Geostatistical Seismic Inversion with Direct Sequential Simulation and Co-simulation with Multi-local Distribution Functions

Stochastic sequential simulation is a common modelling technique used in Earth sciences and an integral part of iterative geostatistical seismic inversion methodologies. Traditional stochastic sequential simulation techniques based on bi-point statistics assume, for the entire study area, stationarity of the spatial continuity pattern and a single probability distribution function, as revealed by a single variogram model and inferred from the available experimental data, respectively. In this paper, the traditional direct sequential simulation algorithm is extended to handle non-stationary natural phenomena. The proposed stochastic sequential simulation algorithm can take into consideration multiple regionalized spatial continuity patterns and probability distribution functions, depending on the spatial location of the grid node to be simulated. This work shows the application and discusses the benefits of the proposed stochastic sequential simulation as part of an iterative geostatistical seismic inversion methodology in two distinct geological environments in which non-stationarity behaviour can be assessed by the simultaneous interpretation of the available well-log and seismic reflection data. The results show that the elastic models generated by the proposed stochastic sequential simulation are able to reproduce simultaneously the regional and global variogram models and target distribution functions relative to the average volume of each sub-region. When used as part of a geostatistical seismic inversion procedure, the retrieved inverse models are more geologically realistic, since they incorporate the knowledge of the subsurface geology as provided, for example, by seismic and well-log data interpretation.     

Geostatistical Seismic Inversion with Self-Updating of Local Probability Distributions

Mathematical Geosciences - Three-dimensional subsurface elastic models inverted from seismic reflection data are the basis of the geo-modeling workflow. These models are often used to predict the...     

Direct Sequential Simulation and Cosimulation

Sequential simulation of a continuous variable usually requires its transformation into a binary or a Gaussian variable, giving rise to the classical algorithms of sequential indicator simulation or sequential Gaussian simulation. Journel (1994) showed that the sequential simulation of a continuous variable, without any prior transformation, succeeded in reproducing the covariance model, provided that the simulated values are drawn from local distributions centered at the simple kriging estimates with a variance corresponding to the simple kriging estimation variance. Unfortunately, it does not reproduce the histogram of the original variable, which is one of the basic requirements of any simulation method. This has been the most serious limitation to the practical application of the direct simulation approach. In this paper, a new approach for the direct sequential simulation is proposed. The idea is to use the local sk estimates of the mean and variance, not to define the local cdf but to sample from the global cdf. Simulated values of original variable are drawn from intervals of the global cdf, which are calculated with the local estimates of the mean and variance. One of the main advantages of the direct sequential simulation method is that it allows joint simulation of N _v variables without any transformation. A set of examples of direct simulation and cosimulation are presented.     

Adding Local Accuracy to Direct Sequential Simulation

Geostatistical simulations are globally accurate in the sense that they reproduce global statistics such as variograms and histograms. Kriging is locally accurate in the minimum local error variance sense. Building on the concept of direct sequential simulation, we propose a fast simulation method that can share these opposing objectives. It is shown that the multiple-point entropy of the resulting simulation is related to the univariate entropy of the local conditional distributions used to draw simulated values. Adding local accuracy to conditional simulations does not detract much from variogram reproduction and can be used to increase multiple-point entropy. The methods developed are illustrated using a case study.     

3维干旱变量联合概率分布研究

研究多变量干旱特性联合分布的推求方法。选择干旱历时、干旱烈度和烈度峰值为水文干旱特性变量。单变量的边际分布参数分别采用矩法、概率权重法、极大似然法和遗传算法进行计算和优化。应用检验、Kolmogorov-Smirnov等6种检验法进行单变量分布的拟合度检验。采用Pearson’s古典相关系数,Spearman秩相关系数,Kendall’s,Chi-Plots和K-Plots进行变量间的相依性度量。选择4种常用的3维Archimedean Copula函数进行干旱特性变量联合分布拟合。根据RMSE、AIC和BIC准则选择最优copula。在此基础上,采用基于Rosenblatt变换的Bootstrap法进行3维copula的拟合度检验。模型应用于渭河流域北洛河状头站径流序列,结果表明:Gumbel-Hougaard copula拟合效果最好,可以描述洛河状头站3维干旱变量的联合分布。     

