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1.
Chemical variation diagrams formed from ratios with a common denominator exhibit induced correlations which can obscure the effects of true compositional variations. Nevertheless, important conclusions have been obtained using Pearce element ratio (and isochron) diagrams, even though these diagrams are formed from axes ratios with a common denominator. In this paper, we consider two approaches to mitigate the effects of induced correlation, and in doing so, demonstrate the validity of geochemical analysis using diagrams formed from ratios with a common denominator. First, we propagate analytical error onto Pearce element ratio diagrams to distinguish chemical variations associated with analytical error from chemical variations related to geological processes. Second, we consider an alternative diagram formed from ratios with different denominators which does not exhibit any induced correlation. We demonstrate both theoretically and by example that results produced using this diagram are identical to those using diagrams with a common denominator. These two lines of evidence confirm that Pearce element ratio (and isochron) diagrams are useful and valid tools in the analysis of geochemical variations.  相似文献   

2.
Analysis of petrologic hypotheses with Pearce element ratios   总被引：6，自引：0，他引：6  
Pearce element ratios can test whether the members of a rock suite are comagmatic and can illustrate the causes of chemical diversity in comagmatic suites. Comagmatic rocks have constant ratios for elements conserved in the system during changes that led to the chemical diversity. In basaltic systems, the incompatible elements, Ti, K, and P, are often conserved. The slope of the trend on a Pearce element ratio diagram is sensitive to the stoichiometry of the crystallizing and segregating phases. A judicious choice of ratios as axes for the diagram provides a signature for the phases involved and estimates of their compositions. In basaltic rocks, diagrams with Ti/K vs P/K can provide a test of the comagmatic hypothesis. Diagrams with 0.5 [Mg + Fe]/K vs Si/K have trends that are distinct for each comagmatic suite and different mineral assemblage. Different suites are distinguished by the intercepts in diagrams, whereas mineral assemblages are recognized by the slopes of the trends. For example, if olivine is the sole crystallizing and segregating phase, the trend will have a slope of 1. Diagrams with [2Ca + Na]/K vs Al/K distinguish plagioclase from augite assemblages and, in conjunction with 0.5 [Mg + Fe]/K diagrams, unravel the crystallization sequences of suites that have suffered three phase crystallization and segregation. Analyses from the Uwekahuna laccolith, Kilauea, the 1955 and 1967–68 eruptions of Kilauea, Diamond Craters Volcanic Field, Oregon, and experimental data on MORB glasses provide illustrations of the interpretations that can be obtained from Pearce element ratios.  相似文献   

3.
Pearce element ratios (PER's) have conserved denominators which have not participated in the material transfer processes that cause chemical variations in rocks. Theoretically, there is no truly conserved element (constituent) which can be used as a PER denominator because in every material transfer process all constituents have non-zero concentrations in the phases that are being transferred. Thus, constituents used as denominators of PERs may have undergone at least a small amount of material transfer. This communication investigates the degree to which a non-conserved PER denominator changes the trend of data produced by a material transfer process from that produced by the same process but plotted on a PER diagram with a truly conserved denominator. An equation is developed that utilizes the partition coefficient as the measure of the degree of involvement of the denominator constituent in the phase undergoing transfer. This equation is examined to determine how the magnitude and direction of a PER diagram data trend change with increasing involvement of the denominator constituent in the transferring phase. A set of plagioclase fractionation examples are presented which use different elements as PER denominators and consider the effects that small amounts of these elements in the plagioclase structure will have on the data trend, as a function of the element partition coefficient between crystal and melt. Results demonstrate that the direction of change in slope of a material transfer data trend is a function of the initial relative magnitudes of the numerator constituents on the PER diagram. Additionally, if the amount of involvement of a PER denominator in a separating phase is very small relative to the amount of the numerator constituents in the separating phase, there is no significant change in the data trend caused by material transfer on a PER diagram. Moreover, if the denominator constituent substitutes for a numerator constituent in the phase undergoing transfer, the intercept of the trend of the data may not converge to zero when there is a large partition coefficient, as would be expected from theory. Thus, statistical tests to determine if a PER denominator is conserved, which evaluate whether the intercept is significantly different from zero, may not be very powerful because a large amount of denominator variation is necessary before the intercept of a data trend is forced through the origin, if at all.  相似文献   

