A New Differentiable Parameterization Based on Principal Component Analysis for the Low-Dimensional Representation of Complex Geological Models

A new approach based on principal component analysis (PCA) for the representation of complex geological models in terms of a small number of parameters is presented. The basis matrix required by the method is constructed from a set of prior geological realizations generated using a geostatistical algorithm. Unlike standard PCA-based methods, in which the high-dimensional model is constructed from a (small) set of parameters by simply performing a multiplication using the basis matrix, in this method the mapping is formulated as an optimization problem. This enables the inclusion of bound constraints and regularization, which are shown to be useful for capturing highly connected geological features and binary/bimodal (rather than Gaussian) property distributions. The approach, referred to as optimization-based PCA (O-PCA), is applied here mainly for binary-facies systems, in which case the requisite optimization problem is separable and convex. The analytical solution of the optimization problem, as well as the derivative of the model with respect to the parameters, is obtained analytically. It is shown that the O-PCA mapping can also be viewed as a post-processing of the standard PCA model. The O-PCA procedure is applied both to generate new (random) realizations and for gradient-based history matching. For the latter, two- and three-dimensional systems, involving channelized and deltaic-fan geological models, are considered. The O-PCA method is shown to perform very well for these history matching problems, and to provide models that capture the key sand–sand and sand–shale connectivities evident in the true model. Finally, the approach is extended to generate bimodal systems in which the properties of both facies are characterized by Gaussian distributions. MATLAB code with the O-PCA implementation, and examples demonstrating its use are provided online as Supplementary Materials.     

Integrating production data under uncertainty by parallel interacting Markov chains on a reduced dimensional space

In oil industry and subsurface hydrology, geostatistical models are often used to represent the porosity or the permeability field. In history matching of a geostatistical reservoir model, we attempt to find multiple realizations that are conditional to dynamic data and representative of the model uncertainty space. A relevant way to simulate the conditioned realizations is by generating Monte Carlo Markov chains (MCMC). The huge dimensions (number of parameters) of the model and the computational cost of each iteration are two important pitfalls for the use of MCMC. In practice, we have to stop the chain far before it has browsed the whole support of the posterior probability density function. Furthermore, as the relationship between the production data and the random field is highly nonlinear, the posterior can be strongly multimodal and the chain may stay stuck in one of the modes. In this work, we propose a methodology to enhance the sampling properties of classical single MCMC in history matching. We first show how to reduce the dimension of the problem by using a truncated Karhunen–Loève expansion of the random field of interest and assess the number of components to be kept. Then, we show how we can improve the mixing properties of MCMC, without increasing the global computational cost, by using parallel interacting Markov Chains. Finally, we show the encouraging results obtained when applying the method to a synthetic history matching case.     

求解大样本核主成分分析模型的Lanczos算法

求解核主成分分析模型的技术关键是确定核矩阵端部的较大特征对。把求解大规模对称矩阵端部特征对问题的基本方法--Lanczos算法应用于核主成分分析模型的求解,设计了大样本核主成分分析模型求解的实用算法。在clapack和nu TRLan两个软件包的基础上,开发了大样本核主成分分析模型求解算法的VC++程序。用高光谱遥感图像数据进行模型求解算法的应用试验研究,证明了大样本核主成分分析模型求解算法的实用性。     

基于主成分分析的致密砂砾岩孔隙度测井评价方法

岩性识别是致密砂砾岩测井评价的重要工作。砂砾岩岩性多样、成分复杂,导致测井识别岩性准确率低、测井解释孔隙度不准确。以东营凹陷北部陡坡带沙四下亚段致密砂砾岩为例,在对其岩石学特征分析的基础上,按照岩石类型和骨架矿物差异给砂砾岩分类,利用铸体薄片资料对测井曲线进行岩性标定,提取各种岩性的测井响应特征,在此基础上建立了基于主成分分析的测井岩性识别方法,并分岩性建立了孔隙度测井评价模型,提高了砂砾岩测井岩性识别和测井孔隙度计算的准确率。     

