Exploring self-affine properties in seismograms

Self-affine properties have been observed in a large variety of rough profiles and time series from natural data sets. In this work, seismograms used for oil prospecting, which contain information of distinct subsurface features collected by seismic waves reflected or scattered at their interfaces, are taken into consideration. It is expected that any self-affine property, measured by the Hurst exponent H, depends on the depth. For each seismic trace, H is evaluated locally within a moving window, which is chosen narrow enough to reveal space dependency but also wide enough to display scale invariance. With the use of color code diagrams, it is possible to draw two-dimensional diagrams that show the local dependence of H for the analyzed seismogram. The reliability of the method is tested by the investigation of seismograms that contain ground roll components, as well as multiple reflections. The effect of different kinds of filter in the scaling properties is also investigated. In this case, comparisons are drawn among the diagrams obtained from original seismograms and those subjected to appropriate filter to eliminate spurious components. Work supported by the Brazilian agencies CNPq, FINEP-CTPETRO and Petrobras.     

Chemical Variations in the Palisade Sill

Walker (1940) considered that the chemical data of the differentiatedPalisade sill could not be treated in variation diagrams becauseof the narrow range of SiO² weight per cent. The present workexamines the same data using a recent graphical technique whichis not subject to such limitations. The results show that thechemical variation is almost exactly that required by crystalfractionation of olivine and pyroxene from a single, relativelyhomogeneous, parent magma. Most other hypotheses of differentationare either unnecessary or not in accordance with the chemicaldata. Generally, the results confirm Walker's earlier conclusionswhich were based mainly on petrography ansd field relations.     

砂岩(砂)的岩相分析和分类标准

定量的砂岩（砂）岩相学分析是重要的岩石学分析手段,有助于探讨沉积物的源区、背景和沉积盆地性质.在过去几十年中,科学家们对于砂岩（砂）的定量碎屑颗粒统计及其潜在地质意义（如沉积碎屑物与源区母岩的关系、沉积过程对碎屑组分的影响、碎屑组分与大地构造背景的关系等）取得了很多进展,但是对于定量的岩相分析方法和命名方案一直缺少系统的总结,导致一些实际工作中的波折和误区.在总结前人文献的基础上,系统描述了砂岩（砂）定量岩相分析的方法,并推荐最优的分类命名方案,希望建立统一的工作规范,本文提升砂岩（砂）碎屑颗粒统计结果的可靠性和数据的可对比性.同时,我们对砂岩构造背景判别图解的适用性进行了探讨,认为图解是展示砂岩碎屑组分统计结果的有效工具,但用于构造背景判断时则需谨慎,最好基于岩石本身的特征并结合其他资料综合探讨.      

Modern pollen spectra from lake sediments in Finland and Finnmark, north Norway

Absolute (APF) and relative surface pollen spectra from 67 moderate-sized lakes in Finland and Finnmark are presented as pollen diagrams and isopoll maps and analysed by multidimensional scaling. The results are applicable to problems of regional vegetational history through comparisons of pollen spectra and the use of R-values. It is shown that relative spectra can discriminate the major vegetational regions. APFs give better resolution among northern forest regions and low APFs characterize tundra. Gradients of tree-pollen percentages in south and central Finland are related quantitatively to the major forest gradients, which are azonal, mainly related to soils, and affected but not obscured by human influence. Forest clearance is reflected in frequencies of various non-tree pollen types. Non-tree pollen and spores also provide vegetational and climatic information in the far north.     