4.
Geochemical data can be quantitatively modelled by means of Pearce diagrams. These are graphs of A/Z vs B/Z where A, B and Z are compositional abundances (e.g. wt.% SiO2, wt.% MgO, and ppm La) and Z has the additional property of having constant absolute abundance. In the terminology of igneous petrology, Z (the common denominator variable) could be an incompatible element. The numerators (A and B) may be complex algebraic combinations of elements, or even CIPW normative abundances. The utility of Pearce diagrams lies in the fact that slopes of data distributions equal the bulk AB ratio of minerals lost or gained from a suite of cogenetic rocks. There is no distortion because these plots correct for data closure. Terms of the form Ai·Z0/Zi (where Z0 is the abundance in a reference sample) remove the scaling to Ai caused by the abundance of a particular choice of Z. Subtraction of these terms for different samples (e.g. Ai·(Z0/Zi)-Aj· (Z0/Zj)) quantifies mineral losses and gains. Mathematical analysis shows that limited compatibility of the denominator variable is permitted. A bulk partition value (D) of 0.1 introduces an error of only 10% in values of Ai***-Z0/Zi, and 10° in slope-angle on Pearce diagrams over a crystallization interval of 50%. For D0.01 the error is minimal for a crystallization interval over 90%.  相似文献   

5.
Pearce element ratios (PERs, of Pearce 1968) express geochemical data in a form where variations in absolute compositions of an igneous suite can be evaluated. Generally the denominator value in the ratio is taken as a major element abundance, but it is argued here that Zr provides a more suitable choice. Zr remains incompatible in magmatic systems up to 68 wt.% SiO2 because zircon fractionation can be suppressed by high melt temperatures and increased volatile contents. The use of Zr thus permits PER modelling to be extended to much higher levels of silica than previously investigated. However, such systems are more complex than those just involving simple basaltic magmas. Besides fractionation, the processes of magma mixing, combined assimilation and fractional crystallization, and the initial degree of partial melting in the mantle source must also be considered. To distinguish and evaluate these processes a set of example suites are investigated from a complex synextensional calc-alkaline province in the western USA. Samples within most individual suites can be modelled by fractionation, however a significant trend orthogonal to the main fractionation vector is also apparent, and open system processes are inferred. Successful modelling is achieved on an inter-suite basis using diagrams with axis functions of ([4(Ca+Na)+0.5(Fe+Mg)]/Zr versus (Si+Al)/Zr). Potential open system evolution paths between mafic end members and crustal contaminants are also displayed and evaluated on these same diagrams. The encouraging results suggest that such PER diagrams may be employed as a versatile tool for investigating the systematics of related igneous suites over a wide area.  相似文献   

6.
A multivariate probability transformation between random variables, known as the Nataf transformation, is shown to be the appropriate transformation for multi-Gaussian kriging. It assumes a diagonal Jacobian matrix for the transformation of the random variables between the original space and the Gaussian space. This allows writing the probability transformation between the local conditional probability density function in the original space and the local conditional Gaussian probability density function in the Gaussian space as a ratio equal to the ratio of their respective marginal distributions. Under stationarity, the marginal distribution in the original space is modeled from the data histogram. The stationary marginal standard Gaussian distribution is obtained from the normal scores of the data and the local conditional Gaussian distribution is modeled from the kriging mean and kriging variance of the normal scores of the data. The equality of ratios of distributions has the same form as the Bayes’ rule and the assumption of stationarity of the data histogram can be re-interpreted as the gathering of the prior distribution. Multi-Gaussian kriging can be re-interpreted as an updating of the data histogram by a Gaussian likelihood. The Bayes’ rule allows for an even more general interpretation of spatial estimation in terms of equality for the ratio of the conditional distribution over the marginal distribution in the original data uncertainty space with the same ratio for a model of uncertainty with a distribution that can be modeled using the mean and variance from direct kriging of the original data values. It is based on the principle of conservation of probability ratio and no transformation is required. The local conditional distribution has a variance that is data dependent. When used in sequential simulation mode, it reproduces histogram and variogram of the data, thus providing a new approach for direct simulation in the original value space.  相似文献   

