Simpson’s Paradox in Natural Resource Evaluation

Reversals of statistical relationships, when two or more groups of data in a cross tabulation are aggregated, were first revealed more than a century ago. The reversal was later named Simpson’s paradox after his reversal examples in a seminal paper drew the attention of the statistical community. However, almost all the published cases have been in sociology and biomedical statistics. Does Simpson’s reversal occur in geosciences? Various examples from petroleum geology and reservoir modeling will be shown in this paper. Boundary conditions for such a reversal will be discussed under a broader framework of sampling analysis. Ecological inference bias, change of support problem, modifiable areal unit problem, and reference class problem will be discussed in relation to the Simpson’s paradox in the framework of spatial statistics. It will be demonstrated that the traditional interpretation of the paradox as a result of disproportional sampling based on a contingency table is not always true in the framework of spatial statistics, and the reversal while theoretically benign is inferentially treacherous. Therefore, emphasis will be on the discussion of combining statistical and scientific inferences in geologic modeling and hydrocarbon resource evaluation under various sampling schemes or support effect with or without a Simpson’s reversal.     

A review of present techniques and methodological advances in analyzing Th in aquatic systems

The short-lived thorium isotope ²³⁴Th (half-life 24.1 days) has been used as a tracer for a variety of transport processes in aquatic systems. Its use as a tracer of oceanic export via sinking particles has stimulated a rapidly increasing number of studies that require analyses of ²³⁴Th in both marine and freshwater systems. The original ²³⁴Th method is labor intensive. Thus, there has been a quest for simpler techniques that require smaller sample volumes. Here, we review current methodologies in the collection and analysis of ²³⁴Th from the water column, discuss their individual strengths and weaknesses, and provide an outlook on possible further improvements and future challenges. Also included in this review are recommendations on calibration procedures and the production of standard reference materials as well as a flow chart designed to help researchers find the most appropriate ²³⁴Th analytical technique for a specific aquatic regime and known sampling constraints.     

A long pollen record from Lac du Bouchet, Massif Central, France: for the period ca. 325 to 100 ka BP (OIS 9c to OIS 5e)

Pollen analysis was carried out on sediments older than the Würm pleniglacial (OIS 4), in two new sequences (H and I) derived from the centre of Lac du Bouchet, Massif Central. The inferred vegetation history enables, for the first time in France, five temperate episodes to be defined which pre-date the last interglacial. These temperate episodes alternate with episodes during which the changes in vegetation are indicative of glacial climates. Comparison of these climatic episodes with the oceanic isotope record shows that the pollen record of sequences H and I from Lac du Bouchet spans the time interval from OIS 9c (Ussel interstadial) to OIS 5e (Ribains/Eemian interglacial). In the organic sediments from the Amargiers interstadial (OIS 9a), a trachytic layer, Ar/Ar dated to ca 275 ka, enables a correlation to be established with the upper part of a sequence derived from the nearby Praclaux crater, the lower part of this sequence being of Holsteinian age (OIS 11c). The cross-dating of the pollen sequences from Lac du Bouchet (cores H, I and D) and from Praclaux provides a complete record from the Massif Central, southern France, of successive glacial and interglacial episodes that span the last ca. 400 ka, that is the interval from the Holsteinian to the Holocene.     

A relational database of global U-Pb ages

Enhanced understanding of how sampling techniques affect estimates of the global U-Pb age-distribution have, in turn, constrained U-Pb database design. Recent studies indicate that each continent has a unique age-distribution, as determined by zircon ages dated by the U-Pb isotope method. Likewise, broad regions within a continent also exhibit diverse age-distributions. To achieve a reliable estimate of the global distribution, the heterogenous composition of the continental crust requires sampling as many regions as feasibly possible. To attain this goal, and to provide a method for calculating age histograms, the records from a recent global U-Pb compilation are supplemented with 281,631 new records. These additions increase the database size to 700,598 records. In addition, the data are now restructured and made available as a relational database. After filtering the records by the six age-models included with the database, the results reveal two problems that might generally be unrecognized. First, an abrupt switch in the best-age at any given point(such as 1000 Ma) from ~(206)Pb/~(238)U ages to ~(207)Pb/~(206)Pb ages artificially depresses the age-distribution at the cutoff point. Second, rejecting analyses based on either absolute discordance or the magnitude of 2σ precision errors artificially depresses the age-distribution between 900 Ma and 2000 Ma. The results indicate that, when estimating the global U-Pb age-distribution, the methods for determining best-age and for rejecting records both require some attention. Possible solutions include using either an Accuracy Model or a Precision Model for estimating best-age, and then including all U-Pb records in the estimate, rather than rejecting any of them.     