全球新生代安山岩构造环境有关问题探讨

20世纪70～80年代,以Pearce为代表的一批科学家先后提出了玄武岩和花岗岩的构造环境判别图,将构造环境与岩石地球化学特征有机地结合起来,为岩浆岩大地构造环境研究开辟了新途径。但学术界对全球广布的安山岩构造环境及相关地球化学特征问题的讨论则相对不足。本文利用GEOROC 和PetDB 两个数据库对全球新生代安山岩进行数据挖掘,讨论了它们的地球化学特征及形成环境。初步将全球新生代安山岩归属为12个形成构造环境,其中67.71%产出于岛弧、陆缘弧等汇聚板块边缘环境,其余安山岩则形成于大陆板内、大陆溢流、洋岛、大陆裂谷、洋中脊等构造环境。研究表明,常用的玄武岩微量元素判别图以及LILE/HFSE 玄武岩判别图均在一定程度上可用于安山岩成因及环境判别, 暗示安山岩地球化学成分也可用于构造环境的判定。采用大数据思维,探索洋岛安山岩（OIA）和岛弧安山岩（IAA）中地球化学元素的关联关系,从获得的近20 000 个OIA-IAA 判别图中选出lg（Cs/Ta）-lg（Cu/Ta）、lg（CaO/Nb）-lg（Cs/Zr）和lg（Cu/Ta）-lg（Co/Nb）等6个图解,能有效限定它们的构造环境,为安山岩成因及形成环境研究提供了新的思路。这些初步成果说明科学大数据的研究方法可成为岩浆岩构造环境及地球化学研究中的重要有效手段。     

Application of light hydrocarbons (C4–C13) to oil/source rock correlations:: a study of the light hydrocarbon compositions of source rocks and test fluids from offshore Mid-Norway

Relatively little work has been published on the correlation between the light hydrocarbon distributions in reservoir fluids and their proposed source rocks [Philippi, G. T. (1981)]. The aim of our work was to study this relationship in detail for samples from Mid-Norway. The main source rocks offshore Mid-Norway are the marine shales of the Late Jurassic Spekk Formation and the coals and paralic shales of the Early Jurassic Åre Formation. Reliable light hydrocarbon (C₄–C₁₃) data for source rock samples were acquired by thermal extraction-GC of the source rocks. Of these, notably the hydrocarbons in the C₆–C₈ range (routinely measured in test fluids) were used to discriminate between the Spekk and Åre Formation samples. A total of twenty-six samples from the Spekk Formation and twenty-four samples from the Åre Formation at different maturity levels and facies were analyzed. In general, the two source rock types differ in their light hydrocarbon composition by the presence of relatively more aromatics and cyclohexanes in the Åre samples, while the Spekk samples are richer in cyclopentanes and acyclic hydrocarbons. We show that source rock facies is a more important indicator of light hydrocarbon composition than maturity variation. Differences in the chemical composition, which can be used to discriminate between the two source rocks, were supported by differences in the carbon isotope composition of individual components of the same fraction, as determined by GHM-IR-MS analysis of eleven samples. Further, the light hydrocarbon compositions of reservoir fluids (oils and condensates) were compared with those for the source rock(s). Sixty-six gas chromatograms of oils and condensates, representing most of the known petroleum accumulations in Mid-Norway, were collected. Of these, five oil samples were selected for detailed isotopic analysis of individual components (GC-IR-MS). When using a classification scheme based on data from sediment samples, data for the light hydrocarbon fraction of oils and condensates indicate that the Spekk Formation is the dominant source for most of the fields from Mid-Norway, with a significant contribution from the Åre Formation being detected principally in one field. Differences in the chemical composition of the C₆–C₈ fractions were supported by differences in the carbon isotope composition of individual components, which also discriminate between the oils. Although the classification diagrams used in this study are based on source rock data from Mid-Norway, the method can be applied to other areas, providing that the diagrams are calibrated with source rock data from the area of interest.     

小秦岭地区太华群斜长角闪岩原岩类型的地球化学研究

通过各种岩石化学图解、微量元素、元素对比值、元素间相互关系以及稀土元素特征的综合分析、判定所研究斜长角闪岩应类似于现代大洋中脊型富铁玄武岩经高级区域定质作用而形成。研究结果表明、地球化学方法是判别深变质岩原岩性质的有效途径之一。     

