Modelling uncertainty in natural resource analysis using fuzzy sets and Monte Carlo simulation: slope stability prediction

The techniques of fuzzy logic and Monte Carlo simulation are combined to address two incompatible types of uncertainty present in most natural resource data: thematic classification uncertainty and variance in unclassified continuously distributed data. The resultant model of uncertainty is applied to an infinite slope stability model using data from Louise Island, British Columbia. Results are summarized so as to answer forestry decision support queries. The proposed model of uncertainty in resource data analysis is found to have utility in combining different types of uncertainty, and efficiently utilizing available metadata. Integration of uncertainty data models with visualization tools is considered a necessary prerequisite to effective implementation in decision support systems.     

Petrogenesis of Evolved Basalts and Rhyolites at Austurhorn, Southeastern Iceland: the Role of Fractional Crystallization

The Austurhorn intrusive complex in southeastern Iceland representsthe evolved hypabyssal remains of an eroded Tertiary (6–7Ma) central volcano. The complex consists of a layered gabbrointrusion, a composite granophyric stock, and abundant maficand felsic dikes. Mineralogical and geochemical trends amongcontemporaneous, compositionally diverse liquids from the complexprovide insight into the genesis of evolved basalts and rhyolitesin Iceland that are difficult to infer from studies of onlylavas. Mafic and felsic samples have comparable ranges in incompatibletrace element ratios (Ba/La and P/Ce) and Sr- and Pb-isotopes(O'Nions and Pankhurst, 1973; B. Hanan, pers. comm., 1988),suggesting derivation from a common parental composition. Majorand trace element variations throughout the Austurhorn suiteare consistent with fractional crystallization of the observedphenocrysts. Quartz-normative basalts were derived from parentalbasalt containing 7.8 wt.% MgO by extensive low-pressure crystallizationof olivine, augite, plagioclase, magnetite, and ilmenite. Thefractionating assemblage is consistent with the observed mineralogyof associated gabbro. Moreover, the cumulus mineralogy of thegabbro provides evidence for fractionation processes in a compositionalinterval not represented by dikes and sills (i.e., 54–63wt.% SiO₂).Diversity among the mafic dikes reflects severaladditional factors: (1) crystallization under conditions ofvariable oxygen fugacity; (2) separate mantle melting eventsthat produce different Ce/Yb values; (3) contamination of somemafic dikes at depth, presumably by interaction with felsicmagmas. Major and trace element trends among most felsic samples canbe modeled by fractionation of the observed mineral phases:plagioclase, K-feldspar, clinopyroxene, ilmenite, apatite, allanite,and zircon. Although crustal melting has been proposed for generatingIcelandic rhyolites, most Austurhorn felsic samples are unlikeliquids derived by melting of hydrated basalts. In particular,apatite and zircon have controlled the abundances of Zr, Hf,and the REE in the felsic rocks, but they are unlikely to beresidual phases during partial melting of basalt. One felsicdike, interpreted as a melt of an evolved source, shows petrographicevidence of in situ anatexis and also has anomalous trace elementabundances and unusually high ₂₀₆Pb/₂₀₄Pb.     

Late-stage calcites in the Permian Capitan Formation and its equivalents, Delaware Basin margin, west Texas and New Mexico: evidence for replacement of precursor evaporites

Comparison of Upper Guadalupian fore-reef, reef and back-reef strata from outcrops in the Guadalupe Mountains with equivalent subsurface cores from the northern and eastern margins of the Delaware Basin indicates that extensive evaporite diagenesis has occurred in both areas. In both surface and subsurface sections, the original sediments were extensively dolomitized and most primary and secondary porosity was filled with anhydrite. These evaporites were emplaced by reflux of evaporitic fluids from shelf settings through solution-enlarged fractures and karstic sink holes into the underlying strata. Outcrop areas today, however, contain no preserved evaporites in reef and fore-reef sections and only partial remnants of evaporites are retained in back-reef settings. In their place, these rocks contain minor silica, very large volumes of coarse sparry calcite and some secondary porosity. The replacement minerals locally form pseudomorphs of their evaporite precursors and, less commonly, contain solid anhydrite inclusions. Some silicification, dissolution of anhydrite and conversion of anhydrite to gypsum have occurred in these strata where they are still buried at depths in excess of 1 km; however, no calcite replacements were noted from any subsurface core samples. Subsurface alteration has also led to the widespread, late-stage development of large- and small-scale dissolution breccias. The restriction of calcite cements to very near-surface sections, petrographic evidence that the calcites post-date hydrocarbon emplacement, and the highly variable but generally ‘light’carbon and oxygen isotopic signatures of the spars all indicate that calcite precipitation is a very late diagenetic (telogenetic) phenomenon. Evaporite dissolution and calcitization reactions have only taken place where Permian strata were flushed with meteoric fluids as a consequence of Tertiary uplift, tilting and breaching of regional hydrological seals. A typical sequence of alteration involves initial corrosion of anhydrite, one or more stages of hydration/dehydration during conversion to gypsum, dissolution of gypsum and precipitation of sparry calcite. Such evaporite dissolution and replacement processes are probably continuing today in near-outcrop as well as deeper settings. This study emphasizes the potential importance of telogenetic processes in evaporite diagenesis and in the precipitation of carbonate cements. The extensive mineralogical and petrophysical transformations which these strata have undergone during their uplift indicates that considerable caution must be exercised in using surface exposures to interpret subsurface reservoir parameters in evaporitic carbonate rocks.     

