Flexible spectral methods for the generation of random fields with power-law semivariograms

Random field generators serve as a tool to model heterogeneous media for applications in hydrocarbon recovery and groundwater flow. Random fields with a power-law variogram structure, also termed fractional Brownian motion (fBm) fields, are of interest to study scale dependent heterogeneity effects on one-phase and two-phase flow. We show that such fields generated by the spectral method and the Inverse Fast Fourier Transform (IFFT) have an incorrect variogram structure and variance. To illustrate this we derive the prefactor of the fBm spectral density function, which is required to generate the fBm fields. We propose a new method to generate fBm fields that introduces weighting functions into the spectral method. It leads to a flexible and efficient algorithm. The flexibility permits an optimal choice of summation points (that is points in frequency space at which the weighting function is calculated) specific for the autocovariance structure of the field. As an illustration of the method, comparisons between estimated and expected statistics of fields with an exponential variogram and of fBm fields are presented. For power-law semivariograms, the proposed spectral method with a cylindrical distribution of the summation points gives optimal results.     

Perceptions of hazard and risk on Santorini

Santorini, Greece is a major explosive volcano. The Santorini volcanic complex is composed of two active volcanoes—Nea Kameni and Mt. Columbo. Holocene eruptions have generated a variety of processes and deposits and eruption mechanisms pose significant hazards of various types. It has been recognized that, for major European volcanoes, few studies have focused on the social aspects of volcanic activity and little work has been conducted on public perceptions of hazard, risk and vulnerability. Such assessments are an important element of establishing public education programmes and developing volcano disaster management plans. We investigate perceptions of volcanic hazards on Santorini. We find that most residents know that Nea Kameni is active, but only 60% know that Mt. Columbo is active. Forty percent of residents fear that negative impacts on tourism will have the greatest effect on their community. In the event of an eruption, 43% of residents would try to evacuate the island by plane/ferry. Residents aged >50 have retained a memory of the effects of the last eruption at the island, whereas younger residents have no such knowledge. We find that dignitaries and municipal officers (those responsible for planning and managing disaster response) are informed about the history, hazards and effects of the volcanoes. However, there is no “emergency plan” for the island and there is confusion between various departments (Civil Defense, Fire, Police, etc.) about the emergency decision-making process. The resident population of Santorini is at high risk from the hazards associated with a future eruption.     

Torngat ultramafic lamprophyres and their relation to the North Atlantic Alkaline Province

Geological mapping and diamond exploration in northern Quebec and Labrador has revealed an undeformed ultramafic dyke swarm in the northern Torngat Mountains. The dyke rocks are dominated by an olivine-phlogopite mineralogy and contain varying amounts of primary carbonate. Their mineralogy, mineral compositional trends and the presence of typomorphic minerals (e.g. kimzeyitic garnet), indicate that these dykes comprise an ultramafic lamprophyre suite grading into carbonatite. Recognized rock varieties are aillikite, mela-aillikite and subordinate carbonatite. Carbonatite and aillikite have in common high carbonate content and a lack of clinopyroxene. In contrast, mela-aillikites are richer in mafic silicate minerals, in particular clinopyroxene and amphibole, and contain only small amounts of primary carbonate. The modal mineralogy and textures of the dyke varieties are gradational, indicating that they represent end-members in a compositional continuum.

The Torngat ultramafic lamprophyres are characterized by high but variable MgO (10–25 wt.%), CaO (5–20 wt.%), TiO₂ (3–10 wt.%) and K₂O (1–4 wt.%), but low SiO₂ (22–37 wt.%) and Al₂O₃ (2–6 wt.%). Higher SiO₂, Al₂O₃, Na₂O and lower CO₂ content distinguish the mela-aillikites from the aillikites. Whereas the bulk rock major and trace element concentrations of the aillikites and mela-aillikites overlap, there is no fractional crystallization relation between them. The major and trace element characteristics imply related parental magmas, with minor olivine and Cr-spinel fractionation accounting for intra-group variation.