稳健主成分分析在地震资料异常值噪声压制中的应用

提高地震数据的信噪比是地震资料处理的重要目标之一。传统的地震去噪方法虽然可以有效压制随机噪声,但对非高斯分布的异常值噪声压制效果欠佳。本研究展示了一种基于稳健主成分分析的地震数据异常值噪声压制方法。该方法在频率-空间域通过对地震数据实施稳健低秩近似来求取理想无噪声数据。在目标函数构建方面,采用核范数最小化模型求取理想的低秩近似数据,并使用l₁范数最小化模型来估计异常值噪声。此外,运用增广拉格朗日乘子法求解该反演问题。最后,模型数据和实际资料的去噪结果验证了本研究方法的有效性,与传统F-XY域预测滤波法去噪结果进行对比,也显示本研究方法在有效压制异常值噪声的同时能更好地保护有效波能量。     

Instability in Principal Component Analysis and the Quantification of Polyphenism in Palaeontological Data

The occurrence of cryptic polyphenism (variation in morphological properties within a single species) in ammonites is used to exemplify the application of the multivariate set of techniques known in analytical chemistry as cross-validation to quantify and isolate deviating specimens (ecomorphs) in a genetically homogeneous sample. A byproduct of the analysis bears on a method of identifying redundant variables. A species of Nigerian Turonian (Cretaceous) ammonites of the genus Thomasites is used in the exemplification.     

雅鲁藏布江流域水文分区研究

青藏高原水系众多,水文站点稀疏,观测资料匮乏,通过水文分区可以将相似流域归为一类,实现其有限测站水文资料向无资料区移用以及达到站网优化设置的目标。以雅鲁藏布江流域(以下简称雅江)为研究对象,利用气象资料和反映下垫面条件的土地利用和地形等物理因子,采用主成分分析、K-Means聚类分析等方法对雅江进行水文分区研究。研究中,根据气候和地形的垂直特征,将雅江划分为5个水文分区,分别为高寒荒漠区、高原温带河谷区、高原峡谷稀林区、高原冰川雨雪区和亚热带山地多雨区,并阐述了各分区的特征。最后,采用斯米尔诺夫检验的方法,选取具有长序列水文资料的站点进行检验,论证了分区结果的合理性。此项成果可为雅江无资料流域水文预测提供依据。     

基于核主成分支持向量机的火成岩QAPF分类——以青海格尔木地区为例

利用核主成分(KPCA)较强的非线性特征提取能力对Hyperion高光谱数据进行降维及光谱特征提取,将特征信息作为支持向量机(SVM)建模样本的观测数据,建立KPCA-SVM回归模型,利用该模型进行研究区岩石氧化物百分含量反演。同时,依据国际地质科学联合会提出的QAPF火成岩分类方案对区内火成岩进行了岩性划分。研究结果表明:KPCA降维后的高光谱数据反演氧化物含量的效果良好;而基于QAPF模型的火成岩划分结果也十分理想,分类结果对已有地质图进行了有效的补充。KPCA-SVM理论模型为利用高光谱遥感数据进行岩性分类提供了一种快速可行的方法。     

基于层次聚类法和主成分分析法的铜陵市大气降尘污染元素来源解析研究

本文采用层次聚类法和主成分分析法对有色金属矿山城市-铜陵市的大气降尘中污染元素,主要是重金属元素的来源进行了识别,并分析了各来源所占的比例。结果显示,铜陵市大气降尘中污染物主要来源于冶金和采矿,其次为燃煤、交通和土壤扬尘等,其贡献率分别为冶金源+采矿源43.29%,燃煤源32.23%,交通源和土壤源10.53%,其他源13.94%。因此,优先控制冶金尘、采矿尘和燃煤尘,可以有效降低铜陵市大气降尘中污染元素的含量。     

主成分分析在地质样品分类与浓度预测中的应用研究

用主成分分析方法研究地质样品的Ｘ荧光光谱强度与浓度的关系,对未知样分类并预测样品浓度。对标准化后的数据计算各样品的主成分得分,根据得分分布图可快速分类样品。对训练样品作主成分回归分析,建立降维的主成分回归模型,用主元回归预测各组分浓度,效果好于多元回归分析方法。     

Identification of Anthropogenic Features Through Application of Principal Component Analysis to Hydrochemical Data from the Sines Coastal Aquifer, SW Portugal

