隧道勘探AMT数据二维非线性共轭梯度反演的关键参数探讨

研究了二维非线性共轭梯度反演对于铁路隧道音频大地电磁(AMT)勘探的适应性。通过模型反演实验,确定控制反演进程的关键参数选取方法,以便于在不损失分辨率的前提下避免假异常。实验结果表明,在类似的地电条件下:①采用TE+TM模式联合反演;②使用浅部细分网格以更好地拟合地形;③不使用1000 Hz以上易受干扰的数据;④使用较小的正则化因子;⑤选用中、浅层电阻率的均匀空间作为初始模型;以上这些手段能提升反演结果的准确性,更适应铁路隧道勘探解释需要。     

CSAMT在巴音戈壁盆地铀储层识别中的应用

在电磁法数值模拟中,正演模拟是认识各种地电条件下的大地电磁响应特征的良好途径,模型正演得到的结论,对于资料处理、反演、解释具有积极的指导作用。通过在巴音戈壁盆地开展可控源音频大地电磁测量(CSAMT),结合巴音戈壁盆地已知钻孔资料,建立了初始地电模型,进行模型正演计算得出正演数据,通过对正演数据进行反演计算,确定合理的反演模型和反演参数,提高资料反演的准确性,最后根据对实测数据的反演计算、资料解释、综合分析结果,推断研究区铀储层巴音戈壁组的空间展布特征,解释结果得到钻孔资料的验证,在砂岩型铀矿勘查中取得较好的效果。     

大定源瞬变电磁一维自适应正则化反演

自适应正则化反演对初始模型要求较低,直接对瞬变电磁响应数据进行反演。正则化因子通过计算每次迭代的数据目标函数和模型目标函数自适应的得到,从而快速获得地下的地电结构。本文采用自适应正则化反演算法对大定源回线瞬变电磁一维层状模型进行反演,使用均匀半空间作为初始模型,首次采用模型对深度的二阶导数极小的模型约束,通过典型理论模型的反演计算,证明了TEM自适应正则化一维反演算法拟合效果好、精度高,由于不用反复搜索正则化因子,并且收敛速度快,体现了良好的稳定性和可靠性。     

起伏地形三维激电连续介质模型快速反演

为提高起伏地形三维激电数据的反演解释精度和处理效率,笔者开展了连续介质模型快速反演方法研究。针对起伏地形连续电性介质模型,提出了四面体单元电性参数分块线性连续变化的参数化方法。在反演中对模型参数施加光滑和背景约束信息,以提高反演的稳定性和分辨率。通过采用降低反问题的维数、压缩存储线性反演方程各矩阵的元素以及将互换原理和拟牛顿法相结合的方式计算偏导数矩阵等手段,可有效地加快反演的计算速度。最后,为验证反演方法的有效性,对2例地电模型进行反演试算,计算结果表明：反演耗费时间较少,仅迭代6次拟合差便趋于稳定,反演结果能较好地刻画异常体形态,编制的反演解释软件可用于实际生产。     

二维平面非恒定流数学模型的遥感水位数据同化

为了在水流计算中定量化利用遥感水位数据,基于偏微分方程最优化控制理论建立了变分模型来融合二维平面非恒定流的数学模型和数据。根据遥感数据空间信息密集的特点,提出遥感水位数据同化的新算法。采用人工合成数据考察了面域遥感数据对于定常参数和时变两类参数的反演效果。试验结果表明,遥感数据提供的空间分布式信息有利于空间分布式参数的反演识别,而且通过引入考虑水面空间变化信息的附加项,可以改善观测信息的同化,更好地辨识时变参数(流量过程)。以Moselle河的RADARSAT卫星遥感水位数据检验了模型的实用性。     

基于柯西先验分布的叠前弹性阻抗反演方法及应用

以贝叶斯反演为代表的概率化反演方法既能考虑观测数据的不确定性,又可以考虑待求解参数的先验信息,在实际地震反演中备受青睐。经研究表明,在柯西先验信息下获取的反演结果更具有稀疏性,且具有高分辨特征。叠前弹性阻抗反演是一种基于多角度部份叠加剖面的叠前地震反演方法,信息量丰富,计算效率高。这里在贝叶斯框架下,实现了基于柯西先验的叠前弹性阻抗反演方法,并提取了对储层流体敏感的弹性参数。实际资料应用表明,基于柯西先验的弹性阻抗反演方法合理可靠,具有较高的分辨能力,且提取的弹性参数能够较好地吻合实际钻遇结果。     

