High-order Statistics of Spatial Random Fields: Exploring Spatial Cumulants for Modeling Complex Non-Gaussian and Non-linear Phenomena

The spatial distributions of earth science and engineering phenomena under study are currently predicted from finite measurements and second-order geostatistical models. The latter models can be limiting, as geological systems are highly complex, non-Gaussian, and exhibit non-linear patterns of spatial connectivity. Non-linear and non-Gaussian high-order geostatistics based on spatial connectivity measures, namely spatial cumulants, are proposed as a new alternative modeling framework for spatial data. This framework has two parts. The first part is the definition, properties, and inference of spatial cumulants—including understanding the interrelation of cumulant characteristics with the in-situ behavior of geological entities or processes, as examined in this paper. The second part is the research on a random field model for simulation based on its high-order spatial cumulants. Mathematical definitions of non-Gaussian spatial random functions and their high-order spatial statistics are presented herein, stressing the notion of spatial cumulants. The calculation of spatial cumulants with spatial templates follows, including anisotropic experimental cumulants. Several examples of two- and three-dimensional images, including a diamond bearing kimberlite pipe from the Ekati Mine in Canada, are analyzed to assess the relations between cumulants and the spatial behavior of geological processes. Spatial cumulants of orders three to five are shown to capture directional multiple-point periodicity, connectivity including connectivity of extreme values, and spatial architecture. In addition, they provide substantial information on geometric characteristics and anisotropy of geological patterns. It is further shown that effects of complex spatial patterns are seen even if only subsets of all cumulant templates are computed. Compared to second-order statistics, cumulant maps are found to include a wealth of additional information from underlying geological patterns. Further work seeks to integrate this information in the predictive capabilities of a random field model.     

Modeling and Fitting of Three-Dimensional Mineral Microstructures by Multinary Random Fields

Mathematical Geosciences - Modeling a mineral microstructure accurately in three dimensions can render realistic mineralogical patterns which can be used for three-dimensional processing...     

Complex-Valued Random Fields for Vectorial Data: Estimating and Modeling Aspects

Complex-valued random fields represent a natural extension of real-valued random fields and can be useful for modeling vectorial data in two dimensions (i.e., a wind field). In such a case, some theoretical issues arise concerning generating and fitting complex covariance functions to be used for prediction purposes. In this paper, some general aspects and properties of complex-valued random fields are summarized and a procedure to fit complex stationary covariance functions is proposed. A case study for analyzing wind speed data is presented.     

A Class of Variogram Matrices for Vector Random Fields in Space and/or Time

This paper studies vector (multivariate, multiple, or multidimensional) random fields in space and/or time with second-order increments, for which the variogram matrix is an important tool to measure the dependence within each component and between each pair of distinct components. We introduce an efficient approach to construct Gaussian or non-Gaussian vector random fields from the univariate random field with higher dimensional index domain, and particularly to generate a class of variogram matrices.     

Equatorial Currents in the Indian Ocean Based on Measurements in February 2017

We analyze the results of measurements of the Tareev equatorial undercurrent in the Indian Ocean in February 2017. Sections from 3° S to 3°45′ N along 68° and 65° E crossed the current with measurements of the temperature, salinity, and current velocity at oceanographic stations. The maximum velocity of this eastward flow was recorded precisely at the equator. The velocity at a depth of 50 m was approximately 60 cm/s. The transport of the Tareev Current was estimated at 9.8 Sv (1 Sv = 10⁶ m³/s).     