二维重磁资料联合正演模拟

重、磁异常的人机联作模拟反演(也称人机联作选择法),是根据选定地质模型及重、磁异常的正演计算公式,由给定的初始模型参数计算出理论场值,并与实际观测场值进行对比,根据对比中确定的不一致性或残差,依靠解释人员的经验来修改模型形状及物性参数,重新计算理论场值进行下一次对比,反复多次直至达到满意为止,人机联作选择法整体为一套计算机软件,并依据支撑条件的不同可分为在人机联作工作站上使用或在一般的微机上使用。人机联作选择法既可应用于二度体重、磁异常,也可以应用于三度体重、磁异常的模拟计算解释。     

The Theoretical Links Between Sequential Gaussian Simulation, Gaussian Truncated Simulation, and Probability Field Simulation

Sequential Gaussian simulation (sgsim), Gaussian truncated simulation (gtsim), and probability field simulation (pfsim) are three algorithms frequently used for conditional stochastic simulation. They were developed independently and are seen as different algorithms in applications. This paper establishes that gtsim and pfsim can be bridged by a simple quantile transform between Gaussian and uniform distributions. As for the sgsim algorithm, the normal score back-transform can be seen as a series of truncations of the simulated Gaussian field. All three algorithms are shown to be applicable to both continuous and categorical variables. In practice, gtsim can be most often replaced by the more CPU-efficient pfsim algorithm.     

Application and Verification of Joint Probability Method in Potential Forecast for Severe Convective Weather in Anhui Province

In consideration of large uncertainties in severe convective weather forecast, ensemble forecasting is a dynamic method developed to quantitatively estimate forecast uncertainty. Based on ensemble output, joint probability is a post-processing method to delineate key areas where weather event may actually occur by taking account of the uncertainty of several important physical parameters. An investigation of the environments of little rainfall convection and strong rainfall convection from April to September (warm season) during 2009-2015 was presented using daily disastrous weather data, precipitation data of 80 stations in Anhui province and NCEP Final Analysis (FNL) data. Through ingredients-based forecasting methodology and statistical analysis,four convective parameters characterizing two types of convection were obtained, respectively, which were used to establish joint probability forecasting together with their corresponding thresholds. Using the ECMWF ensemble forecast and observations from April to September during 2016-2017, systematic verification mainly based on ROC and case study of different weather processes were conducted. The results demonstrate that joint probability method is capable of discriminating little rainfall convection and non-convection with comparable performance for different lead times, which is more favorable to identifying the occurrence of strong rainfall convection. The joint probability of little rainfall convection is a good indication for the occurrence of regional or local convection, but may produce some false alarms. The joint probability of strong rainfall convection is good at indicating regional concentrated short-term heavy precipitation as well as local heavy rainfall. There are also individual missing reports in this method, and in practice, 10% can be roughly used as joint probability threshold to achieve relative high TS score. Overall, ensemble-based joint probability method can provide practical short-term probabilistic guidance for severe convective weather.     

Comparison between Empirical Estimation by JRC-JCS Model and Direct Shear Test for Joint Shear Strength

In order to study the reliability of the empirical estimation of joint shear strength by the JRC(joint roughness coefficient)-JCS(joint compressive strength) model,natural rock joints of dif-ferent lithologic characteristics and different sizes were selected as samples,and their shear strengths under dry and saturated conditions were measured by direct shear test and compared to those esti-mated by the JRC-JCS model.Comparison results show that for natural rock joints with joint surfaces closely matched,the...     

Comparison of Two Probability Distributions Used to Model Sizes of Undiscovered Oil and Gas Accumulations: Does the Tail Wag the Assessment?

Undiscovered oil and gas assessments are commonly reported as aggregate estimates of hydrocarbon volumes. Potential commercial value and discovery costs are, however, determined by accumulation size, so engineers, economists, decision makers, and sometimes policy analysts are most interested in projected discovery sizes. The lognormal and Pareto distributions have been used to model exploration target sizes. This note contrasts the outcomes of applying these alternative distributions to the play level assessments of the U.S. Geological Survey's 1995 National Oil and Gas Assessment. Using the same numbers of undiscovered accumulations and the same minimum, medium, and maximum size estimates, substitution of the shifted truncated lognormal distribution for the shifted truncated Pareto distribution reduced assessed undiscovered oil by 16% and gas by 15%. Nearly all of the volume differences resulted because the lognormal had fewer larger fields relative to the Pareto. The lognormal also resulted in a smaller number of small fields relative to the Pareto. For the Permian Basin case study presented here, reserve addition costs were 20% higher with the lognormal size assumption.     

