The shape of pebbles

A theory of pebble erosion is presented, based on the assumption that the rate of erosion at a point on the surface is a function Vof the curvature there. It is proved that for physically reasonable functions V,the sphere is the only shape of pebble which can maintain its proportions as it wears away. An argument is given which leads to a particular form for the function Vand a few qualitative consequences of this form are indicated. The surface of the pebble at time tmay be described using spherical polar coordinates θ, Φ by the radius function r (θ, Φ, t). This function is given by a highly nonlinear partial differential equation. However, in the case of the erosion of a deformed sphere, when terms which are of second order or higher in the deformation are neglected, the equation becomes linear and is a version of the diffusion equation. The stability of the spherical shape against deformations of the various harmonic types is then easily analyzed.     

Strain analysis using deformed pebbles: The influence of initial pebble shape

Several methods exist for the determination of the finite strain ellipsoid from deformed pebble shapes. These methods are critically evaluated and others are proposed on the basis of calculations which predict both the sectional and three-dimensional shape of pebbles in simple deformed simulated conglomerates. In many cases it is found preferable to use an average pebble shape to estimate the tectonic strain and that the harmonic mean of the ratios of axial lengths yields an average pebble shape which is closest to the strain ellipsoid shape.     

Some methods for statistical analysis of multimodal distributions and their application to grain-size data

Some of the methods used in the resolution of mixed normal distributions are discussed under three headings: analytical, graphical, and numerical methods. Attention is given to their applicability in the analysis of grain-size data as derived from sieving. Comparisons are made by applying several methods to published data. It is concluded that the numerical methods offer most scope, especially the method of nonlinear least squares. Some analyses of beach sediments, using this method, are presented. The adoption of a convention for the number of individuals in the sample increases ease of interpretation.     

Digital filtering as a tool for the study of some flysch deposits from the East Carpathians (Romania)

Results from the application of digital filtering (simple and weighted averaging) to the analysis of sedimentary series are given. Two flysch sequences from the East Carpathians (Upper Eocene, Damacua Valley; and Lower Cretaceous, Sbrancani Valley) were studied. Individual components, affecting the conditions of deposition, were separated, and establishment of the geological significance of the components separated by digital filtering was investigated.     

赣西北三都小型红盆冲积扇体特征及时空分布

红盆内１０９个点砾岩砾石万分、砾径、古流向的系统统计与沉积学研究，确定该红盆历经三期洪积事件，形成了８个冲积扇体。其中期为洪积事件上鼎盛时期，形成５个冲积扇体，并在其内首次发现恐龙蛋化石，属晚白垩世中晚期。     

Operator error in petrographic point-count analysis: A theoretical approach

Operator error in petrographic point-count analysis introduces bias into the estimates of proportion in a thin section. A correction for this bias, leading to an unbiased estimator of the true proportion in that thin section, is here proposed. Operator error also affects the confidence interval, and in this situation, too, an adjustment is possible. The approach proposed requires that the probabilities associated with operator error, categorized into A-type and B-type errors, are known or assumed. The A-type operator error tends to underestimate the true proportion in a thin section, whereas the B-type operator error tends to overestimate it.     

Counting error in petrographic point-count analysis: A theoretical and experimental study

The binomial model, commonly used to estimate counting error in point-count analysis, misestimates this error when the observation points on a grid are positively or negatively correlated. A model, called the cell model, is proposed as an alternative to the binomial model for use in studies, especially with coarse-grained rocks, in which such correlation is known or thought to exist. In the new model the thin section is conceptually partitioned into a number of cells (six is recommended), and the assumption is made that the proportions in the individual cells are statistically independent and that their variance does not differ from cell to cell. Empirical relations obtained from a suite of 200 thin sections of limestones are in reasonable support of the prediction that large particle size adversely affects counting error estimates based on the binomial model.     

现代沉积学理论重大进展综述

现代沉积学重大进展要表现在各种边缘，分支、交叉，横断学科的诞生和发展。其中，层序地层学的进展表现在层序生物地层学、成岩层序地层学、高频层序地层学、高分辨率层序地层学、应用层序地层学、定量层地层学等理论的涌现和发展；资源沉积学从过去的矿产型资源沉积学研究转向了资源的有限性稀有性、资源的永续利用与社会经济持续协调发展研究；环境沉积学从单一的环境科学研究关系转向了对不同板发、规划、管理、保护、防治等相结     