7.
杨蔚华  刘友梅 《沉积学报》1987,5(3):159-170
本文讨论了成矿随机性问题,强调成矿理论应建立在概率论思想的基础上。元素丰度的概率类型,取决于所处环境赋于它的地球化学性质:环境使其具滞呆性时,呈正态;具活泼性时为偏倚型。活泼性元素成矿后其概率分布为正偏倚型,可被分解为若干个正态,具高均值者伴有大的标准差。滞呆性元素成矿后概率分布为负偏倚型,所分解得的正态与活泼性元素的相反,具高均值者带有小的标准差。矿床的空间分布,受多阶段成矿和成矿因素的叠加控制,故不服从泊松律,而为负二项分布。  相似文献   

8.
The most commonly used tectonic discrimination diagrams for granites were introduced by Pearce et al. [Pearce, J.A., Harris, N.B.W., Tindle, A.G., 1984. Trace element discrimination diagrams for the tectonic interpretation of granitic rocks. J. Petrol. 25, 956–983.]. Since then, many studies have shown that some granites defy classification or their geochemical assignment does not fit with the geodynamic environment in which they are thought to have formed. In this paper we evaluate the performance of the Pearce et al. tectonic discrimination method, specifically, the most widely-used Rb-(Y + Nb) diagram, using a new data base of over 250 occurrences worldwide, the tectonic settings of which are fairly well known. We conclude that a correlation of geochemistry and tectonic position exists, but that ambiguities and misclassifications arise from one or both of the following factors. First, complex or polyphase orogeny can mix source rocks of different tectonic provenance. This is common in continental arcs and collisional settings, which can be closely associated in space and time with extensional regimes. Second, differentiation can produce compositional trends which cross field boundaries, especially the VAG to WPG boundary. One can minimize this problem by using less felsic, noncumulate members of cogenetic series.

We demonstrate the inherent weaknesses of trace element tectonic discrimination diagrams. Such diagrams are of little use if applied alone, but they can be valuable in combination with other methods such as dating and geologic assessment.  相似文献   


9.
Apollo和LP伽马射线谱仪获取了全月10种元素的分布图,通过已有的月岩以及陨石的化学成分数据,将伽马射线谱仪探测数据与这些数据融合,用Th-Fe-Mg三角图解定性的获得元素含量与岩石类型的相关性,同时通过以前融合的数据,获得了月海玄武岩、月陆斜长岩、KREEP岩和富镁岩的全月球表面岩石类型分布图。  相似文献   

10.
Intergrowth defects (intercalation of different structure types) are common in some rock-forming minerals and can be demonstrated to affect trace element distributions, especially when new crystallographic site types are introduced by the intercalated structure. Atoms that do not readily substitute into the host crystal may be incorporated within the intercalated structure. Trace element partitioning patterns, EPR data and mineral dislocation densities suggest that dislocations do not exercise primary control on the partitioning of compatible trace elements, but the effects of dislocations on incompatible elements may be important.Intergrowth defects in geologically important materials include disordered intergrowth structures in Sulfides and the stacking and chain-width disorder that is found in pyroxenes and amphiboles from a range of occurrences. Intergrowth defects may range from a few Ångstroms wide to optically resolvable size. It is important to evaluate their effects when interpreting geological trace element data.  相似文献   

11.
It is becoming increasingly important to determine probability distributions of combinations of random variables. Convolution is a technique by which the distribution of a sum of random variables can be determined. This paper presents some simplifications in order to reduce the numerical integrations and computer time. In addition, the method may be used with empirical nonanalytic distributions. While Monte Carlo methods are also appropriate for calculating the distribution, convolution can give at least as much accuracy as Monte Carlo methods with a reduction in computation. Two applications are presented: one approximates the distribution of percent sand in an area, and the other indicates a method of determining sample size when using the distribution of means to approximate normality.  相似文献   