The Generation of Oceanic Rhyolites by Crystal Fractionation: the Basalt-Rhyolite Association at Volcn Alcedo, Galpagos Archipelago

Alcedo volcano is one of six shield volcanoes on Isabela Islandin the western Galpagos Islands. Although Alcedo is dominantiybasaltic, it is unusual in that it also has erupted 1 km³ ofrhyolite. The rhyolitic phase marked a 10-fold decrease in themass-eruption rate of the volcano, and the volcano has returnedto erupting basalt. The basalts are tholeiitic and range fromstrongly to sparsely porphyritic. Olivine and plagiodase arethe liquidus phases in the most primitive basalts. The MgO andNi concentrations in the most primitive basalts indicate thatthey have undergone substantial differentiation since extractionfrom the mantle. The rhyolites contain the assemblage oligoclase-augite-titanomagnetite-fayalite-apatiteand sparse xenoliths of quenched basalt and cumulate gabbros.Intermediate rocks are very rare, but some are apparently basaltrhyolitehybrids, and others resulted from differentiation of tholeiiticmagma. Several modeling approaches and Sr-, Nd-, and O-isotopicdata indicate that the rhyolites resulted from 90% fractionation(by weight) of plagiodase, augite, titanomagnetite, olivine,and apatite from the most primitive olivine tholeiite. The dataare inconsistent with the rhyolites originating by crustal anatexis.The extreme Daly gap may be caused by the large increase inviscosity as the basaltic magma differentiates to intermediateand siliceous compositions; highly evolved magmas are eruptibleonly after they become saturated with volatiles by second boiling.The close association of the hybrid intermediate magmas andmagmatic inclusions with the climactic plinian eruption indicatesmixing between mafic and silicic magmas immediately before eruption.Rhyolite production was favored by the decrease in supply ofbasaltic magma as Alcedo was carried away from the focus ofthe Galpagos hotspot. A three-stage model for the magmaticevolution of a Galpagos volcano is proposed. In the first stage,the supply of basaltic magma is large. Basaltic magma continuallyintrudes the subcaldera magma chamber, buffering the magmas'compositional and thermal evolution. As the volcano is carriedaway from the basaltic source, the magma chamber is allowedto cool and differentiate, as exemplified by Alcedo's rhyoliticphase. Finally, the volcano receives even smaller influx ofbasalt, so a large magma chamber cannot be sustained, and thevolcano shifts to isolated basaltic eruptions. KEY WORDS: Galpagos; oceanic rhyolites; fractional crystallization; Isabela Island ^*Corresponding author, e-mail: Geist{at}IDUI1.csrv.uidaho.edu. Telephone: 208-885-6491. Fax: 208-885-5724     

Cryptotephrochronology of the Eemian and the last interglacial–glacial transition in the North East Atlantic

The Eemian interglacial and the onset of the subsequent glacial period serve as the most recent analogue for the natural operation of the climate system during the current interglacial. Pronounced climatic oscillations occurred during this period, but their nature and pattern are poorly understood due to dating limitations and unknown phase relationships between different regions and archives. Tephrochronology offers considerable potential for precise correlation of disparate palaeoclimatic archives preserving evidence of these rapid climatic transitions through the tracing of common isochronous tephra horizons. We outline the identification of three previously unknown cryptotephra horizons within a marine core from the Rockall Trough, North East Atlantic. This sequence preserves a high‐resolution record of this interval and shard size, geochemical heterogeneity and the co‐variance of shard concentrations with ice‐rafted debris data are utilized to demonstrate that primary airfall was the most likely transport and depositional pathway. The main geochemical populations of these horizons have similar transitional alkali major and trace element compositions, suggesting that they were derived from a common Icelandic source, potentially the Öræfajökull volcanic system. These tephra horizons represent additions to the North Atlantic event stratigraphy for this period and tentative correlations to Icelandic terrestrial deposits are proposed for two horizons.     

