A generalized principal components model in petrology

Principal components analysis of elemental distributions among minerals elucidate chemical, thermal, and equilibrium effects. Previous approaches in applying this multivariate statistical method to petrologic data are united into a single model, so-called three-mode principal components analysis. The major advantage of the model lies in the separate analysis of each of the three modes: element, mineral, and sample. The three sets of principal components are related through a “core matrix”. The model accommodates the ordination of pair-wise combination of the modes, such as samples and minerals in visualization of multidimensional tie-lines. Because of its generality, the model permits great flexibility in the study of petrologic data.     

Editorial: The Future of Mathematical Geology

Mathematical Geosciences -     

Editorial

Mathematical Geosciences -     

储集层非均质性分析的计算机方法:以西弗吉尼亚州下密西西比系油田为例

本文使用几种计算法和统计法研究美国西弗吉尼亚洲中部格兰尼克里克油田大Ｉｎｊｕｎ砂岩储集层的结构及其与采油量的关系。计算机程序根据已出版的资料编写，以适合（ｌ）计算渗透率对孔隙度的回归；（２）标绘三维孔隙度；（３）确定和标绘根据地球物理测井记录推断的相；（４）估算原始储量、累积产量和采油率。因为回归分析显示出测井记录和岩心孔隙度及岩心渗透率间微弱但重要的相关，所以，孔隙度可用干地层渗透率中以构成储集层的模式。也使用定量地层对比和多维定算法来估算在缺乏可用数据的情况下构造的影响。于井间使用克里格法内插绘制的剖面，突出了孔隙度较高的地带。使用地球物理测井资料和岩心描述，用聚类分析确定导电相。原始储量的估算结果与累计产量数据相结合，得出采油率的估算值。这些采油量变量图通常呈现在岩相图上观察到的相同的南北走向。     

Principal components analysis of three-way tables

A three-mode principal components method allows visualization of the structural or taxonomic relationships within three-way data tables. The fundamental model includes three sets of eigenvectors and a core matrix relating the principal components of each mode. Formal relationships between the method and the usual principal components formulation allow calculation of loadings and scores for each mode; taken with the core matrix, these provide a number of points of view in graphical analysis of three-mode data. The model compares favorably with alternative formulations in terms of simplicity of computation, generality, and symmetry of operation among the modes. An organic geochemical example illustrates the method.     

Objective comparison of mass fragmentograms by principal components analysis: method and results

The multivariate statistical method of Principal Components Analysis is used to classify gas chromatographic-mass spectrometric data. The specific examples comprise sterane and triterpane regions of GC-MS analyses of branched/cyclic fractions. The statistical model provides an objective analogue to visual comparison and classification of mass fragmentograms. Sources of experimental error influencing the statistical results include insufficient sample size, short integration times, and peak skewing. The method successfully groups samples of oils, oil sand, and polluted beach sand according to geographic origin: beach sand groups with type of crude spilled; laboratory biodegraded and untreated Nigerian crudes group together. Applications of three-mode Principal Components Analysis can range from study of geologic processes acting on organic compounds to classification of unknown pollutants.