基于粒子群算法的GPR与电测深共同反演及等值现象消除

电测深曲线的同层等值现象普遍存在于观测误差范围内,地电断面的模型参数不同,而对应的电测深曲线却完全相同,给层状介质的电测深反演带来极大困扰。为消除电测深中等值现象,如实反映层状介质的各层电性参数、厚度等信息,这里提出一种改进的多种群粒子群反演算法,增加同等模型下包含探地雷达几何参数信息的新全局极值点,实现电性参数与几何参数的共同反演,消除单一电测深曲线的S等值现象。通过H型和A型三层电测深曲线的S等值现象数值算例,并将改进的多种群粒子群反演结果与标准粒子群进行了分析和对比。结果表明,加载了探地雷达几何参数信息的改进型多种群粒子群算法,能有效地消除等值现象,更准确地反演出地电模型的各层电性参数和几何参数。     

基于多源试验数据空间变异土体参数概率反演及边坡可靠度更新

岩土工程现场勘察试验通常只能获得有限的试验数据,据此难以真实地量化土体参数的空间变异性。提出了考虑土体参数空间变异性的概率反演和边坡可靠度更新方法,基于室内和现场两种不同来源的试验数据概率反演空间变异参数统计特征和更新边坡可靠度水平,并给出了计算流程。此外为合理地描述土体参数先验信息,发展了不排水抗剪强度非平稳随机场模型。最后通过不排水饱和黏土边坡算例验证了提出方法的有效性,并探讨了试验数据和钻孔位置对边坡后验失效概率的影响。结果表明：提出方法实现了空间变异土体参数概率反演与边坡可靠度更新的一体化,基于有限的多源试验数据概率反演得到的土体参数均值与试验数据非常吻合,明显降低了对参数不确定性的估计,更新的边坡可靠度水平显著增加。受土体参数空间自相关性的影响,试验数据对钻孔取样点附近区域土体参数统计特征更新的影响明显大于距离取样点较远区域。     

基于贝叶斯理论面波频散曲线随机反演

面波频散曲线反演是获得地下横波速度结构的重要地球物理方法。常规基于迭代最小二乘等线性反演方法依赖于初始模型,且存在多极值、容易陷入局部最小、反演精度低等问题。基于贝叶斯理论的随机反演方法是一种可以融合先验信息的非线性反演方法,该方法无需人为给定初始模型,仅利用先验信息对模型进行随机采样,根据概率分布筛选接受合适的后验概率密度估计结果,可达到对细节信息的准确估计。本文针对瑞利面波频散曲线,提出了基于GPR数据先验资料约束的贝叶斯马尔科夫蒙特卡洛(MCMC)随机反演方法,通过随机改变模型参数并计算其频散曲线与实际频散曲线的似然函数来选择是否接受新的模型参数,不断重复此过程,最终得到与实际频散曲线拟合效果最佳的最优解以及横波速度解的后验概率密度分布。通过理论模型以及实际数据反演测试,验证了该方法与常规无约束的随机反演相比,可以有效地提高反演速度和反演精度。     

利用一维正则化反演进行大地电磁测深数据拟二维反演解释

大地电磁测深的反演问题是不适定的,其反演结果不稳定,且具有非唯一性。通过在目标函数中采用正则化方法,可以使得不适定反演问题具有稳定的反演结果,并改善解的稳定性和非唯一性问题。为了提高野外大地电磁测深数据的处理效率和初步解释的精度,提出了大地电磁测深数据的一维正则化反演进行拟二维反演解释方法。这里所述的大地电磁测深一维反演解释,与以往的解释方法不同,其思路首先用Bostick反演的深度来控制层参数,使反演计算的模型参数仅存在电阻率;最后采用阻尼高斯-牛顿算法进行反演计算,并将Bostick反演结果作为反演计算的初始模型。通过模型试算,结果表明其处理速度快、解释直观,对野外大地电磁测深数据进行初步反演解释是可行的。     

Bayesian estimation of seismic hazard for two sites in Switzerland

Seismic hazard analysis is based on data and models, which both are imprecise and uncertain. Especially the interpretation of historical information into earthquake parameters, e.g. earthquake size and location, yields ambiguous and imprecise data. Models based on probability distributions have been developed in order to quantify and represent these uncertainties. Nevertheless, the majority of the procedures applied in seismic hazard assessment do not take into account these uncertainties, nor do they show the variance of the results. Therefore, a procedure based on Bayesian statistics was developed to estimate return periods for different ground motion intensities (MSK scale).Bayesian techniques provide a mathematical model to estimate the distribution of random variables in presence of uncertainties. The developed method estimates the probability distribution of the number of occurrences in a Poisson process described by the parameter . The input data are the historical occurrences of intensities for a particular site, represented by a discrete probability distribution for each earthquake. The calculation of these historical occurrences requires a careful preparation of all input parameters, i.e. a modelling of their uncertainties. The obtained results show that the variance of the recurrence rate is smaller in regions with higher seismic activity than in less active regions. It can also be demonstrated that long return periods cannot be estimated with confidence, because the time period of observation is too short. This indicates that the long return periods obtained by seismic source methods only reflects the delineated seismic sources and the chosen earthquake size distribution law.     

