Teacher''s Aide: Modeling Hole-Effect Variograms of Lithology-Indicator Variables

Common variogram models, such as spherical or exponential functions, increase monotonically with increasing lag distance. On the other hand, a hole-effect variogram typically exhibits sinusoidal waves that form peaks and troughs, thereby conveying the cyclicity of the underlying phenomenon. In order to incorporate this cyclicity into a stochastic simulation, hole effects in the experimental variogram must be fitted appropriately. In this paper, we recommend use of several multiplicative-composite variogram models to fit hole-effect experimental variograms. These consist of a cosine function to provide wavelength and phase of cyclicity, multiplied by a monotonic model (e.g., spherical) to attenuate amplitudes of the cyclical peaks and troughs. These composite models can successfully fit experimental lithology-indicator variograms that contain a range of cyclicities, although experimental variograms with poor cyclicity require special considerations.     

The perturbation of alternating geomagnetic fields by discontinuities with high conductivity contrasts

The perturbation of alternating geomagnetic fields by conductivity discontinuities is considered. A numerical method is used to solve the two-dimensional induction problem. Models in which the conductivity contrast between conductive regions is great, such as between oceanic and continental regions, are considered. The perturbation field distributions for models with higher conductivity contrasts are compared with lower conductivity contrast models using a method recently developed by Jones (1972). Total field solutions are obtained for several models by using a very large grid as well as a folding-in technique. Results from the two methods for the various models are compared. It is found that the folding-in technique offers an alternative method for handling higher conductivity contrasts.     

Spectral index determination between 408 MHz and 5 GHz in the northern sky

We present the joint analysis of two 5-GHz interferometric surveys of the northern sky, taken with different baselines. The two surveys were carried out on the Jodrell Bank 5-GHz interferometer based at Manchester. The Maximum Entropy Method is used to check the consistency of the two surveys and the final two-dimensional maps are used, together with low-frequency full sky surveys, to put constraints on the Galactic spectral index. It is found that synchrotron emission is the dominant process at high Galactic latitudes below 5 GHz.     

A computer method to calculate the convolution of statistical distributions

It is becoming increasingly important to determine probability distributions of combinations of random variables. Convolution is a technique by which the distribution of a sum of random variables can be determined. This paper presents some simplifications in order to reduce the numerical integrations and computer time. In addition, the method may be used with empirical nonanalytic distributions. While Monte Carlo methods are also appropriate for calculating the distribution, convolution can give at least as much accuracy as Monte Carlo methods with a reduction in computation. Two applications are presented: one approximates the distribution of percent sand in an area, and the other indicates a method of determining sample size when using the distribution of means to approximate normality.     

A new population of brown dwarfs

In this paper we report the first results from a survey for low-mass stars and brown dwarfs, based on a photographic stack of around 100 Schmidt plates. This survey extends photographic searches by about 2 mag, and covers an area of 25 deg². Some 30 faint objects with large R − I colours were selected for further study, and were found to have very strong molecular absorption in their spectra, but only moderately red infrared colours. Five of these stars were selected for a parallax programme; three of these were found to be at a distance of around 45 pc, implying a very low luminosity. On the basis of their luminosity alone it is clear that these stars are field brown dwarfs, and we discuss their likely evolutionary status in the context of current models of low-mass stellar evolution.     

Foreground separation methods for satellite observations of the cosmic microwave background

A maximum entropy method (MEM) is presented for separating the emission resulting from different foreground components from simulated satellite observations of the cosmic microwave background radiation (CMBR). In particular, the method is applied to simulated observations by the proposed Planck Surveyor satellite. The simulations, performed by Bouchet &38; Gispert, include emission from the CMBR and the kinetic and thermal Sunyaev–Zel'dovich (SZ) effects from galaxy clusters, as well as Galactic dust, free–free and synchrotron emission. We find that the MEM technique performs well and produces faithful reconstructions of the main input components. The method is also compared with traditional Wiener filtering and is shown to produce consistently better results, particularly in the recovery of the thermal SZ effect.