渗透破坏情况下土坡失稳的模糊概率

探讨了渗透破坏情况下土坡失稳的模糊概率的计算方法，工程实例分析表明，该方法优于其他传统的方法。     

Conditional Simulation of Random Fields with Bivariate Gamma Isofactorial Distributions

This work focuses on a random function model with gamma marginal and bivariate isofactorial distributions, which has been applied in mining geostatistics for estimating recoverable reserves by disjunctive kriging. The objective is to widen its use to conditional simulation and further its application to the modeling of continuous attributes in geosciences. First, the main properties of the bivariate gamma isofactorial distributions are analyzed, with emphasis in the destructuring of the extreme values, the presence of a proportional effect (higher variability in high-valued areas), and the asymmetry in the spatial correlation of the indicator variables with respect to the median threshold. Then, we provide examples of stationary random functions with such bivariate distributions, for which the shape parameter of the marginal distribution is half an integer. These are defined as the sum of squared independent Gaussian random fields. An iterative algorithm based on the Gibbs sampler is proposed to perform the simulation conditional to a set of existing data. Such ‘multivariate chi-square’ model generalizes the well-known multigaussian model and is more flexible, since it allows defining a shape parameter which controls the asymmetry of the marginal and bivariate distributions.     

Compositional Scalar-on-Function Regression with Application to Sediment Particle Size Distributions

Mathematical Geosciences - The chemical composition of sediments is controlled predominantly by the sediment grain size, and thus evaluating their relationship is an important task in sedimentary...     

Improving Sequential Simulation with a Structured Path Guided by Information Content

Multiple-point simulation is a newly developed geostatistical method that aims at combining the strengths of two mainstream geostatistical methods: object-based and pixel-based methods. It maintains the flexibility of pixel-based algorithms in data conditioning, while enhancing its capability of reproducing realistic geological shapes, which is traditionally reserved to object-based algorithms. However, the current snesim program for multiple-point simulation has difficulty in reproducing large-scale structures, which have a significant impact on the flow response. To address this problem, we propose to simulate along a structured path based on an information content measure. This structured path accounts for not only the information from the data, but also some prior structural information provided by geological knowledge. Various case studies show a better reproduction of large-scale structures. This concept of simulating along a structured path guided by information content can be applied to any sequential simulation algorithms, including traditional variogram-based two-point geostatistical algorithms.     

考虑起动概率的无粘性均匀沙起动条件

根据无粘性均匀沙起动的力学条件,在已有研究成果基础上,推导出泥沙起动概率与水流条件之间的关系式,得到考虑起动概率的起动切应力及起动流速公式,并将起动条件与起动标准联系分析.通过对现有几个典型无粘性均匀沙起动条件公式分析表明,本文公式较为合理.     

Analysis of Blast Wave Interaction with a Rock Joint

The interaction between rock joints and blast waves is crucial in rock engineering when rock mass is suffered from artificial or accidental explosions, bursts or weapon attacks. Based on the conservation of momentum at the wave fronts and the displacement discontinuity method, quantitative analysis for the interaction between obliquely incident P- or S-blast wave and a linear elastic rock joint is carried out in the present study, so as to deduce a wave propagation equation. For some special cases, such as normal or tangential incidence, rigid or weak joint, the analytical solution of the stress wave interaction with a rock joint is obtained by simplifying the wave propagation equation. By verification, it is found that the transmission and reflection coefficients from the wave propagation equation agree very well with the existing results. Parametric studies are then conducted to evaluate the effects of the joint stiffness and incident waves on wave transmission and reflection. The wave propagation equation derived in the present study can be straightforwardly extended for different incident waveforms and nonlinear rock joints to calculate the transmitted and reflected waves without mathematical methods such as the Fourier and inverse Fourier transforms.