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.     

Integration of reflection seismic and sediment grain-size data from Lake Khubsugul (Northern Mongolia): a reply to Prokopenko and Kendall

Prokopenko and Kendall (J Paleolimnol doi:, 2008) criticise the work presented in Fedotov et al. (J Paleolimnol 39:335–348, 2008), and instead propose an alternative interpretation for the grain-size evolution recorded in the KDP-01 core, retrieved from the central part of Lake Khubsugul. Their interpretation is based (i) on a seismic-stratigraphic re-interpretation of sparker seismic profile khub012 (which they copied from Fedotov et al. (EOS Trans 87:246–250, 2006)), (ii) on the presupposition that changes in lake level are the dominant control on facies distribution in Lake Khubsugul, and (iii) on the invalidation of our age-depth model. In this reply to their comment, we demonstrate that they interpreted seismic artefacts and geometries caused by changes in profile orientation as true stratigraphic features and that the lake-level reconstruction they derive from this interpretation is therefore incorrect. We also demonstrate that their grain-size predictions, which they consider to be predominantly driven by changes in lake level, are inconsistent with the measured sulphate concentration, which is a demonstrated proxy of lake level in Lake Khubsugul, and with the measured grain-size record. Finally, we point out that even if there would be a problem with the age-depth model, this problem would not affect the part of the sedimentary sequence discussed in Fedotov et al. (J Paleolimnol 39:335–348, 2008).     

ON THE GENERATION OF P AND S WAVE ENERGY IN CRYSTALLINE ROCKS*

A seismic source consisting of a 700 kg weight that could be dropped vertically or projected down a ramp inclined at 45° to the vertical was tested as a source of P, SV and SH waves within a crystalline rock body at Chalk River, Ontario. The seismic energy was recorded by arrays of both horizontal and vertical-component geophones at distances between 30 and 600 m from the source, which was operated over glacial overburden varying in thickness from less than a meter to a few tens of meters. Seismic energy was more efficiently generated when the overburden thickness was at least several meters. The signals identified visually as S are generally true S, though some may be the converted wave PS. The SV amplitudes are generally larger than those of P, regardless of the type of shot, while the signal frequencies are roughly 60 Hz and 90 Hz, respectively. The horizontal-component seismograms for the inclined shots showed no evidence of SH polarization, and the SH amplitudes were only rarely enhanced relative to P and SV amplitudes on changing from vertical to inclined shots. These unexpected results are attributed to the combined effect of the high velocity and density contrasts and the irregularity of the boundary between the glacial overburden and the rock body.     

Tsunamis as geological agents

When a tsunami wave series approaches and interacts with a coast, the consequent passage shorewards of great volumes of water and their invasion of the land, especially within bays and up river valleys, results in the disturbance of existing sediment and the removal seawards of land debris and coastal and shallow‐water marine sediments. Tsunami action builds up sequences of peculiar sediments in shallow water; it at least assists in the formation and maintenance of submarine canyons and, through them, produces turbidity currents of a particularly powerful kind. Tsunami action may explain many puzzling sedimentary phenomena, for example, sudden and drastic changes in near‐shore bathymetry; the formation of chaotic sediments such as some paraconglomerates and edgewise conglomerates. It offers solutions to problems arising from the study of turbiditic sequences, both modern and ancient.     

A mass ratio limit for primordial black holes

We augment our scenario for the formation of astronomical objects from macroscopic superstrings by the assumption that the central matter keeps its identity in the fragmentation. From the condition that the angular momentum per mass squared of this matter should be less than the Kerr limit G/c, we obtain upper limits for the ratio of the mass of central black holes M(BH) to the mass M of the host object. This limit is M(BH)/M ≈ 0.001, and, expressed in observed quantities, approximately M(BH)/M ≈ σ²/(v · c) where σ is the r.m.s. velocity, v the rotational velocity and c the velocity of light. The valuesM(BH) agree with the observed behaviour both in order of magnitude and in the variation with velocity dispersion. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The role of prior model calibration on predictions with ensemble Kalman filter

This paper, based on a real world case study (Limmat aquifer, Switzerland), compares inverse groundwater flow models calibrated with specified numbers of monitoring head locations. These models are updated in real time with the ensemble Kalman filter (EnKF) and the prediction improvement is assessed in relation to the amount of monitoring locations used for calibration and updating. The prediction errors of the models calibrated in transient state are smaller if the amount of monitoring locations used for the calibration is larger. For highly dynamic groundwater flow systems a transient calibration is recommended as a model calibrated in steady state can lead to worse results than a noncalibrated model with a well-chosen uniform conductivity. The model predictions can be improved further with the assimilation of new measurement data from on-line sensors with the EnKF. Within all the studied models the reduction of 1-day hydraulic head prediction error (in terms of mean absolute error [MAE]) with EnKF lies between 31% (assimilation of head data from 5 locations) and 72% (assimilation of head data from 85 locations). The largest prediction improvements are expected for models that were calibrated with only a limited amount of historical information. It is worthwhile to update the model even with few monitoring locations as it seems that the error reduction with EnKF decreases exponentially with the amount of monitoring locations used. These results prove the feasibility of data assimilation with EnKF also for a real world case and show that improved predictions of groundwater levels can be obtained.     

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.     

X-ray transient sources

The galactic distribution and physical nature of X-ray transient sources is investigated. Two types of transients are considered. The observational data on 41 X-ray transient sources are given, and the average parameters of hard and soft X-ray transients are estimated.