Uncertainty Estimate in Resources Assessment: A Geostatistical Contribution

For many decades the mining industry regarded resources/reserves estimation and classification as a mere calculation requiring basic mathematical and geological knowledge. Most methods were based on geometrical procedures and spatial data distribution. Therefore, uncertainty associated with tonnages and grades either were ignored or mishandled, although various mining codes require a measure of confidence in the values reported. Traditional methods fail in reporting the level of confidence in the quantities and grades. Conversely, kriging is known to provide the best estimate and its associated variance. Among kriging methods, Ordinary Kriging (OK) probably is the most widely used one for mineral resource/reserve estimation, mainly because of its robustness and its facility in uncertainty assessment by using the kriging variance. It also is known that OK variance is unable to recognize local data variability, an important issue when heterogeneous mineral deposits with higher and poorer grade zones are being evaluated. Altenatively, stochastic simulation are used to build local or global uncertainty about a geological attribute respecting its statistical moments. This study investigates methods capable of incorporating uncertainty to the estimates of resources and reserves via OK and sequential gaussian and sequential indicator simulation The results showed that for the type of mineralization studied all methods classified the tonnages similarly. The methods are illustrated using an exploration drill hole data sets from a large Brazilian coal deposit.     

Sediment hosted lead–zinc deposits of the Neoproterozoic Bambuí Group and correlative sequences, São Francisco Craton, Brazil: A review and a possible metallogenic evolution model

The Proterozoic sediment-hosted Zn–(Pb) sulfide and non-sulfide deposits of the São Francisco Craton, Brazil, are partially syn-diagenetic and epigenetic and were probably formed during extensional events. The majority of the deposits occur within shallow water dolomites. The Pb isotopic data of sulfides are relatively homogeneous for individual deposits and plot above the upper crust evolution curve of the Plumbotectonic model. Some of the deposits are characterized by highly radiogenic lead (²⁰⁶Pb/²⁰⁴Pb ≥ 21) originating from the highly radioactive crust of the São Francisco Craton. Pb and S isotopic data suggest the sources of metal and sulfur for the deposits to be the basement rocks and seawater sulfates in the sediments, respectively. The relatively high temperatures of formation (100 to 250 °C) and moderate salinity (3% to 20% NaCl equiv.) of the primary fluid inclusions in the sphalerite crystals suggest the participation of basinal mineralizing fluids in ore formation. The steep paleo-geothermal gradient generated by the radioactively enriched basement rocks probably assisted in heating up the circulating mineralizing fluids.     

Shallow-marine sediment cores record climate variability and earthquake activity off Lisbon (Portugal) for the last 2000 years

Sea Surface Temperature (SST), river discharge and biological productivity have been reconstructed from a multi-proxy study of a high-temporal-resolution sedimentary sequence recovered from the Tagus deposition center off Lisbon (Portugal) for the last 2000 years. SST shows 2 °C variability on a century scale that allows the identification of the Medieval Warm Period (MWP) and the Little Ice Age (LIA).High Iron (Fe) and fine-sediment deposition accompanied by high n-alkane concentrations and presence of freshwater diatoms during the LIA (1300–1900 AD) (Science 292 (2001) 662) suggest augmented river discharge, whereas higher total-alkenone concentrations point to increased river-induced productivity. During the MWP (550–1300 AD) (Science 292 (2001) 662) larger mean-grain size and low values of magnetic susceptibility, and concentrations of Fe, n-alkanes, and n-alcohols are interpreted to reflect decreased runoff. At the same time, increased benthic and planktonic foraminifera abundances and presence of upwelling related diatoms point to increased oceanic productivity. On the basis of the excellent match found between the negative phases of the North Atlantic Oscillation (NAO) index and the intensified Tagus River discharge observed for the last century, it is hypothesized that the increased influx of terrigenous material during the LIA reflects a negative NAO-like state or the occurrence of frequent extreme NAO minima. During the milder few centuries of the MWP, stronger coastal upwelling conditions are attributed to a persistent, positive NAO-like state or the frequent occurrence of extreme NAO maxima.The peak in magnetic susceptibility, centered at 90 cm composite core depth (ccd), is interpreted as the result of the well-known 1755 AD Lisbon earthquake. The Lisbon earthquake and accompanying tsunami are estimated to have caused the loss of 39 cm of sediment (355 years of record—most of the LIA) and the instantaneous deposition of a 19-cm sediment bed.     