The Torngat ultramafic lamprophyres have a Neoproterozoic age and are spatially and compositionally closely related with the Neoproterozoic ultramafic lamprophyres from central West Greenland. Ultramafic potassic-to-carbonatitic magmatism occurred in both eastern Laurentia and western Baltica during the Late Neoproterozoic. It can be inferred from the emplacement ages of the alkaline complexes and timing of Late Proterozoic processes in the North Atlantic region that this volatile-rich, deep-seated igneous activity was a distal effect of the breakup of Rodinia. This occurred during and/or after the rift-to-drift transition that led to the opening of the Iapetus Ocean.     

Indicator mineralogy of kimberlite boulders from eskers in the Kirkland Lake and Lake Timiskaming areas, Ontario, Canada

Sixteen kimberlite boulders were collected from three sites on the Munro and Misema River Eskers in the Kirkland Lake kimberlite field and one site on the Sharp Lake esker in the Lake Timiskaming kimberlite field. The boulders were processed for heavy-mineral concentrates from which grains of Mg-ilmenite, chromite, garnet, clinopyroxene and olivine were picked, counted and analyzed by electron microprobe. Based on relative abundances and composition of these mineral phases, the boulders could be assigned to six mineralogically different groups, five for the Kirkland Lake area and one for the Lake Timiskaming area. Their indicator mineral composition and abundances are compared to existing data for known kimberlites in both the Kirkland Lake and Lake Timiskaming areas. Six boulders from the Munro Esker form a compositionally homogeneous group (I) in which the Mg-ilmenite population is very similar to that of the A1 kimberlite, located 7–12 km N (up-ice), directly adjacent to the Munro esker in the Kirkland Lake kimberlite field. U–Pb perovskite ages of three of the group I boulders overlap with that of the A1 kimberlite. Three other boulders recovered from the same localities in the Munro Esker also show some broad similarities in Mg-ilmenite composition and age to the A1 kimberlite. However, they are sufficiently different in mineral abundances and composition from each other and from the A1 kimberlite to assign them to different groups (II–IV). Their sources could be different phases of the same kimberlite or—more likely—three different, hitherto unknown kimberlites up-ice of the sample localities along the Munro Esker in the Kirkland Lake kimberlite field. A single boulder from the Misema River esker, Kirkland Lake, has mineral compositions that do not match any of the known kimberlites from the Kirkland Lake field. This suggests another unknown kimberlite exists in the area up-ice of the Larder Lake pit along the Misema River esker. Six boulders from the Sharp Lake esker, within the Lake Timiskaming field, form a homogeneous group with distinct mineral compositions unmatched by any of the known kimberlites in the Lake Timiskaming field. U–Pb perovskite age determinations on two of these boulders support this notion. These boulders are likely derived from an unknown kimberlite source up-ice from the Seed kimberlite, 4 km NW of the Sharp Lake pit, since indicator minerals with identical compositions to those of the Sharp Lake boulders have been found in till samples collected down-ice from Seed. Based on abundance and composition of indicator minerals, most importantly Mg-ilmenite, and supported by U–Pb age dating of perovskite, we conclude that the sources of 10 of the 16 boulders must be several hitherto unknown kimberlite bodies in the Kirkland Lake and Lake Timiskaming kimberlite fields.     

Formation of Paleoproterozoic eclogitic mantle, Slave Province (Canada): Insights from in-situ Hf and U–Pb isotopic analyses of mantle zircons

In-situ Hf isotope analyses and U–Pb dates were obtained by laser ablation-MC-ICP-MS for a zircon-bearing mantle eclogite xenolith from the diamondiferous Jericho kimberlite located within the Archean Slave Province (Nunavut), Canada. The U–Pb zircon results yield a wide range of ages (2.0 to 0.8 Ga) indicating a complex geological history. Of importance, one zircon yields a U–Pb upper intercept date of 1989 ± 67 Ma, providing a new minimum age constraint for zircon crystallization and eclogite formation. In contrast, Hf isotope systematics for the same zircons display an intriguing uniformity, and corresponding Hf depleted mantle model ages range between 2.1 ± 0.1 and 2.3 ± 0.1 Ga; the youngest Hf model age is within error to the oldest U–Pb date.