Bayesian inversion of synthetic AVO data to assess fluid and shale content in sand-shale media

Reservoir characterization of sand-shale sequences has always challenged geoscientists due to the presence of anisotropy in the form of shale lenses or shale layers. Water saturation and volume of shale are among the fundamental reservoir properties of interest for sand-shale intervals, and relate to the amount of fluid content and accumulating potentials of such media. This paper suggests an integrated workflow using synthetic data for the characterization of shaley-sand media based on anisotropic rock physics (T-matrix approximation) and seismic reflectivity modelling. A Bayesian inversion scheme for estimating reservoir parameters from amplitude vs. offset (AVO) data was used to obtain the information about uncertainties as well as their most likely values. The results from our workflow give reliable estimates of water saturation from AVO data at small uncertainties, provided background sand porosity values and isotropic overburden properties are known. For volume of shale, the proposed workflow provides reasonable estimates even when larger uncertainties are present in AVO data.     

先验概率分布及似然函数模型的选择对边坡可靠度评价影响的定量评估

受工程勘察成本及试验场地限制,可获得的试验数据通常有限,基于有限的试验数据难以准确估计岩土参数统计特征和边坡可靠度。贝叶斯方法可以融合有限的场地信息降低对岩土参数不确定性的估计进而提高边坡可靠度水平。但是,目前的贝叶斯更新研究大多假定参数先验概率分布为正态、对数正态和均匀分布,似然函数为多维正态分布,这种做法的合理性有待进一步验证。总结了岩土工程贝叶斯分析常用的参数先验概率分布及似然函数模型,以一个不排水黏土边坡为例,采用自适应贝叶斯更新方法系统探讨了参数先验概率分布和似然函数对空间变异边坡参数后验概率分布推断及可靠度更新的影响。计算结果表明：参数先验概率分布对空间变异边坡参数后验概率分布推断及可靠度更新均有一定的影响,选用对数正态和极值I型分布作为先验概率分布推断的参数后验概率分布离散性较小。选用Beta分布和极值I型分布获得的边坡可靠度计算结果分别偏于保守和危险,选用对数正态分布获得的边坡可靠度计算结果居中。相比之下,似然函数的影响更加显著。与其他类型似然函数相比,由多维联合正态分布构建的似然函数可在降低对岩土参数不确定性估计的同时,获得与场地信息更为吻合的计算结果。另外,构建似然函数时不同位置处测量误差之间的自相关性对边坡后验失效概率也具有一定的影响。     

Unraveling reservoir compaction parameters through the inversion of surface subsidence observations

In an attempt to derive more information on the parameters driving compaction, this paper explores the feasibility of a method utilizing data on compaction-induced subsidence. We commence by using a Bayesian inversion scheme to infer the reservoir compaction from subsidence observations. The method’s strength is that it incorporates all the spatial and temporal correlations imposed by the geology and reservoir data. Subsequently, the contributions of the driving parameters are unravelled. We apply the approach to a synthetic model of an upscaled gas field in the northern Netherlands. We find that the inversion procedure leads to coupling between the driving parameters, as it does not discriminate between the individual contributions to the compaction. The provisional assessment of the parameter values shows that, in order to identify adequate estimate ranges for the driving parameters, a proper parameter estimation procedure (Markov Chain Monte Carlo, data assimilation) is necessary.     

Bayesian approach for calibrating transformation model from spatially varied CPT data to regular geotechnical parameter

Cone Penetration Test (CPT) is widely utilized to gain regular geotechnical parameters such as compression modulus, cohesion coefficient and internal friction angle by transformation model in the site investigation. However, it is challenging to obtain simultaneously the unknown coefficients and error of a transformation model, given the intrinsic uncertainty (i.e., spatial variability) of geomaterial and the epistemic uncertainty of geotechnical investigation. A Bayesian approach is therefore proposed calibrating the transformation model based on spatial random field theory. The approach consists of three key elements: (1) three-dimensional anisotropic spatial random field theory; (2) classifications of measurement and error, and the uncertainty propagation diagram of geotechnical investigation; and (3) the unknown coefficients and error calibration of the transformation model given Bayesian inverse modeling method. The massive penetration resistance data from CPT, which is denoted as a spatial random field variable to account for the spatial variability of soil, are classified as type A data. Meanwhile, a few laboratory test data such as the compression modulus are defined as type B data. Based on the above two types of data, the unknown coefficients and error of the transformation model are inversely calibrated with consideration of intrinsic uncertainty of geomaterial, epistemic uncertainties such as measurement errors, prior knowledge uncertainty of transformation model itself, and computing uncertainties of statistical parameters as well as Bayesian method. Baseline studying indicates the proposed approach is applicable to calibrate the transformation model between CPT data and regular geotechnical parameter within spatial random field theory. Next, the calibrated transformation model was compared with classical linear regression in cross-validation, and then it was implemented at three-dimensional site characterization of the background project.     