12.
M.H. Dodson 《Lithos》1982,15(3):215-219
A general null hypothesis for isotope geochemistry states that the isotopic composition of an element is independent of its concentration or any other geochemical property of the population. ‘Spurious’ correlations between the ratios 87Sr/86Sr and 87Rb/86Sr (orRb/Sr), due to the common denominator effect, may be ruled out because they contradict this null hypothesis. Mixing processes may be regarded as geochemical counterparts of the common denominator effect. In geochronological systems which satisfy the basic assumptions of the Rb-Sr isochron method observed correlations between Sr isotope abundance and Sr concentration must be secondary to the direct causal dependence of 87Sr/86Sr upon Rb/Sr ratios.  相似文献   

13.
Zircon inclusions were separated from the five major rock-forming minerals of the Sherman Granite of southern Wyoming, in order to evaluate the degree of discordance as a possible function of host minerals. U-Th-Pb isotopic ratios were determined for two size fractions of zircon inclusions from each mineral, plus five size fractions from the bulk rock. Isotopic data from the inclusions have more than double the spread of data on a discordia obtained from the bulk sample, thereby yielding better-resolved concordia intercepts. However, isotopic ratios and morphologic characteristics indicate that the Pb/U systematics are complicated by inherited radiogenic lead. Although the data array cannot unequivocally be explained by the armoring process, the proposed methodology has succeeded in identifying groups of zircon with different isotopic characteristics. As such, this technique can be used to decipher complex geologic/isotopic histories and may be a useful addition to routine zircon geochronology.  相似文献   

14.
《Applied Geochemistry》2005,20(10):1857-1874
The authors investigated statistical distributions for concentrations of chemical elements from the National Geochemical Survey (NGS) database of the U.S. Geological Survey. At the time of this study, the NGS data set encompasses 48,544 stream sediment and soil samples from the conterminous United States analyzed by ICP-AES following a 4-acid near-total digestion. This report includes 27 elements: Al, Ca, Fe, K, Mg, Na, P, Ti, Ba, Ce, Co, Cr, Cu, Ga, La, Li, Mn, Nb, Nd, Ni, Pb, Sc, Sr, Th, V, Y and Zn. The goal and challenge for the statistical overview was to delineate chemical distributions in a complex, heterogeneous data set spanning a large geographic range (the conterminous United States), and many different geological provinces and rock types. After declustering to create a uniform spatial sample distribution with 16,511 samples, histograms and quantile–quantile (Q–Q) plots were employed to delineate subpopulations that have coherent chemical and mineral affinities.Probability groupings are discerned by changes in slope (kinks) on the plots. Major rock-forming elements, e.g., Al, Ca, K and Na, tend to display linear segments on normal Q–Q plots. These segments can commonly be linked to petrologic or mineralogical associations. For example, linear segments on K and Na plots reflect dilution of clay minerals by quartz sand (low in K and Na). Minor and trace element relationships are best displayed on lognormal Q–Q plots. These sensitively reflect discrete relationships in subpopulations within the wide range of the data. For example, small but distinctly log-linear subpopulations for Pb, Cu, Zn and Ag are interpreted to represent ore-grade enrichment of naturally occurring minerals such as sulfides.None of the 27 chemical elements could pass the test for either normal or lognormal distribution on the declustered data set. Part of the reasons relate to the presence of mixtures of subpopulations and outliers. Random samples of the data set with successively smaller numbers of data points showed that few elements passed standard statistical tests for normality or log-normality until sample size decreased to a few hundred data points. Large sample size enhances the power of statistical tests, and leads to rejection of most statistical hypotheses for real data sets. For large sample sizes (e.g., n > 1000), graphical methods such as histogram, stem-and-leaf, and probability plots are recommended for rough judgement of probability distribution if needed.  相似文献   