The Jericho eclogites have previously been interpreted as representing remnants of metamorphosed oceanic crust, and their formation related to Paleoproterozoic subduction regimes along the western margin of the Archean Slave craton during the Wopmay orogeny. Hf isotope compositions and U–Pb results for the Jericho zircons reported here are in good agreement with a Paleoproterozoic subduction model, suggesting that generation of oceanic crust and eclogite formation occurred between 2.0 and 2.1 Ga. The slightly older Hf depleted mantle model ages (2.1 to 2.3 Ga) may be reconciled with this model by invoking mixing between ‘crustal’-derived Hf from sediments and more radiogenic Hf associated with the oceanic crust during the 2 Ga subduction event. This results in intermediate Hf isotope compositions for the Jericho zircons that yield ‘fictitiously’ older Hf model ages.     

Pre‐ and post‐impoundment nitrogen in the lower Missouri River

Large water‐sample sets collected from 1899 through 1902, 1907, and in the early 1950s allow comparisons of pre‐impoundment and post‐impoundment (1969 through 2008) nitrogen concentrations in the lower Missouri River. Although urban wastes were not large enough to detectably increase annual loads of total nitrogen at the beginning of the 20^th century, carcass waste, stock‐yard manure, and untreated human wastes measurably increased ammonia and organic‐nitrogen concentrations during low flows. Average total‐nitrogen concentrations in both periods were about 2.5 mg/l, but much of the particulate‐organic nitrogen, which was the dominant form of nitrogen around 1900, has been replaced by nitrate. This change in speciation was caused by the nearly 80% decrease in suspended‐sediment concentrations that occurred after impoundment, modern agriculture, drainage of riparian wetlands, and sewage treatment. Nevertheless, bioavailable nitrogen has not been low enough to limit primary production in the Missouri River since the beginning of the 20^th century. Nitrate concentrations have increased more rapidly from 2000 through 2008 (5 to 12% per year), thus increasing bioavailable nitrogen delivered to the Mississippi River and affecting Gulf Coast hypoxia. The increase in nitrate concentrations with distance downstream is much greater during the post‐impoundment period. If strategies to decrease total‐nitrogen loads focus on particulate N, substantial decreases will be difficult because particulate nitrogen is now only 23% of total nitrogen in the Missouri River. A strategy aimed at decreasing particulates also could further exacerbate land loss along the Gulf of Mexico, which has been sediment starved since Missouri River impoundment. In contrast, strategies or benchmarks aimed at decreasing nitrate loads could substantially decrease nitrogen loadings because nitrates now constitute over half of the Missouri's nitrogen input to the Mississippi. Ongoing restoration and creation of wetlands along the Missouri River could be part of such a nitrate‐reduction strategy. Published 2013. This article is a U.S. Government work and is in the public domain in the USA.     

Linkages between spatio‐temporal patterns of environmental factors and distribution of plant assemblages across a boreal peatland complex

Here we examine the arrangement of plant species across an oligotrophic bog/poor fen peatland complex in the North American boreal plain and the relationships of these species to their physical and chemical environment. A semi‐uniform spatial sampling approach was utilized to describe the species assemblages, pore‐water chemistry and physical condition of 100 plots throughout a single peatland complex. Regardless of sharing the same ground cover of Sphagnum mosses, the remaining species separated into four distinct assemblages, each with unique indicators. These species groups along with associated chemical and physical factors are organized into four ecosites: bog, margin (edge) and two poor fen ecosites. The plant assemblages of this peatland have a complex relationship with numerous gradients, both physical and chemical, including depth to water table, shade, pH, nutrient and base cation. Rather than being homogenous across the landscape, most environmental variables exhibit distinct spatial patterns and do so in relationship to the plant assemblages, forming spatially distinct ecosites across the complex. Base cation concentrations play a smaller role than previously thought in differentiating these ecosites, and in addition to shade and depth to water table, nitrogen in the form of dissolved organic nitrogen was highly related to the placement of these ecosites. Many significant chemical factors appear related to evaporative water loss within the peatland complex, and these chemical factors are used to differentiate the ecosites. However, the mediation of evaporative water loss is due largely to self‐generated responses of the plant assemblages related to shade through plant morphology and peat acrotelm development related to depth to water table. We conclude that plant species and associated environmental gradients act together to form spatially distinct ecosites. The distribution of these ecosites within this large, environmentally complex peatland is largely controlled by differing self‐generated responses along the hydrotopographical gradient of differential water loss.