Joint Consistent Mapping of High-Dimensional Geochemical Surveys

Geochemical surveys often contain several tens of components, obtained from different horizons and with different analytical techniques. These are used either to obtain elemental concentration maps or to explore links between the variables. The first task involves interpolation, the second task principal component analysis (PCA) or a related technique. Interpolation of all geochemical variables (in wt% or ppm) should guarantee consistent results: At any location, all variables must be positive and sum up to 100 %. This is not ensured by any conventional geostatistical technique. Moreover, the maps should ideally preserve any link present in the data. PCA also presents some problems, derived from the spatial dependence between the observations, and the compositional nature of the data. Log-ratio geostatistical techniques offer a consistent solution to all these problems. Variation-variograms are introduced to capture the spatial dependence structure: These are direct variograms of all possible log ratios of two components. They can be modeled with a function analogous to the linear model of coregionalization (LMC), where for each spatial structure there is an associated variation matrix describing the links between the components. Eigenvalue decompositions of these matrices provide a PCA of that particular spatial scale. The whole data set can then be interpolated by cokriging. Factorial cokriging can also be used to map a certain spatial structure, eventually projected onto those principal components (PCs) of that structure with relevant contribution to the spatial variability. If only one PC is used for a certain structure, the maps obtained represent the spatial variability of a geochemical link between the variables. These procedures and their advantages are illustrated with the horizon C Kola data set, with 25 components and 605 samples covering most of the Kola peninsula (Finland, Norway, Russia).     

Petrologic hypothesis testing with Pearce element ratio diagrams: derivation of diagram axes

In petrology, Pearce element ratio (PER) diagrams have been used: i) to determine whether members of a rock suite are co-genetic, ii) to identify the minerals involved in differentiation processes, and iii) to evaluate the extent to which those mineral are involved. The axis coefficients of each diagram are chosen such that sorting of minerals or combinations of minerals will generate unique and predictable trends. Unfortunately, selection of the optimal combination of axis coefficients is a difficult task, especially if the system being investigated has a large number of phases or complicated solid solution minerals. Our work has established a formal set of rules and matrix operations which facilitate the determination of PER diagram axes coefficients. This methodology can be used to determine the unit molar vector displacement caused by the addition or subtraction of a specific mineral, given a set of axis coefficients. It can also be used to create PER diagrams on which minerals have predetermined vector displacements. By designating all vector displacements to be parallel, axis coefficients for assemblage test diagrams can be determined to test the following hypothesis: the observed chemical variation is due to the addition (or removal) of a specific set of minerals. Alternatively, by designating all vector displacements to be mutually perpendicular, phase discrimination diagrams can be created which test whether the observed chemical variations require a specific phase to be involved in differentiation. Phase discrimination diagrams also provide a means to estimate the extent of that involvement. This methodology facilitates construction of powerful yet simple PER diagrams which provide an effective means of testing alternative differentiation hypotheses. Current address: Department of Geological Sciences, Queen's University Kingston, Ontario K7L 3N6, Canada     

Statistical evaluation of tectonomagmatic discrimination diagrams for granitic rocks and proposal of new discriminant-function-based multi-dimensional diagrams for acid rocks

The four tectonic discrimination diagrams of Pearce et al. [Journal of Petrology, v. 25, p. 956–983] for granitic rocks were first evaluated using the literature cited by these authors as well as from our new database. The first diagram (Y?Nb) cannot discriminate volcanic-arc and collision settings. Both Y?Nb and Yb?Ta diagrams have an overlapping field for within-plate and ocean-ridge granitoids. The remaining two diagrams (Y?+?Nb?Rb and Yb?+?Ta?Rb) use a mobile element (Rb) in their y-axis. Although these diagrams successfully discriminate volcanic-arc and within-plate granites, they perform less well for collision tectonics. Besides, felsic or acid rocks are scarce in ocean-ridge settings, which limits the usefulness of these diagrams for this geological environment. Therefore, using an extensive database, we proposed a set of five new discriminant-function-based multi-dimensional diagrams for acid magmas from four tectonic settings (island arc, continental arc, continental rift, and collision). The very similar tectonic settings of island and continental arcs are discriminated for the first time. These diagrams are based on correct statistical treatment of compositional data, because they use natural logarithm transformation of major-element ratios and linear discriminant analysis (LDA). The use of discordant outlier-free samples prior to LDA improved the success rates by about 3–5%. Success rates of these diagrams as inferred from a testing set were between 76% and 88% for island arc, 60% and 92% for continental arc, and 72% and 84% for both continental rift and collision settings. Finally, application of these new diagrams to case studies not compiled in our initial database used for constructing these diagrams provided the following results: a collision setting for the Himalayas at about 30 Ma; an island arc setting for Quaternary acid rocks from geothermal boreholes in El Salvador; an island- or continental-arc setting for northern Italy at 35–52 Ma; a continental-arc setting for the Italy–Austria border at about 30 Ma; either a rift or a collision setting for northern Nigeria at about 164 Ma; a collision setting for central Nigeria at about 144 Ma and for the Cretaceous Masirah ophiolites of Oman; and an island arc setting for the Cretaceous Semail ophiolites of Oman. In spite of the relative mobility of major elements, these applications suggest utility of the new discrimination diagrams for all four tectonic settings.     

