Quantifying Uncertainty in Mineral Resources by Use of Classification Schemes and Conditional Simulations

Mineral inventory determination consists of estimating the amount of mineral resources on a block-by-block basis and classifying individual blocks into categories with increasing level of geologic confidence. Such classification is a crucial issue for mining companies, investors, financial institutions, and authorities, but it remains subject to some confusion because of the wide variations in methodologies and the lack of standardized procedures. The first part of this paper considers some of the criteria used to classify resources in practice and their impact through a sensitivity study using data from a Chilean porphyry copper deposit. Five classification criteria are compared and evaluated, namely: Search neighborhoods, absolute and relative kriging variances, absolute and relative conditional simulation variances. It is shown that some classification criteria either favor or penalize the high-grade areas if the grade distribution presents a proportional effect. In the second part of the paper, conditional simulations are used to quantify the uncertainty on the overall mineral resources. This approach is promising for risk analysis and decision-making. Unlike linear kriging, simulations allow inclusion of a cutoff grade in the calculation of the resources and also provide measures of their joint uncertainty over production volumes.     

Conditioning Simulations of Gaussian Random Fields by Ordinary Kriging

Conditioning realizations of stationary Gaussian random fields to a set of data is traditionally based on simple kriging. In practice, this approach may be demanding as it does not account for the uncertainty in the spatial average of the random field. In this paper, an alternative model is presented, in which the Gaussian field is decomposed into a random mean, constant over space but variable over the realizations, and an independent residual. It is shown that, when the prior variance of the random mean is infinitely large (reflecting prior ignorance on the actual spatial average), the realizations of the Gaussian random field are made conditional by substituting ordinary kriging for simple kriging. The proposed approach can be extended to models with random drifts that are polynomials in the spatial coordinates, by using universal or intrinsic kriging for conditioning the realizations, and also to multivariate situations by using cokriging instead of kriging.     

Reducing fluctuations in the sample variogram

In the analysis of regionalized data, irregular sampling patterns are often responsible for large deviations (fluctuations) between the theoretical and sample semi-variograms. This article proposes a new semi-variogram estimator that is unbiased irrespective of the actual multivariate distribution of the data (provided an assumption of stationarity) and has the minimal variance under a given multivariate distribution model. Such an estimator considerably reduces fluctuations in the sample semi-variogram when the data are strongly correlated and clustered in space, and proves to be robust to a misspecification of the multivariate distribution model. The traditional and proposed semi-variogram estimators are compared through an application to a pollution dataset.     

Benthic diatoms in a Mediterranean delta: ecological indicators and a conductivity transfer function for paleoenvironmental studies

The contemporary distribution of benthic diatoms and their use as ecological indicators were examined in a coastal wetland, the Ebro Delta, as a representative of environmental conditions in Mediterranean coastal wetlands. A total of 424 diatom taxa were identified across 24 sites encompassing a wide range of wetland habitat types (coastal lagoons, salt and brackish marshes, shallow bays, microbial mats and nearshore marine waters) and conductivities. Canonical correspondence analysis showed that water conductivity and water depth were the main factors structuring the diatom assemblages. Cluster analysis identified five habitat types according to the similarity in diatom species composition: salt marshes, brackish marshes, brackish coastal lagoons and bays, coastal lagoons with fresher conditions, and nearshore open sea. For each wetland habitat, diatom indicator species were identified. Partial canonical correspondence analysis showed that water conductivity, a proxy for salinity, was the most statistically significant and independent variable for explaining the distribution of benthic diatoms in the study area. A transfer function, using a weighted average regression model, was developed for conductivity and displayed reasonable performance (r ² = 0.64; RMSEP = 0.302 log₁₀ mS/cm). Our study in the Ebro Delta provides a basis for using diatom assemblages to make quantitative conductivity inferences, and for using diatom indicator species to identify wetland habitats. These approaches are complementary and may be valuable for paleoenvironmental studies of (1) effects of large-scale, natural changes in the Delta (e.g. sea-level fluctuations), and (2) impacts of short-term anthropogenic changes, such as the introduction and development of rice agriculture.     