Geochemical signatures and mechanisms of trace elements dispersion in the area of the Vale das Gatas mine (Northern Portugal)

A geochemical survey involving the collection and analysis of 170 stream sediment samples was carried out in Vale das Gatas area in order to delineate geochemical signatures and to detect pollution hazards due to mining.Factor analysis applied to the data showed that the most important variables accounting for the first factor are Ag, Pb, Bi, As, W, Cd, Zn and Cu. These variables represent the most significant metalliferous elements of the original paragenesis, which still maintain a close relationship in the secondary geological environment. The spatial distribution of the factor scores referred to factor 1 indicates that positive scores occur predominantly in the Vale das Gatas and Sabrosa streams and in the main Pinhão river. The results also show that the Vale das Gatas mine is the most important contamination source in the Vale das Gatas district.In order to study the dispersion, transfer and uptake mechanisms of trace elements from the Vale das Gatas mine, additional sample media were collected, i.e., stream sediments, tailings, coatings, waters (surficial and mine waters) and specific biological species. Four sample stations were selected, namely two in connection with abandoned adits of the Vale das Gatas mine, one located in the Vale das Gatas stream and one located in the Pinhão River. The results show that chemical reactions of leaching and precipitation took place controlling the heavy metals in areas near the Vale das Gatas mine.At the same time, positive anomalous patterns are visible along the Pinhão river for about 20 km. The mineralogical composition of the stream sediments suggests that processes of mechanical dispersion also interfere in the secondary distribution of the metalliferous elements in that media.     

Petrogenesis of the Eocene and Mio–Pliocene alkaline basaltic magmatism in Meseta Chile Chico, southern Patagonia, Chile: Evidence for the participation of two slab windows

The Meseta Chile Chico (MCC, 46.4°S) is the westernmost exposure of Eocene (lower basaltic sequence, LBS; 55–40 Ma, K–Ar ages) and Mio–Pliocene (upper basaltic sequence, UBS; 16–4 Ma, K–Ar ages) flood basalt volcanism in Patagonia. The MCC is located south of the Lago General Carrera-Buenos Aires (LGCBA), southeast from the present day Chile Triple Junction (CTJ), east of the actual volcanic gap between Southern South Volcanic Zone and Austral Volcanic Zone (SSVZ and AVZ, respectively) and just above the inferred location of the South Chile Ridge segment subducted at 6 Ma (SCR-1). Erupted products consist of mainly ne-normative olivine basalt with minor hy-normative tholeiites basalt, trachybasalt and basanite. MCC lavas are alkaline (42.7–53.1 wt.% SiO₂, 3–8 wt.% Na₂O+K₂O) and relatively primitive (Ni: 133–360 ppm, Cr: 161–193 ppm, Co: 35–72 ppm, 4–16.5 MgO wt.%). They have a marked OIB-like signature, as shown by their isotopic compositions (⁸⁷Sr/⁸⁶Sr_o=0.70311–0.70414 and εNd=+4.7–+5.1) and their incompatible trace elements ratios (Ba/La=10–20, La/Nb=0.46–1.09, Ce/Pb=15.52–27.5, Sr/La<25), reflecting deep mantle origin. UBS-primitive lavas have characteristics similar to those of the Eocene LBS basalts, while UBS-intermediate lavas show geochemical imprints (La/Nb>1, Sr/La>25, low Ce/Pb, Nb/U) compatible with contamination by arc/slab-derived and/or crustal components. We propose that the genesis and extrusion of magmas is related to the opening of two slab windows due to the subduction of two active ridge segments beneath Patagonia during Eocene and Mio–Pliocene.     