寒区高等级公路宽幅路基的随机温度场

寒区高等级公路宽幅路面比普通路面吸热面积更大,增加了保证路基稳定性的难度.在对其进行路基温度场的稳定性分析时,传统的有限元方法都是进行确定性分析,没有考虑到边界条件等因素的随机性、变异性,因此不能得知以上随机因素引起温度场的变幅.采用随机有限元法,由温度场的变分原理,通过摄动法建立随机温度场,从而得到随机温度场的有限元格式,理论公式可广泛适用于其他工程随机温度场问题. 将宽幅路基气温边界条件参数设为随机变量,考虑升温效应,对寒区宽幅路基温度场进行计算,分析了温度场均值和方差的分布规律.结果表明：宽幅路基中部聚热效应明显,路基下部出现厚度不均匀的融化盘,可能造成路基不均匀沉降;边界条件的随机性造成温度场方差分布呈明显的边界效应,即越靠近路基上边界温度场方差越大,在一定深度以下趋于零.此外,不论是路基下出现的融化盘,还是温度场方差分布下边界都将随时间增长而扩大.     

含直立裂隙介质的弹性波动方程正演模拟

从具有水平对称轴的横向各向同性（HTI）介质中的弹性波动方程出发,在交错网格空间中采用高阶差分算子对弹性波动方程进行差分离散,得到了HTI介质中地震波正演的高阶有限差分格式,研究并实现了PML吸收边界条件。在此基础上实现了HTI介质中弹性波方程的多波正演。数值算例表明,该方法能够精确模拟弹性波在复杂各向异性介质中的传播过程,得到高精度的正演记录。     

全拖曳式深海直流电阻率法三维任意各向异性正演模拟

高精度、高效率的深海勘探是当前国家海洋资源勘探开发的研究热点之一,设计观测效率高、勘探成本低的探测方式,开发可精确计算海底复杂电性环境的正演模拟算法有助于推进该研究的进展。本文基于前人的研究经验,引入了全拖曳式深海直流电阻率观测方式,同时考虑到海底沉积环境的电各向异性,开发了基于非结构有限元方法的三维任意各向异性深海直流电阻率正演算法,实现了对海底任意电各向异性情况的仿真模拟。本文算法与层状一维模型半解析解的对比验证了算法的精度。对典型各向异性电性模型的仿真模拟和分析,证明了全拖曳式深海探测方式对海底沉积层和矿产资源电各向异性的高分辨率。在此基础上,总结了电导率各向异性主轴沿笛卡尔坐标旋转时视电阻率分布也发生同方向旋转的视电阻率分布特征,并根据海底地形对各向异性探测的影响进行了简单探讨。     

Numerical Modeling of Hydraulic Fractures Interaction in Complex Naturally Fractured Formations

A recently developed unconventional fracture model (UFM) is able to simulate complex fracture network propagation in a formation with pre-existing natural fractures. A method for computing the stress shadow from fracture branches in a complex hydraulic fracture network (HFN) based on an enhanced 2D displacement discontinuity method with correction for finite fracture height is implemented in UFM and is presented in detail including approach validation and examples. The influence of stress shadow effect from the HFN generated at previous treatment stage on the HFN propagation and shape at new stage is also discussed.     

A Mathematical View of Weights-of-Evidence,Conditional Independence,and Logistic Regression in Terms of Markov Random Fields

New light is shed on mathematical methods of potential modeling from the point of view of Markov random fields. In particular, weights-of-evidence and logistic regression models are discussed in terms of graphical models possessing Markov properties, where the notion of conditional independence is essential, and will be related to log-linear models. While weights-of-evidence with respect to indicator predictor variables and logistic regression with unrestricted predictor variables model conditional probabilities of an indicator random target variable, the subject of log-linear models is the joint probability of random variables. The relationship to log-linear models leads to a likelihood ratio test of conditional independence, rendering an omnibus test of conditional independence restricted by a normality assumption obsolete. Moreover, it reveals a hierarchy of methods comprising weights-of-evidence, logistic regression without interaction terms, and logistic regression including interaction terms, where each former method is a special case of the consecutive latter method. The assumptions of conditional independence of all predictor variables given the target variable lead to logistic regression without interaction terms. Violations of conditional independence are compensated exactly by corresponding interaction terms, no cumbersome approximate corrections are needed. Thus, including interaction terms into logistic regression models is an appropriate means to account for lacking conditional independence. Logistic regression exempts from the burden to worry about lack of conditional independence. Eventually, the relationship to log-linear models renders logistic regression with indicator predictor variables optimum for discrete predictor variables. Weights-of-evidence applies for indicator predictor variables only, logistic regression applies without restrictions of the type of predictor variables and approximates the proper distribution in the general case.     

