Some Results on the Spatial Breakdown Point of Robust Point Estimates of the Variogram

The effect of outliers on estimates of the variogram depends on how they are distributed in space. The ‘spatial breakdown point’ is the largest proportion of observations which can be drawn from some arbitrary contaminating process without destroying a robust variogram estimator, when they are arranged in the most damaging spatial pattern. A numerical method is presented to find the spatial breakdown point for any sample array in two dimensions or more. It is shown by means of some examples that such a numerical approach is needed to determine the spatial breakdown point for two or more dimensions, even on a regular square sample grid, since previous conjectures about the spatial breakdown point in two dimensions do not hold. The ‘average spatial breakdown point’ has been used as a basis for practical guidelines on the intensity of contaminating processes that can be tolerated by robust variogram estimators. It is the largest proportion of contaminating observations in a data set such that the breakdown point of the variance estimator used to obtain point estimates of the variogram is not exceeded by the expected proportion of contaminated pairs of observations over any lag. In this paper the behaviour of the average spatial breakdown point is investigated for cases where the contaminating process is spatially dependent. It is shown that in two dimensions the average spatial breakdown point is 0.25. Finally, the ‘empirical spatial breakdown point’, a tool for the exploratory analysis of spatial data thought to contain outliers, is introduced and demonstrated using data on metal content in the soils of Sheffield, England. The empirical spatial breakdown point of a particular data set can be used to indicate whether the distribution of possible contaminants is likely to undermine a robust variogram estimator.     

Influence of initial plastic anisotropy of overconsolidated clays on ground behaviour during tunneling

In order to evaluate the influence of the initial plastic anisotropy in the excavation of a tunnel, a “bubble” bounding surface model for structured soils, formulated by Kavvadas and Belokas (Proc. 10th IACMAG Conf., 2001), was implemented in the explicit finite difference code FLAC. Two different initial stress (K ₀) conditions were considered. The size and shape of the initial bounding surfaces were specified to be consistent with the initial stress field. The distorted and rotated shape of the bounding surface, supported by experimental results, defines the anisotropy of shear strength, which is shown to have a significant influence on the displacements. There is also considerable sensitivity of the soil model to the initial stress field.     

Upper Cretaceous carbonate hosted zinc–lead–barite deposits in Northern Thrust Zone, northern Iraq: petrography and geochemistry

Zinc–lead–barite deposits located in Lefan and Lower Banik localities of about 25 km northeast of Zakho City, Northern Iraq consist of a group of strata-bound sulfides hosted in Upper Cretaceous (Upper Campanian–Maastrichtian) dolomitic limestone. Carbonate-hosted ores contain 3.77% Zn, 2% Pb, and 5% Fe, while in lower Banik, they contain 1.5% Zn, 0.37% Pb, and 1.4% Fe. Diagenetic processes, such as dolomitization and recrystalization in addition to the type of microfacies, provided appropriate physical and chemical conditions that permitted the passage of ore-bearing fluids and participated in precipitation and ore localization. These deposits are precipitated in a platform and developed within the Foreland Thrust Belt. Ore precipitated as infill of intergranular dolomite porosity with replaced dolomite and rudist shells forming disseminated crystals that occupy intergranular pore spaces around dolomite and calcite and as infill of dissolution spaces and fractures.     

Strain-softening behaviour of sand in strain path testing under plane-strain conditions

Experimental data are presented in this paper to study the strain-softening behaviour of sand under plane-strain conditions. K ₀ consolidated strain path tests were conducted using a new plane-strain apparatus. The stress–strain behaviour of medium dense sand under plane-strain conditions was characterized. The test results show that the occurrence of pre-failure strain softening under plane-strain conditions is affected by the void ratio, the strain increment ratio and the initial effective confining stress. This is consistent with previous findings established under axisymmetric conditions. However, a pre-failure strain-softening behaviour in plane-strain tests conducted under high-confining stresses may consist of three stages, namely, material softening, banding softening, and ultimate state. This observation is different from that in triaxial tests where banding softening does not normally occur.     

Attenuation relations for strong seismic ground motion in the Himalayan region

Strong motion data from various regions of India have been used to study attenuation characteristics of horizontal peak acceleration and velocity. The strong ground motion data base considered in the present work consists of various earthquakes recorded in the northern part of India since 1986 with magnitudes 5.7 to 7.2. Using these data, relations for horizontal peak acceleration and velocity, which are $$\begin{gathered} log_{10} a = 1.14 + 0.31M + 0.65log_{10} R \hfill \\ log_{10} v = 0.571 + 0.41M + 0.768log_{10} R \hfill \\ \end{gathered} $$ have been proposed wherea is the peak horizontal acceleration in cm/sec²,v is the peak horizontal velocity in mm/sec,M is body wave magnitude, andR is the hypocentral distance in km. The proposed relations are in reasonable agreement with the small amount of strong ground motion data available for the northern part of India. The present results will be useful in estimating strong ground motion parameters and in the earthquake resistant design in the Himalayan region.     