A thermodynamic model for multicomponent melts,with application to the system CaO-Al2O3-SiO2

A thermodynamic model is proposed for calculation of liquidus relations in multicomponent systems of geologic interest. In this formulation of mineral-melt equilibria, reactions are written in terms of the liquid oxide components, and balanced on the stoichiometry of liquidus phases. In order to account for non-ideality in the liquid, a ‘Margules solution’ is derived in a generalized form which can be extended to systems of any number of components and for polynomials of any degree. Equations are presented for calculation of both the excess Gibbs free energy of a solution and the component activity coefficients.Application to the system CaO-Al₂O₃-SiO₂ at one atmosphere pressure is achieved using linear programming. Thermodynamic properties of liquidus minerals and the melt are determined which are consistent with adopted error brackets for available calorimetric and phase equilibrium data. Constraints are derived from liquidus relations, the CaO-SiO₂ binary liquid immiscibility gap, solid-solid $\text{P-T}$ reactions, and measured standard state entropies, enthalpies, and volumes of minerals in this system.Binary and ternary liquidus diagrams are recalculated by computer programs which trace cotectic boundaries and isothermal sections while checking each point on a curve for metastability. The maximum differences between calculated and experimentally determined invariant points involving stoichiometric minerals are 17°C and 1.5 oxide weight per cent. Because no solid solution models have been incorporated, deviations are larger for invariant points which involve non-stoichiometric minerals.Calculated heats of fusion, silica activities in the melt, and heats of mixing of liquids compare favorably with experimental data, and suggest that this model can be used to supplement the limited amount of available data on melt properties.     

高岭石-伊利石-透辉石体系假相图

采用较纯透辉石岩、高岭石粘土和伊利石粘土作为端元组分,并根据用 DTA、热台显微镜、XRD 方法测定的数据组成了三元体系的假相图。根据假相图说明了有关陶瓷工艺学和变质岩岩石学的一些问题。     

Geochemistry of Two Types of Basalts in the Emeishan Basaltic Province: Evidence for Mantle Plume-Lithosphere Interaction

Based on the temporal-spatial distribution and geochemical characteristics, the Emeishan basalts can be divided into two types: high-P2O-TiO2 basalt (HPT) and low-P2O5-TiO2 basalt (LPT), which differ distinctly in geochemistry: the LPTs are characterized by relatively high abundances of MgO, total FeO and P2O5 and compatible elements (Cr, Ni, Sc), and relatively low contents of moderately compatible elements (V, Y, Yb, Co), LREE and other incompatible elements compared with the HPT. On the diagrams of trace element ratios, they are plotted on an approximately linear mixing line between depleted and enriched mantle sources, suggesting that these two types of basalts resulted from interactions of varying degrees between mantle plume and lithospheric mantle containing such volatile-rich minerals as amphibole and apatite. The source region of the LPT involves a smaller proportion of lithospheric components, while that of the HTP has a larger proportion of lithospheric components. Trachyte is generated by pa     

Statistical comparisons of heavy metal pollutants between seven regions of the Polish exclusive economic zone

