Point-block covariance: A general solution for the two-dimensional stationary random functions

The application of the theory of random functions to problems of ore evaluation may involve computations of the covariance between the mean value of a given block and the functional value at a given point. However, an analytical solution for such a covariance does not exist for nonspherical blocks and for commonly applied models of covariance functions. Further, because this covariance is a function of the spatial arrangements of the block and the point, it has to be evaluated numerically each time for given point—block arrangements. This paper presents a readily available general solution to this problem in the form of a series of graduated curves which, together with some geometric manipulations, may be used to compute the covariance between a pointand a two-dimensional block for all possible point—block arrangements. The availability of the graph thus eliminates the necessity of using the time-absorbing programs on computers for such computations. Finally, many of the approximations that are made in order to avoid cumbersome covariance evaluations are no longer necessary due to the ease of such computations with the help of the graph provided.     

N and O isotope effects during nitrate assimilation by unicellular prokaryotic and eukaryotic plankton cultures

In order to provide biological systematics from which to interpret nitrogen (N) and oxygen (O) isotope ratios of nitrate (¹⁵N/¹⁴N, ¹⁸O/¹⁶O, respectively) in the environment, we previously investigated the isotopic fractionation of nitrate during its assimilation by mono-cultures of eukaryotic algae (Granger et al., 2004). In this study, we extended our analysis to investigate nitrate assimilation by strains of prokaryotic plankton. We measured the N and O isotope effects, ¹⁵ε and ¹⁸ε, during nitrate consumption by cultures of prokaryotic strains and by additional eukaryotic phytoplankton strains (where ε is the ratio of reaction rate constants of the light vs. heavy isotopologues, ^lightk and ^heavyk; ε = ^lightk/^heavyk − 1 × 1000, expressed in per mil). The observed ¹⁵ε ranged from 5‰ to 8‰ among eukaryotes, whereas it did not exceed 5‰ for three cyanobacterial strains, and was as low as 0.4‰ for a heterotrophic α-protoeobacterium. Eukaryotic phytoplankton fractionated the N and O isotopes of nitrate to the same extent (i.e., ¹⁸ε ∼ ¹⁵ε). The ¹⁸ε:¹⁵ε among the cyanobacteria was also ∼1, whereas the heterotrophic α-proteobacterial strain, which showed the lowest ¹⁵ε, between 0.4‰ and 1‰, had a distinct ¹⁸ε:¹⁵ε of ∼2, unlike any plankton strain observed previously. Equivalent N vs. O isotope discrimination is thought to occur during internal nitrate reduction by nitrate reductase, such that the cellular efflux of the fractionated nitrate into the medium drives the typically observed ¹⁸ε:¹⁵ε of ∼1. We hypothesize that the higher in the ¹⁸ε:¹⁵ε of the α-proteobacterium may result from isotope discrimination by nitrate transport, which is evident only at low amplitude of ε. These observations warrant investigating whether heterotrophic bacterial assimilation of nitrate decreases the community isotope effects at the surface ocean.     

Facies Structure and Quantitative Parameters of Pleistocene Sediments of the Bering Sea

Lithofacies zoning is described for the first time for the Neo- and Eopleistocene of the Bering Sea. Four lithofacies sedimentation zones are distinguished: (I) terrigenous; (II) siliceous–terrigenous; (III) siliceous, and (IV) volcanoterrigenous ones. Corresponding maps were treated using Ronov volumetric method to quantify sedimentation parameters for distinguished lithofacies zones (subzones) and types of Pleistocene sediments. It was revealed that terrigenous sediments predominate over other sediments. Accumulation of the terrigenous sediments was more intense (by 1.4 times) in the Neopleistocene than in the Eopleistocene. The sedimentation rate of siliceous sediments of the Bowers Ridge in the Eopleistocene was two times higher than in the Neopleistocene.     

