Singularity and Nonnormality in the Classification of Compositional Data

Geologists may want to classify compositional data and express the classification as a map. Regionalized classification is a tool that can be used for this purpose, but it incorporates discriminant analysis, which requires the computation and inversion of a covariance matrix. Covariance matrices of compositional data always will be singular (noninvertible) because of the unit-sum constraint. Fortunately, discriminant analyses can be calculated using a pseudo-inverse of the singular covariance matrix; this is done automatically by some statistical packages such as SAS. Granulometric data from the Darss Sill region of the Baltic Sea is used to explore how the pseudo-inversion procedure influences discriminant analysis results, comparing the algorithm used by SAS to the more conventional Moore–Penrose algorithm. Logratio transforms have been recommended to overcome problems associated with analysis of compositional data, including singularity. A regionalized classification of the Darss Sill data after logratio transformation is different only slightly from one based on raw granulometric data, suggesting that closure problems do not influence severely regionalized classification of compositional data.     

Hypothesis for a submarine landslide and cohesionless sediment flows resulting from a 17th century earthquake-triggered landslide in Quebec,Canada

Textural isotopic and microfossil data from two gravity cores obtained in Saguenay Fjord, Quebec, suggest that a distinctive sandy clay bed was deposited as the result of a major landslide in the Saguenay River basin. Pb-210 dating of the cores indicate that the bed is of similar age to the magnitude 7 earthquake of February 5, 1663. The slide involved sensitive marine clays and may have occurred in two stages. Slide sediments carried into the Saguenay River channel were probably reworked and subsequently transported down the Fjord basin as two distinct cohesionless mass flows. Fine clay laminae that overlie the older mass flow bed record the modulation of depositional processes by tidal currents for several weeks after this event.     

Community turnover provides insight into variable invertebrate recovery between restored streams with different integrated catchment management plans

ABSTRACT

Understanding temporal patterns in restored environments is important for identifying potential barriers to recovery and improved management of degraded habitats. In this paper, we use temporal beta diversity analyses to compare invertebrate community recovery trajectories in three restored agricultural stream sites under different integrated catchment plans, a native forest reference site, and two unmodified pasture control stream sites over 24 years. The restored sites diverged from their initial community composition over time and became more similar to the reference site community, which was relatively stable over time. Variation partitioning showed that prior to restoration beta diversity was primarily associated with environmental and spatial drivers, whereas post-restoration beta diversity was more influenced by temporal and environmental drivers, including changes in substrate size, fine sediments, water clarity, and nutrients, as well as temperature and flow regime. Species’ contributions to beta diversity varied between sites and years, with sensitive EPT taxa contributing more in reference and control sites. However, contributions of some EPT species, particularly mayflies, increased in restored sites post-ICM. In summary, after nearly two decades of ICM, restored stream sites show recovery towards reference conditions, yet differences persist, indicating that rehabilitation may take longer, depending on the restoration goals.     

Correlations in aftershock and seismicity patterns

Correlations in space and time play a fundamental role in earthquake processes. One direct manifestation of the effects of correlations is the occurrence of aftershocks due to the stress transfer in the vicinity of a main shock. Less obvious and more speculative changes in correlations may occur in the background seismicity before large earthquakes. Using statistical physics it is possible to introduce a measure of spatial correlations through a correlation length. This quantity characterizes how local fluctuations can influence the occurrence of earthquakes over distances comparable with the correlation length. In this work, the physical basis of spatial correlations of earthquakes is discussed in the context of critical phenomena and the percolation problem. The method of two-point correlation function is applied to the seismicity of California. Well defined variations in time of the correlation length are found for aftershock sequences and background seismicity. The scaling properties of our obtained distributions are analyzed with respect to changes in several scaling parameters such as lower magnitude cutoff of earthquakes, the maximum time interval between earthquakes, and the spatial size of the area considered. This scaling behavior can be described in a unified manner by utilizing the multifractal fit. Utilizing the percolation approach the time evolution of clusters of earthquakes is studied with the correlation length defined in terms of the radius of gyration of clusters. This method is applied to the seismicity of California.     

Testing a statistical curve‐fitting procedure for quantifying sediment populations within multi‐modal particle‐size distributions

This paper describes a series of tests designed to evaluate the capacity of a personal computer (PC) based statistical curve‐fitting program called MIX to quantify composite populations within multi‐modal particle‐size distributions. Three natural soil samples were analysed by a Coulter Multisizer, and their particle‐size distributions analysed using MIX software to identify the modes, standard deviations and proportions of their composite populations. The particle‐size distributions of the three natural soil samples were then numerically combined in equal proportions using a spreadsheet program to create synthetic particle‐size distributions of known populations. MIX was then tested on the synthetic particle‐size distributions to see if the modes and proportions it identified were similar to those modes and proportions known to characterize the synthetic particle‐size distributions. The main outcome is that MIX can very accurately describe the modal particle size and proportions of the major composite populations within a particle‐size distribution. However MIX has difficulty in identifying small populations (those contributing <10 per cent of a total particle‐size distribution), particularly when they are located in the central sections of particle‐size distributions, overlain by larger populations, or when positioned in the fine tails of distributions. Despite these minor shortcomings, MIX is a valuable tool for the examination and interpretation of particle‐size data. Copyright © 2005 John Wiley & Sons, Ltd.     

