地球化学图纹理的多重分形模拟

利用一个简单的基于De Wijs模型的多重分形模型, 可以模拟元素富集值的各种地球化学纹理.每种纹理在平均值上是自相似的, 因为将乘积阶次模型(multiplicative cascade model) 应用到任何子区均能得出类似的纹理样式.在其他的试验中, 通过叠加一个二维趋势纹理(2-dimensional trend pattern) 以及把它与一个常值富集模型混合, 原始的自相似纹理就产生畸变.本文将要研究这些畸变是如何改变用三步矩(3-step method of moments) 所估测的多重分形谱(multifractal spectrum).推导出了满足De Wijs模型纹理的离散和连续频率分布模型.这些模拟纹理满足离散频率分布模型, 当乘积阶次模型(multipicative cascade model) 无限细分时, 假设离散频率分布模型的上界是一连续频率分布, 这个离散分布就在形式上逼近该连续频率分布的上边界.这一极限分布在中心是对数正态的, 但有两个巴利多(Pareto) 分布的尾.这种方法在矿产和油气评价中有重要的潜在意义.      

The offshore to backshore environments of the Abu Ballas Formation of the SE Dakhla Basin (Western Desert,Egypt)

The Abu Ballas Formation in the Western Desert of Egypt represents a marine intercalation within fluvial, Nubia-type sandstones. These deposits document an extensive transgression of Aptian age flooding the Dakhla Basin from north to south. Due to this first advance of the Tethyan sea during the Cretaceous, sediments of open and marginal marine provenance were accumulated in the SE of the basin.The sedimentary succession of the open marine facies is divided into five lithostratigraphic units which reflect that deposition was largely controlled by one single transgressive-regressive event. The transgressive sequence in the lower part of the formation comprises sandstones of a backshore to foreshore environment (unit 1) which are overlain by offshore claystones (unit 2). The middle portion of the sedimentary succession consists of silty and sandy strata (unit 3) which are attributed to large-scale redepositional processes due to intensified bottom currents during the maximum extension of the sea. These sediments are capped by offshore originated claystones (unit 4) grading upwards into siltstones and sandstones of transition-zone to backshore environments (unit 5), which indicate a gradual regression.This stratigraphic sequence documenting a retrograding-prograding shoreline due to the transgression and regression of the Aptian sea, interfingers with silty and sandy deposits of the marginal marine facies of the Abu Ballas Formation. Comparable to the lithostratigraphic units 1 and 5 these strata represent a variety of sedimentary environments ranging from the backshore to the transition zone. They were accumulated on the western slope of the Kharga Uplift bounding the Dakhla Basin towards the east, which was partially flooded while the sea had its maximum extension.

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Zusammenfassung Die Abu Balks-Formation in der Western Desert Ägyptens stellt eine marine Einschaltung innerhalb von fluviatilen Sandsteinen Nubischen Typs dar. Diese Schichtenfolge dokumentiert eine weitflächige, nach Süden hin in das Dakhla-Becken vorgreifende Transgression aptischen Alters. Im Verlauf dieses ersten Vorstoßes der Tethys während der Kreide wurden im SE des Beckens Sedimente offen und randlich mariner Provenienz abgelagert.Die Ablagerungen der offen marinen Fazies werden in fünf lithostratigraphische Einheiten unterteilt, deren vertikale Abfolge eine Sedimentakkumulation im Rahmen einer Transgression und einer nachfolgenden Regression widerspiegelt. Die transgressive Schichtenfolge im unteren Teil der Formation umfaßt Sandsteine mit Merkmalen einer Strandsedimentation (Einheit 1), die von Peliten eines untiefen Schelfs (Einheit 2) überlagert werden. Höher folgen siltige und sandige Schichten (Einheit 3), die auf großräumige Umlagerungsvorgänge im Becken durch bodennahe Strömungen während der maximalen Ausdehnung des Meeres zurückgeführt werden. Die regressive Entwicklung setzt ein mit einer erneuten Ablagerung von pelitischen Sedimenten eines flachen Schelfmeeres (Einheit 4). Diese gehen zum Hangenden hin über in Siltsteine und Sandsteine (Einheit 5), die zwischen dem Schelf und dem Strandbereich vermitteln und das Ende der Verflachungsphase andeuten.Diese Schichtenfolge, die auf ein anfängliches Zurückweichen und späteres Vorrücken der Küstenlinie im Rahmen von Transgression und anschließender Regression hinweist, verzahnt sich mit siltigen und sandigen Ablagerungen der randlich marinen Fazies der Abu Ballas-Formation. Ähnlich wie die lithostratigraphischen Einheiten 1 und 5 entstammen sie einem Strandbis küstennahen Schelf-Milieu und wurden während der maximalen Ausbreitung des Meeres an der westlichen Flanke des Kharga-Uplifts akkumuliert. Diese Schwellenregion, die das Dakhla-Becken nach Osten begrenzt, war im Apt vermutlich nur teilweise überflutet.