Horizontal and vertical zones of influence for root systems of four Mojave Desert shrubs

Horizontal and vertical zones of influence for root systems of four Mojave Desert shrubs were characterized using ³²P as a nutrient tracer. Larrea tridentata's horizontal zone of influence was sparse near the plant's stem base, with a maximum probability of accessing ³²P (P_max) of 41%. However, its horizontal zone of influence extended beyond 5 m, and the distance from the stem base at which the probability of accessing ³²P was half P_max (L₅₀3 m) was significantly greater than the other three shrubs. Ambrosia dumosa's zone of influence was dense near the plant's stem base (P_max78%), but was rare at distances >2 m (L₅₀1 m). Zones of influence for Lycium andersonii and Lycium pallidum were intermediate between those of L. tridentata and A. dumosa. For vertical zones of influence, L. tridentata was more likely to obtain ³²P from 5 m soil depths than A. dumosa, but L. pallidum was not significantly different from either A. dumosa or L. tridentata. Horizontal zones of influence did not change with treatments that altered soil water and nitrogen availability, but vertical zones of influence increased with a flood irrigation treatment that increased water availability to 5 m soil depth. These differences among species likely reflect compromises between their shoot growth strategies and their need to acquire spatially and temporally limited soil resources, especially through competitive interactions.     

Influence of wind upon water quality in Liverpool Bay

Comprehensive distribution patterns of physical and chemical characteristics have been obtained from a series of cruises in Liverpool Bay. The marked feature of these distributions was their temporal variability, suggesting that the surface residual circulation is also temporally variable. The influence of wind stress upon the circulation pattern and hence water quality of this sea area is illustrated.     

Linear and planar structure in ordered multivariate data as applied to progressive demagnetization of palaeomagnetic remanence

Summary. Consider a sequence of, say, 10 to 20 vector observations in three-dimensional space. It is suspected that a few subsets of consecutive observations are made up of collinear points. The purpose of this paper is to construct a statistically based algorithm to find such linear segments and to assess their accuracy. A similar assessment is made for coplanar sets of points.
This algorithm is applied here to palaeomagnetic data and is claimed to be superior to previous methods of palaeomagnetic analysis in terms of completeness and balance of analysis, treatment of measurement errors and other sources of scatter, criteria for identification of linear and planar sets of points, and statistical rigour. Stability spectra, with statistically based confidence limits, are obtained as a by-product.     

Density Structure,Isostatic Balance and Tectonic Models of the Central Tien Shan

A new combined satellite-terrestrial model of the gravity field is used together with seismic data for construction of a density model of the lithosphere of the Central Tien Shan and for estimation of its isostatic balance. The Tien Shan is one of the most active intraplate orogens in the world, located about 1,500 km north of the convergence between Indian and Eurasian plate, and surrounded by stable Kazakh platform to the north and the Tarim block to the south. Although this area was extensively studied during recent decades, several principal problems, related to its structure and tectonics, remain unsolved up to now: (1) various geodynamic scenarios have been discussed so far to explain tectonic evolution, such as direct “crustal shortening,” intracontinental subduction and some others, but no definite evidence for any of them has been found. (2) Still, it is not clear why Tien Shan grows so far from the plate boundary at the Himalayan collision zone. Gravity modeling can provide valuable constraints to resolve these questions. The results of this study show that: (1) there exists a very strong deflection of the Tien Shan lithosphere from isostatic equilibrium. At the same time, the patterns of the isostatic anomalies are very different in the Western and Central Tien Shan. The latter one is characterized by much stronger variations. The best fit of the modeling results is found for the model according to which the Tarim plate partially underthrusts the Central Tien Shan; (2) negative density anomalies in the upper mantle under the central block possibly relate to magmatic underplating during the initial stage of the tectonic evolution. Therefore, the weak lithosphere could be the factor that initiates mountain building far away from the collision zone. Alternatively, this might be a gap after detachment of the eclogised lower crust and lithospheric lid, which is filled with the hot asthenospheric material.