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.     

Fractal characterization of the spatial distribution of geological point processes

Geological point processes can be used to model point patterns occurring frequently in a wide variety of geoscience fields, including the study of mineral deposits, oil producing wells, earthquakes, and landslides. Characterization of the spatial distribution of GPP has implications for understanding the properties of the underlying geological processes and events. Three examples of GPP dealing with (1) metallic mineral deposits, (2) oil producing wells, and (3) aftershocks of the Wenchuan earthquake (on 12 May 2008, magnitude 8.0) are presented to illustrate that (1) the spatial distribution of geological point processes generally shows clustering implying rejection of the Poisson model because L(r) > L_Pois(r); (2) the clustering statistics of the underlying geological processes are fractal; and (3) the size distribution of geological point processes is scale invariant. These results indicate existence of a fundamental law concerning the fractal nature of the point distributions generated by geological point processes.     

A review of calcareous nannofossil astrobiochronology encompassing the past 25 million years

This paper presents a review of (astrobiochronological) calibration of Recent to late Oligocene calcareous nannofossil datum events. Biohorizons included in the paper are those of the widely used “standard” nannofossil zonations of Martini, E. [1971. Standard Tertiary and Quaternary calcareous nannoplankton zonation. In: Farinacci, A. (Ed.), Proceedings of the Second International Conference on Planktonic Microfossils Roma. Rome, Ed. Tecnosci. vol. 2, pp. 739–785], and Okada, H., and Bukry, D. [1980. Supplementary Modification and Introduction of Code Numbers to the Low-Latitude Coccolith Biostratigraphy Zonation (Bukry, 1973, 1975). Marine Micropaleontology 51, 321–325], as well as supplementary biohorizons proposed in the literature. The biohorizons have been selected on the basis of the unambiguous taxonomy of the index taxa and their biostratigraphic usefulness. We emphasise the application of rigorous methodology in nannofossil studies which permits an evaluation of biohorizons in terms of reliability, and calibrates their potential correlatability. Astrochronological age estimates rely on the Geologic timescale developed by the ICS in 2004, with some new calibrations included. We provide an overview of the relative position of biohorizons versus the astronomically calibrated ages of magnetic reversals and reference isotope stratigraphies. Surprisingly, there are still few high-resolution quantitative biostratigraphic studies of astrochronologically tuned sections in spite of the central role of such studies in addressing fundamental problems such as the tempo and mode of plankton evolution.     

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.      

Introduction to special issue on mathematical geology in the People''s Republic of China

Geological Survey of Canada Ottawa, Ontario Canada     

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.