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Résumé La formation Abu Ballas du désert occidental d'Egypte représente une intercalation marine dans les grès fluviatiles de type nubien. Cette séquence illustre une large transgression d'âge aptien pénétrant vers le Sud dans le bassin de Dakhla. Au cours de cette première progression de la Téthys pendant le Crétacé, des sédiments d'origine marine et marginolittorale se sont déposés dans la partie SE du bassin.Les couches de facies marin sont diversées en cinq unités lithostratigraphiques, dont la succession verticale refléte une accumulation de sédiments au cours d'une transgression et d'une régression successives. La série transgressive, dans la partie inférieur de la formation, comprend des grès typiques d'une sédimentaion de haute et de basse plage (unité 1), surmontés par des pélites de plate-forme continentale peu profonde (unité 2). Plus haut viennent des chouches silteuses et sableuses (unité 3) qui sont attribuées à des processus de remaniements dans le bassin par les courants de fond pendant l'extension maximale de la mer. La phase régressive commence par un nouveau dépôt de sédiments pelitiques de mer peu profonde (unité 4). Ceux-ci sont suivis vers le haut par des siltites et des grès (unité 5) déposés dans une zône de transition arrière plage/plateforme continentale et indiquant la fin de la régression.Cette série qui indique un recul puis une avancée de la ligne de rivage, par transgression et régression, est interstratifiée de dépôts silteux et sableux de facies marin marginal de la formation Abu Ballas. Semblables aux unités lithostratigraphiques 1 et 5, ces couches témoignent d'un milieu variant de la basse plage à la partie haute du shelf. Elles se sont accumulés au bord ouest du seuil de Kharga au cours de l'extension maximale de la mer aptienne. A cette époque, cette region élevée limitant le bassin de Dakhla vers l'est, n'était probablement inondée qu'en partie.

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Frequency Distribution of Thickness of Sediments Bounded by Cenozoic Biostratigraphic Events in Wells Drilled Offshore Norway and along the Northwestern Atlantic Margin

Sampling for microfossils in exploratory wells in basins with hydrocarbon potential is subject to considerable uncertainty, mainly because the samples usually are small and subject to caving. Biostratigraphic events defined on fossil taxa include their last occurrences of which the depths along the wells generally can be measured with precision. The RASC method for ranking and scaling of stratigraphic events produces an average basin-wide optimum sequence and zonation that can be used for correlation of strata between wells. In this optimum sequence the fossil events are ordered according to their occurrences in geological time. Depth differences between successive events in the optimum sequence satisfy a frequency distribution that is of interest for potentially increasing stratigraphic resolution. In this article the depth difference frequency distribution is modeled for three large Cenozoic microfossil data sets consisting of 30 wells in the North Sea Basin, 27 wells on the Labrador Shelf and Grand Banks, and 11 wells in the western Barents Sea. The shapes of the three frequency distributions satisfy bilateral gamma distributions with similar parameters. These distributions are fitted by the construction of straightlines on normal Q–Q plots of square root transformed average-corrected depth differences. The gamma distribution model is approximately satisfied except for small negative and positive depth differences, which have anomalous frequencies because of the discrete sampling method used in exploratory well-drilling to collect microfossils. It implies not only comparable average stratigraphic order of events, but also comparable average sedimentation rates in the three Cenozoic basins selected for study.     

Principles of Probabilistic Regional Mineral Resource Estimation

Five principal sources of uncertainty in quantitative mineral resource estimation are listed and illustrated by means of a simple example (mosaic model) and a case history study for large copper deposits in the Abitibi area of the Canadian Shield. Abitibi copper potential originally was estimated on the basis of 1968 estimates of production and reserves totalling 3.12 Mt Cu. This prognostication now could be evaluated on the basis of 2008 copper production and reserves totalling 9.50 Mt Cu. An earlier hindsight study performed on the basis of 1977 data (totalling 5.23 Mt Cu) showed seven new discoveries occurring either in the immediate vicinities of known deposits or on broad regional copper anomalies predicted from the 1968 inputs. By 1977, the global geographic distribution pattern of large copper deposits in the Abitibi area had stabilized. During the next 30 years, new copper was essentially found close to existing deposits, much of it deeper down in the Earth's crust. In this paper, uncertainties associated with copper ore tonnage are analyzed by comparison of 2008 data with 1968 data using (a) log-log plots of size versus rank, and (b) lognormal QQ-plots. Straight lines fitted by least squares on these plots show that 1968 slopes provide good estimates of 2008 slopes but 1968 intercepts are much less than 2008 intercepts. In each linear log-weight versus log-rank plot, the slope is related to fractal dimension of a Pareto frequency distribution, and in a lognormal QQ-plot it is determined by logarithmic variance. The difference between 2008 and 1968 intercepts represents the increase in copper ore production and reserves from 1968 to 2008. The Pareto model fits actual copper and massive sulphides increase over the past 40 years better than the lognormal frequency distribution model for 10 km×10 km cells on favorable environments in the Abitibi area.