A new bivariate Gamma distribution generated from functional scale parameter with application to drought data

Univariate and bivariate Gamma distributions are among the most widely used distributions in hydrological statistical modeling and applications. This article presents the construction of a new bivariate Gamma distribution which is generated from the functional scale parameter. The utilization of the proposed bivariate Gamma distribution for drought modeling is described by deriving the exact distribution of the inter-arrival time and the proportion of drought along with their moments, assuming that both the lengths of drought duration (X) and non-drought duration (Y) follow this bivariate Gamma distribution. The model parameters of this distribution are estimated by maximum likelihood method and an objective Bayesian analysis using Jeffreys prior and Markov Chain Monte Carlo method. These methods are applied to a real drought dataset from the State of Colorado, USA.     

Petrogenetic and metallogenetic responses to Miocene slab flattening: new constraints from the El Indio-Pascua Au–Ag–Cu belt,Chile/Argentina

The Eocene–Miocene volcanic and hypabyssal rocks of the El Indio-Pascua Au–Ag–-Cu belt in the southern central Andean flat-slab region are medium–high-K calc-alkaline arc suites, ranging in composition from andesite to rhyolite. A significant transition in magmatic trace element chemistry, coinciding with a pronounced reduction in magma output, occurred in the late-Middle Miocene as documented by ⁴⁰Ar–³⁹Ar geochronology. The upper Eocene–lower-Middle Miocene rocks exhibit low Sr/Y ratios (<50), minor heavy REE fractionation with Sm/Yb ratios not exceeding 3.5 and, in some cases, minor negative Eu anomalies. In contrast, the largely dacitic rocks erupted after ca. 13 Ma are depleted in Y (10 ppm), have generally high, but variable Sr/Y ratios (30–200), exhibit moderate middle and heavy REE fractionation (Sm/Yb: 3.7–5.9) and lack negative Eu anomalies. The latter features are characteristic of adakitic suites (i.e. slab-melts), but the regional temporal and spatial distribution of arc magmatism precludes a major magma source in the downgoing slab. This evolution is interpreted as reflecting a progressive increase in pressure and the availability of water in the lower-crustal site of magma generation, establishing both garnet and hornblende as major stable phases in the residuum. The pressure in the lower crust increased in response to episodic crustal thickening related to the shallowing of the slab, a process recorded by the incision of three regional pediplains over the period 17–6 Ma. Elimination of the subarc asthenospheric mantle and much of the lithospheric mantle by ca. 10 Ma permitted direct incursion of slab-derived, highly oxidised metal- and volatile-rich supercritical fluids into the lower crust, stimulating melting of mafic, garnet amphibolitic and eclogitic assemblages.The igneous suites emplaced from 36–11 Ma were associated with widespread, and locally intense, epizonal hydrothermal activity, but this was barren of base and precious metals. The shallow-crustal availability of abundant water highlighted in earlier models was therefore not a metallogenetic determinant. Moreover, economic Au–Ag–Cu mineralization, associated with small volumes of dacitic magma, was restricted to the interval 9.5–5 Ma, and was not initiated until at least 3.5 my after the inception of high-pressure magma generation. In contrast to previous metallogenetic studies, we therefore suggest that this petrochemical transition was not inherently favourable for ore formation. We propose that the incursion of highly oxidized supercritical fluids from the slab into the lower crust was ultimately responsible for the brief Late Miocene metallogenetic episode.Electronic Supplementary Material Supplementary material is available in the online version of this article at Editorial handling: V. Bouchot     

Pressure effects on regional mean sea level trends in the German Bight in the twenty-first century

The effect of large-scale atmospheric pressure changes on regional mean sea level projections in the German Bight in the twenty-first century are considered. A developed statistical model is applied to climate model data of sea level pressure for the twenty-first century to assess the potential contribution of large-scale atmospheric changes to future sea level changes in the German Bight. Using 78 experiments, an ensemble mean of 1.4-cm rise in regional mean sea level is estimated until the end of the twenty-first century. Changes are somewhat higher for realisations of the special report on emission scenarios (SRES) A1B and A2, but generally do not exceed a few centimeters. This is considerably smaller than the changes expected from steric and self-gravitational effects. Large-scale changes in sea level pressure are thus not expected to provide a substantial contribution to twenty-first century sea level changes in the German Bight.     

Parameters of “Macromaturity” (PMM): novel rank and type related indices from chemical degradation of macromolecular network of coals

Benzene polycarboxylic acids formed upon oxidative degradation of the macromolecular network of a set of French coals with ruthenium tetroxide are proposed as the basis of new coal rank indices. Their distribution probably reflects the degree of condensation of the polyaromatic subunits occurring in the network of the coals. This feature is illustrated in the case of the benzene tetracarboxylic acids. Application of these molecular indices to Gondwana coals, as well as to maceral concentrates indicates that they are also type related. They could prove particularly useful in the case of coals or kerogens having undergone secondary alteration processes.     