This paper addresses three intractable difficulties associated with the statistical analysis of compositional data, such as percentages or ppm. These are: (1) that such data do not follow multivariate normal distributions thus rendering inappropriate, standard parametric statistical tests and estimation procedures, (2) the covariance/correlation coefficients between specific pairs of components are determined in whole or in part by the presence or absence of other components, and, (3) the negative bias property. That is, at least one covariance and therefore at least one correlation, must be negative, hence the remaining correlations are prevented from ranging freely between ?1 and +1. It follows that correlation coefficients formed from compositional data are not only not absolute, but also frequently spurious. Standard multivariate procedures based on them are unreliable, and intrinsic associations between components inferred from strong positive correlations in particular, are potentially false. In a recent 2009 paper, it was reported that 59 surface sediment samples from 7 regions in the Polish exclusive economic zone had been chemically analyzed for 16 elements. Enrichment factors together with crude correlation coefficients between selected elements were presented. All these quantities were computed from the initial raw compositional data resulting from the chemical analyses In this paper, a statistical procedure is presented which is distinctly different to the enrichment factor computations based on the same raw compositional data. The procedure generates a log-ratio measure of the abundance of each element in each of the seven regions, thus enabling comparisons of relative levels of pollution between the regions. Although the two techniques are quite unrelated, it is shown that in general, extremely high or low measures of the relative abundances in the regions are associated with correspondingly high or low values of the enrichment factors in the same regions that were reported in the 2009 paper. That is, the statistical analysis confirms the results of the enrichment factor data in the identification of the most to the least polluted regions. In an additional analysis, the residue term was excluded from each sediment sample by rescaling the 16 element concentrations to sum to 100%, thus forming 59 residue-free sub-compositions. Crude correlation coefficients were computed for pairs of elements of this sub-compositional data. These revealed that certain correlations based on the initial raw data that were reported in the 2009 paper for the same pairs of elements, were not only inconsistent, but sometimes also contradictory. Such contradictions imply that intrinsic geochemical element associations inferred in that paper from such correlations were false.     

THE QUANTITATIVE-MINERAL COMPOSITION OF GRANITOIDS AND ITS IMPORTANCE FOR PROBLEMS OF PETROLOGY AND NOMENCLATURE

Compilations of mineral compositional data from several "classical regions of granitoid" rock in the U.S.S.R. are shown on triangular diagrams with quartz, K-feldspar, and plagioclase at the apices. Names, most of which are more or less according to general usage, are applied to different fields within the diagram. It is concluded that location within the compositions of rocks diagrams from the different massives indicate relationships between compositions and certain geological features of coeval masses and also reflects such things as assimilation, hybridization, and "degree of differentiation."--R. V. Dietrich.     

Variance--Covariance Relations in Some Published Harker Diagrams of Volcanic Suites

Sample statistics for data upon which a number of publishedHarker diagrams are based are reviewed in detail. A convincingHarker diagram—i.e. one in which most of the data pointslie reasonably close to simple curves—seems to requirethat the variance of silica be at least as large as the sumof all other variances. For this situation it can be shown apriori that strong negative correlation is to be expected betweensilica and some or all other oxides making substantial contributionsto the total variance of the array. The data suggest that thelarger the relative contribution to total variance made by anyother such oxide, the stronger its negative correlation withsilica. An excess of silica variance sufficient to generate strong negativecorrelation of silica with oxides of Ca, Mg, Fe, and Al seemscharacteristic of Cenozoic examples of the basalt-andesite-daciteassociation, whether or not they include rhyolitic material,and even when they contain no dacite. It occurs also in abouthalf the examples of the oceanic basalt-trachyte associationso far inspected, but is not found either in the basalt-mugearitesubgroup of trachyte-bearing suites of this association or inoceanic basalt suites lacking salic derivatives. The strong negative correlations of the typical Harker diagramcould be generated by any process which would greatly enlargethe variance of silica relative to other oxides.     

