On the thermal evolution of the terrestrial planets

Physical and chemical constraints for such different planetary objects as the Earth, the Moon and meteorite parent bodies can best be satisfied by thermal history models having high initial temperatures. On the basis of thermal calculations it is suggested that the evolution of the other terrestrial planets (Mars, Venus and Mercury) was also characterized by high initial temperatures. Under these conditions, melting and, consequently, fractionation would set in at an early stage. Because of the resulting redistribution of the long-lived radioactive heat sources and the concentration of these elements in the surface layers, large-scale differentiation could be achieved by partial melting.Paper presented at the Lunar Science Institute Conference on Geophysical and Geochemical Exploration of the Moon and Planets, January 10–12, 1973.     

On a type of solutions for dynamical rupture of the equilibrium of stars

Solutions for dynamical behaviour of unstable stellar models are obtained, in the special case where the velocity of a gaseous element varies asr/t. It is found that the only possible value for the constant of proportionality is 2/3 and that there are only two such stellar configurations.     

A comparison between cokriging and ordinary kriging: Case study with a polymetallic deposit

Cokriging is applied to the estimation of mineral resources in a polymetallic deposit. Several major steps, which should be taken in using cokriging, are highlighted as necessary practical considerations. The case study is related to an ultramafic copper-nickel deposit. Six elements, Cu, Ni, Au, Ag, Pt, and Pd, occurring in the deposit, are partitioned into three subgroups and the elements within each group are simultaneously estimated on the basis of over 4000 drill assays. A comparison was made between ordinary kriging and cokriging methods through cross-validation. The results show that cokriging has significantly improved the estimates of resources by reducing the overall estimation error by over 15% and the variance of error by over 20%.     

Spectrophotometry of Saturn and its rings from 60 to 180 microns

We observed Saturn at far-infrared and submillimeter wavelengths during the Earth's March 1980 passage through the plane of Saturn's rings. Comparison with earlier spectroscopic observations by D. B. Ward [Icarus32, 437–442 (1977)], obtained at a time when the tilt angle of the rings was 21.8°, permits separation of the disk and ring contributions to the flux observed in this wavelength range. We present two main results: (1) The observed emission of the disk between 60 and 180 μm corresponds to a brightness temperature of 104 ± 2°K; (2) the brightness temperature of the rings drops approximately 20°K between 60 and 80 μm. Our data, in conjunction with the data obtained by other observers between 1 μm and 1 mm, permit us to derive an improved estimate for the total Saturnian surface brightness of (4.84 ± 0.32) × 10^?4W cm^?2 corresponding to an effective temperature of 96.1 ± 1.6°K. The ratio of radiated to incident power, P_R/P_I, is (1.46 ± 0.08)/(1 - A), where A is the Bond albedo. For A = 0.337 ± 0.029, P_R/P_I = 2.20 ± 0.15 and Saturn's intrinsic luminosity is L_S = (2.9 ± 0.5) × 10^?10L_⊙.     

Are quasar redshifts randomly distributed?

A statistical analysis of possible clumping (not periodicity) of emission line redshifts of QSO's shows the available data to be compatible with random fluctuations of a smooth, nonclumped distribution. This result is demonstrated with Monte Carlo simulations as well as with the Kolmogorov-Smirnov test. It is in complete disagreement with the analysis by Varshni, which is shown to be incorrect.     

Neutrino emission,population II stars and big-bang cosmology

The spectroscopic determination of the helium abundance in the oldest stars of the galaxy is supported by the theory of stellar evolution when neutrino emission is considered according to the photon-neutrino coupling theory, if it is assumed that the population II stars started their life with a low surface helium content.Receipt delayed by postal strike in Great Britain.     

Improved resolution of complex eigenfrequencies in analytically continued seismic spectra

Summary. The response of the Earth to an earthquake is a transient that is effectively zero several days after the event. A recording of the event, of finite duration in time, has a Fourier spectrum that is an entire, or integral, analytic function of frequency. We present a very simple procedure for computing the Fourier spectrum as a function of complex frequency; the analytically continued spectrum. By investigating the properties of the analytically continued spectrum we show how to extract high- Q modes, how to estimate Q either from the amplitude or from the width of a resonance function, and how to improve the resolution of splitting to the theoretical maximum. Examples of these procedures, using observed data, are presented.     

Grid cell distortion and MODFLOW's integrated finite-difference numerical solution

The ground water flow model MODFLOW inherently implements a nongeneralized integrated finite-difference (IFD) numerical scheme. The IFD numerical scheme allows for construction of finite-difference model grids with curvilinear (piecewise linear) rows. The resulting grid comprises model cells in the shape of trapezoids and is distorted in comparison to a traditional MODFLOW finite-difference grid. A version of MODFLOW-88 (herein referred to as MODFLOW IFD) with the code adapted to make the one-dimensional DELR and DELC arrays two dimensional, so that equivalent conductance between distorted grid cells can be calculated, is described. MODFLOW IFD is used to inspect the sensitivity of the numerical head and velocity solutions to the level of distortion in trapezoidal grid cells within a converging radial flow domain. A test problem designed for the analysis implements a grid oriented such that flow is parallel to columns with converging widths. The sensitivity analysis demonstrates MODFLOW IFD's capacity to numerically derive a head solution and resulting intercell volumetric flow when the internal calculation of equivalent conductance accounts for the distortion of the grid cells. The sensitivity of the velocity solution to grid cell distortion indicates criteria for distorted grid design. In the radial flow test problem described, the numerical head solution is not sensitive to grid cell distortion. The accuracy of the velocity solution is sensitive to cell distortion with error <1% if the angle between the nonparallel sides of trapezoidal cells is <12.5 degrees. The error of the velocity solution is related to the degree to which the spatial discretization of a curve is approximated with piecewise linear segments. Curvilinear finite-difference grid construction adds versatility to spatial discretization of the flow domain. MODFLOW-88's inherent IFD numerical scheme and the test problem results imply that more recent versions of MODFLOW 2000, with minor modifications, have the potential to make use of a curvilinear grid.     

A sediment quality triad assessment of the impact of copper mine tailings disposal on the littoral sedimentary environment in the Atacama region of northern Chile

A sediment quality triad (SQT) assessment was made of the impact of copper mine tailings disposal on littoral meiofaunal assemblages in the Atacama region of northern Chile. This situation is unusual in that the disposal is direct into the high-energy coastal system and not via a river estuary or other low-energy environment. This situation also allows for the examination of the impact of copper mine tailings in the absence of confounding effects from other pollutants. The three components of the SQT were: 1. an analysis of the bioavailable metals in both the sedimentary porewater and the adjacent seawater, 2. a microcosm bioassay of both sediments and seawaters using meiofaunal assemblages, and 3. quantitative field samples of the meiofaunal assemblages. Twelve study sites with varying degrees of impact were used, including three reference sites. The study identified that both the meiofaunal assemblage densities and taxa diversities decrease with increasing levels of bioavailable copper, that the Foraminifera and Harpacticoida are sensitive to copper, and that otoplanid Turbellaria are often characteristic of impacted sites; tailings also have both chemical and physical impacts on the environment. In some cases the physical impact of tailings is more important in excluding some organisms e.g. the interstitial polychaete, Saccocirrus sonomacus, from a site than is their chemical impact.