The Sines coastal sedimentary basin, a tectonic trough with a NE-SW orientation filled with Mesozoic and Cenozoic deposits, has two hydrogeological systems: the Mio-Pliocene and the Jurassic. Both systems are supplying water to the entire region with highly populated and industrialized areas. The aquifers are recharged in the outcrop areas, although the Jurassic aquifer also receives some contribution from the overlying Miocene rocks. The main groundwater flow direction in the Jurassic aquifer is E to W towards the Atlantic Ocean. In order to understand the influence of anthropogenic activities on the water quality, a statistical principal components analysis (PCA) was performed on the physical–chemical data from groundwater samples in both aquifers. Four components were obtained in the Jurassic and three in the Miocene. The principal components analyses indicate water–rock interactions as the major mechanism responsible for the groundwater solutes (mainly calcium-bicarbonate type), from the calcareous and dolomitic units. Anthropogenic contamination was identified in the influence of the water compositions, corresponding to local polluting inputs. These were magnesium, sulfate, nitrate, iron and copper for PC 3 in the Jurassic and sodium, chloride, nitrate and manganese for PC 2 in the Miocene. These account for about 13% of the system total variance in the Jurassic aquifer and near 23% in the Miocene one.     

基于主成分和模糊C-均值聚类算法的农业水资源高效利用综合分区

基于农业生态系统环境要素、水的资源属性、水资源的高效利用内涵、生产力水平、土地利用方式、种植结构及种植模式等因子,选取构建农业水资源高效利用综合分区的指标体系(16个定量指标、4个定性指标),采用主成分分析和模糊C-均值聚类算法为区划方法,对川中丘陵区进行量化分区。研究结果将川中丘陵区16个地级市和一个县级市(简阳)分为农业水资源较低利用区、农业水资源低效利用区、农业水资源中等利用区、农业水资源高效利用区和农业水资源较高效利用区5个区,这对南方季节性干旱区水资源利用规划有较强的借鉴作用。     

基于主成分分析和贝叶斯正则化方法的神经网络年最大洪峰流量预测模型探讨

针时水文预测建模中输入因子过多而导致神经网络结构规模过大,泛化能力差的问题,利用主成分分析和贝叶斯正则化方法对神经网络进行改进,优化网络结构,从而提高泛化能力。以洮儿河流域镇西站年最大洪峰流量预测为例,研究结果表明,改进的神经网络预测方法与传统的神经网络方法相比,泛化能力有显著提高,而且网络的收敛也比较稳定,实际预测中效果良好。     

基于主成分分析和BP神经网络的五道沟水面蒸发计算研究

针为探讨五道沟水面蒸发量与气象因子间的关系,准确估算该地区水面蒸发量,选取五道沟1991—2019年水面蒸发量以及气象因子实测资料,基于主成分法分析水面蒸发量的影响因素,并结合BP人工神经网络算法建立了水面蒸发计算模型.结果表明:主成分分析提取了三个主成分,第一主成分为地表温度、饱和差、绝对湿度、平均气温以及水汽压力差...     

Application of Principal Component Analysis and Spectral Angle Mapper in the Mapping of Hydrothermal Alteration in the Jebal–Barez Area,Southeastern Iran

The southeastern part of the central Iranian Cenozoic magmatic belt contains many areas with copper mineralization. In an analysis of this region, we used the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) and Enhanced Thematic Mapper plus (ETM⁺) images to map the distribution of hydrothermally altered rocks, based on their mineral assemblages. The spectral measurements, based on the field samples and satellite‐image‐derived spectra, show dominantly Al–OH (sericite and clays) and Fe–O absorption features in the visible–near infrared to shortwave infrared regions of the spectrum. Silica–bearing rocks, as well as silicic alteration, show an intense Si–O vibrational feature in the thermal infrared wavelength region. We analyzed ASTER/ETM⁺ images, performed a directed principal component analysis, and used spectral angle mapper to map areas of hydrothermal alteration and iron oxide/hydroxide minerals. The individual principal component images compiled by directed principal component analysis reveal the distribution of individual alteration minerals such as sericite, kaolinite, chlorite, epidote, and quartz. The best results, in terms of mapping the distribution of alteration, were obtained using the spectral angle mapper method. The altered areas were then sampled and the samples subjected to X–ray diffraction analysis, spectral analysis, and thin sections were observed under a microscope. Field observations reveal that more than 98% of the known copper mineralization occurs within the interpreted alteration areas. The present results indicate the great potential of ASTER and ETM⁺ data for mapping the distribution of alteration and exploring for copper mineralization in areas with a similar climate and geological setting to those of the present study.     