Multivariate morphometrics and analysis of shape

Analysis of size and shape has always figured largely in interpretations of multivariate analyses of measurements on organisms, although on premises that are not always unchallengeable. A recent surge of interest has led to important advances in formal analysis of variations in shape (geometric morphometrics) and phylogenetic significance of such changes. In connection herewith, an improved philosophy for the choice of variables suitable for depicting shape variation is evolving. Important results for statistical validity of multivariate analyses now are being made available by several workers (robust estimates of canonical vectors, etc., stability of eigenvectorial elements, effects of deviations from multivariate normality) with special reference to applications in morphometric studies. Such questions have been little considered in the past with the result that many multivariate analyses of biological and geological data are inexact.Contribution Number 2 in a series of review articles by the Mathematical Geologists of United States. Accepted January 8, 1985. Invited lecture delivered to the thematic conference of Geological Shape Analysis, Wood's Hole, Massachusetts, September 8–12, 1984.     

当代沉积学研究的新进展与发展趋势——来自第三十一届国际地质大会的信息

本文为笔者根据第三十一届国际地质大会的200余篇与沉积学相关的论文摘要综合编写而成。评述了当代沉积学研究的最新进展与发展趋势,主要包括:碎屑岩、碳酸盐岩及混合沉积的环境变化及其演变;沉积盆地分析与大地构造沉积学;层序地层学;冰川事件沉积学;全球变化沉积学;环境沉积学;资源沉积学;生物礁及白云岩成因;碳酸盐岩成岩作用等。重点阐明了现代沉积学研究应向多学科交叉渗透、多种高新技术的引用和多领域应用的方向发展。未来沉积学研究以人类的生存与发展所依托的环境、气候和资源为服务对象,才会有更加旺盛的生命力和美好的未来。     

地震沉积学探讨

地震沉积学是用地震手段研究沉积岩及其形成过程的学科,其研究手段主要有90°相位转换和地层切片技术等。90°相位转换使地震相位具有了岩性地层意义,可以用于高频层序地层的解释;地层切片是指对某一层位内进行等比例内插切片之后用来研究各个等时地层单元的沉积体系（相）的平面展布。文章认为：①由于受地震分辨率的限制,地震沉积学目前主要应用于研究宏观的地层、岩石、沉积史和沉积体系,还没有达到全面研究沉积岩及其形成过程的程度,因此,目前的地震沉积学是利用地震手段结合井资料研究宏观的地层、岩石、沉积史和沉积体系的一门学科,它还需要进一步的发展才有可能继地震地层学、层序地层学之后真正成为一门研究沉积岩及其形成过程的新学科;②相位转换技术中转换的角度并不一定局限于90°,可以是其它角度的相位转换,这要根据层位标定的具体情况而定;③地层切片比时间切片和沿层切片更加合理,但是目前的地层切片技术还没有考虑地层的沉积速率随时间的变化,因此,地层切片还不是严格意义上等时的。     

Study of factors influencing variation in size characteristics of fluvioglacial sediments

Factor analysis using promax oblique rotation was used in a study of fluvioglacial sediments of Late Weichsilian (Wurm) age. The use of oblique rotation allowed a more realistic interpretation of the factors and understanding of relationships between sedimentsize classes. At the second-order level, two factors are operatable, one producing variations in the coarse-size range, the other in the fine-size range. The factors are uncorrelated and mutally unrelated. At the first-order level are six factors, four representing aspects of the second-order factor of coarse size and two representing the fine size. The factor producing the variation in the coarse size is the most important one. At the lowest level in the hierarchy scale are the individual size variables. Results show that the number of factors required to account for the variation in a sediment-size data set is a function of the scale at which the problem is examined.     

Some consequences of applying lognormal theory to pseudolognormal distributions

A logarithmic transformation may be used to improve the efficiency of estimates of the mean when observations follow the lognormal distribution. But if this transformation is applied to observations that follow another distribution, bias may be introduced. We consider some consequences of erroneously applying lognormal estimation theory and demonstrate that biased estimates may be obtained for certain classes of distributions. Illustrations of bias obtained in gold sampling are given.     

Paragenesis of mineralization within fractured pebbles in Witwatersrand conglomerates

Mineralized conglomerates in the Witwatersrand goldfields consistently exhibit intense fracturing of quartz pebbles. The fractures are coated with quartz, phyllosilicates, organic matter, uraninite, gold, and base metal sulfide minerals, showing that all of these phases were at least partially epigenetic. Samples from five goldfields (Evander, West Rand, Carletonville, Klerksdorp, Welkom) across the Witwatersrand Basin show comparable paragenetic sequences of fracture-fillings. This implies that fracturing and several episodes of mineral deposition were basinwide events, rather than the result of local processes. Fluid inclusion data for the quartz indicates precipitation from these basinwide fluids at relatively low temperatures (<250 °C), which may be consistent with other evidence for mineralization following the Vredefort Event at 2025 Ma.     