Global optimization of core station networks for space geodesy: application to the referencing of the SLR EOP with respect to ITRF

We apply global optimization in order to optimize the referencing (and consequently the stability) of the Earth Orientation Parameters (EOP) with respect to ITRF2005. These EOP are derived at a daily sampling from SLR data, simultaneously with weekly station positions. The EOP referencing is carried out with minimum constraints applied weekly to the three rotations and over core station networks. Our approach is based on a multi objective genetic algorithm, a particular stochastic global optimization method, the reference system effects being the objectives to minimize. We thus use rigorous criteria for the optimal weekly core station selection. The results evidence an improvement of 10% of the stability for Polar Motion (PM) series in comparison to the results obtained with the network specially designed for EOP referencing by the Analysis Working Group of the International Laser Ranging Service. This improvement of nearly 25 μas represents 50% of the current precision of the IERS 05 C04 PM reference series. We also test the possibility of averaging the weekly networks provided by our algorithm (the Genetically Modified Networks—GMN) over the whole time period. Although the dynamical nature of the GMN is clearly a key point of their success, we can derive such a global mean core network, which could be useful for practical applications regarding EOP referencing. Using this latter core network moreover provides more stable EOP series than the conventional network does.     

Comparison of C and N stable isotope ratios between surface particulate organic matter and microphytoplankton in the Gulf of Lions (NW Mediterranean)

Carbon and nitrogen stable isotope ratios of particulate organic matter (POM) in surface water and 63–200 μm-sized microphytoplankton collected at the fluorescence maximum were studied in four sites in the Gulf of Lions (NW Mediterranean), a marine area influenced by the Rhone River inputs, in May and November 2004. Some environmental (temperature, salinity) and biological (POM, Chlorophyll a and phaeopigments contents, phytoplankton biomass and composition) parameters were also analysed. Significantly different C and N isotopic signatures between surface water POM and microphytoplankton were recorded in all sites and seasons. Surface water POM presented systematically lower δ¹³C (∼4.2‰) and higher δ¹⁵N (∼2.8‰) values than those of microphytoplankton, due to a higher content of continental and detrital material. Seasonal variations were observed for all environmental and biological parameters, except salinity. Water temperature was lower in May than in November, the fluorescence maximum was located deeper and the Chlorophyll a content and the phytoplankton biomass were higher, along with low PON/Chl a ratio, corresponding to spring bloom conditions. At all sites and seasons, diatoms dominated the phytoplankton community in abundance, whereas dinoflagellate importance increased in autumn particularly in coastal sites. C and N isotopic signatures of phytoplankton did not vary with season. However, the δ¹⁵N of surface water POM was significantly higher in November than in May in all sites likely in relation to an increase in ¹⁵N/¹⁴N ratio of the Rhone River POM which influenced surface water in the Gulf of Lions. As it is important to determine true baseline values of primary producers for analysing marine food webs, this study demonstrated that C and N isotopic values of surface water POM cannot be used as phytoplankton proxy in coastal areas submitted to high river inputs.     

Eddy properties in the Southern California Current System

The California Current System (CCS) is an eastern boundary upwelling system characterized by strong eddies that are often generated at the coast. These eddies contribute to intense, long-distance cross-shelf transport of upwelled water with enhanced biological activity. However, the mechanisms of formation of such coastal eddies, and more importantly their capacity to trap and transport tracers, are poorly understood. Their unpredictability and strong dynamics leave us with an incomplete picture of the physical and biological processes at work, their effects on coastal export, lateral water exchange among eddies and their surrounding waters, and how long and how far these eddies remain coherent structures. Focusing our analysis on the southern part of the CCS, we find a predominance of cyclonic eddies, with a 25-km radius and a SSH amplitude of 6 cm. They are formed near shore and travel slightly northwest offshore for ~?190 days at ~?2 km day^?1. We then study one particular, representative cyclonic eddy using a combined Lagrangian and Eulerian numerical approach to characterize its kinematics. Formed near shore, this eddy trapped a core made up of ~?67% California Current waters and ~?33% California Undercurrent waters. This core was surrounded by other waters while the eddy detached from the coast, leaving the oldest waters at the eddy’s core and the younger waters toward the edge. The eddy traveled several months as a coherent structure, with only limited lateral exchange within the eddy.