Principal component analysis and hierarchical cluster analyses of arsenic groundwater geochemistry in the Hetao basin,Inner Mongolia

Although high As groundwater has been observed in shallow groundwater of the Hetao basin, little is known about As distribution in deep groundwater. Quantitative investigations into relationships among chemical properties and among samples in different areas were carried out. Ninety groundwater samples were collected from deep aquifers of the northwest of the basin. Twenty-two physicochemical parameters were obtained for each sample. Statistical methods, including principal component analysis (PCA) and hierarchical cluster analysis (HCA), were used to analyze those data. Results show that As species were highly correlated with Fe species, NH₄-N and pH. Furthermore, result of PCA indicates that high As groundwater was controlled by geological, reducing and oxic factors. The samples are classified into three clusters in HCA, which corresponded to the alluvial fans, the distal zone and the flat plain. Moreover, the combination of PCA with HCA shows the different dominant factors in different areas. In the alluvial fans, groundwater is influenced by oxic factors, and low As concentrations are observed. In the distal zone, groundwater is under suboxic conditions, which is dominated by reducing and geological factors. In the flat plain, groundwater is characterized by reducing conditions and high As concentrations, which is dominated by the reducing factor. This investigations indicate that deep groundwater in the alluvial fans mostly contains low As concentrations but high NO₃ and U concentrations, and needs to be carefully checked prior to being used for drinking water sources.     

Hydrogeochemical evolution of groundwater in a Mediterranean coastal aquifer, Mersin-Erdemli basin (Turkey)

In this study, hydrogeologic and hydrochemical information from the Mersin-Erdemli groundwater system were integrated and used to determine the main factors and mechanisms controlling the chemistry of groundwaters in the area and anthropogenic factors presently affecting them. The PHREEQC geochemical modeling demonstrated that relatively few phases are required to derive water chemistry in the area. In a broad sense, the reactions responsible for the hydrochemical evolution in the area fall into four categories: (1) silicate weathering reactions; (2) dissolution of salts; (3) precipitation of calcite, amorphous silica and kaolinite; (4) ion exchange. As determined by multivariate statistical analysis, anthropogenic factors show seasonality in the area where most contaminated waters related to fertilizer and fungicide applications that occur during early summer season.     

基于主成分分析法与Bayes判别法组合应用的火山岩岩性定量识别:以渤海海域中生界为例

渤海海域中生界火山岩岩石类型复杂多样,且同一岩性受岩石成分、结构差异的影响,因此岩石物理响应特征存在较大差异,为岩性识别增加了难度。本文通过对研究区大量取心资料、壁心资料以及薄片资料的岩电分析,优选出对岩性响应敏感的自然伽马(GR)、补偿中子(CNL)、密度(DEN)、声波时差(AC)以及原状地层电阻率(Rd)等5条曲线。基于主成分分析法,构建了F_1—F_5共5个综合变量,其中F_1和F_2方差贡献率占总贡献率的81.4%,可作为两个主成分有效地反映5个变量的信息。针对主成分信息,利用Bayes判别法,构建了不同岩性的定量解释模型,对研究区9种火山岩进行了岩性识别。对取心井段的回判结果显示,基于主成分分析与Bayes判别的联合识别方法较常规交会图法在岩石成分及结构的识别精度方面均有较大程度的提高。该方法的提出对研究区成像测井、元素测井资料缺少井段的火山岩岩性识别具有重要借鉴作用。     

Metal sources of the Navan carbonate-hosted base metal deposit, Ireland: Nd and Sr isotope evidence for deep hydrothermal convection