电磁波场数值计算中时间域有限差分法与时间域伪谱法的对比研究

为提高电磁波场数值计算精度,对时间域有限差分法与时间域伪谱法进行了对比研究。时间域有限差分法是一种目前流行的电磁场时域数值计算方法,已被广泛应用于求解与时间有关的偏导数方程。对于大规模数值计算,时间域有限差分法需要较多的内存空间。时间域伪谱法基于时间域有限差分法,该方法使用快速傅里叶度换来计算麦克斯韦方程中的空间导数。由于傅里叶变换的准确性,时间域伪谱法使计算精度提高,数值计算时所需的格子数大大减少,这极大地节省了计算机内存空间,适合于大规模正反演问题的数值计算。     

Forward and Inverse Problems in Modeling of Multiphase Flow and Transport Through Porous Media

The paper deals with numerical simulation techniques for forward and inverse modelling in multiphase (multicomponent) flow through porous media. The forward simulation software system MUFTE-UG uses recent discretization techniques and fast solvers. The efficient integration of optimization strategies for the solution of the inverse problems is demonstrated in detail and also applied to practical numerical examples.     

Generative Adversarial Network Applied to Ore Type Modeling in Complex Geological Environments

Mathematical Geosciences - In complex geological environments, the spatial domain characterization of different ore types has been one of the most important challenges in the assessment of mineral...     

基于随机森林建模预测河套盆地高砷地下水风险分布

河套盆地浅层地下水砷污染严重,对当地居民健康造成严重影响。当前对河套盆地浅层地下水高砷分布的研究受限于采样时间和样本数量,难以从宏观角度对河套盆地高砷地下水的空间分布作出较为全面的评价。本文基于研究区506个浅层地下水样品,以9个地表环境参数为初始预测变量,经过最佳变量组合筛选,采用随机森林建模来产生风险概率,评价了预测变量的重要性以及对高砷地下水的影响。以气候因子为动态预测变量,根据模型识别不同季节地下水高砷的概率分布并制作了风险区专题图。结果表明：研究区的地下水样品砷含量为0.05~916.7μg/L,超标率（砷浓度>10μg/L）为50%;地下水高砷风险区主要分布在河套盆地的沉积中心地带,但冬季高砷风险区面积减少1907km2,占研究区总面积14.14%;降水、干旱指数、排灌渠影响、潜在蒸散、温度是影响高砷地下水最重要的指标。研究认为,河套盆地的气候变量（降水、干旱指数）与含水层砷含量显著相关,控制高砷地下水在河套盆地的沉积中心地带发生季节性变化。     

Sampling Strategies for Uncertainty Reduction in Categorical Random Fields: Formulation,Mathematical Analysis and Application to Multiple-Point Simulations

Mathematical Geosciences - The task of optimal sampling for the statistical simulation of a discrete random field is addressed from the perspective of minimizing the posterior uncertainty of...     

Limitations of Lattice Boltzmann Modeling of Micro‐Flows in Complex Nanopores

The multiscale transport mechanism of methane in unconventional reservoirs is dominated by slip and transition flows resulting from the ultra-low permeability of micro/nano-scale pores, which requires consideration of the microscale and rarefaction effects. Traditional continuum-based computational fluid dynamics (CFD) becomes problematic when modeling micro-gaseous flow in these multiscale pore networks because of its disadvantages in the treatment of cases with a complicated boundary. As an alternative, the lattice Boltzmann method (LBM), a special discrete form of the Boltzmann equation, has been widely applied to model the multi-scale and multi-mechanism flows in unconventional reservoirs, considering its mesoscopic nature and advantages in simulating gas flows in complex porous media. Consequently, numerous LBM models and slip boundary schemes have been proposed and reported in the literature. This study investigates the predominately reported LBM models and kinetic boundary schemes. The results of these LBM models systematically compare to existing experimental results, analytical solutions of Navier-Stokes, solutions of the Boltzmann equation, direct simulation of Monte Carlo (DSMC) and information-preservation DSMC (IP_DSMC) results, as well as the numerical results of the linearized Boltzmann equation by the discrete velocity method (DVM). The results point out the challenges and limitations of existing multiple-relaxation-times LBM models in predicting micro-gaseous flow in unconventional reservoirs.     