关于造山带动力沉积学若干问题的思考

造山带动力沉积学是造山带地质学和大陆动力学研究的重要方面。造山带动力沉积学研究的重要基础是识别造山带的原型沉积盆地,认识其大地构造沉积相和原型沉积盆地的演化。造山带动力沉积学研究的主要内容包括造山带区域地层学、沉积学、大地构造学、造山带原型盆地的充填序列或构造层序、古地理和古海洋及建立沉积盆地的动力模式。其研究方法涉及造山带原型盆地的物源和组分分析、沉积相和沉积体系及沉积构型分析、充填序列和构造层序分析、古流向和古地理分析、沉积厚度和沉降分析以及沉积盆地动力模拟等。     

微生物席沉积学:一个年轻的沉积学分支

现代实例和岩石记录的研究表明,微生物席是一个特别的微生物群落,这个特殊的微生物群落就像一个复杂的食物网一样,群落中的每一个组成成员紧密相互依赖,从而构成了地球上形成最早、延续时间最长的生态系.微生物席在沉积岩中留下了丰富而且复杂的记录,在碳酸盐岩中最为典型的产物就是叠层石,在碎屑岩中最具有代表性的产物就是"微生物诱发的...     

The effect of composition and strain on quartz-fabric intensity in pebbles from a deformed conglomerate

Twenty-eight quartz c-axis fabrics from individual pebbles from a single outcrop of deformed conglomerate have been measured. These pebbles vary in composition and have undergone different amounts of strain. Contrary to expectations based on published results of computer simulated deformation by intracrystalline slip of pure quartzites, it is observed that fabrics are not stronger in the more highly deformed pebbles. Instead, the fabric strength is related to the quartz content of the pebbles. Pure quartzites show the strongest fabrics. As the percentage of non-quartz minerals increases up to 25% the strength of the fabrics rapidly decreases, though the influence of composition becomes less marked when impurities exceed 25%. These observations can be explained if the deformation of the impure quartzites included a contribution from a non-intracrystalline mechanism such as grain boundary sliding.

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Zusammenfassung Von einem einzelnen Aufschluß eines deformierten Konglomerates wurden 28 Quarz c-Achsen Gefügebilder aufgenommen, jeweils von verschiedenen Geröllen. Diese Gerölle unterschieden sich in ihrer Zusammensetzung sowie in ihrem Deformationsgrad. Im Gegensatz zu den Erwartungen, basierend auf veröffentlichten Computersimulationen von intrakristallinen Gleitungen in reinem Quarzit, wurde beobachtet, daß die Gefüge von stark deformierten Kieseln nicht entsprechend stärker ausgeprägt sind, sondern, das Gefüge ist abhängig vom jeweiligen Quarzgehalt der Kiesel: reiner Quarzit zeigt das ausgeprägteste Gefüge. Wenn aber die Fremdanteile bis zu 25% betragen, verringert sich die Stärke der Gefügeausrichtung. Dieser Einfluß geht jedoch erneut zurück, sobald der Fremdanteil 25% übersteigt. Diese Beobachtungen können erklärt werden, wenn die Deformation des unreinen Quarzites auch mit nicht intrakristallin bezogenen Mechanismen im Zusammenhang steht, zum Beispiel mit Gleitungen an Korngrenzen.

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Résumé Vingt-huit mesures de fabriques d'axes c de quartz ont été effectuées dans des cailloux différents provenant d'une même affleurement de conglomérat déformé. Ces cailloux varient en composition et ont été déformés à des degrés divers. Contrairement à ce que laissent prévoir les résultats publiés de la simulation par ordinateur de déformations par glissement intracristallin dans des quartzites purs, on constate que les fabriques ne sont pas plus orientées dans les cailloux les plus déformés. En effet, l'intensité de la fabrique est en relation avec la teneur en quartz des cailloux. Les quartzites purs montrent les fabriques les mieux exprimées. Lorsque la proportion des minéraux autres que le quartz augmente jusque 25%, l'orientation de la fabrique décroît rapidement, tandis qu'au-delà de 25%, l'influence de la composition se marque moins. On peut interpréter ces observations en admettant que dans la déformation des quartzites impurs, intervient un mécanisme non intracristallin, tel qu'un glissement le long des surfaces des grains.

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