The Effect of Postcumulus Reactions on Composition of Chrome-spinels from the Jimberlana Intrusion

Chromites in olivine adcumulates, mesocumulates and orthocumulatesfrom drill core of the Jimberlana intrusion have been analysedand related to the cumulate type and to the nature of the surroundingsilicate mineral. Chromites in adcumulates and mesocumulatesshow a restricted range of composition and are high in Mg, Aland Cr. The orthocumulate chromites vary in composition fromthat found in adcumulates to chromites which are much higherin Fe and Ti and with a higher Fe^3?: Fe^2? ratio. The chromitesin orthocumulates vary in composition depending upon the natureof the enclosing silicate mineral. This is believed to reflectthe ability of the enclosing mineral to protect the originalcumulus chromite from reaction with the intercumulus liquid.Thus chromite within early bronzite oikocrysts was protectedfrom reaction whereas that in plagioclase and phlogopite wasprotected at a much later stage and has a higher Fe and Ti contentChromite within olivine appears to have been able to equilibratewith intercumulus liquid until late in the magmatic historyexcept where the olivine enclosing chromite has itself beensurrounded by bronzite. It is suggested that chromite can exchangeelements with intercumulus liquid through the olivine. Thereare two possibilities; either elements such as Cr, Al, Ti andFe^{3 ?} were able to diffuse through the olivine structure orthe apparently enclosed chromite crystals were able to maintaindirect contact with the melt along fine fractures produced bythe differential thermal contraction of olivine and chromite. The average diameters of chromite crystals within orthocumulatebronzite and olivine are 28 and 20 microns respectively whereaschromites in plagioclase and phlogopite have average diametersof 48 and 56 microns. There is no obvious correlation betweenthe size of the chromite and their composition for grains foundwithin a particular silicate. Chromites of every size have beenable to equilibrate with the liquid unless they were protectedfrom reaction. Nucleation of reaction products played an important role indetermining the final composition of any particular chromitecrystal. The significance of reaction and nucleation on a localscale of millimetres is considered with respect to the majorsilicates and to the location of the last liquid. It is suggestedthat the last liquid tended to concentrate in pockets of reactantcrystals, where product crystals failed to nucleate until latein the magmatic history. It is estimated that in rocks withan orthocumulate texture, the intercumulus liquid crystallizedover a temperature range as large as 300 ?C and that it becamesignificantly more oxidizing near the solidus temperature.     

The Cr-minerals of Outokumpu--Their Chemistry and Significance

The massive Cu–Co–Zn sulfide ores at Outokumpu inFinnish Karelia are unusual among Cyprus type deposits by virtueof the high Cr content exhibited by both the ores and the hostrocks. Throughout both the ore horizons and the metasedimentaryhost rock, bulk-rock Cr content averages 0.2 per cent Cr₂O₃.The high Cr contents result in an unusual degree of Cr substitutionin a number of silicate and oxide phases. Cr₂O₃ analyses presentedhere include values up to 3.74 per cent in tremolite, 3.65 percent in diopside, 26.90 per cent in uvarovitic garnet, 15.37per cent in epidote, 24.63 per cent in muscovite, 8.56 per centin biotite, 5.18 per cent in chlorite, 2.99 per cent in staurolite,and 72.65 per cent in chromite. Cr contents of these mineralscan be extremely variable even on the thin-section scale. Thehigh level of Cr in the metasediments, together with that ofNi, reflects their enhanced concentration in the original sedimentsdue to presumed derivation from a Cr-rich komatiite-bearingsubstrate. High levels of both elements in the stock works indicatethat they may have been partly re-distributed by the hydrothermalore-forming fluids. The variability of Cr content within individualsilicate grains suggests that they overgrew small-scale variationsin sedimentary Cr content sufficiently rapidly to preclude diffusivesmoothing of µ_Cr gradients. This suggests that while Crmay be mobile in hydrothermal systems, it is immobile undermetamorphic conditions.