Adsorption of Heavy Metal Cations by Base Metal Sulfides in the Broken Spur and TAG Hydrothermal Fields,Atlantic Ocean

Data on the mineral and chemical composition of samples of sulfide deposits from the Broken Spur and TAG (Mid-Atlantic Ridge) are presented. The main minerals in the Broken Spur field are marcasite, pyrrhotite, pyrite, chalcopyrite, and sphalerite; in sample from TAG: chalcopyrite, pyrite, and marcasite. It has been established that these sulfide minerals of Fe, Cu, and Zn are natural ion exchangers and belong to the class of adsorbents. Exchange capacity of sulfide minerals in terms of heavy metal cations (Ni2+, Co2+, Cd2+, and Pb2+) is 0.022–0.32 mg-equiv/g. In the exchange reaction products, the mineral composition of sulfide deposits is retained, and new phases do not appear. It is suggested that the adsorbed heavy metal cations populate either vacant cationic or interstitial defect sites in the structures of sulfide minerals. Bond strength of the adsorbed heavy metal cations with the main structural elements of minerals is low, which is confirmed by their high extraction in an acid medium. The results of adsorption-desorption experiments indicate two forms of heavy metal cations in sulfide minerals: adsorbed (basic) and chemically bound.     

复杂河流相地层单砂体级沉积时间单元对比方法

采用“重点井沉积时间单元划分”—“标准层控制、参照层借鉴对比”—“切叠河流定界”—“平面井网对比”这一对比方法,可以很好地解决复杂河流相地层沉积时间单元精细对比的难题,采用该方法对大庆长坦喇嘛甸油田目的层301口开发井进行了沉积时间单元的划分与对比,在此基础上精细刻画了SⅢ各沉积时间单元单砂体的分布范围,把原来认为的大...     

The origin of the Pailin Crystalline Complex in western Cambodia,and back-arc basin development in the Paleo-Tethys Ocean

The Pailin Crystalline Complex, which consists of amphibolites, metagabbros, and felsic igneous rocks, is located in western Cambodia. We used the geochemistry of the amphibolites and the zircon UPb ages of felsic igneous rocks to constrain the origin of the Pailin Crystalline Complex and to gain insights into the tectonic framework of Southeast Asia. Geochemical analyses indicate that the amphibolites are normal (N-type) mid-ocean ridge basalts, similar to the Sa Kaeo Back-arc Basin basalts of southeastern Thailand. The zircon UPb ages are 283 ± 2 Ma (anorthosite dike), 280 ± 2 Ma (aplite dike), and 275 ± 2 Ma (plagiogranite). The geochemistry and detrital zircon UPb ages of sandstones adjacent to the Pailin Crystalline Complex suggest that they are sediments that filled the Sa Kaeo Back-arc Basin during the Triassic. We infer that the Pailin Crystalline Complex is part of a dismembered ophiolite related to the back-arc basin, and that the igneous rocks formed during the Early Permian. Most of the metamorphism occurred during continental collision in Southeast Asia. However, the amphibolites of the Pailin Crystalline Complex also experienced ocean-floor metamorphism at a back-arc spreading center, in a tectonic setting similar to that of the mafic metamorphic rocks of the Nan Back-arc Basin, northern Thailand. We conclude that the Pailin Crystalline Complex is the southernmost extension of a back-arc basin related to subduction of Paleo-Tethys oceanic crust and the Sukhothai Arc.