Bayesian Gaussian Mixture Linear Inversion for Geophysical Inverse Problems

A Bayesian linear inversion methodology based on Gaussian mixture models and its application to geophysical inverse problems are presented in this paper. The proposed inverse method is based on a Bayesian approach under the assumptions of a Gaussian mixture random field for the prior model and a Gaussian linear likelihood function. The model for the latent discrete variable is defined to be a stationary first-order Markov chain. In this approach, a recursive exact solution to an approximation of the posterior distribution of the inverse problem is proposed. A Markov chain Monte Carlo algorithm can be used to efficiently simulate realizations from the correct posterior model. Two inversion studies based on real well log data are presented, and the main results are the posterior distributions of the reservoir properties of interest, the corresponding predictions and prediction intervals, and a set of conditional realizations. The first application is a seismic inversion study for the prediction of lithological facies, P- and S-impedance, where an improvement of 30% in the root-mean-square error of the predictions compared to the traditional Gaussian inversion is obtained. The second application is a rock physics inversion study for the prediction of lithological facies, porosity, and clay volume, where predictions slightly improve compared to the Gaussian inversion approach.     

Stochastic prediction in geomorphology using Bayesian inference models

Bayesian inference modeling may be applied to empirical stochastic prediction in geomorphology where outcomes of geomorphic processes can be expressed by probability density functions. Natural variations in process outputs are accommodated by the probability model. Uncertainty in the values of model parameters is reduced by considering statistically independent prior information on long-term, parameter behavior. Formal combination of model and parameter information yields a Bayesian probability distribution that accounts for parameter uncertainty, but not for model uncertainty or systematic error which is ignored herein. Prior information is determined by ordinary objective or subjective methods of geomorphic investigation. Examples involving simple stochastic models are given, as applied to the prediction of shifts in river courses, alpine rock avalanches, and fluctuating river bed levels. Bayesian inference models may be applied spatially and temporally as well as to functions of a random variable. They provide technically superior forecasts, for a given shortterm data set, to those of extrapolation or stochastic simulation models. In applications the contribution of the field geomorphologist is of fundamental quantitative importance.     

Effects of galvanic distortions on magnetotelluric data: Interpretation and its correction using deep electrical data

The non-inductive galvanic disturbances due to surficial bodies, lying smaller than high frequency skin depth, cause serious interpretational errors in magnetotelluric data. These frequency independent distortions result in a quasi-static shift between the apparent resistivity curves known as static shift. Two-dimensional modelling studies, for the effects of surficial bodies on magnetotelluric interpretation, show that the transverse electric (TE) mode apparent resistivity curves are hardly affected compared to the transverse magnetic (TM) mode curves, facilitating the correction by using a curve shifting method to match low frequency asymptotes. But in the case of field data the problem is rather complicated because of the random distribution of geometry and conductivity of near surface inhomogeneities. Here we present the use of deep resistivity sounding (DRS) data to constrain MT static shift. Direct current sensitivity studies show that the behaviour of MT static shift can be estimated using DC resistivity measurements close to the MT sounding station to appreciable depths. The distorted data set is corrected using the MT response for DRS model and further subject to joint inversion with DRS data. Joint inversion leads to better estimation of MT parameters compared to the separate inversion of data sets.     

基于IBUNE方法的水文模型不确定性分析

在贝叶斯理论框架下,根据一种可结合多个水文模型给出模拟或预报结果的IBUNE方法探讨了水文模型的输入、参数以及结构的不确定性问题。将SCEM-UA算法和EM算法嵌入新安江和TOPMODEL水文模型用于参数优化和模型平均,进而将输入与参数的综合不确定性处理后得到的预报量后验分布进行多模型综合,据此对水文模型的不确定性及其对水文模拟结果的影响进行评价。以湖南洣水流域龙家山水文站以上集水区域为例进行了应用研究,结果表明,IBUNE方法能够有效估计水文模型的不确定性,并能给出合理的概率预报区间。