone, and the joint inversion of seismic and electric data are useful to constrain these parameters as well as other glacial system properties. Furthermore, the joint inversion reduces the uncertainty of the model parameters estimates and provides more accurate results.