Spatial orientation of the spin vectors of the disk galaxies in the Virgo cluster I. A catalogue of the disk galaxies in the Virgo cluster

Based on four UK Schmidt Telescope (UKST) IIIa-j direct plates which had been digitized by the Automated Plate Measuring System (APM), a detailed identification of the disk galaxies in the Virgo cluster has been carried out. The certain and possible member galaxies are mainly selected from the updated Catalogue of 2096 Galaxies in the Virgo Cluster Area (VCC). The area of this identification covers a 85 square degree region centered on this cluster. As a result, we compiled a new catalogue of 340 certain and possible member disk galaxies, including 85 lenticulars (SO), 136 spirals (S) and 119 irregulars (Irr), where the APM-measured values of the position angle (P.A.) and diameters of 299 disk galaxies are provided. For at least 149 galaxies, the values of the P.A. and diameters are published for the first time.Comparison between the APM-measured P.A. and diameters of galaxies and those given by the Uppsala General Catalog of Galaxies (UGC) demonstrates the reliability of our data. The statistical properties and completeness of this database are also discussed. Compared with the UGC-given P.A. and diameters which were determined by eyes, our data has no selection effect owing to the instrument measurements. Within our searching region, this might be the largest and relatively complete photometric database published so far for investigating the spatial orientation of the spin vectors of galaxies in the Virgo cluster.     

Gravitational mass of magnetostatic field

Maxwell's displacement current equation is interpreted in the light of recent work to show that static magnetic field in free space should have a colocated and contemporaneous mass that is neither embodied in, nor can be anticipated from, the mass-energy relation. Thus magnetostatic field in the universe represents an invisible mass. Some consequences are discussed.     

Towards a sustainable economy for the Shetland Islands: Development and management issues in fishing and fish farming

Shetland, as an isolated group of islands on the north-west margin of Europe, has always depended in its economy on marine-based resources, and current trends suggest that this will continue for the future. Up to the oil era Shetland depended mainly on the fisheries around it, although for centuries externally-based fishermen have profited more from these fisheries than have the Shetland people. As well as the development of oil from the 1970s there has been the other major economic innovation of fish farming. The oil industry is on massive scale and has greatly changed the economy of the islands and brought notable social benefits; but the direct employment it provides is considerably exceeded by the fish-related industries, which include employment in fish processing and packing plants as well as in fish catching and fish farming. With the oil industry in Shetland now on a settled downward trajectory, the islands are inevitably now having to look more to fish-related employment for their future. In the internal structure of Shetland, fish farming has a notable effect in distributing employment throughout the islands. Activity in fishing and fish processing is more selectively located: fishing is mainly concentrated in certain islands in the archipelago, particularly Whalsay and Burra; and fish processing is mainly in central locations, especially Lerwick and Scalloway. A prominent problem for fish processors is getting reliable supplies in face of higher fish prices at markets on the Scottish mainland. The processors also now face the challenge of putting more value added on their products in an outlying location. For the future there is a major issue in getting more effective measures for conservation of fish stocks in the Shetland area; there is also the related issue of whether Shetland fishermen should get preference in the allocation of fish quotas in this area. For fish farming there is the basic issue of maintaining a pollution-free environment: this was emphasised by the oil spill from the Braer oil tanker, and there is also concern about potential polluution from the prospective development of oil fields in the more difficult deep-water environment to the west of the islands.     

Exclusive rights to fish: Towards a rational fisheries policy

Discusses the tragedy of the commons with regard to fish resources in the North Atlantic, and points to the fact that the Atlantic cod has now been so heavily exploited that a strong regulation of fisheries is needed to preserve an exploitable stock. The author argues for exclusive economic zones dividing up the remaining loopholes among coastal nations and individually transferable quotas.     

Bayesian estimation of seismic hazard for two sites in Switzerland

Seismic hazard analysis is based on data and models, which both are imprecise and uncertain. Especially the interpretation of historical information into earthquake parameters, e.g. earthquake size and location, yields ambiguous and imprecise data. Models based on probability distributions have been developed in order to quantify and represent these uncertainties. Nevertheless, the majority of the procedures applied in seismic hazard assessment do not take into account these uncertainties, nor do they show the variance of the results. Therefore, a procedure based on Bayesian statistics was developed to estimate return periods for different ground motion intensities (MSK scale).Bayesian techniques provide a mathematical model to estimate the distribution of random variables in presence of uncertainties. The developed method estimates the probability distribution of the number of occurrences in a Poisson process described by the parameter . The input data are the historical occurrences of intensities for a particular site, represented by a discrete probability distribution for each earthquake. The calculation of these historical occurrences requires a careful preparation of all input parameters, i.e. a modelling of their uncertainties. The obtained results show that the variance of the recurrence rate is smaller in regions with higher seismic activity than in less active regions. It can also be demonstrated that long return periods cannot be estimated with confidence, because the time period of observation is too short. This indicates that the long return periods obtained by seismic source methods only reflects the delineated seismic sources and the chosen earthquake size distribution law.