On the Use of the Beta Distribution in Probabilistic Resource Assessments

The triangular distribution is a popular choice when it comes to modeling bounded continuous random variables. Its wide acceptance derives mostly from its simple analytic properties and the ease with which modelers can specify its three parameters through the extremes and the mode. On the negative side, hardly any real process follows a triangular distribution, which from the outset puts at a disadvantage any model employing triangular distributions. At a time when numerical techniques such as the Monte Carlo method are displacing analytic approaches in stochastic resource assessments, easy specification remains the most attractive characteristic of the triangular distribution. The beta distribution is another continuous distribution defined within a finite interval offering wider flexibility in style of variation, thus allowing consideration of models in which the random variables closely follow the observed or expected styles of variation. Despite its more complex definition, generation of values following a beta distribution is as straightforward as generating values following a triangular distribution, leaving the selection of parameters as the main impediment to practically considering beta distributions. This contribution intends to promote the acceptance of the beta distribution by explaining its properties and offering several suggestions to facilitate the specification of its two shape parameters. In general, given the same distributional parameters, use of the beta distributions in stochastic modeling may yield significantly different results, yet better estimates, than the triangular distribution.     

The activity of NaCl in seawater of 10–40‰ salinity and 5–25°C at 1 atmosphere

The activity of NaCl in artificial seawater was measured potentiometrically with Na⁺- and Cl^? -sensitive electrodes. The salinity of the solutions, examined at 25°C, ranged from 10–40‰ salinity. The change in the activity from 5–25°C was measured at 35‰ salinity.The molal mean activity coefficient of NaCl in 35‰ seawater at 25°C is 0.667. The relative partial molal enthalpy of NaCl in 35‰ seawater is ?130 ±50 cal mol^?1. This value is in good agreement with the value measured in pure 0.72 M NaCl.The results were compared with activity coefficients predicted by a specific interaction model and by an ion association model. Good agreement was found in both cases.     

Expert systems for automated correlation and interpretation of wireline logs

CORRELATOR is an interactive computer program for lithostratigraphic correlation of wireline logs able to store correlations in a data base with a consistency, accuracy, speed, and resolution that are difficult to obtain manually. The automatic determination of correlations is based on the maximization of a weighted correlation coefficient using two wireline logs per well. CORRELATOR has an expert system to scan and flag incongruous correlations in the data base. The user has the option to accept or disregard the advice offered by the system. The expert system represents knowledge through production rules. The inference system is goal-driven and uses backward chaining to scan through the rules. Work in progress is used to illustrate the potential that a second expert system with a similar architecture for interpreting dip diagrams could have to identify episodes—as those of interest in sequence stratigraphy and fault detection- and annotate them in the stratigraphic column. Several examples illustrate the presentation.     

The carbon dioxide system in the oceans

A model of the carbon dioxide system in nature is derived and is used to further our understanding of the factors which control this system in the oceans, the atmosphere, and the sediments.     

Chemical characteristics of groundwater around two massive sulphide deposits in an area of previous mining contamination, Iberian Pyrite Belt, Spain

A detailed chemical study of groundwater was carried out to elucidate the processes controlling the oxidation and dissolution of sulphide minerals at two massive sulphide deposits in the Iberian Pyrite Belt (IPB), i.e. the mined La Zarza deposit and the unmined Masa Valverde deposit. It was found that major-element compositions varied according to the hydrological regime, La Zarza being in a relatively high area with groundwater recharge (and disturbance due to the human factor) and Masa Valverde being in a relatively low area with groundwater discharge. The variations mainly concern pH, Eh, SO₄ and Na concentrations. Metal concentrations were determined (a) by ICP-MS after filtration, and (b) in some cases by voltammetric measurement of Cu, Pb, Zn, Cd and Mn using the Voltammetric In situ Profiling (VIP) System, which allows detection of only the mobile fractions of trace elements (i.e., free metal ions and small labile complexes a few nanometers in size). If one compares the results obtained by each of the two methods, it would appear that the groundwater shows significant enhancement of metal solubility through complexing with organic matter and/or adsorption onto colloids and/or small particles. In areas of sulphide oxidation, however, this solubility enhancement decreases according to Cu>Zn>Cd>Pb. Under very low redox conditions, the attained metal concentrations can be several orders of magnitude (up to 10⁸–10⁹ for Cu and 10²–10³ for Pb) larger than those expected from equilibrium with respect to sulphide minerals as calculated with the EQ3NR geochemical code; Zn concentrations, however, are close to equilibrium with respect to sphalerite. The implication of these results is discussed with respect both to mineral exploration and to environmental issues.