The Sensitivity of Four Monitoring Well Sampling Systems to Low Concentrations of Three Volatile Organics

Four state-of-the-art ground water sampling systems were analyzed to determine their reliability in providing representative samples of the volatile chlorinated hydrocarbons trichloroethylene (TCE), perchloroethylene (PCE), and 1,1,1-trichloroethane (TCA) from a simulated monitoring well. The sampling systems studied represent four commonly used devices, including a stainless steel and Teflon® piston pump, a Teflon bailer, a Teflon bladder pump, and a PVC air-lift pump.
Controlled laboratory sampling experiments were conducted in a tank and well test chamber designed to approximate field conditions. A well purging and sampling procedure was used in the test apparatus to determine the accuracy and precision of each device for detecting low concentrations of the compounds in ground water. The compounds selected are some of the most ubiquitous hazardous contaminants found in shallow aquifers near hazardous waste sites throughout the United States.
No significant statistical difference was found among the four sampling systems in detecting the compounds.     

Rapid magmatic processes accompany arc–continent collision: the Western Bismarck arc, Papua New Guinea

New U–Th–Ra, major and trace element, and Sr–Nd–Pb isotope data are presented for young lavas from the New Britain and Western Bismarck arcs in Papua New Guinea. New Britain is an oceanic arc, whereas the latter is the site of an arc–continent collision. Building on a recent study of the Manus Basin, contrasts between the two arcs are used to evaluate the processes and timescales of magma generation accompanying arc–continent collision and possible slab detachment. All three suites share many attributes characteristic of arc lavas that can be ascribed to the addition of a regionally uniform subduction component derived from the subducting altered oceanic crust and sediment followed by dynamic melting of the modified mantle. However, the Western Bismarck arc lavas diverge from the Pb isotope mixing array formed by the New Britain and the Manus Basin lavas toward elevated ²⁰⁸Pb/²⁰⁴Pb. We interpret this to reflect a second and subsequent addition of sediment melt at crustal depth during collision. ²³⁸U and ²²⁶Ra excesses are preserved in all of the lavas and are greatest in the Western Bismarck arc. High-Mg andesites with high Sr/Y ratios in the westernmost arc are attributed to recent shallow mantle flux melting at the slab edge. Data for two historical rhyolites are also presented. Although these rhyolites formed in quite different tectonic settings and display different geochemical and isotopic compositions, both formed from mafic parents within millennia.     

Middle Campanian–lowermost Maastrichtian nannofossil and foraminiferal biostratigraphy of the northwestern Australian margin

The middle–late Campanian was marked by an increase in the bioprovinciality of calcareous microfossil assemblages into distinct Tethyan, Transitional, and Austral Provinces that persisted to the end of the Maastrichtian. The northwestern Australian margin belonged to the Transitional Province and the absence of key Tethyan marker species such as Radotruncana calcarata and Gansserina gansseri has led petroleum companies operating in the area to use the locally developed KCCM integrated calcareous microfossil zonation scheme. The KCCM zonation is a composite scheme comprising calcareous nannofossil (KCN), planktonic foraminiferal (KPF) and benthonic foraminiferal (KBF) zones. This paper presents the definitions and revisions of Zones KCCM8–19, from the highest occurrence (HO) of Aspidolithus parcus constrictus to the lowest occurrence (LO) of Ceratolithoides aculeus, and builds on our previous early–late Maastrichtian study. The presence of a middle–upper Campanian disconformity is confirmed by microfossil evidence from the Vulcan Sub-basin, Exmouth and Wombat plateaus, and the Southern Carnarvon Platform. In the Vulcan Sub-basin and on the Exmouth Plateau (ODP Hole 762C) the hiatus extends from slightly above the LO of common Rugoglobigerina rugosa to above the LO of Quadrum gothicum. On the Wombat Plateau (ODP Hole 761B) it spans from above the LO of Heterohelix semicostata to above the LO of Quadrum gothicum; and in the Southern Carnarvon Platform the disconformity has its longest duration from above the HO of Heterohelix semicostata to above the LO of Quadrum sissinghii. A significant revision of the events which define Zones KCCM18 and 19 was necessary owing to the observation that the LO of Ceratolithoides aculeus occurs below the HOs of Archaeoglobigerina cretacea and Stensioeina granulata incondita and the LO of common Rugoglobigerina rugosa. In the original zonation these events were considered to be coincident.     

On the astrometric detection of neighboring planetary systems,II

Extensive testing suggests that astrometric techniques can be employed to detect and study virtually any planetary system that may exist within 40 light years (12.5 parsec) of the Sun. Following the conclusion of Paper I [G. Gatewood, Icarus27 (1976), 1–12], the astrometric group at the Allegheny Observatory began an intensive survey of 20 nearby stars to detect the nonlinear variations in their motion that planetary systems would induce. Several tests conducted to further our understanding of the limitations of this survey indicated that the photographic detector itself is responsible for the majority of the random error. A new photoelectric detector has been designed and a simplified prototype of it successfully tested. The new detector is expected to be able to utilize virtually all of the astrometric information transmitted through the Earth's atmosphere. This is sufficient to determine relative positions to within an accuracy of approximately 1 milliarcsec/hr. Such precisions exceed the design capabilities of the best existing astrometric telescopes, thus a feasibility study has been conducted for the design of an improved instrument. The study concludes that a new ground-based telescope and the new detector combined should be able to study stars as faint as the 17th magnitude with an annual accuracy of a few tenths of a milliarcsecond. However, to obtain the ultimate accuracy possible from current technology, we must place an astrometric system above the Earth's atmosphere. A space-borne instrument utilizing the new detector would in theory have sufficient accuracy to detect any Earth-like planet orbiting any of the several hundred stars nearest the Sun.