The petrological significance of misorientations between grains

Misorientation analysis quantifies microstructural features in tectonites, metamorphic and igneous rocks, and allows hypotheses on their formation to be tested. The misorientation between two lattices can be expressed by a rotation axis and rotation angle. For lattices with symmetry, it is conventional to take the minimum angle that enables one lattice to be rotated into the other. For a group of lattice measurements two types of misorientation distribution can be calculated. Selecting random pairs of grains gives the random-pair misorientation distribution. Selecting neighbouring pairs gives the neighbour-pair misorientation distribution. The forms of both distributions are visualised using histograms or cumulative frequency diagrams. They are strongly influenced by any overall crystallographic preferred orientation and by intrinsic crystal symmetry. In many rocks, the random-pair misorientation distribution and neighbour-pair misorientation distribution are statistically significantly different (quantified using the Kolmogorov-Smirnov test). Differences between the random-pair misorientation distribution and neighbour-pair misorientation distribution imply that adjacent grains have physically interacted or are inherited from a precursor microstructure. Interactions include (1) reduction in surface energy by lattice alignment. We show this may have occurred in garnet clusters in schist, and olivine in a cumulate. It is well-known in metals and may be a common geological process. (2) Nucleation, where those nuclei have influenced the orientation of adjacent nuclei. (3) Mechanical rotations of facetted grains in compacting crystal mushes, so that faces become parallel. (4) Growth twinning. Inheritance includes (1) subgrain rotation recrystallisation in tectonites deforming by crystal plastic processes. (2) Mechanical and transformation-related twinning. (3) Domainal microstructures, e.g. where grains have formed from a few large original grains, may give rise to spurious correlations when the orientation data cover more than one domain. With this proviso, misorientation analysis can be used to investigate many important microstructural processes.     

Amplitude-periodband diagrams and amplitude spectra of teleseismic body waves

The relation between amplitude-periodband (APB) diagrams and Fourier spectra of teleseismic P and S waves was analyzed using displacement-proportional signals derived from magnetic tape records of the feedback-controlled broadband velocigraph operating at the KHC seismic station. Most Fourier spectra and all the APB diagrams of the wave groups investigated exhibit a more or less pronounced maximum and do not correspond to the shape of theoretical far-field spectra for the Brune model. Contrary to Fourier spectra, APB diagrams have an unambiguously defined level and are not influenced by truncation, incorrect zero level and other disturbing effects.     

The statistics of Pearce element diagrams and the Chayes closure problem

Pearce element ratios are defined as having a constituent in their denominator that is conserved in a system undergoing change. The presence of a conserved element in the denominator simplifies the statistics of such ratios and renders them subject to statistical tests, especially tests of significance of the correlation coefficient between Pearce element ratios. Pearce element ratio diagrams provide unambigous tests of petrologic hypotheses because they are based on the stoichiometry of rock-forming minerals. There are three ways to recognize a conserved element: 1. The petrologic behavior of the element can be used to select conserved ones. They are usually the incompatible elements. 2. The ratio of two conserved elements will be constant in a comagmatic suite. 3. An element ratio diagram that is not constructed with a conserved element in the denominator will have a trend with a near zero intercept. The last two criteria can be tested statistically. The significance of the slope, intercept and correlation coefficient can be tested by estimating the probability of obtaining the observed values from a random population of arrays. This population of arrays must satisfy two criteria: 1. The population must contain at least one array that has the means and variances of the array of analytical data for the rock suite. 2. Arrays with the means and variances of the data must not be so abundant in the population that nearly every array selected at random has the properties of the data. The population of random closed arrays can be obtained from a population of open arrays whose elements are randomly selected from probability distributions. The means and variances of these probability distributions are themselves selected from probability distributions which have means and variances equal to a hypothetical open array that would give the means and variances of the data on closure. This hypothetical open array is called the Chayes array. Alternatively, the population of random closed arrays can be drawn from the compositional space available to rock-forming processes. The minerals comprising the available space can be described with one additive component per mineral phase and a small number of exchange components. This space is called Thompson space. Statistics based on either space lead to the conclusion that Pearce element ratios are statistically valid and that Pearce element diagrams depict the processes that create chemical inhomogeneities in igneous rock suites.