Nd and Sr isotope analyses are presented for gangue mineral samples from the giant carbonate-hosted Navan Zn–Pb deposit, Ireland, and for rocks from which Navan metals may have been derived. Analysis of gangue minerals spanning the Navan paragenetic sequence reveals systematic evolution in the composition of the mineralising fluid. Early fluid represented by replacive dolomite exhibits the lowest initial ⁸⁷Sr/⁸⁶Sr ratio (0.7083–0.7086), closest to that of the host limestone and to Lower Carboniferous seawater, and the highest ¹⁴³Nd/¹⁴⁴Nd ratio (0.51161–0.51176). Later generations of dolomite, barite and calcite, which encompass sulphide precipitation, have higher initial ⁸⁷Sr/⁸⁶Sr ratios (maximum 0.7105) and lower initial ¹⁴³Nd/¹⁴⁴Nd ratios (minimum 0.51157). All samples have initial Nd isotope ratios that are too low to have been acquired only from the host limestone. Drill core samples of presumed Ordovician volcanic and sedimentary rocks from beneath the Navan orebody have ¹⁴³Nd/¹⁴⁴Nd and ⁸⁷Sr/⁸⁶Sr ratios at the time of mineralisation of 0.51184–0.51217 and 0.7086–0.7138, respectively. The data are interpreted to indicate mixing of sulphide-rich, limestone-buffered brine, with a metal-bearing hydrothermal fluid, which had passed through sub-Carboniferous rocks, consistent with published fluid inclusion and S isotope data. The ¹⁴³Nd/¹⁴⁴Nd ratio of this basement-derived fluid is too low to have been imparted by flow through the Devonian Old Red Sandstone, as required in models of regional fluid flow in response to Hercynian uplift. Irrespective of whether such regional fluid flow occurred, the hydrothermal Nd must have been derived from sub-Devonian rocks. These conclusions broadly support the hydrothermal convection cell model in which brines, ultimately of surface origin, penetrated to a depth of several kilometres, leaching metals from the rocks through which they passed. The data also support increasing depth of penetration of convection cells with time. Metals were subsequently precipitated in carbonate rocks at sites of mixing with cooler, sulphide-rich fluids. However, comparison of the Navan hydrothermal gangue Nd–Sr isotope data with data from Lower Palaeozoic rocks strongly suggests that the latter cannot alone account for the “basement” signature. As the Navan deposit lies immediately north of the Iapetus Suture, this suggests that the Laurentian margin includes Precambrian basement.     

U–Pb zircon and Re–Os molybdenite geochronology from La Caridad porphyry copper deposit: insights for the duration of magmatism and mineralization in the Nacozari District, Sonora, Mexico

Uranium–lead zircon (laser ablation multi-collector ICP-MS spot analysis) ages from La Caridad porphyry copper deposit in the Nacozari District, Northeastern Sonora, Mexico, suggest a short period of magmatism, between 55.5 and 52.6 Ma. Two U–Pb ages from the mineralized quartz monzonite unit, showing different textural characteristics, yielded indistinguishable crystallization ages (~54 Ma), and indicate that the intrusion responsible for the mineralization occurred as a single large complex unit, instead of multiple pulses of magmatism. Some zircons analyzed also show inherited ages in cores recording dates of 112–124 Ma, 141–166 Ma and 1.4 Ga. The Re–Os molybdenite ages from the potassic and phyllic hydrothermal alteration veins yielded identical ages within error, 53.6±0.3 Ma and 53.8±0.3 Ma, respectively (weighted average of 53.7±0.21 Ma), supporting a restricted period for the mineralization. The geochronological data thus indicate a short-lived magmatic and hydrothermal system. The inherited zircons of Precambrian and Late Jurassic-Mid Cretaceous age found in the intrusive rocks of La Caridad deposit, can be explained considering two possible scenarios within the tectonic/magmatic evolution of the area. The first scenario considers the presence of a Precambrian anorogenic granitic basement that is intruded by Mesozoic (Jurassic–Cretaceous) units present beneath the La Caridad deposit. The second scenario suggests that the Mesozoic Glance Conglomerate Formation of Arizona underlies the Paleocene volcanic-igneous pile in the La Caridad area.