Tri- and tetraterpenoid hydrocarbons in the Messel oil shale

The high molecular weight constituents of the branched and cyclic hydrocarbon fraction of the Messel oil shale (Eocene) have been examined by high resolution gas chromatography and combined gas chromatography-mass spectrometry. The following compounds are present: perhydrolycopene (1; lycopane), together with one or more unsaturated analogues with the same skeleton; a series of 4-methylsteranes (2c) in higher abundance than their 4-desmethyl analogues; two series of pentacyclic triterpanes, one series (C₂₇-C₃₂) based on the hopane structure (3a-e), and the other (C₂₇-C₃₁) based on the 17α-H hopane structure (3a-d, 17αH); and an intact triterpene hop-17 (21)-ene [3c, Δ 17(21)]. Only two additional triterpanes were detected in minor concentrations, viz. 30-normoretane (3b, 21αH) and a C₃₁ triterpane based on the hopane/lupane-type skeleton. The presence of these compounds suggests a significant microbial contribution to the forming sediment. Comparison of the tri- and tetraterpenoid hydrocarbons with those of the Green River Shale indicates differences in the organisms contributing to the two sediments.     

Multi-stage melt–rock interaction in the Mt. Maggiore (Corsica, France) ophiolitic peridotites: microstructural and geochemical evidence

Spinel and plagioclase peridotites from the Mt.Maggiore (Corsica, France) ophiolitic massif record a composite asthenosphere–lithosphere history of partial melting and subsequent multi-stage melt–rock interaction. Cpx-poor spinel lherzolites are consistent with mantle residues after low-degree fractional melting (F = 5–10%). Opx + spinel symplectites at the rims of orthopyroxene porphyroclasts indicate post-melting lithospheric cooling (T = 970–1,100°C); this was followed by formation of olivine embayments within pyroxene porphyroclasts by melt–rock interaction. Enrichment in modal olivine (up to 85 wt%) at constant bulk Mg values, and variable absolute REE contents (at constant LREE/HREE) indicate olivine precipitation and pyroxene dissolution during reactive porous melt flow. This stage occurred at spinel-facies depths, after incorporation of the peridotites in the thermal lithosphere. Plagioclase-enriched peridotites show melt impregnation microtextures, like opx + plag intergrowths replacing exsolved cpx porphyroclasts and interstitial gabbronoritic veinlets. This second melt–rock interaction stage caused systematic chemical changes in clinopyroxene (e.g. Ti, REE, Zr, Y increase), related to the concomitant effects of local melt–rock interaction at decreasing melt mass, and crystallization of small (<3%) trapped melt fractions. LREE depletion in minerals of the gabbronoritic veinlets indicates that the impregnating melts were more depleted than normal MORB. Preserved microtextural evidence of previous melt–rock interaction in the impregnated peridotites suggests that they were progressively uplifted in response to lithosphere extension and thinning. Migrating melts were likely produced by mantle upwelling and melting related to extension; they were modified from olivine-saturated to opx-saturated compositions, and caused different styles of melt–rock interaction (reactive spinel harzburgites, vs. impregnated plagioclase peridotites) depending on the lithospheric depths at which interaction occurred. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Metasomatism of ferroan granites in the northern Aravalli orogen,NW India: geochemical and isotopic constraints,and its metallogenic significance

The late Palaeoproterozoic (1.72–1.70 Ga) ferroan granites of the Khetri complex, northern Aravalli orogen, NW India, were extensively metasomatised ~900 Ma after their emplacement, at around 850–830 Ma by low-temperature (ca. 400 °C) meteoric fluids that attained metamorphic character after exchanging oxygen with the surrounding metamorphic rocks. Albitisation is the dominant metasomatic process that was accompanied by Mg and Ca metasomatism. A two-stage metasomatic model is applicable to all the altered ferroan intrusives. The stage I is represented by a metasomatic reaction interface that developed as a result of transformation of the original microcline–oligoclase (An_12–14) granite to microcline–albite (An_1–3) granite, and this stage is rarely preserved. In contrast, the stage II metasomatic reaction front, where the microcline-bearing albite granite has been transformed to microcline-free albite granite, is readily recognisable in the field and present in most of the intrusives. Some of them lack an obvious reaction interface due to the presence of stage II albite granites only. When studied in isolation, these intrusives were incorrectly classified and their tectonic setting was misinterpreted. Furthermore, our results show that the mafic mineralogy of metasomatised granites has a significant impact on the characterisation of such rocks in the magmatic classification and discrimination diagrams. Nevertheless, the stage I metasomatised granites can be appropriately characterised in these diagrams, whereas the characterisation of the stage II granites will lead to erroneous interpretations. The close spatial association of these high heat producing ferroan granites with iron oxide–copper–gold (IOCG), U and REE mineralisation in the region indicates a genetic link between the metasomatism and the mineralisation. World-class IOCG, U and REE deposits are associated with metasomatised ferroan granites, suggesting that such a relationship may act as a critical first-order exploration target for undiscovered mineral deposits.