Geochemistry and geothermometry of volcanic rocks from Serra Branca, Iberian Pyrite Belt, Portugal

Volcanic rocks from Serra Branca, Iberian Pyrite Belt, Portugal, consist of calc-alkaline felsic and intermediate rocks. The latter are massive andesites, whereas the former include four dacitic to rhyolitic lithologies, distinguishable on spiderdiagrams and binary plots of immobile elements. Zircon thermometry indicates that two felsic suites may have formed from different magmas produced at distinct temperatures, with only limited fractionation within each suite. Alternatively, all the felsic rocks can be related through fractionation of a single magma if the lower zircon saturation temperature obtained for one suite merely results from Zr dilution, mostly reflecting silicification.

The relatively high magma temperatures at Serra Branca ease the classification of felsic rocks based on their HFSE contents and also indicate volcanogenic massive sulfide deposit favorability. This contrasts with other areas of the Belt that register lower magma temperatures and are subsequently barren. However, magma temperatures may have not been high enough to cause complete melting of refractory phases in which HFSE reside during crustal fusion of an amphibolite protolith, implying difficult discrimination of tectonic environments for the felsic rocks. The intermediate rocks were possibly formed by mixing between basaltic magmas and crustal material, compatible with volcanism in an attenuated continental lithosphere setting.     

Collapse of primordial clouds — II. The role of dark matter

In this article we extend the study performed in our previous article of the collapse of primordial objects. We here analyse the behaviour of the physical parameters for clouds ranging from 10⁷ to 10¹⁵ M_⊙. We study the dynamical evolution of these clouds in two ways: as purely baryonic clouds and as clouds with non-baryonic dark matter included. We start the calculations at the beginning of the recombination era, following the evolution of the structure until the collapse (which we defined as the time when the density contrast of the baryonic matter is greater than 10⁴). We analyse the behaviour of several physical parameters of the clouds (e.g. the density contrast and the velocities of the baryonic matter and the dark matter) as a function of time and radial position in the cloud. In this study all physical processes that are relevant to the dynamical evolution of the primordial clouds, such as for example photon drag (due to the cosmic background radiation) and hydrogen molecular production, besides the expansion of the Universe, are included in the calculations. In particular we find that the clouds with dark matter collapse at higher redshift when we compare the results with the purely baryonic models. As a general result we find that the distribution of the non-baryonic dark matter is more concentrated than the baryonic one. It is important to stress that we do not take into account the putative virialization of the non-baryonic dark matter; we just follow the time and spatial evolution of the cloud, solving its hydrodynamical equations. We also studied the role of cooling–heating processes in the purely baryonic clouds.     

A parallelizable method for two‐phase flows in naturally‐fractured reservoirs

A parallelizable, semi‐implicit numerical method is proposed for the study of naturally‐fractured reservoir systems. It has proved to be computationally efficient in producing accurate numerical solutions for the dual‐porosity model for immiscible, two‐phase flow in such reservoirs. The method combines hybridized mixed finite elements, a new version of the modified method of characteristics, a sophisticated operator‐splitting procedure for separating the pressure calculation in the fractures from that of the saturation, another operator splitting to handle the interaction of the matrix blocks and the fractures, and domain decomposition iterative procedures for both the pressure and the saturation. It permits moderately long time steps for the pressure and the saturation in the fractures and matrix blocks by using short, inexpensive microsteps to treat the transport portion of the saturation equation in the fractures. This paper is devoted to the formulation of the method and a discussion of numerical results for five‐spot and vertical cross‐section examples.     

Modelling frequency distributions of 5 minute-averaged solar radiation indexes using Beta probability functions

Summary ¶Five minute-averaged values of sky clearness, direct and diffuse indices, were used to model the frequency distributions of these variables in terms of optical air mass. From more than four years of solar radiation observations it was found that variations in the frequency distributions of the three indices of optical air mass for Botucatu, Brazil, are similar to those in other places, as published in the literature. The proposed models were obtained by linear combination of normalized Beta probability functions, using the observed distributions derived from three years of data. The versatility of these functions allows modelling of all three irradiance indexes to similar levels of accuracy. A comparison with the observed distributions obtained from one year of observations indicate that the models are able to reproduce the observed frequency distributions of all three indices at the 95% confidence level.Received September 2, 2002; revised February 28, 2003; accepted March 16, 2003 Published online September 10, 2003