金矿样品分析中相关问题讨论

依据金矿石特性,探讨样品在分析过程中要特别注意的加工、测试取样量、样品焙烧、载体灰化等几个关键问题,认为只有处理好以上几个关键问题才能得到准确、可靠检测结果。     

取样窗口迹长均值估计方法的讨论

采用窗口取样法测量岩体中随机不连续面的迹长, 相对于无限二维空间的岩体而言存在着不可避免的偏差。因此, 在实际岩体工程中要对实地测量迹长的偏差进行校正, 以获得校正后的平均迹长。本文着重讨论了Kulatilake教授于 1984年提出的不连续面迹长均值估算法, 并对算法作了必要的修正, 使算法更客观, 更完善, 编制的计算机代码可以很方便地求取无限二维岩体不连续面的校正迹长。     

Time-Dependent Reliability Analysis of Offshore Structures

During the life of an offshore structure,its structural strength declines due to various kinds ofdamages related to the time factor.In this paper,four major kinds of damages,including damages causedby fatigue,dent,corrosion and marine life,are discussed.Based on these analyses,formulas for theevaluation of the damaged structure reliability are derived.Furthermore the computer program ISM forthe analysis of structural reliability is developed by the use of Advanced First Order Second Moment meth-od and Monte-Carlo Importance Sampling method.The reliability of a turbular joint and a beam are stu-died as numerical examples.The results show that the theory and the analysis method given in this paperare reasonable and effective.     

Comparison of derivative-free optimization methods for groundwater supply and hydraulic capture community problems

Management decisions involving groundwater supply and remediation often rely on optimization techniques to determine an effective strategy. We introduce several derivative-free sampling methods for solving constrained optimization problems that have not yet been considered in this field, and we include a genetic algorithm for completeness. Two well-documented community problems are used for illustration purposes: a groundwater supply problem and a hydraulic capture problem. The community problems were found to be challenging applications due to the objective functions being nonsmooth, nonlinear, and having many local minima. Because the results were found to be sensitive to initial iterates for some methods, guidance is provided in selecting initial iterates for these problems that improve the likelihood of achieving significant reductions in the objective function to be minimized. In addition, we suggest some potentially fruitful areas for future research.     

Recent Developments in Marine Diamond Mining

The marine diamond deposits of southern Africa owe their existence to fluvial transport down the Orange River to the South Atlantic. On the coast, they were moved, sorted and concentrated by high-energy sea and wind conditions to create a veneer of diamondiferous gravels on the sea floor. Large scale, offshore production by De Beers Marine commenced in 1989 in Namibian waters. The company now acts as a contractor for Namdeb, a corporation owned jointly with the Namibian governments. Some junior public companies also produce diamonds by large-scale mechanized means and conduct extensive exploration programs. Two important developments have occurred recently. Firstly, equipment for the recovery of diamonds from the seabed has been successfully borrowed from other industries. Large drills from onshore civil engineering have been modified for marine sampling and mining. Remotely controlled, seabed-mounted, excavational systems have assumed a major role. The new systems allow both evaluation sampling and subsequent mining to be undertaken by similar or the same equipment, making the results compatible. They permit highly selective extraction and enhanced recovery of the gravels from irregular bedrock in water approaching 200 m deep. But none is universally applicable offshore, each being the preferred system under different conditions. Secondly, the total output of sea diamonds from Namibian waters has increased to 0.8 million carats annually and now exceeds that from all the country's onshore sources. An industry has become established. Corporate and individual perseverence, government encouragement, new technology, shareholders' risk finance, and De Beers' diamond marketing have all played a role in the success. Future diamond production may increase as companies meet the challenge of working lower grade, higher volume deposits, which will require new approaches to the mining process. With a decrease in the physical risk of marine mining, the most variable inputs in operational planning and production forecasting are recovered grade and throughout rate, together with equipment availability. The importance of reliable grade estimation from sufficient sampling density is widely perceived, but the greatest performance risk can involve the predicted excavation rate and 'mineability' of the seabed sediments. Published reserve statements would benefit from a requirement to specify the planned mining method, the consequent cutoff grade to be employed, and whether or not test mining has been undertaken.     

The value of high-resolution nutrient monitoring: A case study of the River Frome, Dorset, UK

The River Frome was sampled at sub-daily sampling interval, with additional storm sampling, through an annual cycle. Samples were analysed for total phosphorus (TP), soluble reactive phosphorus (SRP), total oxidisable nitrogen (TON) and dissolved reactive silicon (Si). The resulting data set was artificially decimated to mimic sampling frequencies from 12 h to monthly time interval. Monthly sampling interval resulted in significant errors in the estimated annual TP and SRP load of up to 35% and 28% respectively, and the resulting data sets were insufficient to observe peaks in P concentration in response to storm events. Weekly sampling reduced the maximum percentage errors in annual load estimate to 15.4% and 6.5%. TON and silicon concentrations were less variable with changing river flow, and monthly sampling was sufficient to predict annual load estimates to within 10%. However, to investigate within-river nutrient dynamics and behaviour, it is suggested that a weekly sampling interval would be the minimum frequency required for TON and Si studies, and daily sampling would be a minimum requirement to adequately investigate phosphorus dynamics. The loss in nutrient-concentration signal due to reduced sampling interval is presented. Hysteresis in the nutrient concentration/flow relationships for all 32 storm events during the study period were modelled and seasonal patterns discussed to infer nutrient sources and behaviour. The high-resolution monitoring in this study identified, for the first time, major peaks in phosphorus concentration in winter that coincide with sudden falls in air temperature, and was associated with biofilm breakdown. This study has shown that to understand complex catchment nutrient processes, accurately quantify nutrient exports from catchments, and observe changes in water quality as a result of nutrient mitigation efforts over time, it is vital that the newly emerging field-based automated sampler/analyzer technologies begin to be deployed, to allow for routine high-resolution monitoring of our rivers in the future.