15.
Parameters of the hypothetical open arrays were computed for a total of 20 published sets of chemical analyses of igneous rocks in oxide, mole, cation, and cation weight-percentage forms. Negative open variances in the full (11 variables) data sets were eliminated by using a linear transformation of the raw data. For the 13 variables (11 oxides, the sum of the alkalies and total iron as FeO) 286 different simple ternary combinations can be formed. The CaO-Na2O-K2O (CNK) and total iron-serum of the alkalies-MgO (FMA) combinations are of frequent use in depicting “differentiation trends” within a series of igneous rocks. In each of the 20 data sets the estimated open variances of Na2O in the CNK and total iron in the FMA combinations are negative. Elimination of negative open variances in the full data array does not eliminate negative open variances in these ternary combinations. Greater than 50 percent of the 29,172 ternary combinations examined contain a negative open variance.  相似文献   

16.
通过对额济纳旗雅干地区二叠系埋汗哈达组进行剖面实测、室内薄片鉴定、化石鉴定、X-衍射、微量元素、粘土矿物、重矿物等的分析,研究了埋汗哈达组主要岩性的岩石学特征。在此基础上,根据岩性特征、古生物化石、微量元素含量及其比值、饱和烃气相色谱地球化学参数等研究了埋汗哈达组的沉积环境,综合分析认为雅干地区二叠系埋汗哈达组形成于半咸水的滨海—浅海的还原环境。  相似文献   

17.
Michael Ed. Hohn 《Lithos》1979,12(4):317-324
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.  相似文献   

18.
The electrical conductivity of rock depends essentially on pore space geometry and connectivity of low resistive components. This paper presents a method to combine lattice conduction with models of pore space geometry in order to predict the conductivity of porous rock. Key parameter in this context is a quantity called connectivity which in practice can be determined from porosity and formation factor of natural rock if micro structural properties of the material are known. Simulation investigations have been performed to determine the connectivity of random lattices. An approximate equation has been developed empirically which fits the simulation data at conductivity ratios within in the range of 0.5 to 0.001. From comparison with laboratory data is concluded that the electrical conductivity of saturated porous rock can be described by means of random lattice conduction.  相似文献   

19.
水城铅锌矿元素组合和变化规律的统计分析   总被引：1，自引：0，他引：1  
杨光龙 《地质与勘探》2014,50(2):303-310
为揭示黔西北水城地区铅锌矿元素组合及变化规律,利用水城铅锌矿青山矿床岩石地球化学样品测试元素进行了R型聚类分析和因子分析。水城铅锌矿主要元素(氧化物)簇分为三类:一是以Pb-Zn-Ba为组合代表的成矿元素;二是以CaO-MgO、K2O-Al2O3、Cu-Ag-Cd为组合的成岩元素;三是成岩元素中受成矿因素影响而发生改造或迁移的元素,即Ag-Cu-Cd组合。由于成矿热卤水的多次活动和断层作用,蚀变围岩中SiO2、As受成矿因子和成岩因子的双重控制,而断层破碎带中则少了受成矿因素影响的元素,代之以Ba、MgO、SiO2为代表的蚀变岩石元素组合,Pb、Zn、Ba的关系更趋于密切。解释认为,它们的组合变化除受淋滤流失、成岩作用等主因子的支配外,还受到成矿热液作用的影响,是构造控矿的直接表现。  相似文献   

20.
Geostatistical analysis of spatial random functions frequently uses sample variograms computed from increments of samples of a regionalized random variable. This paper addresses the theory of computing variograms not from increments but from spatial variances. The objective is to extract information about the point support space from the average or larger support data. The variance is understood as a parametric and second moment average feature of a population. However, it is well known that when the population is for a stationary random function, spatial variance within a region is a function of the size and geometry of the region and not a function of location. Spatial variance is conceptualized as an estimation variance between two physical regions or a region and itself. If such a spatial variance could be measured within several sizes of windows, such variances allow the computation of the sample variogram. The approach is extended to covariances between attributes that lead to the cross-variogram. The case of nonpoint sample support of the blocks or elements composing each window is also included. A numerical example illustrates the application of this conceptualization.  相似文献   

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